Anti-windup_schemes_for_proportional_integral_and_proportional_resonant_controller

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九年级地理环境保护英语阅读理解20题

九年级地理环境保护英语阅读理解20题1<背景文章>Global warming is one of the most serious environmental issues facing our planet. It refers to the long-term increase in the average temperature of the Earth's climate system. The phenomenon of global warming is caused by a variety of factors. One of the main causes is the increase in greenhouse gas emissions, such as carbon dioxide, methane, and nitrous oxide. These gases trap heat in the atmosphere and cause the Earth's temperature to rise.The effects of global warming are far-reaching. Rising sea levels threaten coastal areas and low-lying islands. More frequent and intense extreme weather events, such as hurricanes, floods, and droughts, can cause significant damage to human lives and property. Changes in precipitation patterns can also affect agriculture and water resources.To address global warming, we need to take action on multiple fronts. We can reduce greenhouse gas emissions by using renewable energy sources, such as solar and wind power. We can also improve energy efficiency in buildings, transportation, and industry. In addition, we can protect and restore forests, which absorb carbon dioxide from the atmosphere.1. What is global warming?A. A short-term increase in temperature.B. A long-term increase in the average temperature of the Earth's climate system.C. A decrease in temperature.D. No change in temperature.答案：B。

PID Control System Analysis and Design

➢ Adding an integral term to a pure proportional term increases the gain by a factor.
➢ Increases the phase-lag
➢ Gain margin (GM) and phase margin (PM) are reduced, and the closed-loop system becomes more oscillatory and potentially unstable
Integrator Windup Remedies
➢ Antiwindup can be achieved implicitly through automatic reset.
➢ Explicit Antiwindup implemented explicitly through internal negative feedback.
STANDARD STRUCTURES OF PID CONTROLLERS
➢ A PID controller is a phase lead-lag compensator with one pole at the origin and the other at infinity.
➢ PI-Phase lag.
➢ Unstable system
Remedies
➢ Involves use of filters
Linear low pass filter Velocity Feedback SetPoint Filter Nonlinear median filter
Linear low pass filter
➢ Windup is due to the controller states becoming inconsistent with the saturated control signal, and future correction is ignored until the actuator desaturates

anti-Windup Compensator Designs for Nonsalient Permanent-Magnet Synchronous Motor Speed Regulators

Anti-Windup Compensator Designs for Nonsalient Permanent-Magnet Synchronous MotorSpeed RegulatorsPhil March,Member,IEEE,and Matthew C.TurnerAbstract—This paper presents and compares a number of anti-windup compensator designs which address the problem of current saturation within high-performance permanent-magnet synchronous motor applications.The compensator variants in-clude an integrator reset scheme,back calculation and tracking, and an optimally synthesized low-order dynamic compensator. Performance is comparedﬁrst through simulation tests using a nonlinear nonsalient machine model with multirate discrete time control loops.Second,the results of tests repeated on a hardware implementation are shown.In both simulation and experiment,the back calculation and tracking and low-order designs are shown to exhibit clear performance advantages over the reset strategy.Index Terms—Anti-windup(A W),constraints,current limita-tion,nonsalient,optimal,permanent-magnet synchronous motor (PMSM),saturation,speed regulation.N OMENCLATUREi a,i b,i c Stator phase currents.i d Stator current vector d-axis component.i q Stator current vector q-axis component.V a,V b,V c Stator phase voltages.V d Stator voltage vector d-axis component.V q Stator voltage vector q-axis component.θe Rotor electrical position.θm Rotor mechanical position.ωm Rotor speed(mechanical).ψf Flux linkage.load Rotor load torque.T Electromagnetic torque.P Number of magnetic pole pairs.φPhase advance angle.K e Motor back-EMF constant.B Damping coefﬁcient.R s Stator phase winding resistance.L s Stator phase winding inductance.J Rotor moment of inertia.Paper2008-IDC-078.R1,presented at the2007IEEE International Electric Machines and Drives Conference,Antalya,Turkey,May3–5,and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript submitted for review September18,2008and released for publica-tion March8,2009.Current version published September18,2009.This work was supported in part by the U.K.Engineering and Physical Sciences Research Council and in part by TRW Automotive.The authors are with the Department of Engineering,University of Leicester, Leicester,LE17RH,U.K.(e-mail:phil.march@;mct6@). Color versions of one or more of theﬁgures in this paper are available online at .Digital Object Identiﬁer10.1109/TIA.2009.2027157I.I NTRODUCTIONW ITHIN permanent-magnet synchronous motor(PMSM) control systems,certain constraints are required to safe-guard the motor and the power electronics;for instance,restric-tions on the magnitude of voltages and currents.The inclusion of these constraints in the control system introduces saturation nonlinearities to the plant inputs and states.These saturation constraints can cause controller“windup”problems when the controller attempts to exceed these during operation and lead to performance degradation,particularly in high-performance applications where saturation is more prevalent.Therefore,for maximum performance to be obtained,there is the requirement to consider these saturation constraints in the design of PMSM control systems.The term windup was originally conceived to describe the unrestricted accumulation of an integral controller,observed when a plant input limit renders a set-point reference infea-sible.Since then,the term has been used more broadly,and is used to refer to more general performance degradation ef-fects associated with the violation of plant input limits.This larger class of undesirable saturation effects includes not only the aforementioned“integrator windup”but also includes the performance degradation resulting from saturation with modern control designs that do not have an explicit integral state,and performance degradation with coupled multivariable systems where saturation of one input can affect a number of perfor-mance outputs.A number of different methods,which vary signiﬁcantly in complexity of design and implementation,could be applied to this problem.Perhaps the simplest approach is to use a low-gain linear controller,which will lead to saturation being encountered less frequently.However,due to linearity,this is achieved typically at the expense of limiting performance.An alternative way of avoiding saturation would be to use H∞techniques[1],[2]to produce(possibly multivariable)controllers which can distrib-ute control effort in a more efﬁcient manner.The drawback to both of the aforementioned approaches is that,since they are linear,they treat large-and small-signal behavior in exactly the same way and thus cannot be used to achieve high-performance small-signal behavior,and large-signal behavior which is less prone to saturation simultaneously.An alternative to the above is to use model-predictive-control[3],[4](MPC)techniques in which the control constraints are incorporated into an online ﬁnite horizon optimization procedure,producing controllers which respect the saturation constraints directly.Of course the0093-9994/$26.00©2009IEEEproblem with H∞and,particularly,MPC techniques is that they tend to require more online computation than standard classical control schemes and thus are not well suited to cost sensitive applications.The approach we consider in this paper is referred to as anti-windup(AW)compensation and corresponds to the sec-ond stage in a two-stage controller design process.In stage one,a“nominal”controller is designed to meet the desired performance objectives in the absence of saturation.This con-troller governs the closed loop dynamics exclusively while the saturation constraint is respected.In stage two,a so-called AW compensator is designed with which the control system is augmented.This compensator only becomes active during saturation,and is designed to maintain stability of the closed loop system and minimize the degradation of performance when violation of the saturation nonlinearity leads to the pres-ence of complex nonlinear dynamics.Models of the constraints are included in the controller and saturation of these software constraints activates the compensator to deal with the saturation event.This approach allows for the nominal controller to be designed to provide good small signal performance,and the AW compensator designed subsequently to handle saturation and therefore ensure good large-signal behavior also.Another beneﬁt of AW is that many compensator designs can commonly be implemented as static feedback gains or dynamicﬁlters with just a few states,and therefore do not make large computational demands on the control computer.Thus,in many ways,AW may be the most logical and appealing solution.A large number of AW schemes are in existence and the reader is referred to[5]–[10]and references therein for an overview of some well-known approaches.One crucial advantage of AW is that it only modiﬁes the existing controller’s behavior during and immediately following saturation events and so does not require an existing controller to be completely redesigned.II.S YSTEM U NDER C ONSIDERATIONIn this paper,we apply AW to deal with violation of satura-tion constraints in the model of a PMSM speed control system for an automotive electric actuator.A.PMSM ModelThe PMSM used is a surface mounted design and therefore has very low saliency.Thus,its dynamics can be reproduced quite accurately by the nonsalient model of(1)–(4)in the d–q coordinate system[11]di d dt =1L s[V d−R s i d+P L sωm i q](1)di q dt =1L sV q−R s i q−P L sωm i d−K eωm√3(2)dωm dt =1J[T−load−Bωm](3)T=√32K e i q.(4)A description of the symbols used for this model and for an equivalent model in three phase coordinates[11],[12]is found in the nomenclature.AW design is normally based on linear models of the plant and controller under consideration,and thus we desire to extract a linear model of the plant.To this end,the aforementioned model is linearized about an equilibrium(trim) pointωm(0),i d(0),i q(0),with corresponding input signals V d(0),V q(0),and load(0),giving the linear state-space model of(5)and(6)in deviation variables.It is important to note that the dynamics of the linear model are dependent upon the trim conditions and are most sensitive to changes in the trim speed.Thus,the speed at which the model is trimmed is an important consideration for developing an appropriate linear model.It should also be noted that,as the motor has several inputs,there is not a unique trim point at a given speed;a wide range(a continuum)of voltage vectors can achieve the same trim speed.In addition,the applied load also affects the speed achieved and therefore the trim point.For this reason, trim points were determined from closed-loop simulations with the given controller in place and were chosen to coincide with the steady-state values enforced by this controllerddt⎡⎣δi dδi qδωm⎤⎦=⎡⎢⎣−R sL sPωm(0)P i q(0)−Pωm(0)−R sL sP i d(0)−K eL s√30K e√32J−BJ⎤⎥⎦×⎡⎣δi dδi qδωm⎤⎦+⎡⎣01/L s0001/L s−1/J00⎤⎦⎡⎣δloadδV dδV q⎤⎦(5)δωm=[001]⎡⎣δi dδi qδωm⎤⎦.(6)B.Controller StructureThe constrained three-phase motor control system which we desire to apply AW compensation to is shown in Fig.1. Clarke and Park transformations[12]are used to convert the three-phase current measurements into d–q-axis coordinates, allowing control to be computed in the rotor reference frame, prior to conversion back into three-phase signals to be applied to the plant.The control system consists of an inner current control loop and an outer speed control loop.The inner loop contains two independent PI regulators,used to control the magnitude of the stator current components in the direct and quadrature axes by manipulating the stator voltage vector in d–q coordinates.The outer loop controller is shown in Fig.2and generates the d-and q-axis current demands that are passed to the inner loop. For maximum torque operation,the d-axis current demand is set to zero and a PI regulator in the q-axis exploits the linear relationship between electromagnetic torque and q-axis current(4)to provide speed(ωm)tracking capabilities by manipulating the q-axis current demand.This provides the most efﬁcient operation and enables speeds up to base speed to be attained.For operation beyond base speed,the nonlinear d-axis portion of the speed controller comes into effect which ad-vances the phase of the current demand vector byφelectrical degrees from the q-axis.The angleφis predetermined as a nonlinear function of speed and is usually read from a lookupid _dmd 2+iq _dmd 2≤i _lim.(7)To convert this “multivariable”type of saturation into a more standard saturation problem,it is possible to consider separate scalar saturation functions on the d -and q -axis currentFig.4.d,q-axis current limit.ing knowledge of the phase advance angleφas a function of speed,these limits can be varied separately to restrict the magnitude of the current demand vector idq_dmd to the limit i_lim,while maintaining the desired phase.In this case,we have−i d≤id_dmd≤i d(8)−i q≤iq_dmd≤i q(9) and the d-and q-axis limits¯i d and¯i q are determined by trigonometry to be sin(φ)i_lim and cos(φ)i_lim,respectively. Note that the current limit has now been simpliﬁed from satu-ration of the norm of a vector signal to saturation of two scalar signals,albeit with time varying limits.A graphical depiction of how these d-and q-axis limits vary with the phase advance angle in rotor electrical coordinates is shown in Fig.4.A useful property of this representation of norm saturation is that violation of the circular limit implies that both the d-and q-axis components of the vector exceed their own limits. Conversely,if the q-axis limit is not exceeded,nor is the d-axis limit,and the vector demand lies within the circle.This link between d-and q-axis saturation can be exploited,allowing AW to be applied only to the q-axis.This follows since only the q-axis portion of the speed controller is dynamic,having no states which contribute to windup.The compensator is designed to manipulate the speed controller states during and immediately following saturation,leading the q-axis output, and hence also the d-axis output,out of saturation.This means that for AW design,only the q-axis scalar saturation function need be considered.The d-axis saturation function can then be incorporated as an additional nonlinearity into the d-axis portion of the speed controller.Note that during operation at speeds below0.22normalized units,the d-axis controller is not active and henceφ=0.In this case,the current limit is purely enforced on the q-axis current.III.AW C OMPENSATIONA block diagram showing how a generic AW compensation scheme is applied to the speed control loop is shown in Fig.5.A signal˜u is deﬁned as the difference between saturated and unsaturated control signals,indicating the existence and severity of a saturation event when˜u=0,and normal operation when˜u=0.This signal drives the compensator block AW in some manner to modify the action of the linear q-axis portion of the controller and solve the windup problem.Three AW com-pensation schemes are introduced in this section which interact with the linear portion of the controller in different ways.As previously mentioned,for the work here,it is possible simply to consider the q-axis current saturation for AW design. Furthermore,we have also neglected the nonlinear d-axis con-troller in the design of the AW compensator.Part of the reason for this was that the d-axis controller is not actually active until a speed of0.22normalized units is attained and thus for a por-tion of the motor’s operational envelope is effectively absent. Second,as the d-axis controller is,by its very nature,nonlinear, it is more difﬁcult to handle this within the conventional AW framework.Finally,the linear q-axis controller is arguably the dominant part of the controller and extensive simulation revealed that it was sufﬁcient to consider this component alone for AW design.The authors do accept that the neglect of the d-axis portion of the controller does yield a small gap between the theory of AW compensator design and its application,but this did not appear to be detrimental in either the simulation or test results.To put the design and function of the three compensator candidates in context,weﬁrst introduce a simulation for which saturation without AW causes problematic performance.For the existing control system,a large step change in speed causes saturation of the current limit,as shown in the simulation results of Fig.6.This particular demand causes the q-axis control signal to exceed the limit for the majority of the simulation, leading to poor tracking of the high-speed demand and an overshoot of the subsequent low-speed demand.Note that the q-axis current limit varies with speed,and that only the signals within the controller exceed the limit since the signals passed onto the current controller are limited.A.Reset AWA simple way of preventing integrator windup in PI con-trollers is to reset the integrator state when saturation is ex-perienced and therefore to prevent the integrator accumulating excessive“energy.”When saturation ceases,integration is then allowed to continue either from the previously held value or another value such as zero.For the method considered in this paper,the integrator state is recalculated during saturation such that the controller output is held at the saturation level.When saturation ceases,integration recommences from the value calculated at the previous sample instance and normal linear operation continues.This is described by(10)and(11)where iq_lim represents the q-axis current limit,kp and ki are the speed controller proportional and integral gains,respectively, I(k)and e(k)denote the integrator state and speed error at sample instance k,respectively,andτspd represents the sample period of the speed controlleriq_dmd(k)=kp e(k)+I(k)(10) I(k)=⎧⎨⎩iq_lim−kp e(k),˜u>0I(k−1)+kiτspd e(k),˜u=0−iq_lim−kp e(k),˜u<0.(11)Fig.6.Saturating system without AW.Methods such as this are commonly used in industry to prevent integrator windup,and this method or variations on the theme can be found preprogrammed in off-the-shelf control hardware.This form of AW can be appealing since it is simple to implement and requires no tuning,although its performance could be improved upon.B.Back Calculation and Tracking(BCAT)In this method,the AW compensator adopts the form of a scalar feedback gain F,which is introduced between the signal˜u and the input to the integrator in the PI controller (Fig.7).This feedback reduces the integrator state over a period of time while saturation continues and will therefore prevent integrator windup.The magnitude of the gain F determines the rate at which the integrator state is reduced and can be tuned to improve performance.This method,and systematic ways for choosing F,is described more fully in[13].The main beneﬁt of this method is its simple transparent architecture and simple tuning.It can be applied successfully in many applications, although it is not well suited to multivariable systems and stability guarantees are not easily acquired.It may also not be directly applicable to controllers without an explicit integral state,for example,many H∞designs.Note that the nonlinear d-axis portion of the speed controller has been omitted from the block diagram of Fig.7for simplicity.C.Low-Order Dynamic AWThis method differs from the others in that it is model based, and as such provides the potential for improved performance by accounting for the dynamics of the plant and controller in the design of the compensator.This compensator adopts the form of two discreteﬁltersΘ1andΘ2which modify the control action at both the input and output of the nominal controller,as shown in Fig.8.Although theseﬁlters are discrete,we choose to useand in particular,it was shown that for low-order synthesis M(s)needed to be chosen asM=(I−K2G2)−1(−K2Θ2+Θ1+I)whereΘ1(s)Θ2(s)=F1(s)˜Θ1F2(s)˜Θ2and F1(s),F2(s)are some appropriate transfer functions cho-sen by the designer and˜Θ1,˜Θ2are gain matrices which are synthesized in an optimal fashion.Moreover,in[15],a linear-matrix-inequality(LMI)method was proposed which allowed˜Θ1,˜Θ2to be synthesized such that an upper bound on theL2gain of the operator T p:u lin→y d was minimized.This procedure allows the AW compensator,shown in Fig.8,to be synthesized in an optimal manner.The results presented in this paper are produced using a low-order compensator which has been synthesized in continuous time and then discretized. However,discrete-time synthesis routines are also in existence, as shown in[16].Unlike the other methods hitherto described,low-order AW provides stability and performance guarantees for the closed-loop system and also is applicable to multiple-input–multiple-output systems,for which simpler strategies often perform poorly.The disadvantage of this method is that,given arbitrary ﬁlters F1(s),F2(s),no a priori guarantees of the existence of a compensator are given;this must be checked using the LMI-optmization procedure.However,previous work has indicated thatﬁrst-orderﬁlters often prove to be effective choices,and once a successful set ofﬁlters have been found,the bandwidths can be varied by the designer to tune for the best overall performance.If a feasible solution cannot be found for the low-order synthesis problem,it is always possible toﬁnd a globally stabilizing AW compensator of order equal to the plant using the methods presented in[17]provided that the plant is asymptotically stable.IV.S IMULATION-B ASED A NALYSISFor simulation tests,the following PMSM model in the stator reference frame[11],[12]is used:di a dt =1L sV a−R s i a+K e√3ωm sin(θe)(12)di b dt =1L sV b−R s i b+K e√3ωm sinθe−2π3(13)di c dt =1L sV c−R s i c+K e√3ωm sinθe−4π3(14)dθedt=Pωm(15)dωm dt =1J[T e−load−Bωm](16)T=−K e√3i a sinθ+i b sinθ−2π3+i c sinθ−4π3.(17)The performance of the three AW designs were comparedusing a simulation model built using the aforementioned motormodel,inverse Park and Clarke transformations[12],and thediscrete time control structure presented in this paper.The innercurrent control loop is run at a fast sample rate in order tofaithfully reproduce the sinusoidal phase voltages which havea frequency of P times the maximum motor speed.However,there are still small errors in the stator phase voltages due tosampling and this does affect performance.This is particularlytrue at high speed when the frequency of the sine wave to beapplied becomes closer to the controller sampling frequencysince the errors become larger.With the d–q axis model,thehigh-frequency sinusoids are not reproduced so these samplerate issues are not revealed.A.AW ActionFigs.10–12show the output and control responses of thespeed control system with each type of AW to the same speeddemand as used for Fig.6.With the reset scheme,the q-axis demand exceeds the saturation limit but the integrator isreset at the next sample instance,successfully bringing thecontrol signal to below the limit(Fig.10).However,becausethe proportional action of the controller diminishes as themotor accelerates,the controller output then drops below thesaturation level for a time,leading to a slower rise time.Asimilar effect is observed during the reverse step.While thisresponse is signiﬁcantly better than without AW(Fig.6),it isnot ideal.This undesirable feature of reset AW is dependentupon the system dynamics and the tune of the PI controller andcan usually be eliminated by reducing the proportional gain.However,this restricts the tuning of the controller and mayimpair the small signal response of the system.With the back calculation and tracking method,the integratoris reset gradually,as observed by the smooth decay of the q-axis demand down to the saturation level for both forward andreverse steps(Fig.11).This leads to longer periods of saturationthan with the reset design,but performance is signiﬁcantly bet-ter overall,showing that bringing the system out of saturationas quickly as possible may not be the best approach.The low-order compensator functions differently in that thecompensator can directly alter the controller output.This meansthat bringing the control signal down to the saturation level isless important in the prevention of windup.Note that while thecontrol signal may greatly exceed the saturation limit(Fig.12),the system gracefully recovers tracking performance when sat-uration ceases.B.Simulation Performance ComparisonsResponses to a doublet speed demand of the system aug-mented by each form of AW are shown in Fig.13.The ben-eﬁt of AW compensation can clearly be seen;performance isimproved by all compensator types,although the reset schemeis less effective at limiting performance degradation.Both the“back calculation and tracking”and the“low order”designsachieve signiﬁcantly faster rise times for both positive and neg-ative step speed demands.They also perform very similarly onFig.10.Saturating system with resetAW. Fig.11.Saturating system with BCAT AW.the simulation model,despite their differing design processes and implementation.When a constant load torque is applied such that the full speed reference is infeasible,the designs perform as shown in Fig.14.For the system without AW,the infeasible reference causes an error signal to persist and the integrator continues to accumulate,leading to a q-axis current demand far in excess of the saturation level.When the reverse step is demanded,the integrator state holds the control signal in saturation for a period of time,resulting in a signiﬁcant delay in the response.Again, performance is improved by the application of each form of AW,with the back calculation design performing best,closelyFig.12.Saturating system with low-orderAW.Fig.13.AW responses to a doublet speed demand under no load conditions. followed by the low-order design,and both outperforming the reset strategy.V.E XPERIMENTAL A NALYSISFor practical testing of the AW designs,the controller code was written using TargetLink rapid prototyping software and ﬂashed to a16-bitﬁxed-point arithmetic processor using Vector CANape.A sophisticated pulsewidth modulation(PWM)algo-rithm was adopted to generate the stator phase voltages.This incorporates the use of third harmonic injection techniques to maximize voltageutilization.Fig.14.AW responses to a doublet speed demand under static loading.A.Model AccuracyIt is inevitable that there will be differences between the performance of the model and that of the real system due to parametric uncertainty and unmodeled dynamics.An example of such a discrepancy is shown in Fig.15where performance of the practical system and the simulation model with reset AW are compared in response to the speed reference of Fig.6.In the practical system,the decelerating step reference is rate limited to prevent the motor operating as a generator.This prevents a deceleration demand from causing saturation,and so the adverse effects observed in the simulation response areFig.15.Experimental and simulated performance comparison under no load. not seen in practice.This focuses the analysis of experimental AW performance on speed references which cause the motor to accelerate.For the accelerating step reference,the experimental data show a faster response with a small amount of overshoot. The main source of this discrepancy is considered to be the modeling of the hydraulic load for which a simple linear approximation is used.In practice,this is highly nonlinear and difﬁcult to model accurately.In addition,the PWM strategy is modeled simply by inverse Park and Clarke transformations and a simple gain adjustment.This simpliﬁcation is expected to be least accurate when maximum voltage is demanded,for instance in response to large demands.Another implication of modeling errors relates to the com-pensator design stage.Since the low-order compensator is model based,any signiﬁcant inaccuracies in the model could cause the design to perform more poorly than predicted when applied to the real system.However,the low-order design is observed to perform well in both cases.In addition,the performance trends observed during simulation tuning were also evident in the experimental tests,i.e.,the best performing design on the simulation model also performed best on the real system,giving conﬁdence that the fundamental dynamics of the model are correct.B.Implementation IssuesThe use ofﬁxed-point arithmetic requires aﬁxed range and scaling to be assigned for each signal,state,and gain in the controller.Inevitably,errors are introduced to the representation of each number,but these can become signiﬁcant when the number to be represented is small compared to the range.These errors can propagate through the controller and accumulate over time due to successive arithmetic operations,and so to minimize their effect,consideration needs to be given to the scaling assigned to each signal/state/gain.This is particularly true when implementing state-spaceﬁlters as used in low-order dynamic compensation.A givenﬁlter can be represented by an arbitrary number of state-space realizations with the same input output relationship,but different state and output equation matrices.Inﬁxed point,the choice of state-space realization can affect the accuracy of computations frominput Fig.16.Experimental data—large step speed demand under static load.to state and from state to output,and hence the accuracy of the input output relationship can vary.A further consideration is that errors in the state to output computation will only be present for one sample instance,but errors in the input to state computation will also affect future sample instances since the error is retained in the state.These factors must be carefully considered when selecting the state-space representation to be used,but a good starting point is a balanced realization.For the low-order compensator we present,theﬁlters chosen are stable,strictly proper,and ofﬁrst-order low-pass design.These characteristics make the choice of adequate scalings relatively simple.C.Experimental Performance ComparisonsIn this section,we compare the performance of the three AW designs as observed using the experimental rig.Current demand saturation is induced for quite small step speed demands while operating at high speed,and when large step demands are made at lower speeds.Unless particular comment is made,the performance differences are very similar under no load and static load conditions.Fig.16shows experimental performance comparisons be-tween the different AW controllers for a large step demand under a small static load.While the reset scheme reduces the overshoot compared to the case without AW,performance is improved further by the BCAT method,and further still by the low-order dynamic design.Certainly,overshoot is caused by the baseline controller,but this is accentuated by saturation,and this component can be improved by good AW design.Fig.17shows step tracking performance for a small step demand in the high-speed range.In this case,the reset and BCAT strategies provide very similar performance but the low-order dynamic compensator performs best,roughly halving the overshoot compared with the previous two designs.VI.C ONCLUSIONThe performance of“back calculation and tracking”and “low-order dynamic”AW compensation has been compared to a reset scheme commonly used in industry through simu-lation tests and a practical implementation.Both compensation。

