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南非迈德逊公司自动汽车理论N2洛伊斯·奥斯蒂茨文件说明书

Pearson South Africa (Pty) Ltd4th oor, Auto Atlantic Building,Corner of Hertzog Boulevard and Heerengracht,Cape T own, 8001© Pearson South Africa (Pty) LtdAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright holder.Every effort has been made to trace the copyright holders of material produced in this title. We would like to apologise for any infringement of copyright so caused, and copyright holders are requested to contact the publishers in order to rectify the matter.First published in 2020ISBN 978-1-485-71741-6 (print)ISBN 978-1-485-71819-2 (epdf)Publisher: Amelia van ReenenManaging editor: Ulla SchülerEditor: Alco MeyerProofreader: Magdel PalmArtwork: Claudia EckardBook design: Pearson Media HubCover design: Pearson Media HubCover artwork: T oRyUK. ShutterstockTypesetting: Charlene BatePrinted byAcknowledgements:Photographs:ContentsModule 1: Engine measurement (1)Unit 1 Engine block (2)Unit 2 Cylinder head (9)Module 2: F ive-speed manual gearbox and anintroduction to six-speed gearbox (15)Unit 1 Gearbox components and operations (16)Unit 2 Six-speed gearbox (26)Module 3: Clutches (29)Unit 1 Clutch assembly (30)Unit 2 Clutch mechanisms (37)Module 4: Driveshaft assemblies (43)Unit 1 Front-wheel drives (44)Unit 2 Rear-wheel drives (48)Module 5: F ront- and rear-wheel naldrive assemblies (53)Unit 1 Front-wheel nal drive (54)Unit 2 Rear-wheel nal drive (60)Module 6: Vehicle suspensions (69)Unit 1 Introduction to vehicle suspensions (70)Unit 2 Active suspensions (78)Module 7: Steering systems (83)Unit 1 Steering gear (84)Unit 2 Steering geometry (93)Module 8: Brake systems (99)Unit 1 Hydraulic servo operating system (100)Unit 2 Disc brake assemblies (109)Unit 3 Drum brake assemblies (112)Unit 4 ABS and EBS operating systems (116)Module 9: Fuel supply systems (121)Unit 1 Introduction to fuel supply systems (122)Unit 2 Introduction to different fuel injection systems (144)Module 10: Ignition systems (135)Unit 1 Introduction to ignition systems (136)Unit 2 Introduction to electronic ignition systems (144)Module 11: Auxiliary electrical systems (151)Unit 1 Lighting systems (152)Unit 2 Starting system (158)Unit 3 Charging system (162)Unit 4 Vehicle air conditioning system (166)Glossary (173)Engine1ModulemeasurementWhat is covered?In this module, we cover engine measurement, includingmeasurements taken on parts in the engine block and the cylinderhead. The components in the engine block which need to be measuredare cylinders, pistons, piston rings, crankshaft and bearings. The partsin the cylinder head which need to be measured are the face surface ofthe cylinder head, valve guides and stems, and the valve springs.Learning OutcomesAfter studying this module, you should be able to:■Understand where to measure the cylinder bore for size taper andovality■Explain how all the measurement are taken on the piston■Explain how all the measurements are taken on the crankshaft,both inside and outside the engine block■Explain how the measurements are taken on the connecting rod■Explain how the measurements are taken for thickness andwarpage■Explain how all the measurements are taken for wear on thevalve guide and valve stem■Explain how to check the seating of the valves■Explain how to measure valve spring height and spring tension.1Module 1: Engine measurement2Module 1: Engine measurementLEARNING OUTCOMES■Understand where to measure the cylinder bore for size taper and ovality ■Explain how all the measurement are taken on the piston■Explain how all the measurements are taken on the crankshaft both inside and outside the engine block■Explain how the measurements are taken on the connecting rod.IntroductionAfter extended engine operation and high mileage, it is necessary to service an engine block. Worn piston rings can cause engine smoking, high oil consumption and low compression during combustion. Worn bearings can lead to low oil pressure, bearing knock and complete part failure.T o service a cylinder block, it is necessary to measure the cylinders for wear, inspect the cylinder wall for damage, install core plugs and hone a cylinder. T odetermine the serviceability of parts, the pistons, piston rings, cylinders, crankshaft and bearings need to be measured. These measurements need to be compared to the manufacturer’s speci cations to determine whether they are still able to be of service or useful.Measure a cylinder bore for size taper and ovalityIf a cylinder is not badly scratched, you have to measure the cylinder to ensure that the new rings will seal properly. Piston rings cannot seal in a worn, out of round or tapered cylinder. The cylinder measurement will help you to determine the piston to cylinder clearance. Cylinder taper and ovality or out of roundness are measured with an inside micrometre or a cylinder bore gauge.Figure 1.1 The bore dial gaugeUnit 1: Engine blockKeywordServiceability when something is still able to be of service or useful3Unit 1: Engine blockModule 1When measuring the diameter of a cylinder with a telescopic gauge, the gauge is extended and locked to measure the inside cylinder after whichmeasurements are made using a micrometre.Cylinder taper is thedifference in diameter between the top of a cylinder and the bottom of the cylinder.Cylinder taper is caused by less lubricating oil at the top of the cylinder and more oil splashing at the bottom. Cylindertaper should not exceed the manufacturer’s speci cations, which means it should not go beyond bounds or limits. The manufacturer’s service manualshould be consulted for exact speci cations. Use a bore gauge or inside micrometre to measure the inside diameter of a cylinder. Cylinder ovality or cylinder out of roundness is the difference in diameter between a cylinder being measured side to side and from the front to the rear in the block. Piston thrust action makes the cylinders wear more at the right angles to the centre line of the crankshaft. The positions where to measure a cylinder bore for size taper and ovality is illustrated in Figure 1.3.Measure the diameter of the cylinder at the top and the bottom of the cylinder. Then calculate for cylinder taper and ovality as illustrated in Figure 1.4. Compare the amount of taper and ovality to the manufacturer’s speci cations to determine whether the cylinder is acceptable or if the engine block needs to be bored.Figure 1.4 Calculations for cylinder taper and ovalityFigure 1.2 The telescopic gauge When a cylinder is tapered, either the top or bottom is larger in diameter than the other.topmiddlebottomFigure 1.3 Measurements of thecylinder bore for size taper and ovalitySubtract the two top measurements from each other to calculate the cylinder out of round.3.987– 3.9810.006Subtract the top and bottom readings from each other to calculate the taper.KeywordExceed to go beyond bounds or limits4Module 1: Engine measurementACTIVITY 1.11. Discuss the terms ‘ovality’ and ‘taper’ in a cylinder.2. A four-cylinder diesel engine’s bore diameter speci cations are 86,49 mm– 86,53 mm. The speci ed maximum out of roundness and taper is 0,01 mm. Calculate the taper and out of roundness for the following measurements taken from a four-cylinder diesel engine to determine if the engine is still within the manufacturer’s speci cations.Table 1.1 Cylinder bore measurementsCylinder diameter at the topCalculations Position inside cylinder In line with the crankshaft centre line (D x )Across crankshaft centre line (D y )OvalityTaper in line with crankshaft centre line (D x )Taper acrosscrankshaft centre line (D y )Top 86, 5586, 65D y – D x = 86,65 – 86,53 = 0,12 mm D top – D middle = 86,55 – 86,53 = 0,02 mm D top – D middle = 86,65 – 86,56 = 0,09 mm Middle 86,5386,56D y – D x =D middle – D bottom =D middle – D bottom =Bottom86,5286,54D y – D x =D top – D bottom =D top – D bottom =Measure a pistonPistons are made of aluminium and are easily damaged and worn. When servicing an engine’s bottom end, it is important to check every piston thoroughly. Look for cracked skirts, worn ring grooves, pin bore wear and other problems.Piston size is measured using a micrometre on the piston skirt just below the piston pinhole. Adjust the micrometre for a slight drag as it is pulled over the piston. Piston taper is measured by comparing the piston diameter at the piston pin centre with the diameter at the bottom of the skirt. The difference between the two measurements equals the piston taper. Compare this measurement with the manufacturer’s speci cations. If the piston taper is not within manufacturer’s speci cations, the piston should be replaced. Piston clearance is measured by subtracting the cylinder borediameter from the piston diameter. The difference between the borediameter and the pistondiameter equals thepiston clearance.Figure 1.5 Measuring piston taperPiston taper-measure at piston pin centre and bottom of skirt Piston size-measure ¾ in. below centre line of piston pin hole5Unit 1: Engine blockModule 1Alternatively, the piston clearance can be measured by placing the piston inside the cylinder andmeasuring the clearance with a feeler gauge. Place a long feeler gauge blade on the piston skirt and push the piston into the cylinder. Use a spring scale to pull the feeler gauge out of the cylinder. When the spring scale reading equals the manufacturer’s speci cations, the size of the feeler gauge equals the piston clearance. Piston ring side clearance is the space between the compression ring and the ring groove. Ring groove wear increases this clearance, and if wear is enough, the ring will not be held square against the cylinder wall. T o measure ring side clearance, slide a feeler gauge between the ring and its groove. The largest feeler gauge that ts between the ring and its groove indicates the ringside clearance. Compare this to the manufacturer’s speci cations.Figure 1.7 Measuring piston ring side clearancePiston ring gap clearance is very important. If the ring gap is too small, the ring could lock or score the cylinder upon heating up and expanding . If the gap is too large, the ring tension against the cylinder walls can be too low, causing blow-by. Check the ring gap clearance by pressing the ring into its cylinder. Press the ring in deeper using the piston to square the ring inside the cylinder. The ring gap is then measured with a feeler gauge and compared against the speci cations.Figure 1.6 Measuring piston clearanceFigure 1.8 Measuring ring gap clearancespring scalefeeler strip pistonpiston ring piston ringfeeler gaugefeeler gauge ring grooveKeywordExpand to increase in extend, size or volume6Module 1: Engine measurementMeasure a crankshaftA crankshaft needs to be perfectly clean before installing it. Inspect the big end and main bearing journals carefully for any scratching, scoring or signs of wear. Blow out oil passages with compressed air.Measuring a crank journal for taper will show if one side of the crank journal is worn more than the other. Use an outside micrometre to measure both ends of the journals. The two measurements should be subtracted from each other and compared to the manufacturer’s speci cations. T aper beyond the manufacturer’s limits requires crankshaft turning.Measure a crank journal for out of roundness or ovality by measuring the crank journal form side to side and from top to bottom. Subtract the two measurements from each other and compared to the manufacturer’s speci cations. If the ovality is not within the manufacturer’s limits, the crankshaft should be sent for machining.T o calculate crank taper, use the following formula:T aper 1:= D A – D B and T aper 2: = D C – D DT o calculate crank journal out of roundness, use the following formula:Out of roundness 1: = D A – D C and Out of roundness 2: = D B – D DCheck crankshaft straightness by mounting the crankshaft on V-blocks and mounting a dial indicator against the centre journal. Slowly turn the crank while watching the dial indicator. Dial indicator movement indicates a crankshaft is bent. The crankshaft can also be placed into the block main bearings instead of using V-blocks.Check main bearing oil clearanceT o check the oil clearance for the main bearing and big end bearings, you can either use a plastic gauge or bearing nip or crush. Wipe off any oil on the crank journal surfaces and install the crankshaft by using the manufacturer’s torque speci e a plastic gauge to check the oil clearance between the crankshaft and the main bearing. First, remove the bearing cap and place a small bead of plastic gauge across the surface of the unoiled crankshaft. Replace the bearing cap and tighten the bolts according to the manufacturer’s speci cations. Loosen the bolts again to remove the bearing cap. Then compare the smashed bead of the plastic gauge to the paper scale. If the clearance is not correct, check the crank journal sizes and bearing sizes.T o check bearing nip or crush , make sure the bearing cap bolts have been torqued according to the manufacturer’s speci cations. Then loosen one of the bolts and check theFigure 1.9 Measuring the crank journal for taper and ovalityFigure 1.10 Checking a crankshaft for straightnessFigure 1.11 Checking oil clearance with a plastic gaugeA CBD7Unit 1: Engine blockModule 1clearance underneath the bearing cap using a feeler gauge. Compare the measurement with the manufacturer’s speci cations.Crankshaft end play is the amount of front to the rear movement of a crankshaft in the engine block. Crankshaft endplay is controlled by the clearance between the main thrust bearing and the crankshaft thrust surface. Mount a dial indicator on the block to measure endplay. Place the dial indicator stem parallel to the crank’s centre line and prise the crank back and forth. The dialindicator movement equals crankshaft endplay. Compare the endplay with the manufacturer’s speci cations. If endplay is incorrect, check the thrust bearing.Crankshaft end play can also be checked by using a feeler gauge. Press the crankshaft to the one side and insert the feeler gauge at one of the main bearing journals. The largest feeler gauge that enters the gap equals the crankshaft end oat.Figure 1.13 Measuring the crankshaft end play with a feeler gaugeACTIVITY 1.21. Explain how to measure piston taper.2. Explain the two methods to measure for piston clearance.3. The manufacturer’s speci cations for the diameter of the main bearings of a diesel engine are 56,980 mm–56,995 mm. The maximum allowed out of roundness is 0,015 mm, and the maximum taper is 0,005 mm. Calculate the taper and out of roundness for the journal if the measurements taken are as in the table below. Refer to Figure 1.9.Figure 1.12 Measuring the crankshaft end play with a dial gauge8Module 1: Engine measurementJournal no.Journal diameter Calculations D AD B D C D D OvalityTaper1.56,9956,9456,9956,89D A – D C = 56,99 – 56,94 = 0,05 mm D B – D D = 56,99 – 56,89 = 0,1 mm D A – D B = 56,99 – 56,99 = 0,00 mm D C – D D = 56,94 – 56,89 = 0,05 mm 2.56,9856,9556,9956,92D A – D C =D B – D D =D A – D B =D C – D D =3.56,9956,9256,9856,90D A – D C =D B – D D =D A – D B =D C – D D =4.56,9956,9656,9956,93D A – D C =D B – D D =D A – D B =D C – D D =Measure a connecting rodThe connecting rod is subjected to tons of pressure during engine operation and can wear, bend or break. The old piston and bearing inserts may indicate the condition of the connecting rod. If any piston or bearing abnormalities are found, there may be something wrong with the connecting rod.The small end is measured with a telescopic gauge and a micrometre. If the small end is worn, the rod bush should be replaced in a machine shop and the pin tted.The connecting rod big end is checked after removing the bearings and replacing the bearing cap. Once the bolts are torqued to the manufacturer’sspeci cation, measure the rod bore diameter on both edges and in both directions. Any difference in edge diameter equals taper of the big end. Any difference in cross diameters equals connecting rod big end out of roundness.Figure 1.14 The connecting rod assemblysmall end bearingsmall endbid end bearingbig end connecting rod belts9Unit 2: Cylinder headLEARNING OUTCOMES■Explain how the measurements are taken for thickness and warpage■Explain how all the measurements are taken for wear on the valve guide and valve stem■Explain how to check the seating of the valves■Explain how to measure valve spring height and spring tension.IntroductionThe cylinder head and valve service are very important for engine performance and service life. The valves, cylinder head and cylinder head gasket, work together tocontain the heat and pressure from combustion. Cylinder heads may become warped or cracked which may lead to coolant leaking into the engine oil and the overheating of the engine. When valve guides and valve stem seals are worn, the engine oil will leak past the valve stem into the combustion chamber, which leads to exhaust smoke and oil consumption. Poorly seated, burnt or bent valves negatively in uence combustion pressure and causes a mis re. It is thus important to carry out certain checks and measurements on a cylinder head to ensure an engine performs at its best.Measure a cylinder head for thickness and warpageA warped cylinder head has a bent deck surface which results from engine overheating. Use a straight edge and feeler gauge to measure cylinder headwarpage . Lay the straight edge on the head and try to slip different feeler gauge blade thicknesses under the straight edge. The thickest blade that ts under the straight edge equals the head warpage.Figure 1.15 Measuring cylinder head for warpageUnit 2: Cylinder headKeywordWarpage to bend or twist out of shape10Module 1: Engine measurementIf the warpage exceeds the manufacturer’s speci cations, the cylinder head needs to be machined by doing cylinder head milling in a machine shop. When servicing a cylinder head, it is important to also check for cracks in the cylinder head. Usually, dye penetrant is used to nd cracks on aluminium components at machine shops.Measure a cylinder head for wear on the valve guide and valve stemValve guide wear is a common problem, and it allows the valve to move sideways during operation. T o check valve guide wear, slide the valve into its guide and try to wiggle it from side to side. If the valve moves in any direction, the valve guide or stem is worn. The amount of play can be measured using a dial gauge, as illustrated in Figure 1.16. Mount the dial indicator stem against theside of the valve head and wiggle the valve sideways while reading the indicator. Valve guide wear can also be measured by using a small hole gauge, as illustrated in Figure 1.17.Figure 1.17 Using a small hole gauge to measure valve guideFigure 1.16 Using a dial gauge to measure valve guideand stem wear gaugecylinder headvalve stem guide11Unit 2: Cylinder headModule 1The small hole gauge is used to determine the inside diameter of the valve guide and then measured by using an outside micrometre.Valve stem wear is checked by using an outside micrometre, as illustrated in Figure 1.18.Check the seating of valvesThe measurements on the valve stem should be taken at the top, middle and bottom of the valve stem.Valve seats and valve faces should be checked for burning, pitting, and wear from opening and closing. T o test if a valve is seated correctly and seals effectively, the cylinder head can be turned upside down. Pour paraf n onto the valves to check if any paraf n leaks into the intake or exhaust ports. The valve to seat contact should also be checked, as illustrated in Figure 1.19.The contact width between the valve’s face and the seat of an intake valve should be approximately 1,6 mm. The valve to seat contact of an exhaust valve should be approximately 2,4 mm. The speci cations should, however, be checked according to each manufacturer.Figure 1.18 Using a micrometre to measure valve stem wearFigure 1.19 Checking the valve to seat contactback cut area – exaggeratedarea of valve that seat seals12Module 1: Engine measurementMeasure spring height and spring tension of a valveT o check for valve spring squareness and valve spring height , use acombination square. Place each spring next to the square on a at surface. Rotate the spring and check for a gap between the side of the spring and the square. If the spring is not square, too long or too short, it should be replaced. T o check for valvetension , use a valve spring tester, as illustrated in Figure 1.21.ACTIVITY 1.31. Discuss how you will measure the gasket surface of a cylinder head for warpage.2. Explain how a blown cylinder head gasket in uences engine performance.3. What will you look for when doing a visual inspection of a valve face and seat?Figure 1.20 Measuring valve spring squareness and heightFigure 1.21 Measuring valve spring tension by using a valve spring testersquarevalve spring13Module summaryModule 1Module summary■After extended engine operation and high mileage, it is necessary to service an engine block.■Worn piston rings can cause engine smoking, high oil consumption and low compression during combustion.■Worn bearings can lead to low oil pressure, bearing knock and complete part failure.■T o service a cylinder block, it is necessary to measure the cylinders for wear, inspect the cylinder wall for damage, install core plugs and hone a cylinder. ■The cylinder head and valve service are important for engine performance and service life.■The valves, cylinder head and cylinder head gasket, work together to contain the heat and pressure from combustion.■It is important to carry out certain checks and measurements on a cylinder head to ensure an engine performs at its best.Exam questions1.Describe the TWO measurements you would make on the cylinders of anengine using a sketch. (4)2.Explain how you will measure piston clearance. (2) THREE engine problems expected from having too much clearancebetween the cylinder and the piston rings? (3)4.Explain how a crank journal is measured for out of roundness or ovality. (2) the TWO methods for checking crankshaft bearing oil clearance. (2)6.Sketch to illustrate the positions in which you will measure warpage on acylinder head. (3)[16] 14Module 1: Engine measurement。

