Semiactive Suspension of the Truck with Preview Control

By mandate of the Engineering Meetings Board, this paper has been approved for SAE publication upon completion of a peer review process by a minimum of three (3) industry experts under the supervision of the session organizer.All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE.For permission and licensing requests contact:SAE Permissions400 Commonwealth DriveWarrendale, PA 15096-0001-USAEmail: permissions@Fax: 724-772-3036Tel: 724-772-4028For multiple print copies contact:SAE Customer ServiceTel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-776-1615Email: CustomerService@ISSN 0148-7191Copyright © 2005 SAE InternationalPositions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions.Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. Printed in USAABSTRACTThe present article looks into possibilities for using drive axle semiactive suspension systems of a tractor in a tractor-semitrailer combination. The problem has been studied by means of computer-aided simulation, with ADAMS/Car MSC software. The shock absorbers of the semiactive suspension are provided with closed-loop preview control. Thus, the steering front axle of the tractor functions as a sensor to register road irregularities that the wheels of the drive axle should overcome. There has been suggested a simplified control logic for the semiactive suspension, being based on the outcomes of the study of the closed-loop preview control algorithm. When used for the drive axle of the tractor in the tractor-trailer combination, the semiactive suspension has been demonstrated to reduce the coefficient of variation of dynamic vertical forces on road pavement by 5,5 to 7%, in comparison with the conventional suspension types.INTRODUCTIONIn articulated trucks the operation features of an axle suspension system influence the driver’s comfort, vehicle handling, safety of the transported cargo, dynamic loads on tractor and semitrailer chassis as well as destructive effect exerted by heavy vehicle on road pavement. The above mentioned factors can be changed to a greater or lesser extent, for their eventual improvement, by using controllable (semiactive) shock absorbers instead of the conventional passive suspension types. In doing so, the performance and efficiency of controlled shock-absorbers depends on their control algorithm.This paper consists of four parts. In the first part the choice of the closed-loop preview algorithm is substantiated for the semiactive suspension control; the design of the simulated tractor-semitrailer combination is described. In the second part covers verification of adequacy of the closed-loop prediction performed. Part 3 represents a comparative analysis of the outcomes of the simulation of a tractor-semitrailer with a rear axle semiactive suspension and the one with a passive suspension. An exercise in simplification of the closed-loop prediction algorithm is presented in the fourth part of the paper.DRIVE AXLE SEMIACTIVE SUSPENSION CONTROL OF TRACTORSIMULATION DESIGNSelecting an Algorithm for Semiactive Suspension ControlVarious algorithms are used for the purposes of semiactive suspension control, the most deeply investigated and widely described being the "skyhook" method [1] and its modifications – “groundhook”, “proportional skyhook”, “hybrid control”, “No-jerk skyhook”. The contributions of the Advanced Vehicle Dynamics Laboratory and the Department of Mechanical Engineering of Virginia Tech headed by Dr. Mehdi Ahmadian [2, 3], and his pupils [4, 5, 6] deserve to be mentioned in this respect. This work is based in much on their results.Other approaches to control the active suspension exists. The optimal control methods H f, H2[7], LQR [8], and fuzzy logic control [9] should be reminded here.The majority of the papers on semiactive suspension and its application in motor vehicles are based on simulation results, rather than on real-life experiments. The simulated outcomes allow definite conclusions of improvement in the operating characteristics of a2005-01-3595Semiactive Suspension of the Truck with Preview ControlAndrei A. MazheiScientific-Engineering Enterprise “Belautotractorbuilding”Anton A. RakitskyInstitute for Machine Reliability and MechanicsAlexander A. UspenskiyRepublican Centre for Technology Transfer Copyright © 2005 SAE Internationalsuspension system of a truck after controlled shock absorbers have been substituted for the conventional passive ones. Furthermore, experimental studies frequently bring ambiguous results. There was not noted any significant improvement in vibrational load of the driver’s seat in the paper [4], with four "skyhook" controlled shock absorbers installed on a three-axle