小学上册第十三次英语第3单元测验试卷

小学上册英语第3单元测验试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The _____ (绿色能源) movement promotes plant-based solutions.2.The _____ (cat/dog) is sleeping.3.The ______ (香味) of flowers can be very strong.4.What do we call a scientist who studies the properties of matter?A. ChemistB. PhysicistC. BiologistD. Geologist答案:A5.I want to _____ (see/watch) a movie tonight.6.What is the main language spoken in the USA?A. SpanishB. FrenchC. EnglishD. German答案:C7.The cake is ________ and sweet.8.We share ______ (秘密) with each other.9.I enjoy going ______ (远足) to enjoy the beauty of nature.10.The ______ teaches us about civic responsibilities.11.The chemical properties of an element depend on its ______ structure.12.The country famous for its tango is ________ (阿根廷).13.What is the opposite of 'fast'?A. QuickB. SlowC. SpeedyD. Rapid14.What is the capital of Tunisia?A. TunisB. SousseC. MonastirD. Bizerte答案:A15.What do you call a house made of ice?A. IglooB. CabinC. CastleD. Hut答案:A16._____ (当地植物) can adapt to specific environments.17.Chemical reactions often involve a change in ______.18.The __________ is the layer of skin that helps to protect against injury.19.I enjoy making memories with my toy ________ (玩具名称).20.I can ________ (manage) my time effectively.21.What do we call the opposite of ‘clean’?A. DirtyB. NeatC. TidyD. Clear22. A __________ is a sudden release of energy in the Earth's crust.23.My friend is a ______. He loves to collect stamps.24.My dad shows me how to be __________ (勇敢的) in difficult times.25.What is the largest country in the world?A. CanadaB. ChinaC. RussiaD. India26.The _______ (The Battle of Waterloo) marked the defeat of Napoleon.27.The ____ is a small creature that hides under leaves.28.What do we call the study of the universe?A. BiologyB. AstronomyC. GeologyD. Physics答案:B29.The _____ (果实) develops after a flower blooms.30. Wall of China was built to __________ (保护) the country from invasions. The Grea31.The ant carries food back to its ______ (巢).32.What is 4 + 5?A. 8B. 9C. 10D. 1133.The _____ (水果收成) happens in late summer.34.Many plants have a specific ______ period for blooming. (许多植物有特定的开花期。

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS

iL L + _ e S rL
D + v
_
C R
rC
filter
_

PWM Signal
+
vcon + v ramp _ V ref
feedback
Figure 1. Block diagram of a PFC boost pre-regulator.
Copyright ? 2003 John Wiley & Sons, Ltd. Int. J. Circ. Theor. Appl. 2003; 31:611–624
SUMMARY This paper investigates the fast-scale instability in a power-factor-correction (PFC) boost converter under a conventional average current-mode control. The converter is operated in continuous mode. Computer simulations and theoretical analysis are performed to study the e ects of the time-varying input voltage under the variation of some chosen parameters on the qualitative behaviour of the system. It is found that fast-scale instability may occur during a line cycle, which can cause distortion to the line current and degrade the practical power factor. The results provide useful information for the design of PFC boost converters to avoid distortion due to fast-scale bifurcation. Copyright ? 2003 John Wiley & Sons, Ltd.

高一经济现象英语阅读理解30题

高一经济现象英语阅读理解30题1<背景文章>The market economy is an economic system in which decisions regarding production, distribution, and consumption are guided by the interactions of supply and demand. In a market economy, businesses and individuals are free to make their own economic decisions.One of the key characteristics of a market economy is the role of competition. Competition among businesses leads to lower prices, better quality products, and greater efficiency. When businesses compete, they are forced to find ways to produce goods and services more efficiently in order to lower costs and offer better prices to consumers.Another important aspect of a market economy is the price mechanism. Prices play a crucial role in allocating resources. When the demand for a particular good or service increases, its price tends to rise. This signals to producers that there is a greater need for that product, and they respond by increasing production. Conversely, when the demand for a product falls, its price drops, and producers reduce production.The market economy also promotes innovation. Businesses are constantly looking for new ways to improve their products and processes in order to gain a competitive edge. This leads to the development of newtechnologies and better ways of doing things.In addition, a market economy allows for a wide range of choices for consumers. With many businesses competing for their business, consumers have the opportunity to choose from a variety of products and services at different prices and quality levels.1. One of the key characteristics of a market economy is _______.A. government controlB. lack of competitionC. the role of competitionD. fixed prices答案：C。