自动控制专业英语习题参考答案.doc

自动控制专业英语习题参考答案Lesson 1 Introduction to Control Systems1.Translate the following into Chinese.(1)In 1922 Minorsky worked on automatic controllers for steering ships and showed how stability could be determined from the differential equations describing the system.1922年，Minorsky开发了用于轮船驾驶的自动控制器，并指出根据描述系统的差分方程确定系统稳定性的方法。

(2) A home heating system in which a thermostat is the controller is an example of an automatic regulating system.家用供暖系统是自动调节系统的实例，其中的温度调节装置就是控制器。

(3)An engine which rejected no heat and which converted all the heat absorbed to mechanical work would therefore be perfectly consistent with the first law of thermodynamics.一台不散热并且把吸收的所有热量都转换为机械功的机器就与热力学第一定律完全一致。

(4)In short, a robot can do the dirty work —the dull, repetitious, dehumanizing and sometimes dangerous work that humans won"t or shouldn't do.简言之，机器人能干脏活，即那些人们不愿意或不该做的枯燥的、重复性的、呆板且有时有危险的活。

数控机床FANUC操作手册

G74 左螺纹攻丝循环（攻牙）
G76 精搪孔循环（精密搪孔）
G80 取消 73、74、76、81 至 89 之指令
G81 钻孔循环（直法钻孔）
G82 盲孔钻孔循环（直法钻孔）
G83 步进钻孔循环（啄法钻孔）
G84 右螺纹攻丝循环（攻牙）
G85 铰孔循环（搪孔）
G86 搪孔循环（搪孔）
G87 反搪孔循环（反向搪孔）
G22 软体行程极限“开” 04
G23 软体行程极限“关”
G28 归回机械基准原点
G29 从机械原点到指定点 00
G30 归回第二、第三及第四机械原点
G31 跳段指令
G40 刀具补偿取消
07 G41 刀具左方向补偿
G42 刀具右方向补偿
G43 刀具长度正方向补偿
08 G44 刀具长度负方向补偿
G49 刀具长度补偿取消
0.001——99999.999(毫米)
R
圆之半径
0.0001——3937.0078(英寸)
I、J、K
刀与圆中之距离
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F
进刀速度
1——15000 毫米/分
S
主轴旋转速度
1——5000 转/分（跟据机床定）
M
开关控制
00——99
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072 电脑贮存之程序数量多于 63 或（附加功能）125 个。
073 此程序编号已被用过。
074 程序编号在 1 至 9999 之外
076 在呼叫副程序（M98）或呼叫巨指令（G65）中无 P 指令。
077 副程序呼叫副程序中，已达三或五次。
在 M98、M99、G65 或 G66 中，P 指令的程序编号或段编号， 078

9 Control System Design Using the PID Controller

P{s) = PO + PlS-\-P2S'^-{-" '-\-PriS""
where the coefficients vary in independent intervals
PO G [Xo, 2/o], Pi e [Xi, 2/i], . . . , Pn^
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192
9. Control System Design Using the PID Controller
robust control and use them to provide a constructive procedure for obtaining all P, PI, and PID controllers that stabihze a given delay-free interval plant family. Section 9.3 considers the case of a system with unknown delay that requires the design of a robust PID controller. In Section 9.4 we study the problem of designing a resilient or nonfragile controller. Section 9.5 introduces time domain performance specifications into the PID design.
9.2 Robust Controller Design: Delay-Free Case
We start this section by briefly reviewing some results from the area of parametric robust control. We will only highlight those results that are most relevant to the subsequent development. For an exhaustive treatment, the reader is referred to [5]. Definition 9.1 Consider the set T of all real polynomials of degree n of the form

Vibration Control of the Rotating Flexible-Shaft-Multi-Flexible-Disk System With the EddyCurrent