Volvo tractor. The cause is probably that switching a shock absorber takes a certain amount of time, while the operation algorithms (including the "skyhook" algorithm) require instantaneous response to the motion of both suspended and unsuspended weight, for the proper functioning of a suspension system. The latter requirement concerns magnetorheological and electrorheological shock absorbers, as well as hydraulic shock absorbers with controlled orifice. This is also confirmed by results of [10]. It is seen from [6] that under input signal at 10.5 Hz and response time of shock absorber of 10 µsec, the actual resistance of shock absorber is greatly different from what is required for the “skyhook” algorithm and modifications thereof. The needto integrate the readings of accelerometers and obtain absolute speed values is another drawback of the “skyhook” algorithm. Should any permanent error of the acceleration sensor appear, it will inevitably accumulate and result in a wrong operation of the control system.In relation to the above challenge, several research studies on preview control algorithms are undertaken nowadays. Their underlying principle is that the control action for a shock absorber is initiated with an advanceof 10 to 50 µsec, so that the shock absorber could be adjusted for the upcoming irregularity of the road. Prediction of road surface line can either be based on data received from vertical acceleration sensors of front axle wheels (in which case a front axle is equipped witha conventional passive suspension), or by scanning road surface ahead of a vehicle. Technologies for recognitionof road objects are applied in progressively increasing frequency in vehicles, however the potential capabilitiesof the most advanced systems are limited down to adaptive cruise control, detection of head-on collision risks, tracking of road marking lines [11]. For the time being, it is only in few special experimental vehicle makes [12] that systems for recognition of sporadic sizeable road prominences can be found.Crolla and Abdel-Hady established in [13] that the semiactive suspension is the most efficient, when the front axle of the automobile is a sensor. In this case, the disturbing action on rear axle wheels may be predicted on the basis of the front axle oscillations, and the control unit is generating its control signal in advance, with account of the operating speed of the sensor-control unit-shock absorber system, the automobile speed and the wheelbase. Work [14] considers control of the shock absorber based on the LQR optimal control method with account of the operating speed of the control system and shock absorber. As shown in paper [15], a significant increase in the characteristics of a semiactive suspension system can be achieved by parallel launching of a virtual suspension model simulation, with a time shift sufficient for switching of the shock absorber to the desirable mode. Thus, with certain suspension system conditions predicted by a model simulator for the time shift, finding an optimal control law presents no problem. The authors of [15] specifically refer to two approaches in implementation of the prediction method:x open-loop prediction;x closed-loop prediction (differently named as the run-ahead prediction).The first method is based on computation of the dynamics of a virtual model simulated in t preview seconds ahead of the actual condition of a real vehicle. With this technique, there is no correlation between the variables pertaining to the conditions of a virtual model vehicle and the actual values of acceleration, speed, motion or displacement of the vehicle, which is a disadvantage of the open-loop prediction method. As the real-world operation conditions are different, due to random road disturbances, open-loop prediction is considered to be of mere cognitive importance.The closed-loop prediction method is different in that the current variables of a suspension dynamic system conditions are approached as the initial conditions for a virtual model in computation of the model’s behavior within the aforesaid time shift t preview. This procedure is repeated at every bypass of the program cycle of the semiactive suspension controller. So, much greater adequacy and reliability is provided by the closed-loop prediction method, as a virtual model is always linked to the actual condition of a real vehicle. The weak point of this method is its huge amount of real-time computation, which makes it of little use in the present-day automotive microprocessor systems.The authors offer to study the poorly investigated closed-loop prediction method to virtual simulation of a vehicle in parallel with a simulation of its simplified model designed for the