NOVATEK-ELECTRO LTD 产品说明书：UBZ-301（10-100A）通用感应电机保护

NOVATEK-ELECTRO LTDResearch-and-Manufacture CompanyUBZ-301 (10-100A)UNIVERSAL INDUCTIONMOTOR PROTECTION UNITUSERS MANUALCONTROLS DESCRIPTION AND DIMENSIONS DIAGRAM 4151. Control for nominal current setting, Inom;2. Control for operating current setting, Iop (% Inom);3. Control for T2 (double overload trip) delay setting;4. Combined trip adjustment control for Umin/Umax;5. Control for phase imbalance adjustment, PI;6. Control for trip threshold for the minimum current, Imin (%Inom);7. Control for automatic reset delay setting, Ton;8. Green LED indicating for the mains voltage presence;9,10,11. Red LEDs indicating faults for insulation, overload and U fault respectively;12. Green LED indicating for load energization;13. Output terminals;14. Input terminals (10,11,12 are used for the connection with the BO-01 exchange unit);15. Insulation monitoring terminal.1 APPLICATIONSThe UBZ-301(10-100A)universal induction motor protection unit is designed for the continuous monitoring of the mains voltage parameters and for RMS phase/line currents of 3-Phase AC 380V/50Hz electrical equipment monitoring, primarily, of induction motors whose power is from 5kW up to 50 kW, isolated neutral system included.The unit provides full and effective protection of electrical equipment by a magnetic starter (contactor) coil control.The unit isolates electrical equipment from the running system and/or disables its start. This is performed in the following cases:1. when the mains voltage is of poor quality (unallowable voltage jumps, phase loss, incorrect phase sequence and phase «coincidence», phase/line voltage imbalance);2. when mechanical overloads (symmetrical phase/line current overload) take place. The unit performs overload protection with a dependent time delay;3. when phase/line current asymmetrical overloads induced by faults inside the motor occur. The unit performs protection from phase current imbalance and further disables an automatic reset;4. when phase current asymmetry without overload occurs that is induced by the insulation fault inside the motor and/or the power cable;5.when motor load is lost(«dry stroke»for pumps).The unit provides the minimum start and/or operating current protection;6. when insulation level to frame is abnormally low. The unit performs insulation level test before start and if the insulation is poor the start is disabled.7.when stator winding ground-to-fault occurs during operation. The unit performs the ground leakage current protection.The UBZ-301 (10-100A) provides:•a simple and accurate electromotor nominal current setting by nominal current standard scale;•the electromotor operating current setting that differs from standard values;•overload tripping with a dependent time delay (the current-time characteristic curve is plotted for a conventionally cold motor). The motor heat balance differential equation is being solved in the operation process. This approach enables to take account of the preceding electromotor status and to make a decision on heat overload presence with the maximum validity. This method also permits to allow for a motor start heating and to restrict (at the customer’s option) amount of starts per unit time;•shift of current-time characteristic curve along the current-axis and along time-axis as well;•setting of trip thresholds for the minimum/the maximum voltage,line voltage&phase current imbalance, and also for automatic reset delay at the personal customer’s discretion;•fault type indication, the mains voltage presence indication, current range indication the unit is adjusted to, and load energization indication;•the data exchange and transfer to the local computer network according to the RS-485 MODBUS record through the BO-01 exchange unit (BO-01 is supplied on order).2 DESCRIPTIONThe unit is a microprocessor-based digital device that provides a high degree of reliability and accuracy. The unit doesn’t need any auxiliary supply because it retrieves it's energy demand out of the measurement signal: it’s self-powered by the voltage to be monitored. Simultaneous isolated independent monitoring for the mains voltage and phase currents permits to detect the type of occurring fault and to provide a different decision-making logic for each fault type. When the mains voltage faults occur the unit performs automatic load reset on return voltage parameters to normal operating conditions. If a fault is induced by abnormal condition inside the motor(phase current imbalance at the symmetrical mains voltage,leakage current presence etc.) restart is disabled.The unit is stocked with three toroidal current transducers. Two of them are the phase/line current transducers (TT1, TT2), power phase cables are pulled through them. The third transducer is the differential current transducer(DCT)that has an enlarged diameter,because three power phase cables are pulled through it. By the 6, 7, 8, 9 terminals the unit is connected in parallel to the mains supply to be monitored. The unit output is provided with N.O. and N. C. contacts (the 1, 2, 3, 4 terminals). The output 3-4 terminals are connected in series with the starter coil power supply (with control circuit). The5terminal is designed to monitor the insulation level. The unit wiring diagram is shown below.When the unit trips the load is de-energized by a break in the magnetic starter coil power circuit through the N. C. 3-4 contacts.Table 1 - The 1-2-3-4 output contacts specificationMax. current for~ 250 V A. C.Max. powerMax sustained safevoltage ~Max. current for U = 30V D.C.Cosφ = 0.43A 2000VA 460V 3ACosφ = 1.05ANominal parameters and trip thresholds are set by front-panel screwdriver potentiometers.Nominal current setting. Nominal current is set by № 1 potentiometer. There are eleven positions of the potentiometer. Each position corresponds to the specific standard nominal current scale value (see below Table of Nominal Currents). Each position is characterized by the specific number of blinks that the green «On» LED makes. To set the nominal current one needs to bring out potentiometer control arm to a corresponding position; when the unit is energized the number of blinks «On» LED must correspond to the Table below. One needs to take into account that there are «dead bands» between the positions where «On» LED glows without blinks and where the nominal current is indefinite.In order to set operating value which is different from the nominal one that is specified in the nominal current table, it’s recommended the № 1 potentiometer to set to the position corresponding to the nearest value from the nominal current scale, and by the № 2 potentiometer one can increase or decrease the necessary value in % from the set value.Table 2 - Nominal current tablePotentiometer №1 devisionsNom. current, АGreen LED «On» blink1101bl.- pause 212,52bl.- pause 3163bl.- pause 4204bl.- pause 5255bl.- pause 6326bl.- pause 7407bl.- pause 8508bl.- pause 9639bl.- pause 108010bl.- pause 1110011bl.- pauseNOTE S:1.Continuous green «On» LED glow means that the potentiometer is set in «dead band». One needs to set the potentiometer so as the green LED blinked and the number of blinks corresponded to the set nominal current.2.Nominal currents setting is to be performed correcting for load connections (Wye/Delta), according to ratings of engine.Controls and adjustmentsThe unit has seven independent controls. For user’s convenience screwdriver slots of adjusting potentiometers are brought out to the unit front panel.•№1 – «Inom» - nominal current setting; there are eleven positions and each position corresponds to the specific current from the nominal currents table;•№2 – «Iop» - operating current; it is set in ± 15 percent of nominal current, it has ten scale marks;•№3 – «T2» - overload trip delay when there is double overload for operating current set; in the central position T2 ≈ 58-60 seconds The minimum time delay is 10 seconds, the maximum time delay is 100 seconds. The control shifts current-time characteristic dependence along time axis;•№4 – «Unom(%)» - combined control for Umax/Umin threshold in percent of the nominal voltage; according to this setting before the load energization the unit is checking the mains voltage level and, depending on its value, permits or forbids the load energization; after the load has been energized the voltage monitoring is going on but the load de-energization decision is made for currents;•№5 – «PI%» - trip threshold control for line voltage imbalance and RMS phase current imbalance; it has ten scale marks. The parameter is calculated as the difference between the maximum and the minimum values, in percent of the maximum value. If current imbalance percentage is twice as much as voltage imbalance percentage then it’s supposed that the imbalance is induced by fault conditions inside the motor. The automatic reset is forbidden and the unit is disabled;•№6 – «Imin» - trip threshold control for the minimum operating current, in percent of operating current set. It has ten scale marks from 0% to 75%: in «0» position this control is off;•№7 – «Ton» - automatic reset delay, it is within 0 – 600 seconds range; the scale is logarithmic.Indication•the green «ON» LED indicates that voltage exists in the mains. In the blink mode of glow the blink number between pauses corresponds to the specific nominal current from the nominal current table; there is a continuous glow in a «dead band». One needs to set a nominal current in the blink mode of operation;•the green «Load» LED indicates that the load is energized (the 3-4 terminals are closed);•the red «Insulation» LED lights up with continuous glow before the start if the stator/ power cable winding insulation level is abnormally low (less than 500 kOhms), and also during operation when there is a tripping for differential current; the unit is disabled;•the red «U Fault» LED glows when the mains voltage fault has occurred. The blink mode of operation switches on when there is undervoltage/overvoltage, phase imbalance for the mains voltage, voltage is not present on all three phases;•incorrect phase sequence or phase coincidence induces the mode of operation when all three red LEDs are blinking in turn;•the red «Overload» LED blinks when the average phase current exceeds the nominal one. After the unit has tripped for overload this LED comes to glow during 0.9 AR (automatic reset) delay.4 TECHNICAL BRIEFNominal line voltage, V380Mains frequency, Hz45-55Nominal current range in UBZ-301 10-100, А10-100Operating current setting range, % of nominal±15Double overload delay adjustment range, sec10-100Voltage threshold adjustment range, % of nominal±(5-20)Phase imbalance adjustment range, %5-20Trip threshold adjustment range for the minimum current, % of nominal0-75Automatic reset delay adjustment range ( Тon), sec0-600First energization load delay when Тon= 0, sec2-3Trip delay for current overload According to current-time characteristic curveTrip delay for voltage fault, sec2Trip delay for current fault (overload excluded), sec2 Fixed trip point for leakage current, А 1.0 Insulation resistance threshold, kОhms500±20 Voltage hysteresis, V10/17 Heat hysteresis, % of stored-up heat after load de-energization33Trip threshold accuracy for current, % of nominal current, not more than2-3 Trip threshold accuracy for voltage, V, not more than3 Phase imbalance accuracy, %, not more than 1.5 Operating voltage range, % of nominal one50-150 Power consumption (under load), VA, not more than 3.0 Maximum switched current of output contacts, A5 Output contact life:- under 5A load , operations, no less than - under 1A load , operations, no less than 100 000 1 000 000Enclosure:- apparatus- terminal block IP40 IP20Operating temperature range, °C from -35 to +55 Storage temperature, °C from -45 to +70 Weight, kg, not more than0.200Case dimensions 4 modules of S-typeMounting standard 35 mm DIN-railMounting position arbitrary5 OPERATION1. After supply voltage has been applied to the unit and before the output relay is energized the unit checks:•a stator winding insulation level to frame. If insulation resistance is below 500±20 kOhms, the load is not energized. The red «Insulation» LED glows;•the mains voltage quality,i.e.if voltage is present on all three phases,if the mains voltage is symmetrical, what the RMS line voltage value is like. When any of inhibit factors is present, the load is not energized, the red «U Fault» LED blinks;•a correct phase sequence, and phase «non-coincidence». When any of inhibit factors is present, the load is not energized, all red LEDs are blinking in turn; If all the parameters are normal, the outlet relay will be energized after Ton delay has expired (the 3-4 contacts are being closed and the 1-2 contacts are being opened) - the green «Load» LED glows. If load currents are absent (there are no less 2% of nominal one) the reason is that the load is de-energized. Voltage monitoring and insulation level is going. Output relay of unit is de-energized if inhibit factors are present in pause without currents;2. After the load is energized the unit performs voltage and current monitoring. The decision on load de-energization is made according to the following factors:•RMS current exceeds the nominal (operating) current (set by №№ 1, 2, 3 potentiometers); if there is current overload without heat overload the red «Overload» LED blinks but the load is not de-energized. If current overload induces heat overload the load is de-energized. The red «Overload»LED glows and is ON during 0.9Ton. The automatic reset is permitted;•current imbalance (set by №5 potentiometer) is twice exceeds the mains voltage imbalance; the load is de-energized, all red LEDs glow, the unit is disabled, the automatic reset is forbidden. To enable the unit one needs to remove supply voltage from the unit. It’s supposed that this type of fault is induced by abnormal conditions inside the motor;•current imbalance (set by №5 potentiometer) is less than twice exceeds voltage imbalance; the load is de-energized, the red «U Fault» LED glows, the automatic reset is permitted;•current imbalance (set by №5 potentiometer) is less than voltage imbalance; the load is de-energized, the red «U Fault» LED blinks, the automatic reset is permitted;•the average current value is less than Imin (set by №6 potentiometer); the load is de-energized, all red LEDs blink simultaneously, the unit is disabled, the automatic reset is forbidden. To enable the unit one needs to remove the supply voltage from the unit.Electromotor protection against heat overloadThe electromotor heat balance equation is being solved as the work advances. It’s supposed that:•the motor was cold before start;•during operation the motor releases the heat which is proportional to the current square;•after the stop the motor cools down exponentially.Below is the current-time characteristic curve with different T2 values (set by №3 potentiometer), where:•I/In – current ratio relative to the nominal current;•T/T2 -- actual trip delay relative to T2 (set by № 3 potentiometer).Current-time characteristic dependenceThe current-time characteristic dependence shown in the tables below is given for the standard recommended T2 value (the №3 potentiometer middle position corresponds to 60 seconds when double overload occurs):I/Inom 1.1 1.2 1.4 1.72 2.73456781015Тsec36524714888.66036.424.613.58.5 5.9 4.3 3.3 2.10.9After the load has been de-energized owing to the heat overload it will automatically be energized again:•according to heat hysteresis if time delay Ton=0, i. e. the motor must cool down 33% of the stored up heat;•according time delay Ton (№ 7 potentiometer) if Ton isn’t equal 0.By suitable selection of different Ton values, heat hysteresis considered, one can reduce number of starts per time unit because in the intermittent cycle the unit stores heat quantity released at the start of the motor.6 PRELIMINARY STARTING PROCEDURE AND SERVICE MANUALThe unit produced is completely ready for operation and needs no special pre-starting procedure measures. Owing to digital technology all the unit settings are aligned quite accurate, so no control devices are needed to adjust them. Use of the unit according to specifications above and the present service manual, continuous work included, relieves of preventive maintenance during service life. To put the unit in operation one must follow operating instructions given below:1.To set nominal (operating) current, trip thresholds, trip delays and reset delay by potentiometer's contact arms.2.To connect the unit according to the wire diagram given below:•by the 6(L1), 7(L2), 8(L3), 9(N) terminals the unit is connected in parallel to the mains supply to be monitored;•two current transducers (each one of them is put on two power phase wires that carry the load) are connected to the 13, 14, 15, 16 terminals; in connecting one has to consider the transducers grading;1st transducer– the beginning – the 13 terminal, the end – the 14 terminal;2nd transducer– the beginning – the 15 terminal, the end – the 15 terminal;•a differential current transducer that is put on the three power phase wires must be connected to the 17, 18 terminals (the connection grading is unimportant);•the 5 insulation monitoring terminal is connected to one of the MS output contacts;•output contacts (the 3-4 terminals) are connected to the MS coil power supply circuit (control circuit);•the BO-01 exhange and date transfer unit is connected to the 10, 11, 12 terminals (this unit is supplied on order).3.To apply a voltage to the unit. The correct setting of nominal current is checked by the number of blinks that the green LED makes. After Ton has expired (if there are no factors that can forbid energizing) the output relay of the unit is energized. If Ton=0, the first energizing will occur after 2-3 sec delay has expired.NOTE - The unit must be connected subject to the safety regulations. To set settings is recommended in «off» state. To set settings alive is permitted in the test conditions subject to the safety regulations.ATTENTION!If immediately after the load has been energized the unit de-energizes it and disables it for current imbalance,the incorrect polarity of the current transducers TT1or TT2 connection may be a reason. Then it’s recommended to change one of the transducers connection by reversing the places“the beginning-the end”of the13-16terminals.If the effect pointed above repeats when the load is re-energized it means that the transducers were connected correctly and the imbalance arose from EM and/or power cable fault.NOTES:1 Transducers are mounted by plastic clamps (they are component parts of supplies).2 The phase wires which are passing through the differential transducer to try to symmetrize in the centerof the transducer.WIRING DIAGRAMDT–differential current transducer (differential current transformer);CT1,CT2–current--transducers;BO-01– exchange and date transfer unit (on order)NOTE:1 “START”-button and “STOP”-button can be connected to MSC power supply circuit if necessary;2 The 220V MSC connection is shown here. The 380V MSC power supply circuit is analogous, coil power is applied from different phases through the 3-4 contacts;3 If BO-01 is absent the 10, 11, 12 terminals are not used.7 STORAGE AND SHIPPING CONDITIONSThe unit in manufacturer package should be stored in enclosed rooms at –45 to +70 °C and exposed to no more than 80% of relative humidity when there are no fumes in the air that exert a deleterious effect on package and the unit material. The Buyer must provide the protection of the unit against mechanical damages in transit.8 WARRANTYNovatek-Electro LTD. Company warrants a trouble-free operation of the UBZ-301 (10-100A) unit manufactured by it within 36 months from the date of sale, provided:•the proper installation;•the safety of the inspection quality control department seal;•the integrity of the case, no traces of an opening, cracks, spalls etc.。

2023年12月英语六级听力原文及参考答案

2023年12月英语六级听力原文及参考答案听力稿原文section AConversation 1气候变化和全球经济发展W: Professor Henderson could you give us a brief overview of what you do, where you work and your main area of research？M: Well the Center for Climate Research where I work links the science of climate change to issues around economics and policy。

Some of our research is to do with the likely impacts of climate change and all of the associated risks。

W: And how strong is the evidence that climate change is happening that it‘s really something we need to be worried about。

M: Well most of the science of climate change particularly that to do with global warming is simply fact。

But other aspects of the science are less certain or at least more disputed。

And so we‘re really talking about risk what the economics tells us is thatit’s probably cheaper to avoid climate change to avoid the risk than it has to deal with the likely consequences。

2025年北师大版高考英语试题与参考答案

2025年北师大版英语高考复习试题与参考答案一、听力第一节（本大题有5小题，每小题1.5分，共7.5分）1、Listen to the following dialogue between two students, and answer the question.Student A: Hey, are you planning to follow the exam schedule strictly? Student B: Yeah, I always try to stick to a routine. How about you?Student A: Well, I like to mix it up a bit. It keeps me motivated.Question: What does Student A prefer when it comes to following an exam schedule?A. To follow the routine strictly.B. To mix up the schedule to stay motivated.C. To follow the schedule only when it’s convenient.D. To avoid any schedule altogether.Answer: BExplanation: Student A indicates that they like to mix up the schedule to stay motivated, which is equivalent to choice B.2、 Listen to the following conversation about a school trip, and complete the following sentence with the correct information.Teacher: Ok, everyone, we’re going to have a field trip next week. It’s a science-themed trip to the museum downtown.Student A: That sounds amazing! What are we going to learn there, though?Teacher: Well, you’ll get a behind-the-scenes look at how exhibits are put together, and you’ll interact with some of the curators. Plus, there are interactive displays where you can try out different experiments.Question: What will the students be able to do during the trip to the museum?A. Simply observe the exhibits without participating.B. Work with the curators to put together new exhibits.C. Participate in interactive experiments and discussions.D. Finish the field trip without visiting the museum.Answer: CExplanation: The teacher mentions that the students will be able to participate in interactive experiments and discussions, which corresponds to choice C.3.What does the man suggest doing?A) Having a picnic.B) Going to the cinema.C) Visiting the museum.D) Playing tennis.Answer: A) Having a picnic.Explanation: The woman mentions that it’s a beautiful day and asks the man what he thinks they should do. The man responds by suggesting they take advantage of the weather and have a picnic in the park. Therefore, the correct answer isA) Having a picnic.4.Where are the speakers most likely?A) At home.B) In a restaurant.C) On a bus.D) In a bookstore.Answer: B) In a restaurant.Explanation: The dialogue involves one speaker asking for recommendations on dishes and commenting on the menu, while the other speaker provides suggestions and describes the specials. This context strongly suggests that the conversation is taking place in a restaurant, making B) In a restaurant the correct choice.5、 Listening Section AQuestion: How is the woman going to the airport?A) By bus.B) By taxi.C) By subway.Answer: BExplanation:In the recording, the man asks, “Are you going to the airport by bus or by taxi?” The woman replies, “I decide to take a taxi because it will be faster.” Therefore, the correct answer is B) By taxi.解析：录音中，男士问：“你要去机场是乘公交还是打车？”女士回答：“我决定打车去，因为会更快。