Rong-Fong FungProfessorJung-Hung SunAssociate Professor Department of Mechanical and AutomationEngineering, National Kaohsiung First University of Scienceand Technology,1University Road,Yenchau,Kaohsiung,Taiwan824,ROCShih-Ming HsuGraduate Student, Department of Mechanical Engineering,Chung Yuan Christian University,Chung-Li,Taiwan32023,ROC Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk System With the Eddy-Current DamperIn this paper,the rotatingﬂexible-Timoshenko-shaft/ﬂexible-disk coupling system is for-mulated by applying the assumed-mode method into the kinetic and strain energies,and the virtual work done by the eddy-current damper.From Lagrange’s equations,the result-ing discretized equations of motion can be simpliﬁed as a bilinear system(BLS).Intro-ducing the control laws,including the quadratic,nonlinear and optimal feedback control laws,into the BLS,it is found that the eddy-current damper can be used to suppress ﬂexible and shear vibrations simultaneously,and the system is globally asymptotically stable.Numerical results are provided to validate the theoretical analysis.͓DOI:10.1115/1.1502671͔1IntroductionRecent trends in the components of rotating machines have been directly towards lighter and moreﬂexible due to the modern design requirement for high performance and efﬁciency.The shaft/disk model is an important machine component widely used in many industrial applications:turbine rotors,brake systems,and computer hard disk drive spindle systems,etc.Vibration problems of the rotating shafts with attached disks occur quite frequently, but the dynamic analysis for such systems at present is still re-stricted to theﬂexible-shaft/rigid-disk model.Recently,the ﬂexible-shaft/ﬂexible-disk model has been reviewed,formulated and analyzed by Fung and Hsu͓1͔.When magneticﬂux goes through a rotating conductive disk,an eddy current is induced around the pole area.A retarding braking force is generated by the interaction between the eddy current and the magneticﬂux.Nagaya et al.͓2͔analyzed the theoretical re-sults of the eddy current,braking force and damping coefﬁcient of a magnetic damper consisting of a cylindrical magnet and a plate conductor with arbitrary shape.Kligerman and Gottlieb͓3͔ap-plied an electromagnetic non-contact nonlinear eddy-current damper into the rotating system and also investigated its nonlinear dynamics and stability.Their eddy-current damping coefﬁcient will be adopted in this paper.The BLS comprises perhaps the simplest class of nonlinear sys-tem͑NLS͒.Generally speaking,the control problems for the BLS were studied and presented into three cases͓4͔:͑i͒linear feedback control,͑ii͒quadratic feedback control and͑iii͒optimal feedback control.Lyapunov stability theorem was employed to determine a linear feedback control law͓5͔such that the closed-loop system is asymptotically stable,and toﬁnd the stabilizing feedback control-ler͓6͔for the continuous BLS.The applicability of the quadratic control law͓7͔was extended to the case when the A-matrix has arbitrary eigenvalues.Cebuhar and Constanza͓8͔studied the op-timal control problems for the BLS and solved with a view to approximate analogous problems for the general NLS.The ap-proximation procedure is characterized by a sequence of linear problems converging to the overall optimal control solution.Be-nallou et al.͓9͔designed a nonlinear controller,which is similar to the quadratic feedback controller,based on Lyapunov stability theorem and the solution of Lyapunov equation.Chen͓10͔pro-posed a new nonlinear feedback control such that the close-loop system is not only asymptotically stable but also exponentially stable.To the authors’knowledge,little work has appeared on the dy-namic formulation and analysis of the rotatingﬂexible-shaft/ multi-ﬂexible-disk system with the non-contact eddy-current damper.The co-ordinate transformation is introduced to formulate the kinetic and strain energies.In order to obtain the control ef-forts on theﬂexible vibrations,the assumed-mode method and Lagrange’s equations are employed to derive the discretized equa-tion of motion in the matrix form.The external linearized mag-netic damping forces,generated by the interaction between eddy current and magneticﬂux via Ohm’s law and Lorentz force law, are considered to act on the rotating disks.Then three control laws,including the quadratic,nonlinear and optimal feedback controllers,are applied to suppress theﬂexible and shear deﬂec-tions of the shaft.Finally,numerical results are provided.2Modeling Assumptions and Theoretical Analysis 2.1Assumptions.The analyzed model,shown in Fig.1, consists of aﬂexible shaft carrying M-ﬂexible disks attached to the shaft supported by two end bearings.The shaft is modeled by Timoshenko-beam theory,and each disk is modeled as a uniform ﬂexible circular plate.The assumptions ofﬂexible attachment of shaft and disk͓1͔,and small deformation are made throughout the analysis in the paper.2.2Kinetic and Strain Energies of Rotating Shaft and Disks.In order to obtain the total kinetic and strain energies,the system is conveniently regarded as an assemblage of substructures in which the local reference frames are assigned to describe the rigid-body motions.Then,the elastic deformations are deﬁned as motions relative to the moving local reference frames,and the kinematics of each element can be derived.The detailed descrip-tion and transformation of the co-ordinate systems can be seen in͓1͔.The kinetic and strain energies of the rotating shaft modeled by Timoshenko-beam theory can be written as:KE Sϭ12͵0L͕␳S A S͓͑v˙SϪ⍀w S͒2ϩ͑w˙Sϩ⍀v S͒2͔ϩ␳S I S͓͑␪˙S␩ϩ⍀␪S␰͒2ϩ͑␪˙S␰Ϫ⍀␪S␩͒2͔ϩ␳S I PS⍀2͖dx,(1a)Contributed by the Technical Committee on Vibration and Sound for publication in the J OURNAL OF V IBRATION AND A COUSTICS.Manuscript received October 2001;Vibration and Acoustics revised May2002.Associate Editor:G.T.Flowers.SE Sϭ12͵0L͕E S I S͑␪S␩,x2ϩ␪S␰,x2͒ϩ␬G S A S͓͑v S,xϪ␪S␩͒2ϩ͑w S,xϩ␪S␰͒2͔͖dx(1b)where␳S is the mass density,A S is the cross-sectional area,⍀is the angular speed of the local reference frame OϪX1Y1Z1rotat-ing about the OX1axis as shown in Fig.2,v S and w S are the shaft transverse deﬂections,␪S␩and␪S␰are the slopes of the deﬂection curves due to the bending deformation alone,I S is the diameterarea moment of inertia,I PSϭ͐͐A(y2ϩz2)dA is the polar area moment of inertia,L is the total length,E S is Young’s modulus, G S is shear modulus,and␬is a constant shear coefﬁcient of the Timoshenko shaft.The subscript x denotes a spatial partial derivative.Ignoring the high-order nonlinear terms,the kinetic and strain energies of the i-th rotating disk are expressed respectively as:KE Di ϭ12␳DiA Dih Di͓͑v˙S͑D i͒Ϫ⍀wS͑D i͒͒2ϩ͑w˙S͑D i͒ϩ⍀vS͑D i͒͒2͔ϩ12␳DiI Dih Di͓͑␪˙S␩͑D i͒ϩ⍀␪S␰͑D i͒͒2ϩ͑␪˙S␰͑D i͒Ϫ⍀␪S␩͑D i͒͒2͔ϩ12␳DiI PDih Di⍀2ϩ12͵02␲͵R1iR2i␳D ih Di͕u˙Di2Ϫ2r͓͑␪˙S␩͑D i͒ϩ⍀␪S␰͑D i͒͒cos␪Ϫ͑␪˙S␰͑D i͒Ϫ⍀␪S␩͑D i͒͒sin␪͔u˙D iϪ2r⍀͓͑␪˙S␩͑D i͒ϩ⍀␪S␰͑D i͒͒sin␪ϩ͑␪˙S␰͑D i͒Ϫ⍀␪S␩͑D i͒͒cos␪͔uD i͖rdrd␪,(2a)SE Diϭ12͵02␲͵R1iR2iD iͫͩu D i,rrϩ1r u D i,rϩ1r2u D i,␪␪ͪ2Ϫ2͑1Ϫv Di͒u Di,rrͩ1r u D i,rϩ1r2u D i,␪␪ͪϩ2͑1Ϫv Di͒ͩ1r u D i,r␪ϩ1r2u D i,␪ͪ2ͬrdrd␪,(2b)where␳Diis the mass density,A Diis the area,h Diis the thickness,R1iand R2iare the inner and outer radii,respectively,I Diis thediametral area moment of inertia,I PDiϭ1/4␲(R2i4ϪR1i4)is thepolar area moment of inertia,D iϭE Dih Di3/12(1ϪvD i)is theﬂex-ural rigidity expressed by Young’s modulus E Diand Poisson’sratio v Di,and u Diis the elastic deﬂection of the i-th disk.Theparenthesized superscript notation(D i)is also used for the i-throtating disk.The subscripts r and␪denote the spatial derivatives.The total kinetic and strain energies of the multiple disks can beexpressed as:KE Dϭ͚iϭ1MKE Di,(3a)SE Dϭ͚iϭ1MSE Di,(3b)where M is the total number of disks.2.3Virtual Work of Eddy-Current Damper.The modelof an eddy-current damper shown in Fig.2consists of the electri-cally conductive diamagnetic thin disk attached to the shaft.Thedisk rotates in the air gap of the direct-current excited axial cylin-drical electromagnet and the induced electricﬁeld isgenerated. Fig.1Schematic diagram of a rotating shaftÕdisk coupling systemThe path of the ring cross-section magnetic ﬂux runs perpendicu-larly through the disk.According to Ohm’s law,the current can be propelled by the induced electric ﬁeld which is referred to as the eddy current.The Lorentz force acting on the disk is obtained by volume integration of the cross product of the primary magnetic ﬂux density vector and the eddy current density vector ͓2͔.The virtual work of the i -th eddy-current damper acting on the i -th rotating disk is expressed as:␦W ͑D i ͒ϭF Ry ͑D i ͒␦v S͑D i ͒ϩF Rz ͑D i ͒␦w S͑D i ͒,(4)where the eddy-current damping forces acting in the OY 1and OZ 1axes are:F Ry ͑D i ͒ϭϪc ͑D i ͒v ˙S͑D i ͒,(5a )F Rz ͑D i ͒ϭϪc ͑D i ͒w ˙S͑D i ͒,(5b )In Eqs.͑5a ,b ͒,c (D i )is the eddy-current damping coefﬁcient,as-sociated with the velocities of v S (D i )and w S (D i )of the i -th disk,and can be expressed as ͓3͔:c͑D i ͒ϭ12␲B x i 2͑R ¯2i 2ϪR ¯1i 2͒␴D i h D i ϫͩ1Ϫ͑R ¯2i 2ϪR ¯1i 2͒/R 2i2͓1Ϫ͑v S͑D i ͒2ϩw S͑D i ͒2͒/R 2i2͔2ͪ,(6)where ␴D i is the electrical conductivity of the i -th disk;R ¯1iand R ¯2i are the inner and outer radii of a direct-current excited cylin-drical electromagnet,respectively;and B x i is the axial component of the primary magnetic ﬂux density in the narrow air gap of thecylindrical electromagnet and can be expressed as:B x i ϭ␮0N D i i D i b D i,(7)where ␮0is the permeability of the vacuum,b D i is the air gapwidth of the electromagnet,and N D i is the number of turns of wire carrying a coil current i D i .If the shaft vibration near its equilibrium is small,the coil cur-rent i D i can be given as follows:i D i ϭi D 0i ϩi DC i ,(8)where i D 0i (у0)and i DC i are the constant steady current and the control current,respectively.The eddy-current damping coefﬁ-cient c (D i )can be expanded by Taylor series,assuming that thevalues of v S (D i )and w S (D i )are small enough,as:c ͑D i ͒ϭc ˜͑D i ͒͑i D 0i ϩi DC i ͒2,(9)wherec ˜͑D i ͒ϭ12␲ͩ␮0N D i b D iͪ2␴D i h D i ͑R ¯2i 2ϪR ¯1i2͒ͩ1ϪR ¯2i 2ϪR ¯1i2R 2i2ͪis a constant.Then the total virtual work done by the eddy-current dampercan be expressedas:Fig.2Free-body diagram of the eddy-current damping forces␦Wϭ͚iϭ1M␦W͑D i͒,(10) where M is the total number of the eddy-current dampers.3Discretized Equations of Motion3.1Discretization.Applying the assumed-mode method, the motion of every substructure will be approximated by weighted superposition of admissible functions.The deﬂections of Timoshenko shaft and the i-th disk can be written as͓1͔:v S͑x,t͒ϭ⌿Sd T͑x͒V s͑t͒,(11a)w S͑x,t͒ϭ⌿Sd T͑x͒W S͑t͒,(11b)␪S␩͑x,t͒ϭ⌿S␪T͑x͒⍜S␩͑t͒,(11c)␪S␰͑x,t͒ϭ⌿S␪T͑x͒⍜S␰͑t͒,(11d)u Di ͑r,␪,t͒ϭcos␪⌿DiT͑r͒UD i C͑t͒ϩsin␪⌿D i T͑r͒U D i S͑t͒,(11e)where⌿Sd෈R N Sd,⌿S␪෈R N S␪and⌿Di ෈R N D i are the columnvectors consisting of admissible spatial functions which describe the transverse deﬂections and bending rotations of Timoshenko shaft and transverse vibrations of the i-th disk,respectively;V S෈R N Sd,W S෈R N Sd,⍜S␩෈R N S␪,⍜S␰෈R N S␪,U Di C෈R N D i andU Di S෈R N D i are the column vectors consisting of the correspond-ing time-dependent generalized coordinates;and N Sd,N S␪andN Di are the numbers of admissible functions for the bending andshearing deﬂections of Timoshenko shaft and the transverse de-ﬂections of the i-th disk,respectively.3.2Equations of Motion.Substituting Eqs.͑11a-e͒into Eqs.͑1a,b͒,͑3a,b͒and͑10͒,and using matrix formulation,we have the discretized total energy functions and virtual work, where the detailed expressions are summarized in Appendix.By using Lagrange’s equations,the equations of motion can be de-rived as:͑J pϩz¯T R¯z¯͒⍀˙ϩz¯T A¯T zទϩzថT A¯zថϩ2⍀zថT R¯z¯ϭ0,(12a)A¯z¯⍀˙ϩM¯zទϩS¯z¯Ϫ⍀2R¯z¯ϩ⍀͑A¯ϪA¯T͒zថϭϪ͚iϭ1M c˜͑D i͒N¯͑D i͒zថ͑i D0iϩi DC i͒2,(12b)where z¯ϭ͕V S W S⍜S␩⍜S␰U D1CU D1S¯U D M C U D M S͖T෈R N z¯;M¯෈R N z¯ϫN z¯and S¯෈R N z¯ϫN z¯represent the mass͑inertia͒and stiffness matrices respectively,which are independent of ro-tation;(A¯ϪA¯T)෈R N z¯ϫN z¯represents the gyroscopic matrix;R¯෈R N z¯ϫN z¯and A¯෈R N z¯ϫN z¯represent the rotational and accelera-tional stiffness matrices respectively;N¯(D i)෈R N z¯ϫN z¯represents the damping matrix corresponding to zថ;and N z¯ϭ2(N SdϩN S␪ϩ͚iϭ1M N Di).The details of the value J P,and matrices M¯,R¯,A¯, S¯and N¯(D i)are listed in Appendix.Eqs.͑12a͒and͑12b͒are called as the rigid-body-rotation andﬂexible-vibration equations,respec-tively.The time derivative of the total mechanical energy E(t), which includes the total kinetic and strain energies of the rotating shaft͑1͒and the multiple disks͑3͒,becomes:E˙͑t͒ϭϪ͚ͩiϭ1M c˜͑D i͒N¯͑D i͒zថ͑i D0iϩi DC i͒2ͪT zថ.(13)Therefore,the system is conservative if the eddy-current damping force is not presented.In the rigid-body-rotation equation͑12a͒,it can easily be ob-served that there is no external moment acting in the⍀-direction.Considering the case that the shaft rotates with a constant speed, i.e.,⍀˙ϭ0and⍀ϭconstant,theﬂexible-vibration equation͑12b͒can be rewritten as follows:M¯zទϩ⍀͑A¯ϪA¯T͒zថϩ͑S¯Ϫ⍀2R¯͒z¯ϭϪ͚iϭ1Mc˜͑D i͒N¯͑D i͒zថ͑i D0iϩi DCi͒2.(14) In order to simply the dynamic analysis of theﬂexible-shaft/ﬂexible-disk system,a single thin disk(Mϭ1)acted upon by the eddy-current damper is considered in this paper.Therefore,Eq.͑14͒can be reduced as a single-input system:M¯zទϩ⍀͑A¯ϪA¯T͒zថϩ͑S¯Ϫ⍀2R¯͒z¯ϭϪc˜͑D͒N¯͑D͒zថ͑i D0ϩi DC͒2.(15) Theﬂexible-vibration equation͑15͒can be rewritten in the state-space form,and the bilinear state equation can be obtained as: x˙ϭAxϩN˜x͑i D0ϩi DC͒2ϭA˜xϩN˜x͑i DC2ϩ2i D0i DC͒,x͑0͒ϭx0,(16) where xϭ͕z¯zថ͖T෈R N,A˜ϭAϩN˜i D02,N˜ϭc˜(D)N(D)and Nϭ2N z¯, and the matrices A and N(D)are:Aϭͫ0IϪM¯Ϫ1͑S¯Ϫ⍀2R¯͒Ϫ⍀M¯Ϫ1͑A¯ϪA¯T͒ͬ෈R NϫN,(17a)N͑D͒ϭͫ000ϪM¯Ϫ1N¯͑D͒ͬ෈R NϫN.(17b)In Eq.͑16͒,(i DC2ϩ2i D0i DC)can be treated as the control input. The controller design will be formulated from Eq.͑16͒such that x→0and i DC→0as t→ϱ.4Bilinear Controller DesignThe quadratic,nonlinear and optimal feedback controllers will be designed for the BLS͑16͒in this section.4.1Quadratic Feedback Control.By means of a quadratic Lyapunov function candidate,V(x)ϭ1/2x T Sx,it can be shown that the quadratic feedback control͓6͔:i DC2ϩ2i D0i DCϭϪ␣x T SN˜x,(18) will stabilize Eq.͑15͒.Here␣Ͼ0,and S is a real symmetric positive deﬁnite NϫN matrix that satisﬁes Lyapunov equation:A˜T SϩSA˜ϩQϭ0,(19) where Q is a real symmetric positive semi-deﬁnite NϫN matrix. By using the control constraint:i DC2ϩ2i D0i DCуϪi D02,the control current i DC can be obtained as follows:͑i͒If x T SN˜xϽi D02/␣,i DCϭϪi D0ϩ͓i D02Ϫ␣x T SN˜x͔1/2;(20a)͑i͒If x T SN˜xуi D02/␣,i DCϭϪi D0.(20b) The proof may be obtained from the time rate of change of the quadratic Lyapunov function candidate for Eq.͑19͒.The result is given by:͑i͒If x T SN˜xϽi D02/␣,V˙͑x͒ϭϪ12x T QxϪ␣͓x T SN˜x͔2;(21a)͑i͒If x T SN˜xуi D02/␣,V˙͑x͒ϭϪ12x T QxϪ͓x T SN˜x͔i D02,(21b)where V(x)Ͼ0and V˙(x)Ͻ0for all x 0.Otherwise,it can also be shown͓6͔that the set⌺ϭ͕x෈R N:V˙(x)ϭ0͖has a unique so-lution and contains only trivial trajectories of Eq.͑16͒.Hence,the control current i DC in Eqs.͑20a,b͒globally asymptotically stabi-lizes the bilinear state system͑16͒.4.2Nonlinear Feedback Control.By means of a quadratic Lyapunov function candidate,similar to the quadratic feedback control,it can be shown that the nonlinear feedback control͓10͔:i DC2ϩ2i D0i DCϭͭϪ␳x TʈxʈSN˜xʈxʈ,x 0;0,xϭ0.(22)will stabilize Eq.͑16͒.Here␳Ͼ0,and S is a real symmetric posi-tive deﬁnite NϫN matrix that satisﬁes Lyapunov equation͑19͒. By using the control constraint:i DC2ϩ2i D0i DCуϪi D02,the control current i DC can be obtained as follows:͑i͒If x TʈxʈSN˜xʈxʈϽi D02/␳and x 0,i DCϭϪi D0ϩͫi D02Ϫ␳x TʈxʈSN˜xʈxʈͬ1/2;(23a)͑ii͒If x TʈxʈSN˜xʈxʈϽi D02/␳and xϭ0,i DCϭ0;(23b)͑iii͒If x TʈxʈSN˜xʈxʈуi D02/␳,i DCϭϪi D0.(23c)The time rate of change of the quadratic Lyapunov function can-didate is given by:͑i͒If x Tx SN˜xxϽi D02/␳and x 0,V˙͑x͒ϭϪ12x T QxϪ␳ͫx TʈxʈSN˜xʈxʈͬ2ʈxʈ2;(24a)͑ii͒If x TʈxʈSN˜xʈxʈϽi D02/␳and xϭ0,V˙͑x͒ϭ0;(24b)͑iii͒If x TʈxʈSN˜xʈxʈуi D02/␳,V˙͑x͒ϭϪ12x T QxϪͫx TʈxʈSN˜xʈxʈͬi D02.(24c)Hence,V(x)Ͼ0and V˙(x)Ͻ0for all x 0and the control current i DC in Eqs.͑23a-c͒globally asymptotically stabilizes the bilinear state system͑16͒.4.3Optimal Feedback Control.In order to solve the opti-mal control problem of the bilinear state system͑16͒,we deﬁne the following quadratic performance index:J͑x,i DC͒ϭ12͵0ϱ͓x T Qxϩr͑i DC2ϩ2i D0i DC͒2͔dt(25)where Q is a real symmetric positive semi-deﬁnite NϫN matrix, and r is a real positive value.By using Hamilton-Jacobi-Bellman ͑HJB͒equation͓11͔,Hamiltonian of the system can be formed as:H͑x,V x*,i DC͒ϭ12͓x T Qxϩr͑i DC2ϩ2i D0i DC͒2͔ϩ͑V x*͒T͓A˜xϩN˜x͑i DC2ϩ2i D0i DC͔͒,(26) where V*(x)is a quadratic function of the state.It seems reason-able to guess a solution in the form:V*(x)ϭ1/2x T S(x)x,and the solution of the HJB equation for the inﬁnite-time case is in the form:V x*ϭS(x)x,where the matrix-valued function S(x)is real symmetric positive deﬁnite.According to the necessary condition for a minimum:ץH/ץi DCϭ0andץ2H/ץi DC2у0͓12͔,we obtain the expression for the optimal control current i DC*as the form:͑i͒If͓N˜x͔T S(x)xϽi D02r,theni DC*ϭϪi D0ϩ͓i D02ϪrϪ1͓N˜x͔T S͑x͒x͔1/2;(27a)͑ii͒If͓N˜x͔T S(x)xуi D02r,theni DC*ϭϪi D0.(27b) It can be seen that the designed optimal feedback control law in Eqs.͑27a,b͒is similar to the quadratic feedback control law in Eqs.͑20a,b͒.The matrix-valued function S(x)can be obtained from the time-varying algebraic Riccati equation:A˜T S͑x͒ϩS͑x͒A˜ϪS͑x͓͒N˜x͔rϪ1͓N˜x͔T S͑x͒ϩQϭ0.(28) Substituting i DC*of Eqs.͑27a,b͒into Hamiltonian͑26͒via Eq.͑28͒,it results H(x,V x*,i DC*)ϭ0,and shows that the performance index is minimized by i DC*.The proof of the global asymptotic stability͓11͔is the same as Eqs.͑21a,b͒.Unfortunately,this nonlinear system of algebraic matrix equa-tion͑28͒is hard to solve.In general,it has no analytical solution. However,it has been shown͓8͔that the approximate solutions can be obtained by the iteration method from the convergent sequence of the following linear system:x˙͑0͒ϭA˜x͑0͒,x͑0͒͑0͒ϭx0,jϭ0,(29a) x˙͑j͒ϭA˜x͑j͒ϩB˜͑j͒͑i DC2͑j͒ϩ2i D0i DC͑j͒͒,x͑j͒͑0͒ϭx0,jϭ1,2,¯,(29b) where B˜(j)ϭN˜x(jϪ1).Therefore,the related sequence of the time-varying algebraic Riccati equation and the corresponding optimal control current are listed as follows:A˜T S͑j͒ϩS͑j͒A˜ϪS͑j͒B˜͑j͒rϪ1͓B˜͑j͔͒T S͑j͒ϩQϭ0,jϭ1,2,¯,(30a)͑i͒If͓B˜(j)͔T S(j)x(j)Ͻi D02r,theni DC*͑j͒ϭϪi D0ϩ͓i D02ϪrϪ1͓B˜j͔T S͑j͒x͑j͔͒1/2;(30b)͑ii͒If͓B˜(j)͔T S(j)x(j)уi D02r,theni DC*͑j͒ϭϪi D0.(30c) The trajectories x*(j)are solutions of Eq.͑29b͒associated with i DC*(j)in place of i DC.It has been proved͓8͔that if x*and i DC* represent the solutions of the optimization problem͑16͒and͑26͒, then the sequence͕x*(j)͖converges uniformly to the optimal tra-jectory x*and the sequence͕i DC*(j)͖converges uniformly to the optimal control i DC*.5Numerical Example5.1Model Assumptions5.1.1Parameters of Physical System.In the numerical simu-lations,Runge-Kutta method is employed to solve Eq.͑16͒for a simple-supported Timoshenko shaft and a single thin disk.The parameters are chosen as:͑i ͒Shaft:L ϭ1.0m,r S ϭ0.02m,␳S ϭ7850kg/m 3,E Sϭ210GPa,G S ϭ80GPa,␯S ϭ0.3,␬ϭ5/8,A S ϭ␲r S 2,I Sϭ1/4␲r S 4and I PS ϭ2I S ;͑ii ͒Disk (M ϭ1):h D ϭ0.005m,R 1ϭ0.05m,R 2ϭ0.25m,␳D ϭ2700kg/m 3,E D ϭ70GPa,␯D ϭ0.3,x D ϭL /2,A Dϭ␲(R 22ϪR 12),I D ϭ1/4␲(R 24ϪR 14)and I PD ϭ2I D .͑iii ͒Eddy-current damper (M ϭ1):␮0ϭ4␲ϫ10Ϫ7H/m,␴Dϭ3.82ϫ107mho/m,N D ϭ2000turns,R¯1ϭ0.15m,R ¯2ϭ0.20m,b D ϭ0.05m and i D 0ϭ2A.The optical-type sensors are needed to measure the bendingdeﬂections ␯S (D )(t )and w S (D )(t )at x ϭx D ,and the transverse de-ﬂection u D (R 2)(t )ϭu D (R 2,0,t )at r ϭR 2,while the strain gaugesare used to measure the shearing deﬂections ␪S ␩(O )(t )ϭ␪S ␩(0,t )and ␪S ␰(O )(t )ϭ␪S ␰(0,t )at x ϭ0.It is assumed that the power am-pliﬁers and sensors have perfect dynamics,and the active damp-ing is stable.5.1.2Admissible Functions.In this paper,mode shapes ͓1͔of the non-rotating uniform.Timoshenko beam with hinged-hinged boundary conditions and the non-rotating uniform circular plate with inner-clamped/outer-free boundary conditions are used as the admissible functions for the shaft and disk,respectively. 5.1.3Initial Conditions.In numerical simulations,the initial conditions of the bending and shearing deﬂections of the shaft and the transverse deﬂection of the disk,respectively,are:␯S ͑x ,0͒ϭ0.01sinͩ␲xLͪ,(31a )w S ͑x ,0͒ϭ0,(31b )␪S ␩͑x ,0͒ϭ0.01␲L cos ͩ␲x Lͪ,(31c )␪S ␰͑x ,0͒ϭ0;(31d )u D ͑r ,␪,0͒ϭ0.01⌿D ͑10͒͑r ͒cos ␪,(31e )where the ﬁrst mode is considered as initial condition in eachstructure.5.1.4Convergent Analysis.By calculating the eigenvalues of Eq.͑15͒in free vibration with ⍀ϭ300rpm,a convergent analysis is studied ͓13͔.In order to save the numerical computa-tion time based on the convergent analysis,the number of admis-sible functions for the bending deﬂections N Sd ϭ5,the number of admissible functions for the shearing deﬂections N S ␪ϭ5,and the number of admissible functions for the transversedeﬂectionsFig.3The transient responses of Timoshenko-beam model.…a …Bending deﬂection ␯S …D ……t …,…b …Bending deﬂection w S …D ……t …,…c …Shearing deﬂection ␪S ␩…O ……t …,…d …Shearing deﬂection ␪S ␰…O ……t …,…e …Transverse deﬂection u D …R 2……t …,…f …Total mechanical energy E …t ….…‘‘...’’:free vibration;‘‘’’:quadratic feedback control;‘‘-.-’’:nonlinear feedback control;and ‘‘’’:optimal feedback control ….N Du ϭ2͑the degree of freedom of the total discretized system ϭ24͒are chosen to describe the local deﬂections of the dis-cretized system.5.2Control Parametric Matrices.In view of the controller design for the bilinear systems,the design technique can be sum-marized as the following steps:Step 1.Choose the weighting matrices:Q ϭͫI¯00I ¯ͬ෈R N ϫN(32a )andI ¯ϭͫI00000ͬ෈R N z ¯ϫN z ¯(32b )where I ෈R N Sd is the identity matrix.Step 2.Choose the weighting factors:͑i ͒Quadratic feedback control:␣ϭ104.͑ii ͒Nonlinear feedback control:␳ϭ104.͑iii ͒Optimal feedback control:r ϭ10Ϫ4.Step 3.Solve Lyapunov equation ͑19͒for S or solve the time-varying algebraic Riccati equation ͑28͒for S (x ).Step 4.Obtain the control currents from Eqs.͑20a ,b ͒,͑23a -c ͒and ͑27a ,b ͒.5.3Numerical Results.By using the operating angular speed ⍀ϭ1000rpm,a steady-state current i D 0ϭ2A and the ini-tial conditions ͑31a -e ͒,the free vibrations and control results of Timoshenko-beam model are shown in Figs.3͑a -f ͒,and those of Euler-beam model are shown in Figs.4͑a -f ͒.Figures 5͑a -c ͒show the coil current inputs i D for the quadratic,nonlinear and optimal feedback control laws,respectively.Figures 3͑a ,b ͒show the bending deﬂections ␯S (D )(t )and w S (D )ϫ(t )at x ϭx D ,respectively.Figures 3͑c ,d ͒show the shearingdeﬂections ␪S ␩(O )(t )ϭ␪S ␩(0,t )and ␪S ␰(O )(t )ϭ␪S ␰(0,t )at x ϭ0,re-spectively.The dotted lines represent the case for free vibrations.The dash lines represent the responses under the quadratic feed-back control law ͑20͒.It is found that the controlled responses are asymptotically stable.The dash-dotted lines show the results un-der the nonlinear feedback control law ͑23͒.It can be seen that the amplitudes are also asymptotically stable.The control effort can be changed by adjusting the coefﬁcient ␳and control constraint.The solid lines represent the results under the optimal feedback control law ͑27͒.In our numerical experience,the differences of results between the iteration numbers j and j Ϫ1are smaller as j is larger.Figure 3͑e ͒shows the transverse deﬂection at the point(R 2,0)of the disk plane with u D (R 2)(t )ϭu D (R 2,0,t ).From the disk deﬂections,it is observed that no external force directly acts on it,and the coupling effects from shaft deﬂections are so small that the deﬂections of disk are almost always the same.Figure 3͑f ͒shows the total mechanical energy E (t ).In free vibrations,E (t )is constant.It can be seen that the responses via the nonlinear feed-back control decay fast,and those via the optimal feedback con-trol are the last ones.It is seen that all the total mechanical ener-gies of the three control laws asymptotically decay to zero about 0.05secThe control results of Euler-beam model of the three control laws are compared in Figs.4͑a -d ͒.It can be seen that the control responses shown in Figs.4͑a ,b ͒and the total energy shown in Fig.4͑d ͒are similar to those of Timoshenko-beam model.The transverse vibrations of disk shown in Fig.4͑c ͒still remain the same.The control currents are compared between Timoshenko-beam and Euler-beam models for the three control laws and are shown in Figs.5͑a -c ͒.For the quadratic feedback control,the current converges to the steady-state current i D 0in Fig.5͑a ͒.The coefﬁ-cient ␣in Eq.͑20͒can be chosen according to both the admissible control current input and the time to reach the steady state.In Fig.5͑b ͒,the current i D for the nonlinear feedback control is similar to an unit control,and converges to a steady-state current i D 0but it still chatters.The current i D for the optimal feedback control shown in Fig.5͑c ͒also converges to the steady-state current i D 0,and is smoother than that in Fig.5͑a ͒.However,these closed-loop control laws for both Timoshenko-beam and Euler-beam models are almost the same.From the results of above three closed-loop control laws,itisFig.4The transient responses of Euler-beam model.…a …Bending deﬂection ␯S …D ……t …,…b …Bending deﬂection w S …D ……t …,…c …Transverse deﬂection u D …R 2……t …,…d …Total mechanical energy E …t ……‘‘...’’:free vibration;‘‘’’:quadratic feedback control;‘‘-.-’’:nonlinear feedback control;and ‘‘’’:optimal feedback control ….found that the nonlinear feedback control has the best perfor-mance,and the optimal feedback control law appears to have the smoothest control input current.In practical,it is hard to imple-ment the optimal feedback control law,because the iteration method needs much computation time and cannnot have a imme-diate reaction to suppress vibration.6ConclusionIn this paper,the rotating ﬂexible shaft/disks coupled with theeddy-current damper are formulated by use of the co-ordinate transformation and assumed-mode method.The proposed three feedback control methods are successfully applied to the rotating ﬂexible shaft/disks system via the eddy-current damper.The prob-lem is reduced to the standard form of the bilinear system.It is found that the nonlinear feedback control has the best control effort and decays the amplitudes asymptotically,and is similar to an unit control.The optimal feedback control has the most smooth control current input.AcknowledgmentThe authors are greatly indebted to the National Science Coun-cil of R.O.C.for the support of this research through contract No.NSC-89-2213-E-033-044.AppendixDiscretized Kinetic and Strain Energies and Virtual Work:KE ϭKE S ϩKE D ϭ12J P ⍀2ϩ12͑z ថTM ¯z ថϩ2⍀z ថT A ¯z ¯ϩ⍀2z ¯T R ¯z ¯͒,(A 1)SE ϭSE S ϩSE D ϭ12z ¯T S ¯z ¯,(A 2)␦W ϭϪ͚i ϭ1Mc ˜͑D i ͒N¯͑D i ͒z ថ͑i DC i ϩi D 0i ͒2␦z ¯,(A 3)where the details of the value J P ,and matrices M ¯,R ¯,A ¯and S ¯arederived in Fung and Hsu ͓1͔,and the matrix N ¯(D i )is shown as:N¯͑D i ͒ϭ΄⌿Sd ͑D i ͒⌿Sd ͑D i͒T00000¯000⌿Sd ͑D i ͒⌿Sd ͑D i͒T0000¯00000000¯00000000¯00000000¯00000000¯00]]]]]] ]]000000¯000¯΅.References͓1͔Fung,R.F.,and Hsu,S.M.,2000,‘‘Dynamic Formulations and Energy Analy-sis of Rotating Flexible-Shaft/Multi-Flexible-Disk System with Eddy-CurrentBrake,’’ASME J.Vibr.Acoust.,22,pp.365–375.͓2͔Nagaya,K.,Kojima,H.,Karube,Y .,and Kibayashi,H.,1984,‘‘Braking Forcesand Damping Coefﬁcients of Eddy Current Brakes Consisting of Cylindrical Magnets and Plate Conductors of Arbitrary Shape,’’IEEE Trans.Magn.,20͑6͒,pp.2136–2145.͓3͔Kligerman,Y .,and Gottlieb,O.,1998,‘‘Dynamics of a Rotating System witha Nonlinear Eddy-Current Damper,’’ASME J.Vibr.Acoust.,120,pp.848–853.͓4͔Mohler,R.R.,1991,Nonlinear Systems:Volume II,Applications to BilinearControl ,Prentice Hall.͓5͔Derese,I.,and Noldus,E.,1980,‘‘Design of Linear Feedback Laws for Bilin-ear Systems,’’Int.J.Control,31,pp.219–237.͓6͔Gutman,P.O.,1981,‘‘Stabilizing Controllers for Bilinear Systems,’’IEEETrans.Autom.Control,26͑4͒,pp.917–922.͓7͔Jacobsen,D.H.,1979,Extensions of Linear-Quadratic Control,Optimizationand Matrix Theory ,Academic press.͓8͔Cebuhar,W.A.,and Costanza,V .,1984,‘‘Approximation Procedures for theOptimal Control of Bilinear and Nonlinear Systems,’’J.Optim.Theory Appl.,43͑4͒,pp.615–627.͓9͔Benallou,D.,Mellichamp,D.A.,and Seborg,D.E.,1988,‘‘Optimal Stabiliz-ing Controllers for Bilinear Systems,’’Int.J.Control,48͑4͒,pp.1487–1501.͓10͔Chen,M.S.,1998,‘‘Exponential Stabilization of a Constrained Bilinear Sys-tem,’’Automatica,34͑8͒,pp.989–992.͓11͔Lewis,F.L.,and Syrmos,V .L.,1995,Optimal Control ,Wiley,New York.͓12͔Bryson,A.E,Jr.,and Ho,Y .C.,1975,Applied Optimal Control ,Wiley,NewYork.͓13͔Jia,H.S.,1999,‘‘On the Bending Coupled Natural Frequencies of a Spinning,Multispan Timoshenko Shaft Carrying Elastic Disks,’’J.Sound Vib.,221͑4͒,pp.623–649.Fig.5Coil current input i D for …a …quadratic feedback control law,…b …nonlinear feedback control law,and …c …optimal feedback control law。

Automatic control theory 自动控制原理

1) linear systems versus Nonlinear systems. 2) Time-invariant systems vs. Time-varying systems. 3) Continuous systems vs. Discrete (data) systems. 4) Constant input modulation vs. Servo control systems.
Automatic control theory
A Course ——used for analyzing and designing a automatic control system
Chapter 1 Introduction
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Chapter 1 Introduction
1.5 An outline of this text 1) Three parts: mathematical modeling; performance analysis ; compensation (design). 2) Three types of systems: linear continuous; nonlinear continuous; linear discrete. 3) three performances: stability, accuracy, rapidness. in all: to discuss the theoretical approaches of the control system analysis and design. 1.6 Control system design process

工业自动化与自动化管理技术考试选择题 62题

1. 工业自动化系统中最常用的控制器是：A. PLCB. PCC. MCUD. FPGA2. 下列哪种传感器通常用于检测温度？A. 光电传感器B. 温度传感器C. 压力传感器D. 位移传感器3. 在自动化系统中，SCADA代表什么？A. System Control and Data AcquisitionB. System Control and Data AnalysisC. Supervisory Control and Data AcquisitionD. Supervisory Control and Data Analysis4. 机器人编程中，常用的编程语言是：A. C++B. JavaC. PythonD. RAPID5. 自动化系统中的“反馈”是指：A. 系统输出与期望值的比较B. 系统输入与期望值的比较C. 系统输出与输入的比较D. 系统输入与输出的比较6. 下列哪项技术用于提高工业机器人的精度？A. 机器学习B. 人工智能C. 视觉系统D. 传感器融合7. 在自动化生产线上，下列哪种设备用于物料搬运？A. 机器人B. 传送带C. 升降机D. 分拣机8. 工业自动化中的“闭环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制9. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP10. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database11. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器12. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database13. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统14. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机15. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制16. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP17. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database18. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器19. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database20. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统21. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机22. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制23. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP24. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database25. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器26. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database27. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统28. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机29. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制30. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP31. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database32. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器33. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database34. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统35. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机36. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制37. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP38. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database39. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器40. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database41. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统42. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机43. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制44. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP45. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database46. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器47. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database48. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统49. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机50. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制51. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP52. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database53. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器54. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database55. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统56. 在自动化生产线上，下列哪种设备用于产品检测？A. 机器人B. 传送带C. 检测机D. 分拣机57. 工业自动化中的“开环控制”是指：A. 只有输入信号的控制B. 只有输出信号的控制C. 输入信号和输出信号的控制D. 输入信号、输出信号和反馈信号的控制58. 下列哪种通信协议常用于工业自动化网络？A. HTTPB. FTPC. ModbusD. SMTP59. 在自动化系统中，下列哪种设备用于数据存储？A. PLCB. HMIC. SCADAD. Database60. 机器人操作中，下列哪种传感器用于检测物体的位置？A. 温度传感器B. 压力传感器C. 视觉传感器D. 声音传感器61. 在自动化系统中，下列哪种设备用于人机交互？A. PLCB. HMIC. SCADAD. Database62. 下列哪种技术用于提高工业自动化系统的安全性？A. 机器学习B. 人工智能C. 视觉系统D. 安全控制系统答案1. A2. B3. C4. D5. A6. C7. B8. D9. C10. D11. C12. B13. D14. C15. A16. C17. D18. C19. B20. D21. C22. A23. C24. D25. C26. B27. D28. C29. A30. C31. D32. C33. B34. D35. C36. A37. C38. D39. C40. B41. D42. C43. A44. C45. D46. C47. B48. D49. C50. A51. C52. D53. C54. B55. D56. C57. A58. C59. D60. C61. B62. D。

FANUC 0i mate C 数控铣床电气控制系统及PLC控制设计

Abstract Can be
CNC milling machine is a common milling machine used digital control system the control of the program code accurately for milling machining
Key words :FANUC 0i mate C;CNC milling machine; Frequency conversion governor; PLC;Servo drive
FANUC 0i mate C 数控铣床电气控制系统及 PLC 控制设计
目录
引言.....................................................................1 1 FANUC 0i mate C 系统构成...............................................2 1.1 FANUC 0i mate C 系统组成及功能....................................2 1.2 FANUC 0i mate C 系统的配置........................................3 1.3 FANUC 0i mate C 系统的功能连接....................................6 2 系统硬件配置............................................................8 2.1 主轴电机的选型.....................................................8 2.2 交流异步电动机的调速方法...........................................8 2.3 变频调速器工作原理和基本构成......................................10 2.4 变频调速器的选择..................................................12 2.5 变频调速器的参数设置..............................................13 2.6 CNC 变频调速器的连接框图..........................................16 2.7 数控机床进给伺服系统的组成和功能特点..............................16 2.8 伺服电机的选型....................................................19 2.9 进给伺服单元的选型................................................24 3 电气控制系统电路图设计.................................................26 3.1 主轴控制原理图....................................................26 3.2 供电原理图.......................................................26 3.3 CNC 主板............................ ............................27

仿昆虫微飞行器仰俯姿态伺服控制器的设计

仿昆虫微飞行器仰俯姿态伺服控制器的设计收稿日期:2009-12-17基金项目:浙江省自然科学基金资助项目,(Y6090639)颜幸尧,张洪军,苏中地,孙在(中国计量学院计量测试工程学院,杭州 310018)摘要:在风洞实验中,为动态地研究仿昆虫微飞行器的仰俯姿态控制方法,微飞行器的仰俯姿态需要根据安装于其上的微型多维力传感器的输出扭矩进行实时调节,为此设计了本伺服控制器。

控制器采用STC 增强型51单片机作为本控制器的核心,用模拟SP I 接口与多维力传感器进行数据采集,采用电位器作为姿态角传感器,外接模数转换电路对姿态角度进行采样;采用步进电机实现对仰俯姿态角角速度的动态调节,并采用P I D 算法对姿态角角速度进行闭环反馈控制,以确保仰俯姿态角速度的控制精度。

关键词:仿昆虫;M AV (M icro-A eria-l V ehicle);仰俯姿态;风洞中图分类号:TM 275;TM 38316 文献标志码:A 文章编号:1001-6848(2010)07-0001-03Design on a Servo Controller for P itch A ttit ude Control of Insect Ins piredMAVsYAN X ing -yao ,Z HANG H ong -j u n ,SU Zhong -d,i SUN Zai(C ollege o f M etrology Technology and E ng ineering,China J iliang Universit y ,H angzhou 310018,China )Abst ract :For t h e conven ience for p itch attitude contro lm ethod stud ies of i n sect inspiredMAV s ,t h e pitch attitude o f a MAV in w i n d tunnel need to be adjusted i n stantaneously accord i n g to the force and m o m en ts m easured by a mu lti d i m ensional force sensor wh ich w as mounted on the body o fMAV,this g i v es rise the de -si g n of this contro ller .An enhanced STC M CS-51m i c ro -chip w as token as the CPU of the who l e circu i,t SPI i n terface w as used to get the data fr o m the mu lti d i m ensional force sensor and an adjustable resister to -gether w ith an analog to dig ita l converter c ircu itw ere used to get rea l pitch attitude ofMAV.S tep m oto rw as taken to rea lize the contr o l o f t h e p itch attitude dyna m ically ,and PI D algorith m w as used i n a feedback con -tro l loop of pitch angu lar veloc ity ,wh ich i m prove the accuracy o f the pitch angular velocity greatly .K ey W ords :Insect i n sp ired ;MAVs ;Pitch attitude ;W i n d tunnel0 引言随着尺寸的缩小,各类常规微飞行器都在气动效率和机动性能上遇到了难于逾越的障碍。

自动控制原理第十章

Compensation 补偿、校正

The alteration or adjustment of a control system in order to provide a suitable performance is called compensation. Compensation is the adjustment of a system in order to make up for deficiencies or inadequacies(不足).
1 1
A phase-lead network
R2 ( R1Cs 1) V2 ( s ) R2 Gc ( s ) R R R1 R2 V1 ( s ) R R // 1 1 2 Cs 1 2 1 Cs R1 R1 R2 R2
Type of compensation

Cascade compensation
feedback compensation

Output compensation
input compensation
10.2 Approaches to system design

Frequency domain---Bode diagrams Time domain---Root locus
Ts 4 sec, 0.45
4 Ts 4 n 0.45n 4
n 2.22
B 1.33n 3
For uncompensated system
K1 G (s) 2 s
G ( j ) 10 ( j ) 2
n K1
n 2.22

2 K1 n 10

圆筒状超磁致伸缩致动器磁场研究与仿真

圆筒状超磁致伸缩致动器磁场研究与仿真范文涛;林明星;鞠晓君;王庆东【摘要】为设计圆筒状超磁致伸缩致动器(GMA),采用基于磁路的方法对圆筒状超磁致伸缩材料(GMM)内的磁场强度进行计算,基于Maxwell软件建立了圆筒状GMA的3D模型并对磁路结构中各部件尺寸及GMA筒内构件的磁导率对磁场的影响进行了仿真研究.结果表明:在闭合的磁路结构中,对于给定的线圈匝数和激励电流,GMM筒中磁场强度大小受GMM筒轴向长度影响较大且为负相关.磁场均匀性方面,影响较大的是穿过圆筒状GMA构件的磁导率和导磁环轴向长度,二者均与磁场不均匀度正相关.%In order to design a cylindrical giant magnetostrictive actor (GMA), the magnetic field intensity in the cylindrical GMM is calculated using magnetic circuit method.The 3D model of the cylindrical GMA is established by Maxwell software and the influences of the size of each unit in the magnetic circuit are studied.The results show that in a closed magnetic circuit with specific coil turns and current, the length of the GMM has great negative correlation with the magnetic field intensity inside the cylindrical GMM.As for the uniformity, the biggest correlation factors, both of which are negative, are the magnetic permeability of the body through the cylindrical GMA and the length of the magnetic conducting ring.【期刊名称】《功能材料》【年(卷),期】2017(048)005【总页数】7页(P5054-5060)【关键词】圆筒状超磁致伸缩致动器;磁路设计;磁场;仿真【作者】范文涛;林明星;鞠晓君;王庆东【作者单位】山东大学机械工程学院,济南 250061;山东大学机械工程学院,济南250061;山东大学机械工程学院,济南 250061;山东大学机械工程学院,济南250061【正文语种】中文【中图分类】TP202超磁致伸缩材料(GMM)是近来发展迅速的新型功能材料，拥有比同类材料更加突出的优点，如能量密度高、响应速度快、应变系数大、居里温度高、输出力大等，在机械领域取得了广泛应用[1]。

过程装备与控制工程专业外语(原文+翻译)

Unit 21Pumps1. IntroductionPump, device used to raise, transfer, or compress liquids and gases. Four' general classes of pumps for liquids are described below t In all of them , steps are taken to prevent cavitation (the formation of a vacuull1), which would reduce the flow and damage the structure of the pump, - pumps used for gases and vapors are usually known as compressors . The study of fluids in motion is called fluid dynamics.1．介绍泵是提出，转移或压缩液体和气体的设备。

下面介绍四种类型的泵。

在所有的这些中，我们一步步采取措施防止气蚀，气蚀将减少流量并且破坏泵的结构。

用来处理气体和蒸汽的泵称为压缩机，研究流体的运动的科学成为流体动力学。

Water Pump, device lor moving water from one location to another, using tubes or other machinery. Water pumps operate under pressures ranging from a fraction of a pound to more than 10,000 pounds per square inch. Everyday examples of water pumps range from small electric pumps that circulate and aerate water in aquariums and fountains to sump pumps that remove 'Water from beneath the foundations of homes.水泵是用管子或其他机械把水从一个地方传到另一个地方。

基于AMEsim_Simulink的电液伺服比例控制的同步回路建模与仿真研究

2
同步系统组成及原理
电液伺服比例阀控非对称液压缸同步系统的原理图如图 1 所示。两个液压缸的结构和参数完全相同，用电液伺服比例阀控制，设定值与速度传感器输出信号的差值作，为阀的控制信号，系统的控制策略采用“同等方式 ” 即两个同步液压缸同时跟踪设定的理想输出，分别受
收稿日期： 2012 － 04 － 20 作者简介：于宗振（ 1987 －），男，山东临沂人，在读硕士，主要从事机电系统控制方面的研究。
2 2 1
2（ 1 + n ） βe A Vt
槡
2 Vt （ 1 + n2 ） β e m
]
的固有频率，该值可从产品样本提供的伯德图上查到； ξ sv 为伺服比例阀的阻尼比；由式（ 7 ）～（ 10 ）可绘出对称阀控非对称液压缸位置控制系统方框图如图 2 所示。由图 2 可求得对称阀控非对称液压缸位置控制
*
（ 3 ）有些产品为了解决零漂问题，设置了第 4 位，还可实现断电时的安全保护。伺服比例阀内装放大器，具有伺服阀的各种特 — — — 、、，性零重叠高精度高频响其工作频宽和性能已达高性能伺服阀，而成本仅为伺服阀的 1 /3 ，对油液清洁度要求比伺服阀低，工作更可靠，可用于位置、压［1 ］力等要求无零位死区的闭环控制。笔者以电液伺服比例阀控非对称液压缸为研究建立了电液伺服比例阀液压同步控制系统的数对象，学模型，设计了 PID 控制器对同步系统的控制性能进行优化。并利用 AMESim 和 Simulink 软件对双缸同步液压系统进行了联合仿真，仿真结果表明，采用伺服比例阀可以实现较高精度的同步控制。
·机械研究与应用· 2012 年第 3 期（总第 119 期）

Client-Server Design and Implementation Issues in the Accelerator Control System Environmen