prediction purposes. With virtual simulation, the dynamic processes do not take place in the real-time mode, therefore higher demands of computer hardware resources are not relevant. By using the output data of the closed-loop prediction simulation it is possible to do analyses and develop empiric laws for semiactive suspension control that would require some lower real-time computation features of hardware.Virtual Model of Tractor-Semitrailer Combination in ADAMS/CarWe performed the work in the ADAMS/Car special computer simulation environment designed by the MSC Software (USA), which is a generally recognized simulation tool of automobile dynamic processes and its road behavior [16]. By means of the ADAMS/Car software package, it is quite easy to build a completedynamic model of the automobile. The designer disposes of a library of automobile system templates, which are easy to modify, and the tools of parameterization and visual 3D designing. By virtue thereof, the user is dealing not with abstract structural elements but with actually-dimensioned graphic subsystem images.There has been a tractor-semitrailer combination model created for the study in the ADAMS/Car environment(Fig. 1).Fig.1. Tractor-semitrailer assembly in the ADAMS/CarBasic parameters of the simulated vehicle are listed in Table 1. Model is based on truck templates provided by MSC Software [17]. However, they underwent a series of design changes related to the cab, cab suspension and driving axle suspension of the truck tractor. According to Table 1, changes were made in masses, dimensions and characteristics of the elements.The tires were built on the basis of a simple Fiala-model. The Fiala-type tire model is fairly nicely describing the normal reaction forces and tire deformations at the straight-line movement of the automobile.There are strong grounds to believe that continuous adjustment of shocks is not necessary here. This assumption is proved by the results of the study [18]. In the authors’ opinion, it is enough to have just three probable damping characteristics of a shock absorber: "soft", "hard" and medium (semi-hard). Switching between the "soft" and "hard" modes is performed by control algorithms, while the medium mode may be constantly used with the automatic suspension control off.The paper [4] mentions the damping characteristics of a base passive shock absorber and those of an experimental controllable magnetorheological shock absorber, both installed on a class 8 Volvo tractor. These damping characteristics were taken as the basis for the simulation. The damping characteristic curve of the base passive shock absorber in ADAMS/Car was approximated with a spline; the "soft" and "hard" curves were obtained as products of the base curve and multipliers 0.286 and 2.476, respectively. Let us define these multipliers as the relative damping coefficients. The coefficient values are chosen so that the "soft" damping curve corresponds to the damping curve of a magnetorheological shock absorber with the coil poweroff. To obtain more obvious results, the reaction forcesof "hard" curve were doubled, in comparison to thereaction forces of the magnetorheological shockabsorber with control current set at 3A (Fig.2).Table 1. Basic vehicle parametersFig. 2. Damping curves assumed for investigationParameter UnitsValueBase (B1+B2) mm3,506 Distance from front axle to centerof gravity (B1) mm1,100Height of centre of gravity of tractor mm 1,266Track width(2 L) mm1,808Distance from front axle to fifthwheel mm2,764 Mass (weight) of tractor M s kg5,340Mass (weight) of front (steering)axle kg325 Mass (weight) of drive axle kg 427Mass (weight) of twin wheels ofdrive axle kg 600Mass (weight) of front axle wheelof tractor kg 270Distance from fifth wheel to frontaxle of semitrailer mm 7,481Interaxle distance of semitrailer mm 1,245Distance from fifth wheel to centerof gravity of semitrailer mm 5,690Height of center of gravity ofsemitrailer mm1,814 Mass (weight) of fully loadedsemitrailer kg 28,800Mass (weight) of axle of semitrailer kg 783Mass (weight) of twin wheels ofsemitrailer kg600 Stiffness coefficient of dampingelement of drive axle N/mm 1,170Stiffness coefficient of tires N/mm 1,500Damping coefficient of tires N sec/mm 0.4The ADAMS/Car environment does not allow changing stiffness of its standard damping elements in the process of a single virtual experiment, therefore these elements have been replaced with different ADAMS/Car standard elements (Point-to-Point Actuators) that set up the force),()(V f V V f V F base shock D (1)with V standing for velocity across the shock absorber, f base (V) for reaction force corresponding to the velocity V with the base curve, Į for relative damping coefficient. Switching