IEC61400-1-2005风电机组设计要求标准英汉对照

Consolidated editions The IEC is now publishing consolidated versions of its publications. For example, edition numbers 1.0, 1.1 and 1.2 refer, respectively, to the base publication,the base publication incorporating amendment 1 and the base publication incorporating amendments 1and 2.
需要什么文档直接在我的文档里搜索比直接在网站大海捞针要容易的多也准确省时的多
INTERNATIONAL STANrbines – Part 1:
Design requirements
Publication numbering As from 1 January 1997 all IEC publications are issued with a designation in the 60000 series. For example, IEC 34-1 is now referred to as IEC 60034-1.
Further information on IEC publications The technical content of IEC publications is kept under constant review by the IEC, thus ensuring that the content reflects current technology. Information relating to this publication, including its validity, is available in the IEC Catalogue of publications (see below) in addition to new editions, amendments and corrigenda. Information on the subjects under consideration and work in progress undertaken by the technical committee which has prepared this publication, as well as the list of publications issued,is also available from the following: IEC Web Site (www.iec.ch) Catalogue of IEC publications The on-line catalogue on the IEC web site (www.iec.ch/searchpub) enables you to search by a variety of criteria including text searches,technical committees and date of publication. Online information is also available on recently issued publications, withdrawn and replaced publications, as well as corrigenda. IEC Just Published This summary of recently issued publications (www.iec.ch/online_news/justpub) is also available by email. Please contact the Customer Service Centre (see below) for further information. Customer Service Centre If you have any questions regarding this publication or need further assistance, please contact the Customer Service Centre: Email: custserv@iec.ch Tel: +41 22 919 02 11 Fax: +41 22 919 03 00 .

用于逆变器的比例-谐振控制器的抗饱和方案

1
引言
比例 -谐振（ PR）控制器，自从被提出之后，便
[1-2]
的方式。文献提出了一种抗饱和的方法，也可以归为跟踪积分的方式，只是文中并未做详细的分析。总体来看，跟踪积分可以达到 PR 控制器抗饱和的目的，但是需要设计一个反馈系数。本文从等效电路的角度出发，提出一种 PR 控制器的抗饱和新方案。从结构上看，此种策略结合了条件积分和跟踪积分，属于混合式结构。这种策略有物理意义明确，简单，容易实现的优点。仿真和实验结果验证了本方案的有效性。
(3)
当等效电路中各个元器件的参数分别为：
2
1 s
rP K P , rR Ki , CR
路阻抗为：
2 Kic 1 时，电 , LR 2 Kic 2
图2
另一种 PR 控制器的形式
当控制器输出被限幅电路限制时，控制器中的积分器就可能出现饱和的现象。而 PR 控制器中包含了两个积分器，因此饱和现象同样是存在的。
GPR ( s) K p
2 Kic s s 2c s 2
2
(2)
同样，这种 PR 控制器也可以用两个积分器组
成，如图 2 所示。
e
Kp
电路，如图 4 所示。其阻抗的传递函数为：
+ +
Z ( s) rP
2c
+ 1 s
2c K i
rR LR s CR rR LR s 2 LR s rR
2c K i
yr
-
+
2
1 s
PR Controller
1 Kp
图6
本文提出的抗饱和方案
新的控制方案便基于此等效电路，如图 6 所示。虚线框中为 PR 控制器，图中 y 表示 PR 控制器的输出， yp、yr 分别表示输出 y 的比例部分和谐振部分。他们之间的关系满足：

克罗韦尔简便紧凑的电机启动解决方案规格产品说明书

Technical DataOriginal InstructionsEasy and Compact Motor Starting SolutionsBulletins 140MP, 100-K, and 193-KOverviewBulletin 140MP Motor Protection Circuit Breakers (MPCBs) or Motor ProtectiveSwitching Devices (MPSDs) provide magnetic short circuit and thermal overloadprotection up to 32 A. They are tested in combination with Allen-Bradley® Bulletin100-K contactors to create two-component motor starters.Our easy and compact motor starting solutions are designed to ensure the smoothoperation of your motors, thereby enhancing the overall productivity of yoursystems. They offer a high degree of flexibility, allowing for precise adjustments tomatch the specific requirements of your motors. This precision, coupled with therobust protection features, helps prevent motor damage and extends the lifespan ofyour equipment.These devices are UL Listed as Manual Motor Controllers (with optional approvals forSuitable as Motor Disconnect and Suitable for use in Group Installation). Groupmotor installations eliminate the need for individual branch short circuit protectivedevices for each motor circuit, reducing panel space, installation and wiring time,and costs. There is only one Branch Circuit Protective Device (BCPD) for the “Group”.Features and Benefits Ratings•Protection and Control Functions:•UL group motor and IEC Type 1 and Type 2 ratings -Overload protection•CE, cULus, CCC, KC, EAC certifications-High short-circuit protection•Devices meet MPSD requirements per IEC 60947-4-1-Disconnect function•Devices meet circuit breaker standards per IEC 60947-2 -Phase loss protection•Rated up to 690V AC•Adjustable current setting for overload protection•Temperature compensation from -25…+55 °C (-13…+131 °F)•Suitable for three-phase and single- phase application•Suitable for use outside North America•Easy to install, snap-on mounting of accessories and modules•Provides disconnecting means for motor branch circuit •Modular Accessories•Offers short-circuit protection (magnetic protection)•Ideal for industrial or commercial application where space isat a premium•Provides overload protection (thermal protection)•Allows manual switching (motor control means)•Less panel depth requirements than standard IEC contactors•Budget-friendly motor starting solutiontwo-component starterbimetallic overload relayEasy and Compact Motor Starting Solutions Technical DataQuick Motor Starter SelectionThe two-component motor starter is a simple setup that includes a motor protection circuit breaker with a built-in thermal overload relay and a motor contactor. This combination provides protection and control for the motor. This is the most compact and most popular motor starting configuration.The three-component motor starter offers a more flexible solution. It consists of a motor circuit protector or fuses, a motor contactor, and a motor thermal overload relay. This configuration provides enhanced protection options in the separate thermal motor overload relay. When building a three-component motor starter, you can use either fuses or a motor circuit protector without thermal overload, such as the 140MT motor circuit protector.The following tables list a popular subset of these devices. More main device features, sizes, and accessory options are available. See publications 140-TD005, 100-TD013, and 193-TD010 at rok.auto/literature.Step 1: Choose Circuit Breaker and Optional Connection ModuleStep 2: Configure ContactorAfter you select your contactor in the preceding table, complete your contactor cat. no. by using the codes below for coil voltage and auxiliary contact configuration.Example: for a 24V DC contactor with integrated diode and 1 N.O. contact, Cat. No. 100-K09⊗✪ becomes Cat. No. 100-K09DJ10Step 3 (Optional): Select Motor Overload RelayRated Operating Current[A]Thermal Trip AdjustmentRange [A]MPCB(1) Cat. No.Optional ConnectingModule Cat. No.Contactor Cat.No.0.160.1…0.16140MP-A3E-A16140MP-A-PEK12100-K05⊗✪0.250.16…0.25140MP-A3E-A250.400.25…0.40140MP-A3E-A400.630.40…0.63140MP-A3E-A6310.63…1.0140MP-A3E-B101.6 1.0…1.6140MP-A3E-B162.5 1.6…2.5140MP-A3E-B254 2.5…4.0140MP-A3E-B406.3 4.0…6.3140MP-A3E-B63100-K09⊗✪10 6.3…10.0140MP-A3E-C10100-K12⊗✪128.0…12.0140MP-A3E-C121610.0…16.0140MP-A3E-C16(1)140MP devices have built in Trip Class 10 protection, and do not require a separate motor overload relay unless you change the motor protective device to fuses or a circuit breaker withoutthermal overload protection.140MP-A-PEK12100-K140MP⊗ Coil Voltage Code(1)(1)Additional coil voltages are available. See publication 100-TD013.✪Auxiliary ContactsCode Description Code DescriptionD120V AC, 60 Hz and 110V AC, 50 Hz10 1 N.O.B480V AC,60Hz011N.C.KJ24V AC, 50/60 HzKF230V AC, 50/60 HzDJ24V DC with integrated diodeThermal TripAdjustment Range[A]Overload RelayCat. No.For Use WithContactor0.1…0.16193-KA16100-K05…-K120.16…0.25193-KA250.25…0.40193-KA400.35…0.50193-KA500.55…0.80193-KA800.75…1.0193-KB100.90…1.3193-KB131.1…1.6193-KB161.4…2.0193-KB201.8…2.5193-KB252.3…3.2193-KB322.9…4.0193-KB403.5…4.8193-KB484.5…6.3193-KB635.5…7.5193-KB757.2…10.0193-KC109.0…12.5193-KC122Rockwell Automation Publication 140MP-TD002A-EN-P - August 2024Rockwell Automation Publication 140MP-TD002A-EN-P - August 20243Easy and Compact Motor Starting Solutions Technical DataAccessoriesApproximate DimensionsDimensions are shown in millimeters (inches). Dimensions are not intended for manufacturing purposes.100-K Miniature Contactor with 193-K Overload RelayCat. No. 140MP-A3E… ≤16 AAdditional ResourcesThese documents contain additional information concerning related products from Rockwell Automation. You can view or download publications at rok.auto/literature .Popular Accessories for 140MP MPCBsDescriptionCat. No.Front-mounted Auxiliary Contact •1 N.O.-1.N.C.•No additional space required 140MP-A-AFA11Front-mounted Auxiliary Contact•1N.O.•No additional space required140MP-A-AFA10Compact Bus Bars•UL: 600V, 60 A; IEC: 690V, 65 A •45 mm (1.77 in.) spacing •For use with front-mounted auxiliary contact •2 x 3 connections 140MP-A-W452Bus Bar Feeder Terminal (Flat)•Supply of compact bus bars •Increases terminal capacity 140MP-A-WTNEnclosure•Up to three padlocks in OFF position•Protection Class: IP65; UL/CSA Type 12•Red/yellow handle140MP-A-ENY65Popular Accessories for 100-K ContactorsDescriptionCat. No.Front-mounted Auxiliary Contacts •2 N.O.-2 N.C.•4-pole version•Mirror Contact performance per IEC 60947-4-1100-KFC22Front-mounted Auxiliary Contacts •1 N.O.-1 N.C.•2-pole version•Mirror Contact performance per IEC 60947-4-1100-KFC11Power Wiring Kit•For Reversing and Star/Delta combinations. Star-point bridge not included.•Min. interruption time 50 ms 100-KPRDC Diode Suppressor •12…250V DC •Plug-in type•Limits surge voltage on coil drop-off100-KFSD250Mechanical Interlock•For interlocking of two adjacent contactors•No added width to contactor assembly•Front mount plug-in type •Optional auxiliary contactblocks and suppressor modules mount onto the interlock100-KMCHResourceDescriptionIEC Contactor Specifications, publication 100-TD013Provides product selection and specifications for IEC contactors.Motor Protection Circuit Breaker and Motor Circuit Protector Specifications, publication 140-TD005Provides product selection and specifications for Bulletin 140MP/MT motor protection circuit breakers and motor circuit protectors.Bimetallic Overload Relay Specifications,publication 193-TD010Provides product selection and specifications for 193-K and 193-T1 bimetallic overload relays.Product Certifications website, rok.auto/certificationsProvides declarations of conformity,certificates, and other certification details.Publication 140MP-TD002A-EN-P - August 2024Copyright © 2024 Rockwell Automation, Inc. All rights reserved. Printed in the U.S.A.Rockwell Automation SupportUse these resources to access support information.Documentation FeedbackYour comments help us serve your documentation needs better. If you have any suggestions on how to improve our content, complete the form at rok.auto/docfeedback .Technical Support CenterFind help with how-to videos, FAQs, chat, user forums, Knowledgebase, and product notification updates.rok.auto/support Local Technical Support Phone Numbers Locate the telephone number for your country.rok.auto/phonesupport Technical Documentation CenterQuickly access and download technical specifications, installation instructions, and user manuals.rok.auto/techdocs Literature LibraryFind installation instructions, manuals, brochures, and technical data publications.rok.auto/literature Product Compatibility and Download Center (PCDC)Download firmware, associated files (such as AOP, EDS, and DTM), and access product release notes.rok.auto/pcdcRockwell Automation maintains current product environmental compliance information on its website at rok.auto/pec .Allen-Bradley, expanding human possibility, and Rockwell Automation are trademarks of Rockwell Automation, Inc.Trademarks not belonging to Rockwell Automation are property of their respective companies.Rockwell Otomasyon Ticaret A.Ş. 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2005-SCL-L2 anti-windup for linear dead-time systems