Client-Server Design and Implementation Issues in the Accelerator ControlSystem Environment *S. Sathe, L. Hoff, T. CliffordBrookhaven National LaboratoryUpton, NY, 11973-5000, USAAbstractI n distributed system communication software design, the Client-Server model has been widely used. This paper addresses the design and implementation issues of such a model, particularly when used in Accelerator Control Sys-tems. In designing the Client-Server model one needs to decide how the services will be deﬁned for a server, what types of messages the server will respond to, which data formats will be used for the network transactions and how the server will be located by the client. Special consideration needs to be given to error handling both on the server and client side. Since the server is usually located on a machine other than the client, easy and informative server diagnostic capability is required. The higher level abstraction provided by the Client-Server model simpliﬁes the application writing, but ﬁne control over the network parameters is essential to provide the performance required. These design issues and implementation trade-offs are discussed in this paper.1. IntroductionVery large scale integration and the advent of data communication networks have made desktop computers an afford-able alternative to centralized facilities. Data-communication networks connect the computers together, allowing the exchange of information and the sharing of resources between different computers on the network. Resources can now be concentrated in the computer that best provides the resource and that computer can make the resource avail-able to other computers via the network. An application is no longer conﬁned to the resources available on the local computer, but can now use the resources available to the network.An accelerator control application is an example of such a paradigm. It uses various services such as the database, accelerator device control, alarm handling, data archiving, data display and user interface services. To perform these services one or more of each type of server is available. These servers are distributed across the network and need to be accessible to the application. An application user should be able to access these services on the network without explicitly requesting the network transactions. The computer software should automatically locate the resource and transfer the information to and from the service. In other words, access to the services on the network needs to be transparent. A standard model for such distributed applications is a Client-Server model.2. Client-Server ModelIn a Client-Server model, the server offers the services to the network which the client can access. The term client and server do not necessarily imply computers; they can be thought of as a client process and a server process. In certain cases even a server process may perform a client’s role in addition to its server role and vice versa. A Client Server relationship is not symmetrical[1]. This means that they are coded differently. The server is started ﬁrst and never ter-minates unless it is forced to.* Work performed under the auspices of the U.S.Department of EnergyA server typically opens a communication channel and waits for a client request to arrive at the well known address. Upon the arrival of a request, the server executes it in the context of the server process or in a separate one and sends back the results to the client. Then it goes back in the wait state to receive more client requests. The client, knowing the server address, opens a communication channel, connects to it, and then sends request messages to the server and receives the responses. When done, the client closes the communication channel.A Client-Server model is considered to be part of the session layer and presentation layer of the well-known Open System Interconnect(OSI)[2] Model. This layer hides the application layer from some networking details and differ-ences in data formats between various computer architectures. These higher level abstractions namely Client and Server provide an appropriate interface which makes the distributed application writing simpler.3. Server DesignA server typically provides a number of services. A service is a piece of code that accomplishes the desired function-ality. A Service can be fully deﬁned by its name, input parameters and the results produced. Such a service can be executed in the context of the server process and is called an iterative service, or it can be executed in the context of another process and is called a concurrent service. The iterative services are used when the time to handle a request is known ahead of time. In the case of a concurrent service, the amount of time required to handle the service is unknown or is too long to hold the server process from accepting new requests. Concurrent services need to be reen-trant and, if they have to share any global data, a proper locking mechanism is required. Accelerator controls device services such as setting the setpoint of a device or getting the readback from a device are examples of the concurrent type services, as the time required for these services varies with which control device is being used. However, the ser-vice that gets server diagnostic information can be of an iterative type of service.A server can be stateless or stateful. A stateless server does not maintain any information or state about the clients. However a stateful server accumulates client information to function properly. In the case of a stateless server crash, the client comes to know about it and can retry to contact it. The server can just be restarted and then functions nor-mally. However if a stateful server crashes in the middle of its operation, the server alone has the information to know where to resume operation. Server crash recovery can be complicated. A stateful server also needs to know about a client crash so that it can clean up the client information held with it. An accelerator controls device server that sends back a number of replies for a single client request needs to remember the client address and therefore is an example of a stateful server. However a display server is a stateless server since it does not have to remember any client infor-mation.Another issue in server design is security. Should the server need to identify the client before accepting the request? If the server does employ some identiﬁcation checking scheme, it should report security faults to some authority. Accel-erator control facilities that give control system access to a large user community tend to have some kind of security scheme built in their system.The issue of heterogeneity is important in the server design. Several kinds of heterogeneity need to be considered: machine architecture independence, operating system independence, software vendor implementation independence and server release independence. Different machine architectures have different data representations. Using higher level languages can solve this problem. The use of standards and portable compilers give the operating system inde-pendence. The server release independence implies that the client should be able to run independently of which ver-sion of the service is available. Vendor dependencies must be eliminated to increase the portability of the application. Accelerator controls applications can be written using C or C++ languages to achieve the machine architecture inde-pendence. The use of a portable compiler such as GNU (provided by Open Software Foundation) C or C++ compiler gives operating system independence. The use of standard libraries such as POSIX gives vendor independence. In accelerator control applications it is common that a server and/or a client needs to be updated after it has been released. This need may be because of added functionality or a bug ﬁx in the server code. It is often desirable that the old and new versions of server should coexist such that the new server can service the requests from the old or the new clients. The clients should be prepared to use the new server if it exists or should try the old one.Error reporting is one of the important features of the server. A server needs to return the good or bad status of the ser-vice executed. A well deﬁned interface to deﬁne all the service-related errors is crucial.4. Client DesignA client is an entity that requests services from a remote or a local server. The client assembles a request message and transmits it to the server to initiate some action by the server. The ﬁrst step in a client design is to determine how the client will ﬁnd the server process to which it wants to send the requests. Some kind of a database is usually employed to hold this information.The request messages sent by a client to a server can be broadly categorized as send-only, blocked, callback, batch and broadcast[1]. A send-only type message originates at the client end and is sent to the server. There is no reply expected from the server for this message. A client request sent to the display server to update the data to be displayed is an example of a send-only type message. When a blocked message is sent to the server, the client blocks until the reply is received from the server. A request to get the control device server diagnostic information is an example of such a type of message. When a callback message is sent to the server, one or several replies are expected from the server at a later time. To receive such delayed replies, the client now has to become a server and the server has to become a client while originating the replies. For example, an accelerator control device client sends a callback request to a server to receive the data from a device based on a hardware or a software event. A broadcast message is sent to probe the network for servers matching a certain address. The servers matching this address acknowledge the request by sending a reply back to the client. A batch message keeps the requests at the client side until the client lets them go over the network. An advantage of sending requests in batches is that it reduces the network overhead. A sin-gle reply for all the requests is sent by the server. Accelerator control clients use batching of request messages to improve overall performance.There are some issues to consider while determining the timeout values for the client. Servers are likely to take vary-ing amounts of time to service individual requests, depending on factors such as server load, network routing and net-work congestion. The client should be prepared for the worst conditions or for a variation of service time-outs.A client can fail to communicate to a server for various reasons. For example, the client may not ﬁnd the address of the server, or the network between the server and client may not be operational, or the machine on which the server runs may not be up, or the server itself may not be running. The client needs to detect and report these errors in a well-deﬁned fashion.A client and server running on two computers having different architectures pose a data interpretation problem. T o overcome such a problem various strategies can be used. The client can ﬁlter the data into a machine-independent for-mat before sending it to the server. The server on receiving the request ﬁlters it in its native format. When sending the reply back to the client, the server ﬁlters the data in the machine independent format and the client ﬁlters it back into the native format.A second strategy could be that the server always makes the data right after receiving and before sending. This strat-egy assumes that the server knows about its native architecture data formats as well as the client’s architecture data format. Another strategy is that the client always makes the data conversions before sending and after receiving. In this case the client has to know about its native as well as servers’s architecture data format. It is also possible to have the receiver always making the data right. In such a case both client and server have to know the architecture of the machine from which the data came. Accelerator control applications can choose from one of the above mentioned techniques that is suitable for their environment. However the technique that converts the data to machine indepen-dent format or the case where the receiver always makes the data right are supported by standard industry tools such as RPC[1][3].5. Client Server PerformanceAs with any software design, performance is an issue in the design of the server. Numerous client requests can quickly affect a servers’s performance, if the server has to do a lot of processing for each request. By keeping the request short and the amount of work required by the server for each request low, the performance can be improved, especially in the case of the iterative server. If the service takes a long time to ﬁnish, the server performance can be improved by making it concurrent. If the concurrent service uses a globally shared resource, care should be taken to lock it at the lowest possible level of granularity to avoid delays and assure smooth working of the server.A client should try to group small requests into one batch and then send it to the server in one network transaction to avoid the overhead involved in sending individual small requests.One of the parameters that has a big impact on the server performance is ﬂow control. Flow control assures that the client does not overwhelm the server by sending requests at a faster rate than the server can process them. The size of the request message and the rate at which the message is sent need to be tuned for the given network conﬁguration.Proper network parameter selection is important both on the client and the server side. In the accelerator control applications, the message size typically varies from application to application. It ranges from a few bytes to a few hundred kilobytes. The time required to send and receive the message is mainly dependent on the size of the message for the same distance. It is desirable to be able to set the timeout suitable for a given request. The network receive buffer size for the server is a function of the largest message size, as well as how many clients are expected to com-municate to the server simultaneously. The network send buffer size needs to be set as well, depending upon the size of the message and the rate at which they are sent. To help the user to get a handle on the network transaction timing, the client needs to provide the timing statistics for the messages being sent and the reply messages being received.Last but not least, the network components play an important role in improving the client server performance. High performance network elements such as bridges and routers and high band-width networks, specially for consoles that collect data from a number of front ends, are crucial.A server health checking mechanism is necessary to be built in the server design. Some diagnostics about the server request handling are highly desirable.6. Client Server ImplementationOne of the major decisions that the implementor needs to make in the beginning is what network transport is appro-priate for a given Client Server model. User Datagram Protocol (UDP) and Transmission Controls Protocol (TCP/IP) are widely used transports in accelerator control system. The size of the messages to be exchanged, network topology and reliability of the message delivery are important determining factors amongst many others. UDP seems to be suit-able for smaller size messages, typically less than 1000 bytes and for the smaller network. The smaller message size and smaller network ensure a minimal packet loss with normal network trafﬁc. TCP/IP is desirable in case of large message sizes and for the wider networks. It provides a reliable data delivery and also does the ﬂow control so that the sender does not overload the receiver by sending data at a rate faster than it can handle. TCP/IP being a connection oriented protocol, the client needs to reconnect after a server crash.Having selected the transport, one proceeds to choose the interface to be used to implement the Client Server Model. Remote Procedure Call(RPC) is a well known mechanism that is used to invoke a procedure on a remote system. The RPCs prevent the client and servers from having to worry about details such as sockets, network byte order etc. which makes distributed application writing easier. Some accelerator control system designers choose to write their own RPCs while others utilize the standard ones. Standard RPCs enable the writing of servers and clients in a uniform way. Typically, they provide standard ways for ﬁnding the server process on a given host. The standard RPCs provide a mechanism to deﬁne the request and reply messages which is vital to any distributed application. Each type of mes-sage can be deﬁned by its name. The request and reply data also can be deﬁned in terms of single data items or anarbitrary structure. Errors are handled and reported via a well deﬁned interf ace. Security mechanisms, both on the server and the client side are provided by the RPC interface. Since RPCs are available on various Unix as well as Real Time systems, the client server code becomes portable. V arious machine architecture heterogeneity is taken care of by the standard RPCs. They also provide a uniform health checking mechanism crucial to any distributed application. RPCs provide a mechanism to structure the request and reply data in an arbitrary, user deﬁned fashion. RPCs in gen-eral are well suited for synchronous type of communication, where the client blocks until the reply from the server is received. To implement the callback type of message delivery, which is asynchronous in nature, takes extra efforts on the part of the implementor.Using the concepts described above, a Client-Server model has been designed and implemented for the AGS and RHIC control systems. There are two different implementations, one for each control system, because of different requirements and historic reasons. UDP transport was found suitable for AGS, because of the message size of 512 bytes and a small network of about 40 front ends. As UDP does not support the ﬂow control, the clients needed to introduce the ﬂow control explicitly. As the RHIC supports large message sizes and is planned to have of the order of 150 front ends, TCP/IP was a natural choice. Both the AGS and RHIC accelerator device servers are designed to be stateful. Since TCP is a connection-oriented protocol, the design needed to provide mechanisms for cleaning up the client information from the server as the clients crash. Both iterative and concurrent services are supported by the servers. As the vendor supplied software does not give a handle on the client-server connection timeout, a Unix signal is used to interrupt the system connect call. In the case of a server crash, the TCP-based clients need to reestablish the connection with the server. In contrast, UDP based clients do not have to worry about it. Both blocked and callback type client messages are supported. Client-server implementation is a C++ class library and is portable across Unix and VxWorks operating systems. The class library is based on the standard SUN Open Network Computing(ONC) RPC communication interface. The capability of adjusting the network buffer size and time-outs is also provided. The rpcinfo program supplied by RPC is used for checking the health of the server. To get a handle on more server spe-ciﬁc information, the server diagnostics provides information such as start-up time, the machine name on which it is running, the number of synchronous and asynchronous messages it has handled from the start-up time and so on. It also provides the information about callback clients. Typical diagnostic information is as follows:ADOIF SERVER DIAGNOSTICS INFO-----------------------------------------------Host Name: startupTime: THU OCT 19 08:30:28 1995RPC Program Number: 1000002RPC Version Number: 0TCP Socket Number: 19Port Number: 990Receive Queue Size: 10000 bytesSend Queue Size: 10000 bytesSynchronous Messages handled: 2784Asynchronous Messages sent out: 9178Asynchronous Active Requests: 328Async Clients Being Served: 4Async Client Addresses being used by the ADOIF Server----------------------------------------------------------------Client Address No 0----------------------Host Name: RPC Program Number: 1073742096RPC Version Number: 1Server Port Number: 10998Process Id: 16272Client Address No 1----------------------Host Name: RPC Program Number: 1073742226RPC Version Number: 1Server Port Number: 12741Process Id: 1402Client Address No 2----------------------Host Name: RPC Program Number: 1073742231RPC Version Number: 1Server Port Number: 12744Process Id: 1407Client Address No 3----------------------Host Name: RPC Program Number: 1073741829RPC Version Number: 1Server Port Number: 44807Process Id: 260057. ConclusionsThe Client-Server Model is a standard model used in the accelerator controls applications. There are various server and client design issues. They include concurrent versus iterative services, stateless versus stateful servers, message security, machine architecture, software vendor and server version independence. The design of built-in mechanisms to send and receive different types of messages such as send-only, blocked, callback, broadcast etc. is necessary. To improve the server performance, proper ﬂow control on the client side is necessary. Selection of network time-outs and selection of proper network buffer sizes is a key to performance tuning. Standard RPCs are well suited to imple-ment a Client-Server model as it addresses most of the design and implementation issues of such a model. A Client-Server model implementation that handles callback type messages tends to be more complex and involved than one that handles only synchronous type messages.References[1] J. R. Corbin, The Art of Distributed Applications, Springer-Verlag New York[2] W. Richard Stevens, Unix Network Programming, Prentice Hall[3] W. Rosenberry, D. Kenney, G. Fisher, Understanding DCE, O’Reilly Associates, Sebastopol, CA[4] J. Bloomer, Power Programming with RPC, O’Reilly Associates, Sebastopol, CA。

测控专业英语考试作文

测控专业英语考试作文精选英文测控专业英语考试作文：Title: The Role of Instrumentation and Control Engineering in Modern Industrial AutomationIn the dawn of the 21st century, where technology advancements are reshaping every aspect of our lives, Instrumentation and Control Engineering (ICE) stands as a pivotal discipline, driving the wheel of modern industrial automation forward. This interdisciplinary field, at the nexus of electronics, computer science, and mechanical engineering, plays a crucial role in enhancing productivity, ensuring safety, and optimizing processes across diverse industries.The Foundation of AutomationAt its core, ICE revolves around the design, installation, maintenance, and optimization of measurement systems, control systems, and automation technologies. These systems are the backbone of any automated industrial process, enabling precise monitoring, data acquisition, and dynamic adjustment of process variables in real-time. From temperature and pressure sensors to complex programmable logic controllers (PLCs) and supervisory control and data acquisition (SCADA) systems, ICE professionals integrate these components to create intelligent, self-regulating systems.Boosting Productivity and EfficiencyOne of the most significant contributions of ICE to modern industries lies in its ability to significantly boost productivity and efficiency. By automating repetitive and labor-intensivetasks, companies can allocate human resources more effectively, focusing on strategic decision-making and innovation. Furthermore, precise control over process parameters ensures consistent product quality, reducing waste and enhancing overall operational efficiency. This, in turn, leads to cost savings and increased competitiveness in the global market.Ensuring Safety and ReliabilitySafety is paramount in any industrial setting, and ICE plays a vital role in mitigating risks and ensuring the reliable operation of systems. By implementing robust safety instrumentation systems (SIS) and integrating failsafe control strategies, ICE professionals ensure that even in unforeseen circumstances, processes can be safely shut down or diverted to prevent accidents. Additionally, real-time monitoring and predictive maintenance capabilities enable early detection of potential issues, further enhancing system reliability and reducing downtime.Facilitating Smart ManufacturingAs the Industry 4.0 revolution gains momentum, ICE becomes even more indispensable. Smart factories, powered by the Internet of Things (IoT), big data analytics, and advanced automation technologies, rely heavily on ICE expertise to design and implement intelligent systems that can learn, adapt, and optimize processes autonomously. From cyber-physical systems to autonomous mobile robots, ICE professionals are at the forefront of transforming traditional manufacturing into agile, flexible, and sustainable smart manufacturing ecosystems.ConclusionIn conclusion, Instrumentation and Control Engineering is a cornerstone of modern industrial automation, driving innovation, enhancing productivity, ensuring safety, and facilitating the transition to smart manufacturing. As technology continues to evolve, the demand for skilled ICE professionals will undoubtedly grow, making this field an exciting and rewarding career choice for those passionate about leveraging technology to shape the future of industries worldwide. By continually advancing our knowledge and embracing emerging technologies, we can unlock even greater potential in automation, creating safer, more efficient, and sustainable industrial processes for generations to come.中文对照翻译：标题：仪表与控制工程在现代工业自动化中的作用在21世纪初，技术进步正在重塑我们生活的方方面面，仪表与控制工程（ICE）是一门关键学科，推动着现代工业自动化的发展。