of the shock absorbers in the ADAMS/Car environment was provided by altered value of Į variable (0.286 or 2.476), according to output data of a prediction module.With changing the control signal, the resistance of the shock absorber fails to take the required value at once. Various studies take this value called reaction (response) time to be equal to 15-50 µsec. Therefore, the actual value of F actual , created by the Point-to-Point Actuator element is defined by integrating the derivative F actual (2):)()(actual shock actual F F dtF d H , (2) where H is the coefficient selected for a particular value of the step size of simulation such as to have F actual attain 95% of F within 40 µsec.There was a prediction module devised and created for the purposes of analysis of the closed-loop prediction algorithm. The prediction module is a user-written Fortran subroutine linked to the ADAMS/Car library. The core of the prediction module is a simplified model of thetractor-semitrailer combination shown on Fig. 3Fig. 3. Simplified model of tractor-semitrailercombination To avoid adding dynamic motion equations of the semitrailer to the simplified model, the trailer effect will be replaced by a weight located above the fifth wheel point. In doing so, the centre of gravity of the tractor is displaced and shifted closer to the drive axle, in the distance S offset .Another essential assumption iselimination of tires in the simplified model. Thus, vertical movements and velocity of the wheel hubs are calculated by the ADAMS/Car software, with the account of the tire effect upon the entire model vehicle (with the tires, as shown on Fig.1) assumed as the external disturbance factors for the simplified mode, rather than the road ordinates. Also, an assumption was made that the vertical movements of the steer axle wheel hubs are equal to those of the drive axle wheel hubs at crossing a single road bump at the same speed. It allows creating the prediction module for the simplified model behavior, with the initial conditions at both axles for the period of time that it takes the vehicle to run the distance equal to the wheel base length. As was mentioned above, the closed-loop prediction algorithm is constantly linked to the current actual state of the system, so the aforesaid assumptions do not produce notable effect on the result of algorithm.The initial data for the simplified model system are presented in Table 2.Table 2. Initial data for the simplified modelWith the dynamic system of the simplified model, the Lagrangian equation of 2nd kind is applicable:,)(i ii i Q q P q T q T dt d w w w w w w (3) with q i standing for generalized coordinate, T for kinetic energy of the system, P potential energy, Q i for generalized external force, to i th coordinate). By choosing Z S , Z I , Z T for the generalized coordinates, while taking into account the absence of external forces, weParameter Variable Units Value L mm 908 B1 mm 2,465 Center of gravity arrangement B2 mm 1,142D Kf5.9 Damping coefficient of front (K f ) and rear (K r )springing elements D KrN sec/ mm 0.286 5.9 or 2,476 5.9Cf N/ mm 1,170 Stiffness of a front (C f ) and rear (C r )springing elementsCr N/ mm 1,170Mass (weight) of vehicle Ms kg 20,000 I I kg*mm 2 1.078E+007 Respective moments of inertia, tolongitudinal (I I )and lateral (I M )axesI Mkg* mm 21.944E+010arrive at a set of differential equations that describe the simplified model:,T A T A T A T A z I L,A L A L A L A z I ,A A A A z m 24132211ijij4321șș4321s s (4)with A i determined by the expressionui f i f i z c D k A ,(5) where:.,,,424313222111u r s u r s u f s u f s z z B z l z D z z B z l z D z z B z l z D z z B z l z D I T I T I T I T (6) t switch = 0.05 sec. is accepted as the time for switching ofthe controllable shock absorber. Prediction of vertical motions of the vehicle will then be provided for the period of time t preview = 2t switch = 0.1 sec. Thus, the shock absorber will securely have the time sufficient for switching, whenever demanded by the prediction algorithm.To solve the combined differential equations, there was IVPAG subroutine taken from the set of IMSL Library mathematical subroutines of Compaq Visual Fortran software package and used for the prediction module. The step constant for solving of the set of equations (2) is 0.005 sec. Accordingly, prediction of the simplified model behavior for 0.1 second is done in 20 steps. The following initial values of the variables (Table 3) pertaining to the state of the system are required for solution of the simplified model dynamics equations: Table 3. Variable conditions of the simplified model Z U1, Z U3 Vertical displacement of left hub and right hub of front (steer) axledZ U1/dt,dZ U3/dt,dZ U2/dt,dZ U4/dt Vertical velocity of the wheel hubs Z T Roll angle Z MPitch angledZ T /dt Roll angular velocity dZ M /dt Pitch angular velocityZ s Vertical displacement of center of gravity dZ s /dt Vertical velocity of center of gravityZ U2 Z U4Vertical displacement of left hub and right hub of drive axleBefore the start of the prediction process the values of the above listed variables are equal to the corresponding values of the ADAMS/Car virtual sensors. In the process of prediction the variables are changed by the solution of the equations describing the movement of the virtualmodel. Z U2 and Z U4 are the exceptions; at everyprediction step vertical displacement values of the left and right hubs of the drive axle at the moment of time t are replaced with the displacement values of the wheel hubs of the steer axle at the moment of time t - (B1+B2)/v , where t stands for the actual time, (B1+B2)for the tractor base, v for the vehicle speed.Along with the solution of the movement equations of the model for the period t preview at varying relative damping coefficient values, there is a criterion deduced to determine the choice of the prediction algorithm between the "soft" or "hard" damping modes.The authors have taken O as the aforesaid criterion, determined by the expression12i ni ci Za Z I O ¦ (7)in which ci Zand i Z I stand for the predicted value vertical acceleration of the tractor’s center of gravity andthe pitch angular velocity at the i th step of prediction series, a stands for weight coefficient, n =20 is the number of steps in the prediction procedure.The damping mode required of the shock absorbers corresponds to the lower value of the criterion.The authors have deduced the criterion expression (7) empirically, by calibration of the virtual model. The background idea of the calibration was that O values should always be the smallest at the bigger values of the relative damping coefficient, when a vehicle rides on an absolutely smooth surface. In other words, in these conditions the algorithm should set the shock absorbers to the "hard" mode, for reduced pitch and roll at acceleration, braking or at cornering. Yet, with this, the weighting coefficient should not be as big as to pass thehigher values ci Zof the "rigid" suspension mode when bumps or pot holes (notably influencing the comfort ofpassengers) are ridden over.Testing track and test conditionsTractor-semitrailer combinations are normally used on high-quality motorways. Therefore an asphalt pavement surface should be modeled for the virtual testing.The road microprofile is determined by a statistical method. The determined normalized correlation function [19] for an asphalt pavement of average quality is as follows:)6,0cos(15,085,0)(05,02,0x e e x R x x (8)Simulation of the stochastic process for the given normalized correlation function should be based on thecentral limit theorem. The variable of stochastic process will be referred to as the ordinate of the road profile. Having assumed that the ordinates of the road profile are identical for the left and the right wheels, 3D road profiles of two testing roads are modeled in the TiemOrbit format for ADAMS/Car.The virtual test was run in MDI_SDI_TESTRIG in compliance with the parameters in Table 4. Ɍable 4. Virtual testing parametersType of test Straight-line acceleration (Acceleration value and acceleration algorithm) 0.1g;closed-loop Initial speed, km/h 50 Simulation time, sec. 20 Number of simulation steps4000VERIFICATION OF PREDICTION ADEQUACYThe first step in the analysis of the created model was the verification checkup of the prediction algorithm regarding adequacy of the predicted state of the dynamic system. The data collected from the ADAMS/Car chassis acceleration sensors have been put to the profiles (curves) of acceleration of the center of gravity and presented in Fig. 4, along with the predicted (estimated) acceleration curve. The estimated acceleration curve has been shifted to the left, by t preview = 0.1 secFig. 4. Vertical accelerations of the tractor's center of gravity (solid line - actual values, dashed line - predicted for 0.1 sec.)Apparently, as seen in Fig. 4, the closed-loop prediction method is sufficiently adequate, in terms of the systemstate prediction, even at essential simplifications of the dynamic system.SIMULATION RESULTSWith reference to the predicted state of the dynamic system, one of the two possible alternative relative damping coefficients is chosen by the algorithm, according to the criterion described above. The resulting switching data are diagrammed in fig. 5. The described algorithm will be hereinafter denoted "Preview Full". It is a complex algorithm that requires a significant number of sensors and