Systems&Control Letters54(2005)1205–1217/locate/sysconleL2anti-windup for linear dead-time systemsLuca Zaccarian a,∗,1,Dragan Neši´c b,2,Andrew R.Teel c,3a Dip.di Informatica,Sistemi e Produzione,University of Rome,Tor Vergata,00133Rome,Italyb Department of Electrical and Electronic Engineering,The University of Melbourne,Parkville,3010,Victoria,Australiac Department of Electrical and Computer Engineering,University of California,Santa Barbara,CA93106,United StatesReceived19December2003;received in revised form12October2004;accepted7April2005Available online2June2005AbstractIn this paper,we address and solve the problem of anti-windup augmentation for linear systems with input and output delay.In particular,we give a formal deﬁnition of an optimal L2gain based anti-windup design problem in the global,local, robust and nominal cases.For each of these cases we show that a speciﬁc anti-windup compensation structure(which is a generalization of the approach in the Proceedings of the Fourth ECC,Brussels,Belgium,July1997)is capable of solving the anti-windup problem whenever this solvable.The effectiveness of the proposed scheme is shown on a simple example taken from the literature,in which the plant is a marginally stable linear system.©2005Elsevier B.V.All rights reserved.Keywords:Anti-windup;Input-delay;Input-saturation1.Introduction1.1.Input saturation and anti-windupAs the research activity in automatic control pro-gresses,several mathematical tools and nonlinear∗Corresponding author.Tel.:+390672597429;fax:+390672597427.E-mailaddresses:zack@disp.uniroma2.it(L.Zaccarian),d.nesic@ee.mu.oz.au(D.Neši´c),teel@(A.R.Teel).1Research supported in part by ASI and MIUR through PRIN project MATRICS and FIRB project TIGER.2Research supported by the Australian Research Council underthe large grants scheme.3Research supported in part by AFOSR Grant number F49620-03-1-0203and NSF Grant number ECS-0324679.0167-6911/$-see front matter©2005Elsevier B.V.All rights reserved. doi:10.1016/j.sysconle.2005.04.009control ideas become increasingly applicable to prac-tical control problems.One such area deals with the so-called“anti-windup”strategy,where signiﬁcant progress has been made over the past decade.Anti-windup denotes the design of a compensator which “augments”an existing controller on a plant subject to input saturation.In particular,in the anti-windup problem statement it is assumed that a controller has already been designed disregarding the saturation ef-fect,so that the corresponding closed loop behaves very desirably for small enough signals.The goal of anti-windup is then to recover as much as possible that “unconstrained”performance(and,at the very least, stability)also for large signals,for which the satura-tion nonlinearity operates in its nonlinear region.1206L.Zaccarian et al./Systems&Control Letters54(2005)1205–1217The anti-windup design problem has been qualita-tively stated already from the1950s both in the analog [14]and in the digital control framework[6].How-ever,the arising solutions were at that time mainly application oriented and not applicable to large classes of control systems.It was only in the1980s that some design techniques applicable to large classes of con-trol systems were formalized(see,e.g.,[10,1,20]), although the issue of performance characterization and improvement was still mostly unsolved.Inter-esting surveys of these techniques can be found in [9,11].In the past decade,a great deal of attention has been devoted to the formalization and solution of the anti-windup problem using modern control theory techniques and several recent papers have charac-terized thoroughly the linear anti-windup design technique for linear systems(see[21,7]).Moreover, several nonlinear solutions have been given to the non-linear anti-windup design problem for linear plants (see,e.g.,[29,30,2])and to the nonlinear anti-windup problem for nonlinear plants(see,e.g.,[18,19]).1.2.Anti-windup for dead-time systemsWhile,on one hand,actuator saturation is a ubi-quitous phenomenon which makes anti-windup useful in any control system where a sufﬁciently high accu-racy is needed(this typically happens in aggressive high-performance designs),another phenomenon that is often found in conjunction with saturation is the presence of time delays at the input and at the output of the plant.Similar to the saturation effect,the delay phenomenon becomes crucial when the control task is aggressive enough so that the phase roll-off may destroy the stability(and/or performance)properties of the closed-loop system.For these saturated and re-tarded systems,it is of interest to address the corre-sponding generalization of the anti-windup problem. This can be intuitively seen as follows:assume that a predesigned controller(possibly including internal delays)is available for the delayed plant without in-put saturation;then build an anti-windup compensator that,when interconnected to the existing control sys-tem is capable of1.reproducing the responses induced by that pre-designed controller when signals are small enough not to activate actuator saturation;2.recovering the stability(and,partially,the perfor-mance)that would be otherwise lost due to the non-linear effects of saturation,for all other signals. The solution to this anti-windup problem is appealing because it makes it possible to implement control laws for delayed systems without saturation also on satu-rated and delayed plants.Many such tools are available in the literature.See,e.g.,the many generalizations of the Smith predictor structure,ﬁrst proposed in[25]. Note that the anti-windup problem described above is different from the problem of bounded stabilization of input delayed systems,where signiﬁcant amount of work has been done,especially in recent years. (See,for example the preliminary work in[24]and also recent contributions in[12,13,5,16,27].)Although interesting on their own sake,bounded stabilizers for input delayed systems are not sufﬁcient to solve the anti-windup problem addressed here because they do not necessarily fulﬁll the requirement(at item1above) that the closed-loop system behaves locally as required by the given unconstrained controller,which is part of the problem speciﬁcation,rather than a degree of freedom in the design.When focusing on the anti-windup design problem for dead-time systems,a very natural solution can be obtained by suitably generalizing(in a straightfor-ward way)the classical Internal Model Control(IMC) technique for anti-windup[32],where the stability problem is fully solved for the case where the open-loop plant is characterized by a Hurwitz matrix.How-ever,it is known that IMC-based anti-windup designs may lead to poor performance,which leaves space for signiﬁcant improvement over this straightforward construction.Anti-windup design for linear dead-time control systems was also addressed in[22],where a solution to the problem is given,once again for the case where the open-loop plant is characterized by a Hurwitz matrix and also under some additional tech-nical assumptions.Despite the work of[22]and the IMC extension mentioned above,very little has been done so far on anti-windup design for dead-time linear control systems.Nevertheless,these ideas have been proven to be successful on several applications,in-cluding active queue management in TCP networks [23]and other experiments discussed in[4].It is also noted in the work in[27]that a static anti-windup gain is included within a saturated control design task forL.Zaccarian et al./Systems&Control Letters54(2005)1205–12171207a dead-time plant.In[27],the anti-windup goal is not directly addressed because the controller is not con-sidered as a design constraint but rather as a degree of freedom within the control system design.Never-theless,that underlying technique could be easily gen-eralized for static anti-windup design whenever the unconstrained controller is a linear system without delays.1.3.ContributionIn this paper,we address the anti-windup design problem for dead-time control systems.The proposed solution is applicable to any linear control system,in-cluding the case where the unconstrained controller contains internal time delays(such as in the case where it arises from a Smith predictor design).Moreover,a global solution is given to the problem under the(nec-essary)property that the plant state matrix has eigen-values with nonpositive real part,thus extending pre-vious results to the case of poles on the imaginary axis. As compared to the solution in[22],the approach pro-posed here is stronger because it holds under weaker conditions(these conditions are actually shown to be necessary for the solvability of the problem).More-over,whenever the approach in[22]is applicable,it can be interpreted as a special selection among a fam-ily of solutions parametrized within the framework proposed here.As compared to the potential static anti-windup solution residing in the approach of[27],note that our result provides a general solution to the prob-lem,whereas the results in[27]are only applicable if certain matrix inequalities are satisﬁed.The paper is organized as follows.Weﬁrst formal-ize the anti-windup design goal(which is based on a generalization of the delay-free ideas in[29])intro-ducing the global,local,robust and nominal problem statements in Section2.Then in Section3we prove necessary and sufﬁcient conditions for the solvability of the problem and provide a general framework for the corresponding solution(whenever it exists).In this framework,speciﬁc selections of a stabilizing signal are shown to solve the different instances of the anti-windup problem.In Section4we apply our design to an example where the plant state matrix is non-Hurwitz(so that previous techniques are not applica-ble)and show the desirable performance induced by the proposed anti-windup strategy.1.4.NotationThe following deﬁnitions will be useful to clarify the notation used throughout the paper.•Given a vector w∈R n and a set S⊂R n,the distance of the vector w from the set S is deﬁned asdist(w,S):=infs∈S|w−s|.•Given numbers a a b b and a function w:[a,b]→R n,the L2norm of w(·)restricted to the interval[a,b]is deﬁned asw[a,b] 2:=ba|w( )|2d .If[a,b]=[0,∞),to simplify notation we will often use w 2in place of w[0,∞) 2.We will denote w[0,∞) 2as the L2norm of w(·)and, if w[0,∞) 2<∞,we will say that w(·)∈L2.•Given a constant t d>0and a function s: [−t d,∞)→R n,then for all t 0,the functional s d(·)is deﬁned as s d(t):={s( ), ∈[t−t d,t]}.Moreover,for each t 0,the norm|s d(t)|is deﬁned as|s d(t)|:=max ∈[t−t d,t]|s( )|.•Let K>0and >0be given.A nonlinear func-tional differential equation of the form˙x=f(x d(t),w d(t)),y=g(x d(t),w d(t))isﬁnite gain L2stable from w to y if for all functions w(·)and initial conditions x d(0),the following bound holds for all t 0y[0,t] 2 K|x d(0)|+ w[−td,t]2.2.Problem statementConsider a linear time-invariant plant subject to in-put and output delays:˙x(t)=Ax(t)+B sat(u(t− I))+B d d(t)+ x(t), y(t)=Cx(t− O)+D sat(u(t− I− O))+D d d(t− O)+ y(t),z(t)=C z x(t)+D z sat(u(t− I))+ z(t),(1)1208L.Zaccarian et al./Systems &Control Letters 54(2005)1205–1217Fig.1.The unconstrained closed-loop system.where I >0is a uniform delay at the plant control input u ∈R m , O >0is a uniform delay 4at the plant output measurement y ∈R p ,z represents the performance output (without loss of generality we can assume that this output is not delayed)and d represents a disturbance input.The three extra signals x , y and z can be stacked in a single vector representing the output of the following linear system (represented in the Laplace domain)(s):=x (s)y (s) z (s) := (s) x(s)u(s)d(s) = xx (s) ux (s) dx (s) xy (s) uy (s) dy (s) xz (s) uz (s) dz (s) x(s)u(s)d(s) (2)which may be inﬁnite dimensional (it may have inter-nal delays)and represents unmodeled dynamics and/orparameter uncertainties in model (1).The system cor-responding to the perturbed plant (1),(2)is repre-sented by the dashed box in Fig.1.We will need the following assumption for system (1),(2).Assumption 1.The pair (C z ,A)is detectable .5Sys-tem (2)is ﬁnite-gain input /output L 2stable from (x(·),u(·),d(·))to (·)with L 2gain equalto .Assume that a linear controller (deﬁned,in general,by linear functional differential equations)has been4Note that,by the uniformity property,the two delays at theplant input and output can be lumped in a single time delay,either at the input or at the output of the plant,therefore slightly reducing the notation in this paper.We use,however,this type of notation here to parallel the notation ﬁrst used in [22]and to compare our results to those reported therein.5This assumption is only needed to prove the necessity of the results of Theorem 1.The sufﬁciency statements still hold when (C z ,A)is not detectable.designed for the following linear dead-time system without input saturation˙x(t)=Ax(t)+Bu(t − I )+B d d(t)+ x (t),y(t)=Cx(t − O )+Du(t − I − O )+D d d(t − O )+ y (t),z(t)=C z x(t)+D z u(t − I )+D dz d(t)+ z (t)(3)and that the controller equations can be written as˙x c (t)=f (x c,d (t),u c,d (t),r d (t)),y c (t)=g(x c,d (t),u c,d (t),r d (t)),(4)where f (·,·,·)and g(·,·,·)are linear functionals.6In particular,controller (4)is assumed to enforce a desirable closed-loop behavior on the unconstrained plant (3)when interconnected through the following unconstrained interconnection equations u(t)=y c (t),u c (t)=y(t).(5)The corresponding closed-loop system (3),(4),(5)is represented in Fig.1and will be referred to as the unconstrained closed-loop system henceforth.More-over,its response will be called unconstrained re-sponse .The following assumption will hold for the unconstrained closed-loop.Assumption 2.There exists a small enough gain >0such that the unconstrained closed-loop system (3),(2),(4),(5)is well-posed (namely ,unique solu-tions exist for al linitialstates and for al linputs )and ﬁnite-gain L 2stable from the input =( x , y , z )to the closed-loop state and output ,uniformly over all selections of system (2)satisfying Assumption 1.We will address in this paper the anti-windup prob-lem arising when saturation is present at the plant input,so that the unconstrained performance of the closed-loop (3),(2),(4),(5)is only feasible for small enough signals.For simplicity,we will consider de-centralized saturation functions,although the results can be extended in a straightforward way to the more general class of nonlinearities characterized in6As deﬁned in the notation Section 1.4,the subscripts d denotethe dependence of the functional on the past history of the signal under consideration.L.Zaccarian et al./Systems&Control Letters54(2005)1205–12171209Fig.2.The anti-windup closed-loop system. [29,Assumption2].Similar to the approach in[29],toproperly formalize the anti-windup problem,we needto introduce a subset U of the plant input vector spaceR m,which is a strict subset of the linear region of thesaturation function,namely∃ >0,s.t.u+ v|v|∈{w∈R m:w=sat(w)},∀u∈U,v∈R m.(6) Based on this set U and following the anti-windup approach for undelayed linear plants,the main anti-windup goal will address the design of the anti-windup compensator AW of Fig.2with the goal of recovering as much as possible the“response without saturation”(herein called unconstrained response) on the saturated(and compensated)closed-loop of Fig.2(this will be called anti-windup closed-loop system henceforth).In the following,for any selec-tion of the external signals r(·),d(·),given initial conditions for plant(3)and for controller(4),we will denote the unconstrained closed-loop response using overlines.Moreover,given the same initial conditions for the saturated plant(1)and controller(4),we will denote the corresponding anti-windup closed-loop response without overlines.Deﬁnition1.Given a plant(1)and a controller(4) satisfying Assumption2,and a set U∈R m satisfy-ing(6),an anti-windup compensator AW solves the corresponding•robust global anti-windup problem if there existsa continuous positive nondecreasing function :R 0→R 0and a(sufﬁciently small)L2gainfor the unmodeled dynamics(2)such that forall initial conditions and all external inputs,7z−z 2 ( sat(u)−u 2);(7)•nominalgl obalanti-windup probl em if thebound(7)holds with ≡0(namely,in theabsence of unmodeled dynamics);•robust local anti-windup problem if the bound(7)holds for small enough values of the initialconditions of the anti-windupﬁlter AW and ofsat(u)−u 2.Remark1.Note that(7)enforces a bound on the out-put mismatch(z−z)(·)based on the energy spent by the(ideal)unconstrained input response outside the saturation limits.This characterization is reason-able because that input energy cannot be instantly re-covered on the saturated control system,regardless of what the anti-windup compensation is.Therefore,(7) successfully captures the intuitive performance recov-ery goals of the anti-windup design.Note also that (7)implicitly enforces the property that all the uncon-strained trajectories that never exceed the saturation limits(so that sat(u)−u 2=0),will be exactly re-produced by the anti-windup closed-loop system.In-deed,in that case,(7)implies that z−z 2=0,namely z(·)≡z(·).3.Main resultIn this section,we will address the anti-windup problem of Deﬁnition1and give necessary and suf-ﬁcient conditions for its solvability,together with a7For simplicity of notation,in Eq.(7)and throughout the proof of the paper,the L2bounds are all given omitting the initial conditions.1210L.Zaccarian et al./Systems &Control Letters 54(2005)1205–1217Fig.3.The proposed anti-windup scheme.constructive solution whenever the problem is solv-able.For the solution of this problem,we will select the ﬁlter AW as the following dynamical system:˙x aw (t)=Ax aw (t)+B(sat (u(t))−y c (t)),v 1(t)=f aw (x aw (t),sat (u(t))−y c (t)),v 2(t)=Cx aw (t − I − O )+D(sat (u(t − I − O ))−y c (t − I − O )),(8)where the selection of the function f aw (·,·)will be speciﬁed later.This ﬁlter will modify the intercon-nection between the plant (1)and the controller (4)through the following equations u(t)=y c (t)+v 1(t),u c (t)=y(t)−v 2(t).(9)The corresponding closed-loop system is represented in Fig.3.The effectiveness of structure (8),(9)of the anti-windup compensator in solving the anti-windup prob-lem of Deﬁnition 1is based on the fact that (at least in the case where ≡0)the arising closed-loop sys-tem can be transformed into the cascade interconnec-tion between the functional differential equation cor-responding to the unconstrained closed-loop (3),(4),(5)and an extra subsystem consisting of the ﬁlter (8)which needs to be stabilized by suitably designing the compensation signal v 1in (9).This scheme arises from a generalization of the scheme adopted in [29]for anti-windup design for linear undelayed systems.Indeed,the same tools introduced in [29]for the design of the signal v 1can be also used in the framework (8),(9).To this aim,we report in the following the result in [29,Lemma 1],which will be useful next.As reported in [29],this lemma can be proven by combining the results in [17]and [28].Lemma 1.For the controlsystem ˙x aw =Ax aw +B(sat (v + (t))− (t)),where (A,B)is stabilizable ,and U satisﬁes (6),1.there always exists a globally Lipschitz feedback v =k(x aw )such that if dist ( ,U ) 2and |x aw (0)|are sufﬁciently small ,then x aw (·)∈L 2and the L 2gain from dist ( (·),U )to x aw (·)is ﬁnite ;2.if all the eigenvalues of A have nonpositive real part ,then there exists a globally Lipschitz feedback v =k(x aw )such that if dist ( (·),U )∈L 2,then x aw (·)∈L 2;moreover ,if A is critically stable ,i.e.,if there exists P =P T >0such that A T P +P A 0,then the function k(·)can be taken to be the lin-ear function x aw →k(x aw ):=−B T P x aw .Finally ,when A is Hurwitz ,the L 2gain from dist ( (·),U )to x aw (·)is ﬁnite .We are now ready to state our main result.Theorem 1.Suppose Assumptions 1and 2hold for the plant (1),(2)and for the controller (4).Then ,according to Deﬁnition 1,the following holds :1.the local robust anti-windup problem is always solvable ;2.the global nominal anti-windup problem is solvable if and only if A has poles in the closed left half plane ;3.the global robust anti-windup problem is solvable if and only if A is Hurwitz ;4.whenever any of the anti-windup problems is solvable ,the anti-windup ﬁlter (8)with the inter-connection equations (9)and with the selection f aw (x aw ,sat (u)−y c )=k(x aw )according to theL.Zaccarian et al./Systems&Control Letters54(2005)1205–12171211constructive result of Lemma1,is well-posed and is a solution to the problem.Proof.Necessity:The necessity in item2can be proved by contraposition.Indeed,if A has poles in the open right-hand plane,the open-loop system is exponentially unstable.Well-known results(see,e.g., [26])state that saturated exponentially unstable plants are not globally null controllable,hence there exist large enough initial conditions for the plant such that the response with saturation will diverge regardless of the anti-windup action.Consequently,since by As-sumption2the unconstrained response will always be bounded,by the detectability property of Assumption 1,bound(7)will not hold.The necessity in item3follows by selecting xx(s)= I and all the other entries of the matrix transfer function in(2)equal to zero,where >0 is arbitrarily small.Then,the state matrix of the per-turbed system will be A+ I,with >0.There-fore,if A is not Hurwitz,this new state matrix will have poles in the open right-hand plane(regardless of how small the gain is).Finally,the proof of the necessity can be completed similar to the case at item 2proven above.Sufﬁciency:The proof of the sufﬁciency is construc-tive and is based on the structure(8),(9)with f aw(·,·) selected as f aw(x aw,sat(u)−y c)=k(x aw)according to Lemma1.Due to space constraints,we will only address here the case where the unmodeled dynamics (2)are absent(namely, ≡0).The proof extends to the robust case by small gain arguments similar to those carried out in[29].Consider the anti-windup closed-loop(1),(4), (8),(9),write the closed-loop dynamics in the co-ordinates(e(t),x c(t),x aw(t))=(x(t)−x aw(t− I),x c(t),x aw(t))as follows(here,y e(t)=y(t)−v2(t); moreover,z e and z aw are new outputs of the closed-loop system):˙e(t)=Ae(t)+By c(t− I)+B d d(t),y e(t)=Ce(t− O)+Dy c(t− I− O)+D d d(t− O),z e(t)=C z e(t)+D z y c(t− I)+D dz d(t),˙x c(t)=f(x c,d(t),y e,d(t),r d(t)),y c(t)=g(x c,d(t),y e,d(t),r d(t)),(10a)˙x aw(t)=Ax aw(t)+B(sat(u(t))−y c(t)),v1(t)=K(x aw),z aw(t)=C z x aw(t)+D z(sat(u(t))−y c(t))u(t)=y c(t)+v1(t).(10b) It is evident that the closed-loop(10)is a cascade interconnection of two subsystems,where(10a)coin-cides exactly with the unconstrained closed-loop sys-tem(3),(4),(5).Therefore,if the initial condition of (8)is x aw,d(0)=0,then8y c(t)=u(t),∀t 0.(11) Moreover,the additional output z e of(10a)satisﬁes z e(t)=z(t)for all times.Consider now the additionaloutput z aw of the second subsystem(10b)and notice that,since by deﬁnition e(t)=x(t)−x aw(t− I),then z e(t)=z(t)−z aw(t− I)for all times.Therefore, z(t)−z(t)=z aw(t− I),∀t I,(12) and consequently,9(z−z) 2= z aw 2.(13) Since u(t)=y c(t)+k(x aw(t)),by the global Lips-chitz property of the saturation function,we have for all t 0,|sat(u(t))−y c(t)| |k(x aw(t))|+|sat(y c(t))−y c(t)|. Therefore,since by Lemma1k(·)is globally Lips-chitz,substituting the previous bound in the third equa-tion of(10b),it follows that there exists >0such that for all t 0|sat(u(t))−y c(t)|(|x aw(t)|+|sat(y c(t))−y c(t)|).(14) Finally,the proof of the theorem is completed by applying Lemma1with (·)≡y c(·)and8In the case when xaw,d(0)=0there will be an additional term depending on the initial condition in the L2bound(7).To keep the discussion simple,we are omitting the initial conditions in the L2bounds of this paper(the corresponding relations are a straightforward generalization of the initial condition-free ones).9Note that due to the presence of the input delay,since the plant initial conditions are assumed to be the same in the unconstrained and in the anti-windup case,then z(t)−z(t)=0 for all t∈[0, I).1212L.Zaccarian et al./Systems&Control Letters54(2005)1205–1217combining the resulting L2bound with Eqs.(11), (13)and(14).Remark2.The selection for v1proposed in Lemma 1is sufﬁcient to solve the anti-windup problems of Deﬁnition1.However,from a performance perspec-tive,alternative selections may be more desirable because they improve the unconstrained response recovery transient.To this aim,a useful property arising from structure(8),(9)is that as shown in the proof of Theorem1(see Eq.(12)),regardless of the selection of v1,the mismatch between the uncon-strained and the actual performance response is given by the extra output z aw in(10b).Therefore,v1can be selected by only focusing on the stabilization of the (undelayed!)subsystem(10b)and on the performance seen at this particular output z aw.In the past years,several techniques have been pro-posed in the context of the undelayed anti-windup problem to improve the corresponding transient re-sponses.Most of these results correspond to linear matrix inequality(LMI)formulations of convex opti-mization problems.Fortunately,the same approaches can be applied also to the time-delayed problem ad-dressed here because of the cascade structure(10)in-duced by theﬁlter(8).Among these techniques,non-linear scheduled techniques were proposed in[30]and sampled-data techniques were proposed in[2].More-over,in[31]the selection of the function f aw(·,·)is optimized among the family of linear functions:f aw(x aw,sat(u)−y c)=Kx aw+L(sat(u)−y c),(15) where the gains K and L arise from suitable LMIs easily solvable by convex optimization.The difference between(15)and the selection proposed in Lemma1 (at least for the Hurwitz case)is in the presence of the feedthrough term L,which evidently enforces an algebraic loop around the saturation.It is commonly acknowledged(see,e.g.,[21])that this algebraic loop may signiﬁcantly improve the transient performance of the control system,especially in the MIMO case. Although the LMI-based selection of K and L proposed in[31]guarantees that the interconnection is well-posed,the corresponding optimal solution might often lead to values of L that are very close to a nonwell-posed interconnection.In those cases,it is useful to augment the LMIs of[31]with an extra matrix in-equality of the form2( −1)W− X2− X T2 X T2X2−2W>0,(16)where ∈(0,1)and > .Based on the results of [8],this bound will ensure that the explicit solution to the implicit equation imposed by the algebraic loop in (8)is Lipschitz of levelM(W)m(W)(where M(·), m(·)denote the maximum and mini-mum singular value of the matrix at argument,respec-tively),thereby not allowing the arising anti-windup solution to be ill-posed.Remark3.The approach given here can be easily seen as a generalization of the construction in[22]. This generalization allows to remove the technical As-sumption(A3)in[22](thus solving the anti-windup problem also when Assumption(A3)does not hold), it allows to establish stability of the arising closed-loop whenever the plant is Hurwitz and it allows,in general,to guarantee improved performance by way of the degrees of freedom in the selection of v1. Indeed,by suitable loop transformations and some tedious calculations,it can be shown that the anti-windup solution proposed in[22]for dead-time plants is equivalent to usingﬁlter(8)with the selectionv1(s)=−D c(s)v2(s),(17) where the matrix D c(s)corresponds to the input–output link of the unconstrained controller.In particu-lar,in[22,Section3],the unconstrained con-troller is a delay-free LTI system and D c(s)=L is its(constant)input–output matrix;in[22,Sec-tion4],the unconstrained controller has a spe-ciﬁc structure with an internal time delay 3and D c(s)=L3L1(I−e−s 3L2L1)−1is the correspond-ing term10related to the generalized input–output link(see[22]for details).10Actually,in[22,Section4],D c(s)is deﬁned as L u:= L3[I+e−s 3L1(I−e−s 3L2L1)−1L2]L1.However,it can be shown that this last expression is equivalent to the more intuitive one reported above.。