移动机器人系统设计与实现：监控与控制说明书

6th International Conference on Mechatronics, Computer and Education Informationization (MCEI 2016)Study on using design circuits to implement a Mobile Robot systems forMonitoring and ControlChanggeng Yu 1,a, Xiangxu Xie1,b,*, Fulian Li1,a 1School of Mechanical and Electronic Engineering, Hezhou University, No.18, xihuan Road,Hezhou,Chinaa********************,b***************Keywords: Mobile robot; Arduino platform; Video monitoring; Wireless transmission Abstract. The mobile robot system can actually be applied to some of the places reconnaissance and monitoring, and the use of wireless networks, making the operating system more flexible, so that movement of the machine by monitoring and investigation without the shackles of cable. In this paper, we present the design and implementation of a mobile system with wireless for remote monitoring and control. It was composed of a multiple sensors, a control board, a camera video capture and a wireless communication module. The robot prototype was manufactured and experimented. Experiment results of typical cases verified its flexibility and reliability.IntroductionWith the progress of science and technology, mobile robot for monitoring are palying more and more important roles[1]. A wide range of automation, control equipment and other equipment for centralized interconnected has become a trend in many field, such as factory automation, machinery, and manufacturing, if use of Internet technology and processing equipment, robotics, control systems, and on-site linking, you can achieve Internet environment automation[2]. Undoubtedly, the robot control and network technology will have a very important theoretical significance and wide application prospect. Classical control theory, we know that the basic control system typically comprises modules, such as information detection module, the controller module, and actuator module. These key module state is directly related to the effectiveness and stability control systems. With the increasing level of multi-functional smart device technology, more and more enterprises, the company began research and design of intelligent robot platform, with further research, greatly accelerated the pioneering research in the field of multi-directional intelligent robot devices.Self-localization is a basia issue in the mobile robots[3-7]. As the diversity of monitoring mobile robot module. By installing different hardware sub-module, one can save costs, on the other hand can make the model of refining. In order to improve the degree of artificial intelligence of the mobile robot, and can respond quickly in the implementation process given the task order, then the mobile robot has a necessary prerequisite is to have the ability to carry different types of sensor functions. Mobile robots get information from the sensor, and its data is processed in the microcontroller through the relevant algorithm after obtaining the policy, then the appropriate action to achieve through the implementation of the module [8].Through the modular structure of the hardware was designed, according to the actual situation of need, ready to install sensors to achieve the different functions and monitoring mobile robot has wireless network communication capabilities. In order to monitor real-time health of the mobile robot, and the need to move the robot status information and run dynamic information, including road run dynamic status, motor information, servo information, speed information, etc. sent to the host computer, in order to obtain these useful Real-time monitoring of running status information to the mobile robot, while the host computer can control the operation of the mobile robot, such as acceleration, change of direction, set various parameters related to the mobile robot to achieve manual control. A good, convenient, and user-friendly surveillance mobile robot allows us to gather critical data in a timely manner, and the data necessary processing.System OverviewThis system mainly consists of two parts: the lower part of the mobile robot machine and PC main control section. The next bit machine mobile robot part, mainly consists of two parts: the network portion and the camera portion Arduino control board, the webcam is mainly used for video information collection, Arduino control board is mainly used for steering gear, DC motor control and sensor control, movement control and sensor information collection car. Master PC-side main control software system, the next crew to operate the mobile robot control, at the same time, be able to obtain information on the webcam video, webcam can be controlled, and the camera capture the information processing software. Relationship links the system shown in Fig 1.The design of robot can be divided into five steps:(1) According to the design requirements, determine the control program. (2) the use of Altium Designer designed hardware schematic diagrams. (3) Draw program flow chart, using the C programming language, Arduino simulation debugging. (4) Each element is soldered on the PCB, and is programmed into the microcontroller. (5) In order to debug control functions.Hardware DesignMobile surveillance robot consists of Arduino UNO R3 MPU circuit, Robot-Link V4.0 AR WIFI module, L298N drive module, motor, car chassis, power supply modules and other components[9]. ThecomputerserverFigure 1. System link Figure 2. control system structure(1) Arduino MPU Circuit. The main control circuit board: Arduino UNO R3 MPUs ATMEGA328P chip as a control unit. Arduino is a USB interface based on open source Simple I / O interface board (including 12-channel digital GPIO, 4-channel PWM output, channel 10bit ADC input channel 6-8), and has a similar use Java, C language IDE integrated hardware and software. Arduino UNO is the latest version of the Arduino USB interfaces series. Fig 3 is a development board Arduino UNO and parameter descriptions.Figure 3. Arduino UNO parameters(2) Wireless Wifi Routing Module. Wireless WiFi routing module used in processing chip is MT7620N, this router is Open WRT system, Open WRT is a highly modular, highly automated embedded Linux systems, components, and has a strong network scalability is often used industrial equipment, telephone, small robots, intelligent home, routers and VOIP devices. The routing module can be used as forwarding station to achieve load USB camera and serial communication with the microcontroller.(3) Video Capture System. Video capture system by installing cameras at the remote scene of the completion of the real-time monitoring, and make the appropriate controls based on the collected information and feedback, when the abnormal situation occurs, it is possible rapid response, positive response to help the operator to provide the right decisions. Video surveillance technology based on embedded technology have many advantages, such as small size, high stability, disorderly site duty, real good and simple structure, the video surveillance system consists of Video Capture System, PTZ camera control system, A signal transmission system and a video processing system.(4) The Motor Drive Module. Multifunctional motor-driven drive module: using as the L298N motor driver chip. L298N has a high voltage, high current, high frequency response of the full-bridge driver chip, one can control four L298N DC motor, and with a control enable. The motor driver chip drives capability, easy operation, good stability, excellent performance. L298N enable terminal can add level control; you can also take advantage of MCU software control to meet the needs of complex circuits. L298N is an internal H-bridge with two high voltage and high current full-bridge driver chip that can be used to drive DC motors, stepper motors. In addition, L298N drive power is larger, according to the input voltage and the output of different voltage and power to solve the problem of insufficient load capacity [10].(5) Power Module. Power module: from 2200mAh 7.4 8A Lithium battery protection board composition. By 7805 chip regulator by 0.1uF and 470μF capacitor filter.Software DesignPC control program uses C# programming language, can be realized by Robot-Link V4.0 AR WIFI module sends a command to the next crew and reception. But also through Wireless Module PTZ image signal transmission to the host computer image display window.Lower machine Arduino control board uses the Arduino IDE development. Arduino language is based on wiring language development, is avr-gcc library of the second package, the microcontroller does not require much basic programming foundation. Because all the advantages of Arduino, a growing number of professional hardware developers have started using Arduino or to develop their projects, products; more and more software developers to use Arduino to enter the field of hardware development, networking and so on.PC clients running control terminal control program must first establish a connection request to wait for the server-side response, the connection is successful you need to complete the function shown in Fig. 4.Figure 4. PC control terminal overall function block diagramPC Remote Control client software overall function, contains three main parts: The video image decoding display, data processing and display, and transmit control information data.Under-Bit machine is the executive body of the robot, the direct control of various external devices and sensors, mainly responsible for receiving serial commands, parse serial command, the drive hardware work. At the same time, sensor data collection, according to the agreement package, sent from the serial port to the server, which runs on the microcontroller, the main program flow shown in Fig 5. Under normal operating conditions, the procedure loops, receiving commands, parse the command, execute the command, returns the result, according to the parameters set PWM control commands to control DC motor speed to control the speed and direction of movement of the robot.No Figure 5: Lower computer program execution flowPrototype and ExperimentsAfter complete the system design, it is necessary to repeatedly test various parts of the found a potential problem and provide the basis for improving design, system testing is an important step design meets the requirements of the verification. System testing required by the functions and modules, the first test of the hardware system, ensure a stable operating environment, followed by the test system software to ensure the normal start the server application, and then test the control terminal, ensure the normal response to user actions, send the right control command and parsing the video data, and finally test the real-time communication protocols and systems to ensure accurate real-time data transmission. Mobile monitoring robot is shown in Fig 6.Test system hardware including system power test, each module input voltage testing. Positive and negative components before soldering with a multimeter to test the power system short-circuit phenomenon exists, then soldering the power supply part of the circuit, the test two outputs 5V voltage is normal, and so on.Software debugging mainly to the lower part of the control program into the device, and directly connected to the microcontroller serial port to PC, PC to send via serial debugging assistant according to the agreement on the control command to debug the system control section. Whether the controller can properly parse the command and returns the requested data. Control client software were installed into the PC computer before opening the software, the first network connected to the robot's wireless "hot spots", the control terminal and the robot end consisting of a wireless local area network connection parameter settings control terminal for the IP address of the machine the server and port number, if the control terminal after a successful connection, you can preview the real-time video images. Send control commands to test whether the normal motion, video recording and save the picture is normal. The field of video images as shown in Fig 7.Figure 6: Mobile robot physical map Figure 7: Real time video imageBased on mechanical design, hardware selection, the mobile robot prototype photographs were developed in the lab. The robot mechanism implemented using four fixed wheels four DC motor control. Arduino UNO R3 microcontroller generates a PWM signal to control the speed and direction of. The robot is given by the command-driven software in the computer system and key algorithms run. SummaryThis paper is designed and implemented a web-based control of mobile surveillance robots, and describes the implementation of hardware and software. Specific tasks include:(1) Analysis of the current situation and development trend of robotics technology, combined with the current rapid development of embedded technology and mobile Internet technology, paper proposesa mobile monitoring robot.(2) Completed the design and commissioning of robot hardware circuit.(3) The whole system software and hardware test results meet the design goals.(4) For robot movement in a wireless network environment.AcknowledgementThis work was financially supported by the National Natural Science Foundation of China (Grant No. 6154055), the Doctor's scientific research foundation of Hezhou University (No.HZUBS201506). References[1] Kovadic, Z., Cukon, M., Brkic, K., et al, "Design and control of a four-flipper tracked exploration& inspection robot", Control & Automation (MED), 2013 21st Mediterranean Conference on , 2013, pp.7-12.[2] Kasim M. Al-Aubidy, Mohammed M. Ali, Ahmad M. Derbas, et al, "GPRS-Based RemoteSensing and Teleoperation of a Mobile Robot", 10th International Multi-Conference on Systems, Signals and Devices (SSD), Hammamet, Tunisia, 2013,pp.1-7.[3] Marin, L., Valles, M., Soriano, A., et al, "Event-Based Localization in Ackermann SteeringLimited Resource Mobile Robots", Mechatronics, IEEE/ASME Transactions on, vol.19, no.4, 2014, pp.1171-1182.[4] Han Xiao; Payandeh, S., "Experimental design and analysis in kinematic-based localization inwireless mobile platform network", Systems Conference (SysCon), 2012 IEEE International, 2012, pp.1-6.[5] Dey, G.K.; Hossen, R.; Noor, M.S. , et al, "Distance controlled rescue and security mobile robot",Informatics, Electronics & Vision (ICIEV), 2013 International Conference on, 2013, pp.1-6. [6] Guangming Song, Kaijian Yin, Yaoxin Zhou, et al, "A surveillance robot with hopping capabilitiesfor home security", Consumer Electronics, IEEE Transactions on, vol.55, no.4, 2009, pp.2034-2039.[7] Sourangsu Banerji, "Design and Implementation of developed an Unmanned Vehicle using a GSMNetwork with Microcontrollers", International Journal of Science, Engineering and Technology Research (IJSETR) Volume 2, Issue 2, 2013, pp.367-374.[8] Schmid, K., Hirschmuller, H., "Stereo vision and IMU based real-time ego-motion and depthimage computation on a handheld device", Robotics and Automation (ICRA), 2013 IEEE International Conference on, 2013, pp.4671-4678.[9] Schwartz, F. P., Benac, C., Rocha, V. R. S. , et al, "Microcurrent Stimulation Device Controlledby ATMEGA328P-PU Chip and Android App", 2016 Global Medical Engineering Physics Exchanges/Pan American Health Care Exchanges (GMEPE/PAHCE), 2016.[10] D erbas, A.M., Al-Aubidy, K.M., Ali. Et al, "Multi-robot system for real-time sensing andmonitoring", 15th International Workshop on Research and Education in Mechatronics (REM), El Gouna, Egypt, 2014, pp.1-6.。

高功率模型用的 servo 说明书

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STEERING CONTROLLER DESIGN FOR INTELLIGENT VEHICLES

S TATE OF THE A RTS:S TEERING C ONTROLLER D ESIGN FOR I NTELLIGENT V EHICLES-- White Paper Report onIntelligent Vehicle Steering Controller Design Technology伊利诺伊大学的一个华人教授，带过我一段时间。