considerable control system hardware resources.The left hub acceleration diagram displays the vertical acceleration values of the left rear wheel hub.The results of the simulation provide the grounds for the conclusion that the influence of the damping features of shock absorbers (damping curve) on vertical acceleration of a fully loaded tractor and trailer is insignificantly small, in view of their high mass inertia. Root-mean-square vertical accelerations at passive "soft", passive "hard" and semiactive suspension modes are, respectively, 824.0 mm/ sec 2, 765.0 mm/sec 2, 802.4 mm/sec 2.In cases of fifth-wheel coupling, the influence of the damping characteristics of shock absorbers is considerably higher on the normal forces in the wheel-to-road interaction and on the vertical force of the tractor-to-semitrailer coupling.To evaluate the damage of the tractor’s drive axle to the pavement, the authors resort to the tire force variation coefficient (i.e. the dynamic load coefficient, DLC) [18]. The DLC factor is determined by the formula,FDLC V(9)with ı for the standard deviation of the normal force, F for the normal force of a wheel. Since the road profile ordinates are identical for left and right wheels, table 5 brings the ı and DLC values for the sum of the normal forces of the drive wheels on the road.Table 5. Variation of the sum of the normal forces Damping curve “Hard” passive “Soft” passiveSemiactive V , N13,931 13,770 12,981 DLC 0.166 0.164 0.155 Vertical force variation in fifth wheel coupling can be approached in a similar way of analysis (please, refer to table 6).Table 6. Vertical force in fifth wheel couplingDamping curve “Hard”passive“Soft”passiveSemiactiveV, N 13,598 9,187 11,044 DLC 0.160 0.108 0.130Thus, if exposed to the load of about 8 tons, the semiactive suspension system of the drive axle of the tractor reduces the on-pavement dynamic load variation by 5.5 to 7%; the vertical force variation span in fifth wheel coupling is narrowed to a somewhat lesser degree. With the tractor and semitrailer fully loaded, the vertical acceleration features of the tractor's center of gravity do not change essentially, due to the big mass inertia of the tractor and semitrailer combination. SIMPLIFICATION OF ALGORITHM OF CONTROLThere was a suggestion of development of a simple empirical control algorithm based on the switching diagram (shown in fig. 5). It should be noted that significant vertical acceleration of rear wheel hubs are, as a rule, contemporized with switching to the "soft" mode. Authors propose simplified prediction algorithm, which is hereinafter named “Preview Lite“, which requires only vertical acceleration values of steer wheel hubs and vehicle speed for the initial data. More details on Preview Lite operation are given in paper [20]. After registering accelerations in front axle wheels, which exceed the preset sensitivity threshold, upon expiry of the calculated time interval, the shock absorbers of the rear axle are switched over into the "soft" mode. The delay is defined by the algorithm on the basis of the automobile speed and response time of the shock absorbers. Fig.6 brings an example of variation of shock absorber switches by the Preview Lite on the same test track.The results of the comparative analysis of Preview Full and Preview Lite, under their equal testing conditions, are summarized in table 7.The analytical findings make it apparent that Preview Lite, with certain given switching settings, is intermediate between Preview Full and passive “soft” suspension. Table 7. Comparative data of the Preview Full andPreview Lite algorithmsAlgorithm PreviewFullPreviewLite Normal forces of drive wheels in the wheel-roadinteractionV, N 12,981 13,086DLC 0.1550.156Vertical force in fifth wheel couplingV, N 11,044 9,859DLC 0.1300.116This fact determines the decrease in DLC values for thefifth wheel coupling, in comparison with the resultsobtained by Preview Full. However, considering the DLCcoefficient as a criterion of higher importance, thePreview Lite algorithm ranks insignificantly lower thanPreview Full (with Preview Lite the DLC is 0.156, whilewith Preview Full the DLC is 0.155).The advantages of the Preview Lite control algorithm areas follows:1. Essential simplification and cheapening of thesemiactive suspension design. The “skyhook” algorithm(and most similar ones) requires absolute speeds ofboth sprung and unsprung masses as its inputparameters. It means that in this case we need a doublenumber of acceleration sensors.2. The algorithm uses acceleration values as input data.Therefore, we are rid of acceleration sensor's erroraccumulation at integration of its readings.3. There are no tough requirements to operation speedof the shock absorber.。