小学上册第十三次英语第3单元期末试卷

小学上册英语第3单元期末试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.What is the primary color of the sun?A. BlueB. YellowC. WhiteD. RedB2.My friend is a ______. She loves to do puzzles.3.My dog loves to dig ______ (洞) in the sand.4.What is the name of the famous mountain in the United States?A. Mount EverestB. Mount RushmoreC. Mount KilimanjaroD. Mount Fuji5.What do we call the study of numbers?A. MathematicsB. GeometryC. AlgebraD. Statistics6.What is the name of the famous explorer who sailed around the world?A. Ferdinand MagellanB. Christopher ColumbusC. Vasco da GamaD. Captain CookA7.My dog loves to play fetch in the ______ (公园).8.What is the term for the distance around a circle?A. AreaB. DiameterC. CircumferenceD. RadiusC9.I want to be a _______ (职业) when I grow up. It’s my dream job.10.The chemical symbol for thulium is ____.11.I like to make homemade ________ (果汁) during the summer to stay cool.12.What is the capital of Colombia?A. MedellínB. BogotáC. CaliD. CartagenaB13.The ancient Romans celebrated games in honor of the god ______ (朱庇特).14.arctic) is known for its cold climate. The ____15.What do you call the place where you can buy groceries?A. StoreB. MallC. SupermarketD. MarketC16. A ladybug has ______ spots.17.The ancient Romans had a complex system of _____.18.The __________ (历史的责任) shapes our choices.19.The sun is ______ (shining) brightly today.20.My favorite drink is _______ (牛奶).21. A __________ is a type of reaction that releases energy.22.What is the main source of energy for the Earth?A. WindB. SunC. WaterD. CoalB23.The manatee is often found in warm ______ (水域).24.Chemical reactions can be affected by _____, concentration, and surface area.25.We have a pet ___. (hamster)26.What is the capital of Jamaica?A. KingstonB. Montego BayC. Ocho RiosD. Negril27.I like to watch the ______ (云彩) change shapes.28.Which instrument is used to measure the speed of the wind?A. AnemometerB. BarometerC. ThermometerD. HygrometerA29.Elements are found on the ______ table.30.The _____ (大象) is a gentle giant.31.I can ______ (进行) research effectively.32.What do we call the main ingredient in a salad?A. DressingB. LettuceC. CroutonsD. CheeseB33.The _______ (The Gold Rush) brought many settlers to California in the 1840s.34.I enjoy ___ (drawing) with chalk.35.I love to _______ (了解)新事物。