智能行走机械的控制器设计Qin Zhang(qinzhang@)Department of Agricultural and Biological EngineeringUniversity of Illinois at Urbana-Champaign2005Table of Contents1. I NTRODUCTION (1)2. D ESIGN OF T ASK C ONTROLLERS (2)2.1. Human Operator Performance Model-Based Task Controller (2)2.2. Other HIL-Type Task Controllers (4)2.3. Fuzzy Adaptive Task Controllers (5)3. N INE P RIMARY I MPLEMENT C ONTROLLERS (7)3.1. PID Controller (7)3.2. FPID Controller (10)3.3. LQR Controller (12)3.4. H Controller (13)3.5. Predictive Controllers (15)3.6. Adaptive Controllers (16)3.7. Sliding Mode Controller (19)3.8. Fuzzy Controller (21)3.9. Neural Networks Controller (23)3.10. A Brief Discussion on Controller Selection (25)4. S TEERING S YSTEMS M ODELING AND I DENTIFICATION (26)4.1. An Overview on Steering Systems Modeling (26)4.2. An Overview on Steering Systems Identification (27)5. S UMMARY (28)R EFERENCES (30)1.I NTRODUCTIONIntelligent vehicles are designed to travel and perform specific operations in various types of terrains. Automated path tracking is one of the fundamental operations for such vehicles. To achieve accurate path tracking for intelligent ground vehicles, an appropriately designed vehicle steering controller is essential.An automatic controller is an electronic device used to convert an operational command into a control signal to drive an implement actuator for maintaining or adjusting the work status of a plant in achieving the operation goal of the plant. In general, a control method works by modifying the implementing control signal in terms of the operational command and feedback signals along three paths: forward, feedforward and feedback. Figure 1 shows a general steering control system. The major difference among various control systems is their method in modifying the command and feedback signals.Because of the wide variation in operation conditions, the major challenges in designing a high performance controller for intelligent vehicle steering systems include how to create appropriate steering command to navigate the vehicle under a specific operating condition and how to design a proper steering controller to implement the steering command. One solution to solve this problem is the design of an intelligent steering controller, consisting of a navigation controller and a steering implementation controller. As illustrated in Figure 2, the basic feature of such design approach is to separate the design process for the navigation controller and the steering controller. This design approach divides the control goal for the intelligent steering controller into two separate sub-goals of searching for the most appropriate steering command in terms of vehicle posture and accomplishing the desired steering actions promptly and accurately.It allows us to design a navigation controller independent to the steering actuating system and design a steering controller without worry about the dynamics of the vehicle turning. This design approach can not only greatly simplify the design process, but also result in more robust and higher performance intelligent steering controllers.This white paper will review the basic methodologies for designing both navigation and steering controllers. To provide a wider coverage on potential technologies for designing intelligent steering controllers, the methodologies reviewed here may not necessary based on vehicle steering applications. In this white paper, the design methods for navigation (or task) controllers will first be reviewed. Then, the design method of seven types of primary steering (or implement) controllers, from PID controllers to neural network-based controllers, will be discussed. The information presented in this white paper is collected from an extensive literature review on technologies developed for designing various types of navigation (task) and steering (implement) controllers in the past decade.2.D ESIGN OF T ASK C ONTROLLERSTask (or say navigation) control is a fundamental function of intelligent vehicle. One attractive feature of intelligent tasks control is its capability of incorporating human maneuvering behaviors in control loop, namely the human-in-the-loop (HIL) control. However, to incorporate human maneuvering behaviors in design process in an industrial controller design process, there are a few obstacles to overcome. The first obstacle is to provide a satisfactory interactive design environment by integrating control dynamics and human maneuvering dynamics in the design process. The second obstacle is the need for a trainable real-time model to represent human operator performance consistently. The third obstacle is the need for an appropriate adaptive algorithm that adjusts the control system parameters automatically for realizing optimal machine performance. This section will introduce a few methods for designing intelligent task controllers.2.1.Human Operator Performance Model-Based Task ControllerDr. William Norris, a Deere engineer, proposed a human operator performance model (HOPM) based controller design process during his Ph.D. study at the University of Illinois (Norris, 2001). As a task-orientated controller, this HOPM-based controller can incorporate human‘s machinery maneuvering behaviors to modify the input control signals to the steering controller for achieving better vehicle maneuvering performance. To effectively present these concepts, an introduction of the topology design and operation principles of the human-in-the-loop (HIL) design tool is briefly discussed here.In principle, a HIL controller design tool applies a learning loop to incorporate human operator‘s machinery maneuvering habits in the controller design process. Figure 3 illustrates the system topology of the design tool developed to design the steer-by-wire control system for an articulated off-road vehicle. The core loop of the HIL design tool consists of a virtual operator, a virtual vehicle, and a virtual road. The virtual operator is designed to create different driving behaviors of human operators in an attempt to drive an off-road vehicle along a desired path. The virtual vehicle consists of a steering controller and a vehicle dynamics model to represent the responses of the vehicle to the operator‘s driving behavior. The v irtual road is a predefined desired path for the vehicle. Switch S1 (Figure 3) can either be set to train the virtual operator using the steering error between the virtual vehicle and the virtual road or set to engage the virtual designer to optimize the steering controller based on the steering error and the virtualtrainer is actually a machine-learningalgorithm designed to train the virtualoperator to distinguish the maneuverpattern of a human driver based on thecharacteristics of a feedback steeringerror. The virtual designer is anautomated control optimizer that tunesthe controller adaptively according to theoperator‘s driving behavior.The HIL design tool uses training,design, and implementation to performthe required functions. In the trainingphase, the design tool closes switch 1(S1) and opens switch 2 (S2) asillustrated in Figure 3, and the virtualdesigner is disconnected from the loop.Therefore, the virtual vehicle is fixed inthis phase. The feedback steering error is determined based on the differences between theoutputs from both the virtual vehicle and the virtual road. The steering error is sent to both thevirtual trainer and the virtual operator as the training sample to tune the virtual operator. Afterbeing trained, the virtual operator is capable of providing a consistent steering pattern torepresent certain driving behaviors of a human operator.In the design phase, the design opens switch S1 is open and closes switch S2 to inactivatethe virtual trainer and activate the virtual designer to tune the steering controller adaptively according to the operator‘s driving behavior. During the tuning process, the virtual designer will adjust controller parameters according to the input control signal from the virtual operator and the resulting errors in vehicle trajectory based on the current set of controller parameters. To incorporate human driving behaviors in the controller design process, an adaptive algorithm was used to adjust controller parameters of the control system (Norris et al., 2002).In the implementation phase, the switch settings are the same as in the design phase. Themain differences between the design and implementation phases are that a human operator willreplace the virtual operator, and the virtual designer is used to tune the controller parametersadaptively to a human operator‘s driving habit. This is done to accomplish the predefinedsteering operation. During implementation, the virtual designer will continuously optimize the VMC in accordance with the operator‘s driving behavior and steering error.Due to the complicated nature of steering an intelligent vehicle, it requires to have a highdegree of granularity to cover all possible combinations of operating conditions. In order to meetreal-time simulation requirements, Norris et al. (2005) have proposed a hierarchical fuzzy relations control strategy (FRCS) to reduce the size of the virtual operator‘s rule-base. This strategy could incorporate the priorities of relevant parameters with appropriate control strategy to build a minimal size rule base without loss of the completeness of the steering controlleroperation range.As summarized above, HOPM is an intelligent controller design tool developed toautomatically adjust steering signals generated by human operators to a steering controller to achieve more consistent maneuvering, and therefore is suitable for designing intelligent vehicle controllers. Based on this design-tuning approach, interested vehicle system parameters could be configured by means of simulation analysis.2.2. Other HIL-Type Task ControllersOther than the HOPM based controller, a few HIL-type task controllers based ondifferent approaches to incorporate human maneuvering behaviors have been introduced by other researchers (Looney and Tacker, 1990; Glass and Wong, 1998; Fales et al., 2003; Cummings and Guerlain, 2004; Stanciu and Oh, 2005; Ren and Beard, 2005). It indicates an increased interest on incorporating human maneuvering patterns in controller design for achieving better planning, higher-level operations, and contingency interventions for difference types of vehicles. Because of the uncertain and hard-to-predict nature of maneuvering vehicles in open fields, researchers often choose fuzzy logic and neural networks as the tools to model the human performance in a control system.One approach proposed by Looney and Tacker (1990) is the use of neural networks torecognize control tasks and use of a human model (knowledge base) to assess and verify the identified tasks for implement (Figure 4). The core elements in this HIL controller are two majority vote neural networks (MVNN) which select the most applicable control task from all potential ones based on the majority votes for implementing. The neural networks based model presents situation-response frames to the HIL controller, and the outputs from this HIL controller are selected control commandsmost suitable for the identified situation. In principle, this MVNN based HIL controller can be adopted as a high level tasks controller for implementing automated control functions on many types ofintelligent vehicles because of its capability on recognizingoperating situations andgenerating appropriate control commands for such situations.Such a model can reduce performance requirements on actuator controllers for purpose of achieving robust control performance under variousoperating situations.An approach of symbolic control for tasks control for a complicated dynamic plant was introduced by Glass and Wong (1988). This approach uses an artificial intelligent reasoning technology to replace some of the functionalities of human operators in the identification and control of certain complex dynamic plants. It applies a symbol-processing technique tosupervise and reconfigure conventional implement controllers. As illustrated in Figure 5, theLower Level Signal Processing Feature Extraction High Level Signal ProcessingLow Level NN of Recognizer High Level NN ofRecognizer/Assessor Knowledge BaseHigh Decoder Human-in-the-Loop Command Sequence Generator External System Figure 4. Majority vote neural networks based human-in-the-loop control modelconstructed by three hierarchicallevels of controls: the supervisorycontrol, the tasks control and theimplement control. Thesupervisory control aims atsearching for the optimal controlcommands corresponding to thedetected operating conditions. Thetasks controller either convert thecontrol commands into controlsignals as control inputs to lowerlevel implement controllers oradjust parameters for the classicalcontrollers to make those controlleradaptive to operating conditions.In this symbolic controller,the knowledge base serves an important role on replacing human operators in condition identification. This knowledge base can carry conditionally-applicable knowledge, such as decision-making, trouble-shooting and diagnosis, in a set of rules. Other than offer flexibility in modifying, adding to or deleting from the knowledge base, the rules offer the best understandability to people across the board on how the system is working. In many cases, a high performance tasks controller may also require some means of utilizing algorithmic or procedural knowledge to create optimal control commands. Such knowledge can always be represented by methods attached the slots of model or rule of sequences.In implementing symbolic control, the selection of proper search technique is important. Generally, there are two search approaches of backward and forward-chaining, being commonly used in control applications. The backward-chaining is often used over the parameter rule set, and the forward-chaining is frequently used for the model identification rule set. This difference is largely due to the constraints of real-time behavior in parameter and model identification. In parameter identification, it often needs to complete within a short time interval, the backward-chaining technique allows choosing a proper parameter with limited number of inference. As comparison, in model identification, active values are often propagated from the observed values and states through the model, and the forward-chaining deduction rules are more suitable for matching the plant changes at either system or subsystem level of abstraction. The nature of symbolic control is to identify the specific plant change, and select or adjust the implement controllers for executing most satisfied controls.2.3.Fuzzy Adaptive Task ControllersInstead of creating proper control commands to an implement controller for various operating conditions, a different approach of task control is to tune the controller always at an optimal setting for different operating conditions (Zhang et al. 1999). The major challenge in designing such an adaptive controller for an intelligent vehicle is to find an appropriate means for tuning the steering controller parameters with respect to changes in system dynamics or disturbances. The measure of success in adaptive control is the improvement in steeringperformance, including the reduction in system deadband and the improvement in commandmodulation. In a hydraulicallythe system deadband is defined asthe command level correspondingto the first motion of the cylinderactuator. Command modulationquality includes gain variationand linearity on velocity controlunder varying loads.Applying the fuzzyadaptive approach, the reportedtask controller modulates theinput control signal in response tovariations in external load byadjusting valve transform. Asillustrated in Figure 6, the fuzzyadaptive HIL-type controllerconsists of an actuator operationidentification function and an executive valve transform tuning function. Because the steering rate control of a hydraulic actuator is closely interrelated with the magnitude and the direction of system load. The operating conditions in this controller are identified based on the levels of load magnitude and direction. Functionally, the fuzzy tuning algorithm needs to check the system load magnitude and actuator motion direction, select appropriate valve transforms, and derive an executive valve transform for optimal control.In adaptation, the operation identification function classifies the conditions of actuator operation based on the identified external load, and selects appropriate valve transforms from the database for the identified condition. The load quantifier is a key component in the fuzzy adaptive control scheme. It converts a real-valued system load into a couple of fuzzy-valued ones for both providing operation information for fuzzy reasoning and resolving non-linearity for steering control. With consideration of load levels, a common sense model of fuzzy tuning was to classify operating conditions. In most circumstances, two operating conditions could be identified at the same time. The valve transform database kept potential valve transform sections suitable for various operating conditions. A confidence factor is assigned to each selected valve transform. When two valve transforms were obtained from the fuzzy reasoning process, the controller applies a defuzzification on those valve transforms for getting a definite executive one.Comparing to conventional controls, the fuzzy adaptive control can tune the executive valve transform accurately for identified operation conditions, compensate high non-linearity effectively and consequently achieve prompt and accurate velocity control on a hydraulic steering actuator. One very distinguishable feature of the fuzzy adaptive control is its generality, being capable of controlling different actuator systems with similar operations. Such generality is the product of the common sense of the system maneuvering on which the control model is based. Such a feature makes one model applicable to all similar operations with little or even nomodification.3.N INE P RIMARY I MPLEMENT C ONTROLLERSAfter separating the task control from implement control, the execution of implement control will be reduced to simple steering actuator control problem. This approach makes it possible to design a simple implement controller to execute the steering commands created in the tasks controller. The design objective for such a controller will change to simply realize the desired actuating actions accurately and promptly according to the input steering commands. It allows us to use the existing control methods to achieve satisfactory steering control performance. This white paper will introduce seven types of primary controllers, including PID, FPID, LQR,H∞, adaptive, predictive, sliding mode, fuzzy and neural-network based controller. This section will discuss the basic features, tuning approaches and their strength/weakness.3.1.PID ControllerPID controller stands for Proportional-integral-derivative controller, and it is a classical control method with well-developed controller design and tuning technologies. PID controller is one of the most commonly applied control methods in many fields of automation, including vehicle steering control. For example, Dong et al. (2002) used a PID controller to control an electrohydraulic (E/H) steering system on an agricultural vehicle. A group of researchers from Lancaster University in UK had successfully developed PI, PID and PIP (proportional-integral-plus) controllers to control the bucket position of an intelligent excavator (Gu et al., 2004) in performing automated foundation digging. PID controllers may also be implemented under varying gains to achieve more robust performance under changing operation conditions, such as a robust PID control can improve the tracking performance of a robot manipulators with elastic joints (Alavarez-Ramirez et al., 2001). In practice, PID controller can be integrated with other control methods such as fuzzy control to minimize the effects of some abnormal disturbances.As illustrated in Figure 7, a PID controller achieves its control goal by means of utilizing a feedback signal reflecting the actual operational state of the plant to be controlled. While aPID controller receives a control command, the controller will first compare with the feedback signal to identify the difference between the desired setpoint and the actual state, then to make a correction to the plant via a control actuator. Because of its capability to make control adjustments in terms of the actual plant operation states, a PID controller can also correct the undesirable behaviors on the plant operation induced by external disturbances.Figure 7 also shows that a PID controller uses three error correction methods to achievecalculated in terms of the identified error:()()()()dt t de k dt t e k t e k t u D I P ++=⎰ (1)where, ()t u is the control signal, ()t e is measured control error, P k , I k and D k are proportional, integral and derivative gains, respectively.In most automated steering control applications, PID controllers are often implemented in a discrete form as expressed below:))2()1(2)(()())1()(()1()(-+--++--=--k e k e k e k k e k k e k e k k u k u D I P (2)where, u (k ) and e (k ) are sampled number sequences of control signal and error.The design of a PID controller is mainly to determine the appropriate control gains for correcting the error promptly and accurately. Among three control modes, the proportional control forms a control signal directly reacting to the error for correcting it. Thus, proportional control is simple to implement and simple to tune, but has a performance limitation that its fast responses to system errors may easily cause over-correction and result in an offset. The integral control forms a control signal in response to the integral of the error and provides a means to perform effective control with an error of zero mean. However, its phase lag of 90︒ in control signal may cause a reduction in the stability of control system. The differential control reacts to the rate change in the controlled variable (measured by the derivative of the error) and is used to stabilize the system. As illustrated in Figure 8, when a PID controller receives a step command to increase its setpoint, the proportional segment of the controller reacts quickly to the deviation between the setpoint and the plant output in attempting, but often allows a steady-state error. The integral segment is sensitive to small errors and is used to eliminate the steady-state error, but its high sensitivity to small error may causes instability on system behavior. The differential segment is only sensitive to abrupt changes in control error. A proper combination of P, I and D segments in a PID controller can achieve satisfied performance by compensating for the shortcomes of the individual segments as illustrated in the figure.integral and/or derivative control modes in its forward path. It means that a PID type controller can contain all three modes, or contain any combination of two modes: PI, PD, ID, or contain only a single mode of P, I and D. The feedback path in a PID type controller always employs a proportional terms.There are a few different design approaches commonly typically applied in designing a PID controllers. One of the most common approaches in designing a PID controller is to identify the transfer function of plant being controlled either theoretically or experimentally. This approach is applicable to plants of single variable and capable of being modeled as linear time-invariant and lumped. A number of design tools are available for designing a PID controller based on this approach. Some of the examples are phase and gain margin method (Paraskevopoulos, 2002), optimal method (Anderson and Moore, 1990) and predictive method (Camacho and Bordons, 1995). The challenge is when one needs to design a PID controller for plants cannot be represented using a linear model, such as nonlinear plants. One of the very common design approaches for such plants is to Linearize the plant model, then design the PID based on the linearized model as if the plant is a linear one. Other approach often used in industry is to adjust the parameters of a PID controller in hope of obtaining a satisfactory overall system. There are a few design methods, such as phase-plane method (Astróm, 2001), describing function method (Nassirharand et al., 1988) and the Lyapunov stability method (Arimoto et al., 1988), being reported to be suitable for designing controllers for various types of nonlinear plants. Unfortunately, there is still lack of a simple and general method for designing all nonlinear controllers.A well-functioned controller must be tuned to ensure the stability and to meet other performance requirements. Normally, the tuning criteria include five performance measures of stability, response rate, noise ratio, disturbance rejection capability and parameter sensitivity. Over the years, there are many tuning methods being developed. In general, the controller tuning process will first search for proper gains to ensure a desired stability and response, then to calculate disturbance rejection and parameter sensitivities. Normally, a complete system tuning process is a two-step procedure of identifying initial gains based on the open-loop system, and modifying those gains based on the closed-loop system.For tuning PID controller, there are tuning tools available commercially, such as control system toolbox and optimization toolbox in Matlab (Nise, 1995, The Mathworks Inc., 2004). Among those methods, the Ziegler-Nichols method (Astróm and Hagglund. 1995) is one of most commonly used. Based on this method, PID gains can be determined in the following way: First set both integral and differential gains to zero as if the controller is a proportional controller, and increase the proportional gain from a very low level slowly until the system reaches instable. Identify two critical values of the proportional gain at the points of the system starts to oscillate (the oscillate point) and when it reaches instable (the instable point). Then, both integral and differential gains are determined based on the identified critical proportional gains. Because of its multiple loops in determining a set of proper PID gains, Ziegler and Nichols method has both technical and economical disadvantages in tuning many industrial controllers. To solve this problem, many efforts have been made in attempt to create tuning methods more suitable for industrial applications while retaining the simplicity of Ziegler and Nichols method. Astróm and Hagglund (2004) demonstrated the use of a few simple tuning rules to ensure robust performance by adjusting controller parameters in terms of system behaviors corresponding to step responses.tuning methods for optimizingcontroller gains automaticallyeither for initial setup or inresponse to operation conditionchanges. For an example, Astrómand Wittenmark (1973) proposeda self-tuning method for PIDcontrollers. Based on theirmethod, the self-tuning controllerconsisted of two loops of an innercontrol loop and an outer tuningloop as illustrated in Figure 9.The self-tuning is performed interms of on-line model analysisresult that reveals plant dynamicresponses. In performing the on-line analysis, the tuning unit collects both control output, u, and plant output, y, and estimates an optimal set of controller gains by utilizing proper optimal criteria. Isermann (1982, 1987) has also reported a self-adaptive controller capable of tuning PID controllers adaptively in terms of a quadratic performance criterion. Based on Isermann‘s approach, a recursive least square method is used to identify process model and a rule-based supervision function is used to check the agreement of the identified model with the actual process. This tuning method can automatically adjust PID gains when the process model can be verified.There are other methods for tuning PID controllers being reported in the literature. Some of the examples are instant Ziegler and Nichols method (Miller et al., 1967), pole placement method (Gawthrop, 1986), Nyquist based design method (Astróm and Hagglund, 1988), fuzzy tuning method (Kazemian, 1998), genetic algorithm tuning method (Mitsukura et al., 1999), neural networks tuning model (Omatu et al., 1998), and expert system-based method (Ravichandran, 2001).3.2.FPID ControllerA FPID controller consists of a feedforward loop and a conventional PID loop (Figure10). The feedforward loop is used to create basic implementing control signal in terms of an identified relationship between the control input and the system response, which is oftenpresented in a form of an inversed transform function of the plant being controlled. Based on theRFigure 10. System diagram of a typical feedforward-plus-PID controller。

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$This work was partially supported by MURST scientiﬁc researchfunds under the framework of a COFIN2000project.*Corresponding author.Tel.:+39-0521-905752;fax:+39-0521-905723.E-mail address:guarino@ce.unipr.it(C.Guarino Lo Bianco).0967-0661/02/$-see front matter r2002Elsevier Science Ltd.All rights reserved. PII:S0967-0661(02)00036-92.Feedforward design via dynamic inversion Generally speaking,an effect position control for a servomechanism should satisfy the following requirements:*fastest possible transient(minimum settling time);*reduced overshoot(if possible,zero)to a step command;*reduced steady-state error(if possible,zero);*the controller output must never saturate.The next subsection brieﬂy describes a classic proportional and derivative(PD)-type feedback con-troller design.Section 2.2shows how the servo performances can be improved by using the proposed inversion-based synthesis of the command input.2.1.The PD feedback controllerThe controlled plant is composed of a permanent magnet dc motor coupled to the output shaft by means of a reduction gear.Various approximations are usually made in order to design the controller.Firstly,the design is completely based on the nominal plant. Secondly,plant equations do not take into account various nonlinear effects introduced by friction(stiction, Stribeck effect,hysteresis,etc.)and backlash.Notwith-standing,such effects are particularly relevant in affecting the steady-state behavior especially when the velocity error constant of the control loop is not high(cf.Section4).The design is then based on the reduction of the following classical dc motor model (Kuo,1995,p.171):d id t¼ÀR mL miÀK m K gL mo0þv inL m;d o0d t¼K m K gJ eqiÀF mJ eqo0;d y0d t¼o0:ð1ÞThe motor transfer functionY0ðsÞv inðsÞ¼K m K gs½L m J eq sþðR m J eqþF m L mÞsþðR m F mþKmKgÞð2Þresulting from model(1)can be simpliﬁed by neglecting the fastest dynamic.By assuming that L m¼0;the following reduced transfer function is obtained:G pðsÞ:¼Y0ðsÞin¼K m K gm eq m m m g¼1sða sþbÞð3Þwhere a¼ðR m J eq=K m K g and b:¼R m F mþK2mK2g=K m K gÞ: The position control system is schematically shown in Fig.1.It uses a simple PD controller that will be digitally implemented.The zero-order hold can be taken into account by considering a delay time equal to T samp=2:Moreover,an additional delay of T samp=2is added to consider also the latency delay caused by the discrete-time implementation of the controller.As usual, aﬁrst-order approximation may account for these delays so that the zero-order hold can be substituted by the transfer function:G sðsÞ:¼1T samp sþ1:The control scheme also evidences a feedback low-pass ﬁlter whose purpose is to cut off the noise deriving from the potentiometer used to detect the position of the output shaft.Its transfer function isG fðsÞ:¼1f:In this control scheme,no current feedback is provided (i.e.the torque loop is missing)while atachometricfeedback is obtained through a discrete derivative of the position.The proportional gain K p and the derivative gain K d are selected to assign the position of the closed-loop dominating poles.More precisely their damping ratio d is directly assigned whereas their natural frequency o n can be indirectly evaluated by imposing the peak time ðt p ¼p =ðo n ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1Àd 2p ÞÞof the closed-loop step response.The controller is tuned by selecting a combination of d and t p in order to obtain the best-possible performances in response to a step-function reference.However,owing to the amplitude limitation on the maximum motor feeding voltage,a restriction on the feasible location of the dominant closed-loop poles emerges (cf.Section 4).Hence,a trade-off between overshoot and settling time arises and we note that to completely eliminate the output overshoot,the servo system exhibits an unacceptably large settling mand signal design via dynamic inversion The performances of the PD controller described in the previous subsection can be improved by synthesizing an appropriate command signal r ðt Þfor the closed-loop system of Fig.1to substitute the customary step command.This will determine a sharp reduction of both the overshoot and the settling time.Firstly,we choose the family of transition polynomials introduced in Piazzi and Visioli (2001b)as desired signals.Secondly,we solve the dynamic inversion problem by determining the command signal that causes the desired output.This approach has also been investigated in Piazzi and Visioli (2001a,c)and it is brieﬂy summarized herein.Denote r and y ;respectively,as the input and the output signals of a proper minimum-phase linear plant deﬁned by its transfer function:G ðs Þ:¼b m s m þb m À1s m À1þ?þb 0s þa n À1s þ?þa 0:ð4ÞWith the purpose of planning a smooth outputtransfer between two assigned output set-points (namely y 0and y 1),we adopt the parameterized family of transition polynomials of Piazzi &Visioli (2001b)to attain a desired motion without any oscillatory modes and with travelling time equal to the parameter t :y ðt ;t Þ:¼y 0;t o 0;y 0þðy 1Ày 0Þð2k þ1Þ!ðk !Þ2t 2k þ1R t 0v kðt Àv Þk d v ;0p t p t ;y 1;t >t8>>><>>>:ð5ÞThe positive integer k appearing in (5)can be freely chosen to ensure that y ðt ÞA C k over ðÀN ;þN Þ:Thetime derivative of (5)is given by y ð1Þðt ;t Þ¼ðy 1Ày 0Þð2k þ1Þ!ðk !Þ2t2k þ1t kðt Àt Þk ;t A ½0;t :ð6ÞThe above expression (6)shows that y ðt ;t Þis monotonically increasing or decreasing depending on the sign of y 1Ày 0exclusively.In particular,this guarantees that the planned output has no overshoot.Relying on the stability of the zero dynamics of (4),the synthesis of the command signal is straightforward usingR ðs ;t Þ¼G À1ðs ÞY ðs ;t Þ;ð7Þwhere Y ðs ;t Þ:¼L f y ðt ;t Þg and R ðs ;t Þ:¼L f r ðt ;t Þg ;here,and in the following we set y 0¼0without any loss of ing polynomial division rewrite G À1ðs Þas follows:G À1ðs Þ¼g r s r þg r À1s r À1þ?þg 0þH 0ðs Þ;ð8Þwhere r :¼n Àm is the relative order (or relative degree)of G ðs Þand H 0ðs Þis the strictly proper stable transfer function representing the zero dynamics:H 0ðs Þ:¼d m À1s m À1þd m À2s m À2þ?þd 0b m s m þb m À1s m À1þ?þb 0:ð9ÞDeﬁne Z 0ðt Þ:¼L À1f H 0ðs Þg and from (7)and (8)immediately deriver ðt ;t Þ¼g r y ðr Þðt ;t Þþg r À1y ðr À1Þðt ;t Þþyþg 0y ðt ;t ÞþZ tZ 0ðt Àv Þy ðv ;t Þd v ;t X 0:ð10ÞIt is known (Polderman &Willems,1998,p.112;Piazzi &Visioli,2001b)that the command signal r ðt Þis of class C l if and only if y ðt Þis of class C l þr :Hence,the appropriate choice of k in (5)makes it possible to obtain an arbitrarily smooth command signal.For the servo system considered in this paper,we have set y y 0and introduced the transfer function of the closed-loop control scheme of Fig.1as G o ðs Þ:¼Y o ðs ÞR ðs Þ¼K p ð1þt f s Þs ð1þt f s Þð1þt s s Þða s þb ÞþsK d þK p:ð11ÞThis G o ðs Þis supposed to be stable owing to the controller synthesis proposed in the previous subsection and has relative order r ¼3:By means of the polynomial division,it is possible to obtain the g i parameters and the explicit expression of Z 0ðt Þ:g 3¼t s a K p ;g 2¼t s b þa K p ;g 1¼b K p ;g 0¼K dt f K p ;Z 0ðt Þ¼1ÀK d t f K pe Àt =t ft f:C.G.L.Bianco,A.Piazzi /Control Engineering Practice 10(2002)847–855849The system command signal can be thus explicitly given byrðt;tÞ:¼0;t o0;g3yð3Þðt;tÞþg2yð2Þðt;tÞþg1yð1Þðt;tÞþg0yðt;tÞþR tZ0ðtÀvÞyðv;tÞd v;0p t p t;g0y1þR tZ0ðtÀvÞyðv;tÞd vþy1R ttZ0ðtÀvÞd v;t>t;8>>>>>>>>><>>>>>>>>>:ð12Þwhere,having chosen k¼3to obtain a continuous command signal,for t A½0;tyðt;tÞ¼y0þ140y1t7Àt77þt t62À3t2t55þt3t44;ð13Þyð1Þðt;tÞ¼140y1tðÀt6þ3t t5À3t2t4þt3t3Þ;ð14Þyð2Þðt;tÞ¼420y1t7ðÀ2t5þ5t t4À4t2t3þt3t2Þ;ð15Þyð3Þðt;tÞ¼840y1tðÀ5t4þ10t t3À6t2t2þt3tÞ:ð16ÞOne degree of freedom still remains for the complete deﬁnition of the command signal rðt;tÞ:the transient time t:An obvious choice is to minimize t to get the fastest possible transient.This meansﬁnding the minimum t under the constraint of saturation avoidance for the motor feeding voltage.To this end let us denote with v inðt;tÞthe motor voltage input caused by the command input rðt;tÞ:Hence the following semi-inﬁnite generalized optimization problem is considered:tÃ¼arg f min t:j v inðt;tÞj p V lim;8t A½0;t g;ð17Þwhere V lim is the power converter saturation voltage.It is worth noting that function v inðt;tÞdoes not depend on the controller parameters but it is exclusively linked to the motor transfer function G pðsÞ(3)through the relation:v inðt;tÞ¼LÀ1½GÀ1pðsÞYðs;tÞ :Hence,applying the dynamic inversion procedure delineated in(7)–(10)and taking into account the structure of G pðsÞgiven by(3),we obtainv inðt;tÞ¼g p2yð2Þðt;tÞþg p1yð1Þðt;tÞ;ð18Þwhere g p1and g p2are appropriate real coefﬁcients. Problem(17)can be solved using speciﬁc algorithms for semi-inﬁnite optimization(Teo,Rehbock,&Jen-nings,1993;Guarino Lo Bianco&Piazzi,2001a, 2001b).However,for the case of yðt;tÞA C3;it is possible to equivalently reformulate problem(17)to obtain a standardﬁnite optimization problem.Indeed,with the help of tools for symbolic manipulation,theﬁve possible relative extrema of v inðt;tÞover the domain½0;t can be expressed in closed form;we denote them with#v iðtÞ;i¼1;y;5:Therefore,problem(17)is equivalent totÃ¼arg f min t:j#v iðtÞj p V lim;i¼1;2;y;5gð19Þand can be solved with standard nonlinear program-ming tools or with a more straightforward bisection-type algorithm(Piazzi&Visioli,2001b).The previous considerations make it evident that tÃdepends only on the plant transfer function and on the proﬁle chosen for the output plant.This is an interesting feature of the proposed dynamic inversion approach.On the contrary,adopting a purely feedback control scheme with a traditional step command,the avoidance of the voltage saturation should be sought by imposing constraints on the controller parameters.3.Coordinated feedforward/feedback design using dynamic inversionIn the following it will be supposed,in agreement with adopted inversion-based approach,that the output signal has already beenﬁxed as yðt;tÃÞ;the optimal transfer deﬁned by(17)and(19).Hence,the insertion of a feedback controller is justiﬁed in order to reduce the sensitivity of the servo system to variations in the motor plant parameters and to unmodelled dynamics(such as friction and other nonlinear phenomena)(Horowitz, 1963,p.94).As a consequence,the controller design should follow these guidelines:(a)closed-loop stability is attained,(b)the controller bandwidth is as large as possible,and(c)the loop velocity error constant K v is as high as possible.Using these guidelines it will be possible to greatly reduce,as noted in Piazzi and Visioli(2001a),the effects of the plant uncertainties over the range of frequencies of the command signal.It is worth noting that a controller designed according to the proposed approach will be quite different from a controller synthesized according to the traditional setup with step-command signals.In particular,the new approach makes it possible to obtain high values for K v with respect to that of a traditional controller.For the case at hand,an appropriate control scheme of the servo system is shown in Fig.2.Theﬁxed-structure controller G cðsÞis chosen to cancel the two‘‘slowest’’plant poles and to have a pair of complex poles according to a Butterworth conﬁguration:G cðsÞ:¼K cð1þl sÞð1þt s sÞ1þﬃﬃﬃ2ps=o cþs2=o2c;ð20Þwhere l:¼a=b is the plant time-constant dominating pole and t s is the equivalent time constant of the zero-order hold.The controller design parameters are then K c;the controller static gain that is proportional to the velocity error constant K v;and o c;the Butterworth natural frequency of the controller poles.C.G.L.Bianco,A.Piazzi/Control Engineering Practice10(2002)847–855 850In accordance with the above,design guidelines proceed as follows:(1)Firstly,choose the highest o c value compatible with the digital implementation and in any case the factor o c l should not be too high(in general,the time constants of the controller should not be too small compared with those of the plant).(2)Secondly,assign the minimum damping ratio d lim for the closed-loop dominant poles and then choose the maximal K c for which the corresponding dominant poles have a damping ratio greater or equal to the assigned d lim: The choice of the maximal K c is illustrated in Fig.3 showing a schematic root locus.We remark that the assigned damping ratio d lim can be chosen to be much smaller than the usual values related to a traditional controller design because,having adopted the dynamic inversion approach,the actual over-shooting of the set-point transfer has no relation to the closed-loop dominant poles.Theﬁnal design step is the determination of the command signal rðt;tÃÞthrough dynamic inversion. Considering that the pertinent closed-loop function isG0ðsÞ:¼Y0ðsÞRðsÞ¼K cð1þt f sÞb sð1þt f sÞð1þﬃﬃﬃ2pðs=o cÞþs2=o2cÞþK c;ð21Þthen we obtain the feedforward command signal asrðt;tÃÞ¼LÀ1½GÀ1oðsÞYðs;tÃÞ :According to the dynamic inversion procedure describedin(8)–(10)we explicitly derive the command signal asrðt;tÃÞ¼bo2cK cyð3Þðt;tÃÞþbﬃﬃﬃ2po c K cyð2Þðt;tÃÞþbK cyð1Þðt;tÃÞþ1t fZ teÀðtÀvÞ=t f yðv;tÃÞd v:ð22Þ4.Experimental resultsTo validate the approach proposed in this paper,weused the experimental setup developed by QuanserConsulting.The test bench is based on a personalcomputer controlling,by means of a built in I/O boardand an external power converter,a dc servo motor(seeFig.4).The personal computer acts as a rapid proto-typing station:the controller is introduced as a Simulinkscheme and converted by the Real Time Workshoppackage into an actual digital controller.For all theexperiments,the sampling timeðT sampÞis5Â10À3s andthe cut-off frequency of the inputﬁltering is25Hz(corresponding to t f=6.37Â10À3s).Continuous timecontrollers have been automatically discretized,usingthe Runge–Kutta solver,by the Real Time Workshop toobtain equivalent discrete time implementations.The nominal plant coefﬁcients used for the controllerdesign are listed in Table1.They are derived from theQuanser Handbook with the sole exception of thefriction coefﬁcient F m which was not available andwhich has been experimentally estimated.The threeplant poles,evaluated from the parameters listed inTable1,are located at0,À61.84andÀ14387.47sÀ1.According to the simpliﬁcation proposed in Section2.1,the fastest plant pole has been neglected by posingL m¼0:The resulting transfer function has twopolesFig.4.The experimental test bench at the Automatica lab of theUniversity of Parma.C.G.L.Bianco,A.Piazzi/Control Engineering Practice10(2002)847–855851placed,respectively,at 0and À61.60s À1and a plant velocity constant b À1=1.72s À1(cf.(2)and (3)).In the following,the control strategies presented in the previous sections are veriﬁed and compared on the actual plant.The robustness of the achieved perfor-mances is discussed in Section 4.3where further experiments on a perturbed plant are reported.4.1.Experimental results with the standard PD controller synthesisDuring this ﬁrst stage the dynamic inversion ap-proach is not used.Consider the simple controller of Fig.1and optimally tune its parameters in accordance with the procedure proposed in Section 2.Choose y 0¼01and y 1¼451:Several values of d A ½0:7;1Þhave been tested and,for each of them,the minimum t p compatible with the limit on the maximum voltage has been selected.Hence,the PD controller used for the experi-ments has been synthesized on the basis of the best compromise between overshoot,settling time and steady-state error.Its resulting parameters are K p ¼6:234V/rad and K d ¼À0:1190V s/rad.Conse-quently,the dominating poles of the closed-loop system have a damping ratio d ¼0:95and the loop velocity error constant is K v ¼15:73s À1.The resulting step response of the closed-loop system is shown in Fig.5.By deﬁning the settling time t s as the minimum time for which the output deﬁnitely belongs to the 72%range of the steady-state value,it results that t s ¼0:3103s.The experimental experience indicates that a large propor-tional gain K p has to be chosen in order to achieve fast transients,to increase the velocity constant K v and to reduce the steady-state error.Unfortunately,a value of K p which is too large will saturate the controller output since it has a strong,direct impact on the peak of the feeding voltage.Moreover,the larger the value of K p ;the larger the overshooting will be.Another drawback induced by large values of K p can be seen in Fig.6.The motor feeding voltage has a sharp discontinuity at the beginning of each transient owing to the step input combined with a relevant proportional action.As a result,the mechanical gears and the motor are particularly stressed.Another relevant detail can be immediately detected from Fig.5:the steady-state error is not zero despite the integrator term of the motor model.An average absolute steady-state error equal to 0.38671has been measured.Such an error is mainly due to the non-modelled nonlinear friction.It is particularly relevant for the servo system considered and its inﬂuence is evident especially for low rotor velocities (static friction).The asymmetric behavior of friction is also evident:the average steady-state error depends on the direction of motion.Still using the previously synthesized PD controller (K p ¼6:234V/rad and K d ¼À0:1190V s/rad),the per-formances of the servo system can be improved by means of the dynamic inversion approach proposed in Section 2.2.As a ﬁrst step,the minimum transient time t Ãis evaluated for the family of output transfers y ðt ;t Þdeﬁned in accordance with (13).By adopting the system parameters of Table 1and solving the optimization problem (19),we obtained t Ã=0.2134s.In Fig.7,the resulting plot of the output signal is shown super-imposed on the plot of the input commandsignalFig.6.Actual motor feeding voltage for the PD controller with step input.Table 1DC motor and load parametersK m ¼7:67Â10À3N m/A or V/(rad/s)K g ¼70J eq ¼0:195Â10À2kg m 2F m ¼0:95Â10À2N m s L m ¼0:18Â10À3H R m ¼2:6O V lim ¼5VC.G.L.Bianco,A.Piazzi /Control Engineering Practice 10(2002)847–855852obtained via dynamic inversion.The system overshoot has been reduced but not completely suppressed.This is a consequence of the inevitable uncertainties concerning the plant parameters and of the unmodelled dynamics (nonlinear friction effects).The settling time has been slightly reduced(t s¼0:2953s)while a better improve-ment has been obtained on the average absolute steady-state error(j e s j=0.26131).4.2.Experimental results for the coordinated feedforward/feedback design using dynamic inversionIn accordance with the new servo control system design presented in Section3,the desired output signal is yðt;tÃÞ:This is the optimal set-point transfer satisfying a voltage saturation avoidance constraint which has already been computed in the previous subsection (tÃ=0.2134s)in agreement with(17)and(19).The coordinated feedback controller(20)is designed byﬁrst ﬁxing o c=220rad/s and then by choosing d lim=0.48for the damping ratio of the closed-loop dominant poles we infer K c¼30V/rad.Consequently,having determined the ideal optimal output yðt;tÃÞand feedback controller G cðsÞ;we compute the command signal rðt;tÃÞ(cf.(22)) by dynamic inversion.The experimental results are best described in Fig.8 where the plot of the actual output signal is shown.The servo system has(almost)no overshoot and the settling time(t s¼0:1653s)has been greatly reduced with respect to the previously attained values(cf.Section 4.1).It is worth noting the substantial similarity between the output signal and the command signal rðt;tÃÞin Fig.8,whereas a corresponding marked difference is shown in Fig.7relative to the uncoordinated feedfor-ward/feedback design.This feature of the coordinated servo scheme is both due to the controller’s large bandwidth and a high loop velocity error constant (K v¼55:88sÀ1).Another advantage obtained with this scheme is a sharply decreased steady-state error (j e s j=0.06021).The simulated shape of the motor supply voltage is shown in Fig.9compared with the shape of the actual voltage.Owing to the chosen dynamic inversion approach,v in is continous so that mechanical stress is reduced.As designed,the power converter neversaturates.mand signal(dashed line)obtained via dynamic inversionand output signal(solid line)for the closed-loop system with the PDcontroller.Fig.9.Simulated and actual plot of the motor feeding voltage v in:C.G.L.Bianco,A.Piazzi/Control Engineering Practice10(2002)847–8558534.3.Experimental results with a perturbed plant The performances of all the three control strategies described in the paper are compared against the variation of the load inertia.More precisely,an additional arm is added to the output shaft of the dc motor (see Fig.10).Its equivalent inertia(0.982Â10À3kg m 2)is about 50%of the system nominal inertia.The command signals and the con-troller parameters used for these experiments are thesame as those used for the unperturbed plant cases.The experimental results on the perturbed plant are shown in Fig.11.In all three experiments,both the system overshoot and the settling time are increased with respect to the values obtained for the unperturbed cases but the new inversion-based coordinated control still performs better than the control with the PD controller (comprising both the standard step input case and the inversion-based feedforward case).Numerical results derived from all the servo experi-ments are shown in Table 2.Overshoots,settling times,and average absolute steady-state errors are reported for both the unperturbed and perturbed cases.These results bear out the advantages of using an inversion-based servo control scheme with a coordinated feedforward/feedback design.5.ConclusionsThe basic idea of dynamic inversion is quite simple.Considering a given system,ﬁrst determine a desired output signal and then,by means of an inversion-based procedure,determine the input that causes the desired output.In this paper,we exploited this idea for the servo position control of a dc motor with speciﬁcations requiring the minimizing of settling time whileachievingFig.10.The dc motor with an additional load at the outputshaft.Fig.11.Plots of the input commands and corresponding output responses for the cases:(a)standard PD controller,(b)PD controller with inversion-based feedforward,(c)new inversion-based coordinated control.C.G.L.Bianco,A.Piazzi /Control Engineering Practice 10(2002)847–855854(if possible)zero overshooting,(if possible)zero steady-state error,and a voltage saturation ing transition polynomials(Piazzi&Visioli,2001b)for the output planning,two servo designs have been presented: *a feedforward design for a traditional PD controllerscheme;*a new coordinated feedforward/feedback design using a high-gain controller.The experimental results included in the article show how the coordinated design—for the unperturbed or original plant—outperforms the uncoordinated design with at least a44%reduction of settling time and negligible overshooting and steady-state error.Consider-ing an artiﬁcially perturbed plant(a50%increased load inertia),the coordinated design still performs better than the uncoordinated design from the standpoint of over-shooting,settling time,and steady-state error(see Table2). Pursuing more general set-point regulation problems, inversion-based coordinated feedforward/feedback de-signs can be found in Piazzi and Visioli(2001c)and Piazzi and Visioli(2001a)for minimum-phase and nonminimum-phase plants,respectively.ReferencesEnns,D.,Bugajski,D.,Hendrick,R.,&Stein,G.(1994).Dynamic inversion:An evolving methodology forﬂight control design.International Journal of Control,59(1),71–91.Guarino Lo Bianco, C.,&Piazzi, A.(2001a).A semi-inﬁnite optimization approach to optimal spline trajectory planning of mechanical manipulators.In:M.Goberna,&M.L!opez(Eds.), Semi-inﬁnite programming:Recent advances.Dordrecht,The Netherlands:Kluwer Academic Publishers,57,271–297. Guarino Lo Bianco,C.,&Piazzi,A.(2001b).A hybrid algorithm for inﬁnitely constrained optimization.International Journal of Sys-tems Science,32(1),91–102.Horowitz,I.(1963).Synthesis of feedback systems.New York: Academic Press.Kuo,B.(1995).Automatic control systems(7th ed.).Englewood Cliffs, NJ:Prentice-Hall.Meyer,G.,Hunt,L.,&Su,R.(1995).Nonlinear system guidance, Proceedings of the34th IEEE conference on decision and control, New Orleans,LA(pp.590–595).Perez,H.,&Devasia,S.(2001).Optimal output transitions for linear systems.Proceedings of the IEEE conference on decision and control, Orlando,F L(pp.3164–3174).Piazzi,A.,&Visioli,A.(2000).Minimum-time system inversion based motion planning for residual vibration reduction.IEEE Transac-tions on Mechatronics,5(1),12–22.Piazzi,A.,&Visioli,A.(2001a).Optimal inversion-based control for the set-point regulation of nonminimum-phase uncertain scalar systems.IEEE Transactions on Automatic Control,46(10), 1654–1659.Piazzi, A.,&Visioli, A.(2001b).Optimal noncausal set-point regulation of scalar systems.Automatica,37(1),121–127. Piazzi, A.,&Visioli, A.(2001c).Robust set-point constrained regulation via dynamic inversion.International Journal of Robust and Nonlinear Control,11(1),1–22.Polderman,J.,&Willems,J.(1998).Introduction to mathematical system theory.New York,NY:Springer.Teo,K.,Rehbock,V.,&Jennings,L.(1993).A new computational algorithm for functional inequality constrained optimization problems.Automatica,29(3),789–792.Table2Comparisons of performances on the original plant and on the perturbed plant.Overshoot(%)t s(s)j e s j(deg.)(Original)(Perturbed)(Original)(Perturbed)(Original)(Perturbed)Case(a)14.523.80.3100.5200.38670.4583 Case(b) 6.513.90.2950.3500.26130.6990 Case(c) 1.48.30.1650.2700.06020.1948The cases refer to:(a)standard PD controller,(b)PD controller with inversion-based feedforward,and(c)new inversion-based coordinated control.C.G.L.Bianco,A.Piazzi/Control Engineering Practice10(2002)847–855855。