IB A-LEVEL经济学词汇中英文对照

经济学词汇--中英文对照A--------------------------------------------------------------------------------accounting:会计accounting cost:会计成本accounting profit:会计利润adverse selection:逆向选择allocation配置allocation of resources:资源配置allocative efficiency:配置效率antitrust legislation:反托拉斯法arc elasticity:弧弹性Arrow's impossibility theorem:阿罗不可能定理Assumption:假设asymetric information:非对称性信息average:平均average cost:平均成本average cost pricing:平均成本定价法average fixed cost:平均固定成本average product of capital:资本平均产量average product of labour:劳动平均产量average revenue:平均收益average total cost:平均总成本average variable cost:平均可变成本B--------------------------------------------------------------------------------barriers to entry:进入壁垒base year:基年bilateral monopoly:双边垄断benefit:收益black market:黑市bliss point:极乐点boundary point:边界点break even point:收支相抵点budget:预算budget constraint:预算约束budget line:预算线budget set预算集C--------------------------------------------------------------------------------capital:资本capital stock:资本存量capital output ratio:资本产出比率capitalism:资本主义cardinal utility theory:基数效用论cartel:卡特尔ceteris puribus assumption:“其他条件不变”的假设ceteris puribus demand curve:其他因素不变的需求曲线Chamberlin model:张伯伦模型change in demand:需求变化change in quantity demanded:需求量变化change in quantity supplied:供给量变化change in supply:供给变化choice:选择closed set:闭集Coase theorem:科斯定理Cobb—Douglas production function:柯布--道格拉斯生产函数cobweb model:蛛网模型collective bargaining:集体协议工资collusion:合谋command economy:指令经济commodity:商品commodity combination:商品组合commodity market:商品市场commodity space:商品空间common property:公用财产comparative static analysis:比较静态分析compensated budget line:补偿预算线compensated demand function:补偿需求函数compensation principles:补偿原则compensating variation in income:收入补偿变量competition:竞争competitive market:竞争性市场complement goods:互补品complete information:完全信息completeness:完备性condition for efficiency in exchange:交换的最优条件condition for efficiency in production:生产的最优条件concave:凹concave function:凹函数concave preference:凹偏好consistence:一致性constant cost industry:成本不变产业constant returns to scale:规模报酬不变constraints:约束consumer:消费者consumer behavior:消费者行为consumer choice:消费者选择consumer equilibrium:消费者均衡consumer optimization:消费者优化consumer preference:消费者偏好consumer surplus:消费者剩余consumer theory:消费者理论consumption:消费consumption bundle:消费束consumption combination:消费组合consumption possibility curve:消费可能曲线consumption possibility frontier:消费可能性前沿consumption set:消费集consumption space:消费空间continuity:连续性continuous function:连续函数contract curve:契约曲线convex:凸convex function:凸函数convex preference:凸偏好convex set:凸集corporatlon:公司cost:成本cost benefit analysis:成本收益分cost function:成本函数cost minimization:成本极小化Cournot equilihrium:古诺均衡Cournot model:古诺模型Cross—price elasticity:交叉价格弹性D--------------------------------------------------------------------------------dead—weights loss:重负损失decreasing cost industry:成本递减产业decreasing returns to scale:规模报酬递减deduction:演绎法demand:需求demand curve:需求曲线demand elasticity:需求弹性demand function:需求函数demand price:需求价格demand schedule:需求表depreciation:折旧derivative:导数derive demand:派生需求difference equation:差分方程differential equation:微分方程differentiated good:差异商品differentiated oligoply:差异寡头diminishing marginal substitution:边际替代率递减diminishing marginal return:收益递减diminishing marginal utility:边际效用递减direct approach:直接法direct taxes:直接税discounting:贴税、折扣diseconomies of scale:规模不经济disequilibrium:非均衡distribution:分配division of labour:劳动分工distribution theory of marginal productivity:边际生产率分配论duoupoly:双头垄断、双寡duality:对偶durable goods:耐用品dynamic analysis:动态分析dynamic models:动态模型E--------------------------------------------------------------------------------Economic agents:经济行为者economic cost:经济成本economic efficiency:经济效率economic goods:经济物品economic man:经济人economic mode:经济模型economic profit:经济利润economic region of production:生产的经济区域economic regulation:经济调节economic rent:经济租金exchange:交换economics:经济学exchange efficiency:交换效率economy:经济exchange contract curve:交换契约曲线economy of scale:规模经济Edgeworth box diagram:埃奇沃思图exclusion:排斥性、排他性Edgeworth contract curve:埃奇沃思契约线Edgeworth model:埃奇沃思模型efficiency:效率，效益efficiency parameter:效率参数elasticity:弹性elasticity of substitution:替代弹性endogenous variable:内生变量endowment:禀赋endowment of resources:资源禀赋Engel curve:恩格尔曲线entrepreneur:企业家entrepreneurship:企业家才能entry barriers:进入壁垒entry/exit decision:进出决策envolope curve:包络线equilibrium:均衡equilibrium condition:均衡条件equilibrium price:均衡价格equilibrium quantity:均衡产量eqity:公平equivalent variation in income:收入等价变量excess—capacity theorem:过度生产能力定理excess supply:过度供给exchange:交换exchange contract curve:交换契约曲线exclusion:排斥性、排他性exclusion principle:排他性原则existence:存在性existence of general equilibrium:总体均衡的存在性exogenous variables:外生变量expansion paths:扩展径expectation:期望expected utility:期望效用expected value:期望值expenditure:支出explicit cost:显性成本external benefit:外部收益external cost:外部成本external economy:外部经济external diseconomy:外部不经济externalities:外部性F--------------------------------------------------------------------------------Factor:要素factor demand:要素需求factor market:要素市场factors of production:生产要素factor substitution:要素替代factor supply:要素供给fallacy of composition:合成谬误final goods:最终产品firm:企业firms’demand curve for labor:企业劳动需求曲线firm supply curve:企业供给曲线first-degree price discrimination:第一级价格歧视first—order condition:一阶条件fixed costs:固定成本fixed input:固定投入fixed proportions production function:固定比例的生产函数flow:流量fluctuation:波动for whom to produce:为谁生产free entry:自由进入free goods:自由品，免费品free mobility of resources:资源自由流动free rider:搭便车，免费搭车function:函数future value:未来值G--------------------------------------------------------------------------------game theory:对策论、博弈论general equilibrium:总体均衡general goods:一般商品Giffen goods:吉芬晶收入补偿需求曲线Giffen's Paradox:吉芬之谜Gini coefficient:吉尼系数goldenrule:黄金规则goods:货物government failure:政府失败government regulation:政府调控grand utility possibility curve:总效用可能曲线grand utility possibility frontier:总效用可能前沿H--------------------------------------------------------------------------------heterogeneous product:异质产品Hicks—kaldor welfare criterion:希克斯一卡尔多福利标准homogeneity:齐次性homogeneous demand function:齐次需求函数homogeneous product:同质产品homogeneous production function:齐次生产函数horizontal summation:水平和household:家庭how to produce:如何生产human capital:人力资本hypothesis:假说I--------------------------------------------------------------------------------identity:恒等式imperfect competion:不完全竞争implicitcost:隐性成本income:收入income compensated demand curve:收入补偿需求曲线income constraint:收入约束income consumption curve:收入消费曲线income distribution:收入分配income effect:收入效应income elasticity of demand:需求收入弹性increasing cost industry:成本递增产业increasing returns to scale:规模报酬递增inefficiency:缺乏效率index number:指数indifference:无差异indifference curve:无差异曲线indifference map:无差异族indifference relation:无差异关系indifference set:无差异集indirect approach:间接法individual analysis:个量分析individual demand curve:个人需求曲线individual demand function:个人需求函数induced variable:引致变量induction:归纳法industry:产业industry equilibrium:产业均衡industry supply curve:产业供给曲线inelastic:缺乏弹性的inferior goods:劣品inflection point:拐点information:信息information cost:信息成本initial condition:初始条件initial endowment:初始禀赋innovation:创新input:投入input—output:投入—产出institution:制度institutional economics:制度经济学insurance:保险intercept:截距interest:利息interest rate:利息率intermediate goods:中间产品internatization of externalities:外部性内部化invention:发明inverse demand function:逆需求函数investment:投资invisible hand:看不见的手isocost line:等成本线，isoprofit curve:等利润曲线isoquant curve:等产量曲线isoquant map:等产量族K--------------------------------------------------------------------------------kinded—demand curve:弯折的需求曲线L--------------------------------------------------------------------------------labour:劳动labour demand:劳动需求labour supply:劳动供给labour theory of value:劳动价值论labour unions:工会laissez faire:自由放任Lagrangian function:拉格朗日函数Lagrangian multiplier:拉格朗乘数，land:土地law:法则law of demand and supply:供需法law of diminishing marginal utility:边际效用递减法则law of diminishing marginal rate of substitution:边际替代率递减法则law of diminishing marginal rate of technicalsubstitution:边际技术替代率law of increasing cost:成本递增法则law of one price:单一价格法则leader—follower model:领导者--跟随者模型least—cost combination of inputs:最低成本的投入组合leisure:闲暇Leontief production function:列昂节夫生产函数licenses:许可证linear demand function:线性需求函数linear homogeneity:线性齐次性linear homogeneous production function:线性齐次生产函数long run:长期long run average cost:长期平均成本long run equilibrium:长期均衡long run industry supply curve:长期产业供给曲线long run marginal cost:长期边际成本long run total cost:长期总成本Lorenz curve:洛伦兹曲线loss minimization:损失极小化1ump sum tax:一次性征税luxury:奢侈品M--------------------------------------------------------------------------------macroeconomics:宏观经济学marginal:边际的marginal benefit:边际收益marginal cost:边际成本marginal cost pricing:边际成本定价marginal cost of factor:边际要素成本marginal physical productivity:实际实物生产率marginal product:边际产量marginal product of capital:资本的边际产量marginal product of1abour:劳动的边际产量marginal productivity:边际生产率marginal rate of substitution:边替代率marginal rate of transformation边际转换率marginal returns:边际回报marginal revenue:边际收益marginal revenue product:边际收益产品marginal revolution:边际革命marginal social benefit:社会边际收益marginal social cost:社会边际成本marginal utility:边际效用marginal value products:边际价值产品market:市场market clearance:市场结清，市场洗清market demand:市场需求market economy:市场经济market equilibrium:市场均衡market failure:市场失败market mechanism:市场机制market structure:市场结构market separation:市场分割market regulation:市场调节market share:市场份额markup pricing:加减定价法Marshallian demand function:马歇尔需求函数maximization:极大化microeconomics:微观经济学minimum wage:最低工资misallocation of resources:资源误置mixed economy:混合经济model:模型money:货币monopolistic competition:垄断竞争monopolistic exploitation:垄断剥削monopoly:垄断，卖方垄断monopoly equilibrium:垄断均衡monopoly pricing:垄断定价monopoly regulation:垄断调控monopoly rents:垄断租金monopsony:买方垄断N--------------------------------------------------------------------------------Nash equilibrium:纳什均衡Natural monopoly:自然垄断Natural resources:自然资源Necessary condition:必要条件necessities:必需品net demand:净需求nonconvex preference:非凸性偏好nonconvexity:非凸性nonexclusion:非排斥性nonlinear pricing:非线性定价nonrivalry:非对抗性nonprice competition:非价格竞争nonsatiation:非饱和性non--zero—sum game:非零和对策normal goods:正常品normal profit:正常利润normative economics:规范经济学O--------------------------------------------------------------------------------objective function:目标函数oligopoly:寡头垄断oligopoly market:寡头市场oligopoly model:寡头模型opportunity cost:机会成本optimal choice:最佳选择optimal consumption bundle:消费束perfect elasticity:完全有弹性optimal resource allocation:最佳资源配置optimal scale:最佳规模optimal solution:最优解optimization:优化ordering of optimization(social)preference:(社会)偏好排序ordinal utility:序数效用ordinary goods:一般品output:产量、产出output elasticity:产出弹性output maximization产出极大化P--------------------------------------------------------------------------------parameter:参数Pareto criterion:帕累托标准Pareto efficiency:帕累托效率Pareto improvement:帕累托改进Pareto optimality:帕累托优化Pareto set:帕累托集partial derivative:偏导数partial equilibrium:局部均衡patent:专利pay off matrix:收益矩阵、支付矩阵perceived demand curve:感觉到的需求曲线perfect competition:完全竞争perfect complement:完全互补品perfect monopoly:完全垄断perfect price discrimination:完全价格歧视perfect substitution:完全替代品perfect inelasticity:完全无弹性perfectly elastic:完全有弹性perfectly inelastic:完全无弹性plant size:工厂规模point elasticity:点弹性post Hoc Fallacy:后此谬误prediction:预测preference:偏好preference relation:偏好关系present value:现值price:价格price adjustment model:价格调整模型price ceiling:最高限价price consumption curve:价格费曲线price control:价格管制price difference:价格差别price discrimination:价格歧视price elasticity of demand:需求价格弹性price elasticity of supply:供给价格弹性price floor:最低限价price maker:价格制定者price rigidity:价格刚性price seeker:价格搜求者price taker:价格接受者price tax:从价税private benefit:私人收益principal—agent issues:委托--代理问题private cost:私人成本private goods:私人用品private property:私人财产producer equilibrium:生产者均衡producer theory:生产者理论product:产品product transformation curve:产品转换曲线product differentiation:产品差异product group:产品集团production:生产production contract curve:生产契约曲线production efficiency:生产效率production function:生产函数production possibility curve:生产可能性曲线productivity:生产率productivity of capital:资本生产率productivity of labor:劳动生产率profit:利润profit function:利润函数profit maximization:利润极大化property rights:产权property rights economics:产权经济学proposition:定理proportional demand curve:成比例的需求曲线public benefits:公共收益public choice:公共选择public goods:公共商品pure competition:纯粹竞争rivalry:对抗性、竞争pure exchange:纯交换pure monopoly:纯粹垄断Q--------------------------------------------------------------------------------quantity—adjustment model:数量调整模型quantity tax:从量税quasi—rent:准租金R--------------------------------------------------------------------------------rate of product transformation:产品转换率rationality:理性reaction function:反应函数regulation:调节，调控relative price相对价格rent:租金rent control:规模报酬rent seeking:寻租rent seeking economics:寻租经济学resource:资源resource allocation:资源配置returns:报酬、回报returns to scale:规模报酬revealed preference:显示性偏好revenue:收益revenue curve:收益曲线revenue function:收益函数revenue maximization:收益极大化ridge line:脊线risk:风险S--------------------------------------------------------------------------------satiation:饱和，满足saving:储蓄scarcity:稀缺性law of scarcity:稀缺法则second—degree price discrimination:二级价格歧视second derivative:--阶导数second—order condition:二阶条件service:劳务set:集shadow prices:影子价格short—run:短期short—run cost curve:短期成本曲线short—run equilibrium:短期均衡short—run supply curve:短期供给曲线shut down decision:关闭决策shortage短缺shut down point:关闭点single price monopoly:单一定价垄断slope:斜率social benefit:社会收益social cost:社会成本social indifference curve:社会无差异曲线social preference:社会偏好social security:社会保障social welfare function:社会福利函数socialism:社会主义solution:解space:空间stability:稳定性stable equilibrium:稳定的均衡Stackelberg model:斯塔克尔贝格模型static analysis:静态分析stock:存量stock market:股票市场strategy:策略subsidy:津贴substitutes:替代品substitution effect:替代效应substitution parameter:替代参数sufficient condition:充分条件supply:供给supply curve:供给曲线supply function:供给函数supply schedule:供给表Sweezy model:斯威齐模型symmetry:对称性symmetry of information:信息对称T--------------------------------------------------------------------------------tangency:相切taste:兴致technical efficiency:技术效率technological constraints；技术约束technological progress:技术进步technology:技术third—degree price discrimination:第**价格歧视total cost:总成本total effect:总效应total expenditure:总支出total fixed cost:总固定成本total product:总产量total revenue:总收益total utility:总效用total variable cost:总可变成本traditional economy:传统经济transitivity:传递性transaction cost:交易费用U--------------------------------------------------------------------------------uncertainty:不确定性uniqueness:唯一性unit elasticity:单位弹性unstable equilibrium:不稳定均衡utility:效用utility function:效用函数utility index:效用指数utility maximization:效用极大化utility possibility curve:效用可能性曲线utility possibility frontier:效用可能性前沿V--------------------------------------------------------------------------------value:价值value judge:价值判断value of marginal product:边际产量价值variable cost:可变成本variable input:可变投入variables:变量vector:向量visible hand:看得见的手vulgur economics:庸俗经济学W--------------------------------------------------------------------------------wage:工资wage rate:工资率Walras general equilibrium:瓦尔拉斯总体均衡Walras's law:瓦尔拉斯法则Wants:需要Welfare criterion:福利标准Welfare economics:福利经学Welfare loss triangle:福利损失三角形welfare maximization:福利极大化Z--------------------------------------------------------------------------------zero cost:零成本zero elasticity:零弹性zero homogeneity:零阶齐次性zero economic profit:零利润。

BT学院 2017年12月CFA一级模拟考试试卷(AM)

【答案】A 【解析】准则 III(B)公平，指的是公平对待每一位客户，对于 discretionary accounts （基金经理可支配的账户）在交易分配时要公平对待，要提前披露分配政策。题干中按照开户时间，不足一年的客户被 disadvantage，没有公平对待，注意陷阱在于提前披露了这一位客户。【考点】 Guidance for Standards I-VII 6. Nicholas Bennett, CFA, is a trader at a stock exchange. Another trader approached Bennett on the floor of the exchange and verbally harassed him about a poorly executed trade. In response, Bennett pushed the trader and knocked him to the ground. After investigating the incident, the exchange cleared Bennett from any wrongdoing. Which of the following best describes Bennett's conduct in relation to the CFA Institute Code of Ethics or Standards of Professional Conduct? Bennett: A. B. C. violated both the standard relating to professionalism and integrity of capital markets. did not violate any of the Code of Ethics or Standards of Professional Conduct. violated the standard relating to professionalism.

Lifting schemes for biorthogonal modulated filter banks

LIFTING SCHEMES FOR BIORTHOGONAL MODULATED FILTER BANKSTanja KarpUniversity of MannheimB6/26D-68131Mannheim,Germany karp@rumms.uni-mannheim.deAlfred Mertins University of Kiel Kaiserstr.2D-24143Kiel,Germany am@techfak.uni-kiel.deABSTRACTIn this paper we connect the design of biorthogonal mod-ulated ﬁlter banks with the idea of lifting schemes,which were proposed for the construction of biorthogonal wa-velets.Based on this formulation,we derive a lattice-like structure for the polyphase components.As the rotation-based structures for the design and implementation of pa-raunitary modulated ﬁlter banks,our structure automati-cally guarantees the PR property of the ﬁlter bank.The coefﬁcients can be freely chosen and used for ﬁlter opti-mization.1.INTRODUCTIONModulated ﬁlter banks are very popular since they pro-vide a very efﬁcient realization.They consist of two mainstages:the polyphase ﬁlters of the prototype and a dis-crete cosine or Fourier transform.Figure 1shows theanalysis part of an-channel cosine modulated ﬁlter bank.C O S I N E M OD U L A T I O N1Figure 1:Cosine-modulated-channel analysis bankBiorthogonal modulated ﬁlter banks (when compared toparaunitary ones)provide the advantage that the overall system delay can be chosen independently of the ﬁlter length,thus resulting in low-delay ﬁlter banks.They have recently been studied in literature by several authors [1,2,3,4,5].While Schuller and Smith describe the ﬁlter bank by a cascade of selﬁnverse sparse matrices and a modulation matrix,the approach derived by Nguyen et al.is based on constraints on the polyphase ﬁlters of a common pro-totype ﬁlter for analysis and synthesis.Based on this formulation for the PR constraints,we here derive a construction scheme for the polyphase ﬁlters thatresults in a lattice-like structure for the polyphase com-ponents.Like the rotations proposed in [6]for the case of paraunitary modulated ﬁlter banks,our structure auto-matically guarantees the PR property of the ﬁlter bank.The obtained coefﬁcients can be used for ﬁlter optimiza-tion,i.e.reduction of the stopband energy of the fre-quency response,or in order to design ﬁlters with integer-valued coefﬁcients.As shown in [5]the analysis and synthesis ﬁlters,and ,of an -channel cosine-modulated ﬁlter bank can be derived from a prototype according to(2)The ﬁlter length,,and the overall delay,(where and ),can be chosen arbitrarily.The ﬁlter bank is PR if the type-1polyphase ﬁlters ,,ofthe lowpass prototypesatisfy the constraints given in (3)-(6),see [5]for a proof.Each PR constraint depends on maximally four type-1polyphase components.The overall system delay can be chosen independently of the ﬁlter length.In the follow-ing,we restrict ourselves to the caseand such that the PR constraints reduce to (5)and all polyphase ﬁlters are of the same length .2.THE LIFTING SCHEMEThe lifting scheme is a systematic way for the construc-tion of biorthogonal wavelets [7,8].One starts with short ﬁlters,or simply with the polyphase transform,and suc-cessively increases the ﬁlter length.A single lifting step consists of increasing the length of one ﬁlter from a PR ﬁlter pair while keeping the PR property.Such a step is typically followed by a dual lifting step where the length of the second ﬁlter is increased.Overall,one alternates lifting and dual lifting to construct long biorthogonal wa-velets from short ones.We here apply the lifting scheme to the polyphase ﬁltersof the prototype ﬁlter.Thus the ﬁlter length can be increased while keeping the ﬁlter bank PR.for(3)for(5)2.1.Increasing the Filter LengthLet us start with a given set of four polyphaseﬁlters thatsatisfy the PR constraint according to(5).Using the lift-ing scheme described in[7,8]for the construction ofbiorthogonal wavelets,we can construct longer polyphaseﬁlters and therefore longer prototypeﬁlters(with–hope-fully–better frequency responses)that are still PR andhave the same delay as the initialﬁlters.Writing(5)in matrix form,we obtainwith and for oddand for even(18)TTICE-LIKE STRUCTURE Connecting lifting and dual lifting to single steps results in the lattice-like structures depicted in Figure2(lifting that does not increase the delay)and Figure3(liﬁng that maximally increases thedelay).Figure2:Lattice structure realizing lifting and dual lift-ing with andFigure3:Lattice structure realizing lifting and dual lift-ing with and resulting in an in-crease of the delay by2samplesWhen realizing the polyphaseﬁlters in VLSI,the lattice-like structure can be directly used and results in an im-plementation that is not only extremly regular but also designated for a parallel implementation.5.DESIGN EXAMPLEFigure4shows the frequency responses for different pro-totypeﬁlters for8-channel cosine-modulatedﬁlter banks. In all cases,the overall system delay is31samples.The frequency responses have been obtained using nonlinear optimization starting with a short prototype and succes-sively increasing the length.A signiﬁcant reduction of the stopband energy can be noticed for longer prototypes.6.CONCLUSIONSIn this paper we have shown that prototypeﬁlters for PR biorthogonal modulatedﬁlter banks can be constructed using lifting schemes.When changing the length of the polyphaseﬁlters by one in each lifting step a lattice like structure can be derived for the polyphaseﬁlters.ThedBFigure4:Frequency responses of prototypes forwith different lengths resulting in the sameﬁlter bank delaycoefﬁcients are robust to quantization and the proposed lifting scheme can be used in order to design integer co-efﬁcient prototypes.7.REFERENCES[1]K.Nayebi,T.P.Barnwell III,and M.J.T.Smith.Low delay FIRﬁlter banks:Design and evalua-tion.IEEE Trans.on Signal Processing,SP-42:24–31,January1994.[2]G.T.D.Schuller and M.J.T.Smith.A newframework for modulated perfect reconstructionﬁl-ter banks.IEEE Trans.on Signal Processing,SP-44, August1996.[3]G.Schuller.A new factorization and structure forcosine modulatedﬁlter banks with variable system delay.In Proc.30th Asilomar Conference on Sig-nals,Systems and Computers,Paciﬁc Grove,USA, November1996.[4]T.Q.Nguyen and P.N.Heller.Biorthogonal cosine-modulatedﬁlter bank.In Proc.IEEE International Conference on Accoustics,Speech,and Signal Pro-cessing,Atlanta,USA,May1996.[5]P.N.Heller,T.Karp,and T.Q.Nguyen.A generalformulation for modulatedﬁlter banks.Submitted to IEEE Trans.on Signal Processing,1996.[6]P.P.Vaidyanathan.Multirate Systems and FilterBanks.Prentice Hall,Englewood Cliffs,1993. [7]W.Sweldens.The lifting scheme:A custom de-sign construction of biorthogonal wavelets.Journal of Appl.and Comput.Harmonic Analysis,3(2):186–200,1996.[8]I.Daubechies and W.Sweldens.Factoring wavelettransforms into lifting steps.Technical report,Bell Laboratories,Lucent Technologies,1996.。

高二英语世界历史中的伟大人物与事件阅读理解25题

高二英语世界历史中的伟大人物与事件阅读理解25题1<背景文章>Alexander the Great is one of the most renowned figures in history. His conquests spanned a vast territory, leaving a lasting impact on the world. Born in Pella, Macedonia, Alexander was the son of King Philip II. From a young age, he showed great courage and leadership.Alexander's army was highly disciplined and skilled. They defeated many powerful kingdoms and empires. His conquests included Persia, Egypt, and parts of India. Along the way, he established many cities and spread Greek culture.One of Alexander's greatest achievements was his ability to blend different cultures. He encouraged his soldiers to marry local women and promoted the exchange of ideas and traditions. This led to a rich cultural synthesis that influenced future generations.Alexander's leadership style was also remarkable. He was known for his bravery in battle and his ability to inspire his troops. He led from the front and was always willing to take risks. His strategic thinking and military genius allowed him to overcome seemingly insurmountable obstacles.The impact of Alexander's conquests was far-reaching. He opened uptrade routes and promoted cultural exchange. His empire became a center of learning and innovation. Many of the ideas and institutions that emerged during his reign had a profound influence on the development of Western civilization.1. Alexander the Great was born in ___.A. AthensB. SpartaC. PellaD. Rome答案：C。

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Anti-windup Schemes for Proportional Integral and Proportional Resonant ControllerAnirban Ghoshal and Vinod JohnDepartment of Electrical Engineering,Indian Institute of Science,BangaloreEmail:anirban@ee.iisc.ernet.in,vjohn@ee.iisc.ernet.inAbstract—Problems like windup or rollover arise in a PI controller working under saturation.Hence anti-windup schemes are necessary to minimize performance degradation.Similar situation may occur in a Proportional Resonant(PR)controller in the presence of a sustained error input.Several methods can be employed based on existing knowledge on PI controller to counter this problem.In this paper few such schemes are proposed and implemented in FPGA and MATLAB and from the obtained results their possible use and limitations have been studied.Index Terms—Anti-windup,Proportional resonant con-trol,PI control,Current control.I.I NTRODUCTIONIn a PI controller windup or rollover is a widely studied problem[1–5].Typically this problem arises if the input error to the controller is large or the input error remains nonzero for a long time.The controller output may saturate either because of large error input or because of nonzero error which makes the integrator output keep on accumulating.A controller under sat-uration may give delayed response to any change in the input and this delay would be more if the con-troller goes into deeper saturation level.Again digital implementation of controller using DSP or FPGA having ﬁxed word length asks for careful choice of per unit values and saturation level of the controller to prevent windup phenomena.Hence it becomes necessary to employ anti-windup strategy to prevent the controller from going into deep saturation and to check windup or rollover of controller output.Anti-windup schemes for PI controller are a well researched topic though newer and innovative methods are still coming up.Several such schemes for PID controllers utilizing limited or conditional integration method and tracking anti-windup method have been discussed in[1].A modiﬁed tracking anti-windup method for PI controllers used in variable speed motor drives is described in[2].Design of an anti-windup scheme utilizing the beneﬁts of both conditional integration and tracking or back-calculation method is shown in[3].A survey on current controlled techniques [4]shows that for control of electric drives and grid connected inverter systems,popular controller strategies use PI controllers.Anti-windup strategies for PI con-trollers used in such applications were under study for long.In recent times current control strategies such as Proportional Resonant(PR)Controller are gaining popu-larity for their advantages over PI controller particularly for control of grid connected inverters[6,7].Here the controller operates on AC signal whereas in popular d-q control or the synchronous reference frame based control the PI controller works on DC signal.It can be shown that under certain condition a PR controller can become prone to windup phenomena.In this paper studies on few‘Anti-windup’schemes for PI controller and their applicability in solving windup problem in PR controller are discussed.These methods were simulated in MATLAB and then implemented on a FPGA based digital controller.This digital controller board uses Al-tera’s‘Cyclone’series FPGA.A word length of16bit, 1pu=3F F F h which is equivalent to5V when viewed through DAC and sampling rate of10kHz were used for implementation.II.PI CONTROLLER WITH ANTI-WINDUPA.PI controllerTransfer function of a PI controller is expressed asG P I(s)=K p+K iFig. 1.Block diagram representation of a PI controller with saturation.So the variables can attain values between certain ﬁnite range and any value out of that range will lead to roll over and output of controller (y )would show it as a sudden jump from positive to negative or vice versa.Such undesirable condition can arise if the error (e )is too large or it remains non-zero for long duration during which the integrator causes the roll over.To limit the output a saturation block can be used at the outputterminal as shown in Fig.1.Here output (y ′)can be expressed asy ′=yfor Y max >y >Y min Ymax for y ≥Y max Yminfor y ≤Y min(3)But the above approach would lead to problem if theinput ‘e ’remains non-zero for long and during that period the integrator output keeps on accumulating.This may either introduce delay in response when the input error changes or even lead to roll over of output ‘y ’as can be seen in Fig.2.To avoid this it is necessaryFig.2.Output of PI controller with saturation implemented in FPGA for error input e =1.25.Here Kp =1.33and Ki =20.7.Upper saturation limit Y max =5V and lower saturation limit Y min =−5V .to check the integration process during such situations which is in general known as anti-windup.In this paper study has been carried out on two schemes using condi-tional integration and tracking anti-windup.Discussionson these commonly adopted anti-windup schemes for PI controllers are in the next subsections.B.Conditional IntegrationThe ﬁrst method,shown in Fig.3is by stopping the integration process when the output y has reached the saturation limit.This method can also be considered asFig.3.Block diagram representation of a PI controller with anti-windup scheme described in Conditional Integration.a variable structure PID control method discussed in [5].This ensures that while the controller is experiencing saturation there is no further increase in the value of output ‘y ’.If the error reduces below certain level for which output comes out of saturation,the integrator starts working again.The results are shown in Fig.4.In this method the PI controller output never goes beyond the saturation limit.Upon reaching saturation the value at which the integrator output is held,depends on input er-ror magnitude and the proportional constant.A variation of this method can be by forcing the integrator output to some predetermined value whenever the controller output getssaturated.Fig. 4.Output of PI controller with anti-windup scheme of Conditional Integration implemented in FPGA for an error input e =1.25.Here Kp =1.33and Ki =20.7.Upper saturation limit Y max =5V and lower saturation limit Y min =−5V .C.Tracking Anti-windupFig.5shows another way of controlling the extent of saturation.Here the difference of actual output (y )andsaturated output (y ′)is fed back through a gain (K lim )to reduce the amount of error input e going intointegrator.Fig.5.Block diagram representation of a PI controller where thedifference between actual output (y )and saturated output (y ′)is used as a feedback signal through a gain (K lim )to reduced the input to integrator.Thus rate at which the output of integrator would have increased is reduced.Under normal situation the anti-windup path does not contribute in any way as y =y ′.The results are shown in Fig.6.Choice of limiting gain (K lim )depends on acceptable restriction on integrator output.Higher value of K lim keeps the actual output (y )close to the saturated output (y ′)which in turn enables the controller to come out of saturation quickly when theFig.6.Output of PI controller with anti-windup scheme of Tracking Anti-windup implemented in FPGA for an error input e =1.25.Here K p =1.33,K i =20.7and K lim =1.Upper saturation limit Y max =5V and lower saturation limit Y min =−5V .The steady state value of output ‘y ’is of interest for choosing K lim .Considering a situation where y >Y max following relationships can be derived to get an indi-cation of steady state and dynamic behaviour of the PI controller under saturation with tracking anti-windupcontrol.If the output of integrator is x ,thendxdt=−K i K lim x +K i (1−K lim K p )e +K i K lim Y max(6)Solution to the above differential equation for a constant error input e (t )=E gives x (t )=(X 0−EKlim+Y max −K p ×E )(7)Here X 0is the initial value of state ‘x ’.Now output ‘y ’can be expressed as y (t )=(X 0−EKlim+Y max )(8)If steady state value of ‘y ’is Y ss ,thenY ss =Y max +Es 2+ω2(10)HeresK iFig.7.Frequency response of the resonant part of a PR controller.Here K i =2000and ω=314rad/sec .(13)for a stable realisation are obtained using Eulers modiﬁed method.Here ∆T is the integration step size.p [n +1]=p [n ]+K i ×∆T ×e [n ]+ω×∆T ×q [n ](11)q [n +1]=q [n ]−ω×∆T ×p [n +1](12)y [n +1]=K p ×e [n ]+p [n +1](13)Fig.8.Block diagram representation of PR controller.Present literatures on PR controller shows several other ways of realisation.In the most commonly used form the resonant part is realized by a second order transfer function with a non-zero damping factor.In this realisation the resonant controller output is bounded for any sinusoidal input but error input is never actually zero.Here choice of damping factor would decide on error magnitude.Also,design of controller should take account of maximum allowable error input for a given damping factor to prevent roll over.The way of imple-mentation where damping factor is zero,shown in Fig.8and implemented by equations (11),(12)and (13),works ﬁne as the error ‘e ’goes to zero at steady state.Butif error ‘e ’,typically a sinusoidal signal,persists for long because of some operating situations then output of resonant part can show unstable behaviour.The time domain expression for output of resonant part i.e.‘p ’,can be expressed as follows p (t )=A 0sin(ωt +φ0)+A ×K i ×t2ωsin(ωt )sin(φ)(14)where,e (t )=A ×sin(ωt −φ)(15)A 0=Q 0)(17)P 0and Q 0are the initial conditions of the states p and q .The above expression shows that if the error is present continuously then output of resonant part would keep on increasing and after sometime the entire controller output y would experience roll over.So it becomes necessary for the controller to limit the output under such situations.Therefore use of anti-windup logic need to be looked into.In this regard the schemes that ﬁnd use in case of a PI controller can be used with a PR controller and their suitability and limitations of the proposed methods can be studied.B.Method 1The scheme of Fig.3would not directly work for a PR controller as stopping of integrator will introduce large DC offset into controller output.Fig.9represents an anti-windup scheme where the resonant part is withdrawn from the control loop and the integrator outputs are forced to zero if the output of controller goes out of desired range.This can be considered reasonable in situations where feed-forward terms and proportional terms are responsible for a large portion of the control action and the integral terms are responsible only to zero out long term output error.The results are shown in Fig.10.It can be observed that due to the proportional part the output from the controller will not be zero.Reappointing the controller has to be done according to the application,from a higher level master control system,or a manual reset can be a solution for this method.In general to minimize the burden on controller the grid voltage is added as a feed-forward term.The desired range of controller output can be derived from the steady state drop of voltage across the ﬁlter between inverter and grid,in case of a grid connected application.Now ifFig.9.PR controller with anti-windup scheme of‘Method1’.Fig.10.Output of a PR controller implemented in FPGA with anti-windup scheme using‘Method1’.Here K p=0.8,K i=125,and ω=314rad/sec.Here Y max=2.5V and Y min=−2.5V.the error is very large and hence the contribution from proportional part becomes signiﬁcantly high then entire controller output should be forced to zero.C.Method2The second scheme shown in Fig.11uses the dif-ference of actual output y and saturated output y′to be used as feed back signal through a gain K lim.As the saturated output y′would bea clipped sinusoidal wave so feed back through K lim would contain higher order harmonics.But the resonant part of the controller provides low gain other than the resonant frequency. Therefore it can be expected that the output y would not be distorted.However higher value of K lim ensures that output y is small.So,value of K lim can be selected based upon desired range of y for maximum error input e.If value of K lim is high then the magnitudes of harmonics also get increased which in turn distorts the output y.Again for a lower magnitude error input e the Fig.11.PR controller with anti-windup scheme of‘Method2’. saturated output y′follows the output y for longer time.Fig.12.Output of a PR controller implemented in FPGA with anti-windup scheme using‘Method2’.Here K p=0.8,K i=125, K lim=10andω=314rad/sec.Here Y max=2.5V and Y min=−2.5V.The result shown in Fig.12shows that the saturated output is almost following the unsaturated output.Here the input value taken is0.1pu.So for lower input value the output y can be used asﬁnal output but for higher input value output y becomes signiﬁcantly distorted. Also if the saturation level chosen are smaller such as10%of rated voltage then level of distortion would increase.IV.E XPERIMENTAL R ESULTTo verify the operation of PR controller a3phase4 wire test setup of inverter with resistive-inductive load was chosen.The neutral point of the load was connected to the dc bus mid point.A current command of4A r.m.s. was given as the input to the current controller.The overall control strategy contains three individual current controller for each phase.The result in Fig.13shows that the controller is capable of tracking the reference current.During the experiment DC bus was held constantat 600V and the load was series connection of of 35Ωresistance and 84mH inductance in each phase.Fig.13.Phase current tracking using the proposed PR controller.Here K p =1.0,K i =1000,K lim =10and ω=314rad/sec.Here Y max =5.0V and Y min =−5.0V .V.C ONCLUSIONThe present paper tries to address the windup or rollover problem that can occur in a PR controller.Two anti-windup schemes have been proposed for PR controller on the basis of the understanding on anti-windup schemes for PI controller.It is shown that a direct extension of the anti-windup mechanism is not feasible.The proposed methods for PR anti-windup implementation indicate that it is possible to obtain an approximate anti-windup performance.The controller logic has been implemented in hardware and results are shown.R EFERENCES[1] C.Bohn and D.P.Atherton,”An analysis package comparingpid anti-windup strategies,”IEEE systems magazine,15(2):34-40,April 1995.[2]H.B.Shin,”New anti-windup PI controller for variable speedmotor drives,”IEEE Transactions on Industrial Electronics,V ol.45,No.3,Page(s)445-450,June 1998.[3] A.Visioli,”Modiﬁed anti-windup schemes for pid controllers,”IEE Control Theory and Application,150(1):49-54,January 2003.[4]M.P.Kazmierkowski and L.Malesani,”Current control tech-niques for three-phase voltage-source PWM converters:a sur-vey,”in Industrial Electronics,IEEE Transactions on,V olume 45,Issue 5,Oct 1998Page(s)691-703.[5] A.Scottedward Hodel and C.E.Hall,”Variable-structure pidcontrol to prevent integrator windup,”IEEE Transactions on Industrial Electronics,48(2):442-451,April 2001.[6] D.N.Zmood and D.G.Holmes,”Stationary frame currentregulation of PWM inverters with zero steady-state error,”Power Electronics,IEEE Transactions on V olume 18,Issue 3,May 2003Page(s):814-822.[7]Y .Xiaoming and W.Merk,”The non-ideal generalised amplitudeintegrator (NGAI):interpretation,implementation and applica-tions,”Power Electronics Specialist Conference,2001.PESC.2001IEEE 32nd Annual V olume 4,17-21June 2001Pages(s):1857-1861.Anirban Ghoshal received B.E.degree in Electrical Engineering from the Bengal En-gineering College,Shibpur and M.Tech degree from the Indian Institute of Technology,Delhi.Currently he is working towards his Phd at the Indian Institute of Science,Bangalore.His areas of interests include power electronics,distributed generation anddrives.Vinod John received B.Tech.degree in Elec-trical Engineering from the Indian Institute of Technology,Madras,M.S.E.E.degree from the University of Minnesota,Minneapolis,and Ph.D.from the University of Wisconsin,Madi-son.He has worked in research and de-velopment positions at GE Global Research,Niskayuna,NY and Northern Power,VT.He is currently working as an Assistant Professorat the Indian Institute of Science,Bangalore.His primary areas of interests are in power electronics and distributed generation,power quality,high power converters and motor drives.。