Sohn_00_Semi-Active Control of the Macpherson Suspension System HIL

8/6/2019 Sohn_00_Semi-Active Control of the Macpherson Suspension System HIL

1/6

WP4-6 5:OO ,Proceedingsof the 2000 IEEEInternational Conference on Control ApplicationsAnchorage, Alaska, USA September 25-27,2000Semi-Active Control of the Macpherson Suspension System: Hardware-in-the-Loop Simulations

Hyun-Chul Soh*,Keum-Shik Hong**, and J. Karl Hedrickt* Department of Mechanical and Intelligent Systems Engineering, Pusan National University, San 3 0 Changjeon-dong, K umjeong-ku,Pusan, 609-735, Korea. Tel: +82(51) 510-1481, Fax: +82 (51) 514-0685, Email: [email protected]** School of Mechanical En gineering & Research Institute of Mechanical Technology, Pusan National University, 30 Changjeon-dong,Kumjeong-ku, Pusan, 609-735, Korea. Tel: +82 (5 1) 5 10-2454, Fax: +82 (5 1) 514-0685, Email: [email protected] Department of Mechanical Engineering, University of Califomia, Berkeley, C A 94720-1 740, USA. Tel.: +1(510) 642-2482, Fax:+1(5 10) 642-6163, Email: [email protected]

AbstractA modified skyhook control for the semi-active Macphersonsuspension system is considered. A new quarter-car model, whichincorporates the rotational motion of the unsprung mass, isintroduced. A feedback control law in the form of a modifiedskyhook control is derived. Two filters to estimate the absolutevelocity of the sprung mass and the relative velocity of the rattle

space are designed. By including the actual semi-active damper inthe loop of com puter simulation, the nonlinearity, time-delay, andunmodeled dynamics of the continuously variable damper havebeen incorporated. The control performances of the semi-activesystem and a passive one have been compared.1. Introduction

The performance of a suspension system is characterized by theride quality, the drive stability or maneuverability, the size of therattle space, and the dynamic tire force. The prime purpose ofadopting an activekemi-active suspension system is to improve theride quality and the drive stability. To improve th e ride quality, it isimportant to isolate the sprung mass from the road disturbancesand to decrease the resonance peak of the sprung mass, near 1 Hz,which is known to be a sensitive frequency to human body. On theother hand, to improve the drive stability, it is important to keepthe tire in contact with the road surface and therefore to decreasethe resonant peak near 10 Hz, which is the resonant frequency ofthe unsprung mass. For a given suspension spring, the betterisolation of the sprung mass from the road disturbances can beachieved with a soft damping by allowing a larger suspensiondeflection. However, the better road con tact can be achieved with ahard damping by not allowing unnecessary suspension deflections.Therefore, the ride quality and the drive stability are twoconflicting criteria in the control system design of suspensionsystems.Since the skyhook control strategy was introduced by Kamoppet al. [ 5 ] , in which an artificial damper was inserted between thesprung mass and the stationary sky as a tool to suppress thevibratory motion of the sprung mass and to calculate the desireddamping force, a number of innovative control methodologieshave been proposed to implement this strategy. The skyhookcontrol can reduce the resonant peak of the sprung mass quitesignificantly and thus achieving a good ride quality. But, in orderto improve both the ride quality and the drive stability, bothresonant peaks of the sprun g mass and the u nsprung mass need tobe reduced. It is known, however, that the skyhook damper alonecannot reduce both resonant peaks at low level. From this point ofview, Besinger et al. [2] proposed a modification of the skyhookcontrol, which includes a passive part as well as a skyhook damperin the process of calculating the desired control input. Novak andValasek [8 ] and Valasek et al. [l o] have proposed a groundhook0-7803-6562-3/00$10.0002000EE E

control, which assumes an additional artificial damper between theunsprung mass and th e ground besides the skyhook damper, for thepurpose of decreasing the dynamic tire force.Compared to the control techniques appeared in the literature,the issues related to the modeling of suspension systems are rare.Jonsson [121 conducted a finite e lement analysis for evaluating thedeformations of suspension components. Stensson et al. [9]proposed three nonlinear models for the Macpherson strut wheelsuspension for the analysis of motion, force, and deformations.These models would be appropriate for the analysis of mechanics,but are not adequate for control system design. In th e conventionalquarter car model, only the up-down movements of the sprun g andunsprung masses are assumed. In the conventional model, the roleof the control arm is completely ignored. From this point of view,a new control-oriented model, which considers the rotationalmotion of the control arm of the Macpherson strut suspension, hasbeen introduced by Ho ng et al. [4].As an actuator for generating the semi-active control force, acontinuously variable damper (CVD) is used. Hence, controlforces are adjusted by changing th e size of an orifice of the CV Dwith a solenoid valve. The damping force characteristics of theCVD are highly nonlinear. The damping force of the extensionmotion is much larger than that of the compression motion. It isalso noted that w ith a semi-active suspension the control action isapplied only when the control force is opposite to the direction ofsuspension deflection.One way of designing a control system for the semi-activesuspension is to figure out all the nonlinearities of the semi-activeactuator and then to design an appropriate control law byconsidering both the vehicle dynamics and the actuator dynamics.For this, the fluid dynamics of the variable damper has to beinvestigated. However, it is not simple to know the completenonlinear characteristics of the variable damper including thesolenoid valve dynamics. Another way is to isolate the mostsignificant nonlinear component, which is the variable damper inour case, and use the real damping force when designing acontroller and evaluating the control performance, which is thehardware-in-the-loop design and simulation. In this case, theprimary controller is designed by using a linear model in which thenonlinear component is treated as a linear one with hardconstraints.Recently, the computer aided control system design (CACSD)has been the subject of focus. The CACSD is often named as therapid control prototyping (RCP) or the hardware-in-the-loopsimulations (HILS) [3]. In the RCP, the plant dynamics and/or thecontroller are implemented in a digital signal processing board,which allows an easy adjustment of various parameters of the plantand/or the controller. If actual hardwares are used in simulating thedynamic performance of a controller and/or a plant model, theword HILS is particularly used. Through the CACSD, the total

982
mailto:[email protected]:[email protected]


2/6


3/6

where

T O I o oa21 a230 0 0 1

r 0 1

"msktIc cos(-Bo)m,m,@ +m:lE sin2(-eo)

041 , and a43 .Remark 2: Comparing the linearized equation (4) with the

conventional model, in which only the vertical movement of boththe sprung and the unsprung masses are considered, the transferfunction of the conventional model and that of (4) becomeidentical if I , = C , 1, = I A c o s a , nd Bo = 0" Therefore, theconventional model is a special case of the new model in the sensethat the same transfer function can be achieved by restrictingI , = C and Bo= 0 . For the detailed comparison, Hong et al. [4]is referred.Now, because Zs is measured, the output equation by definingy = Zs is derived as follows:where

y ( t )= CX(~)Qfs +& z r ?r

Remark 3: It is remarked that the parameter values required inthe control law are the absolute velocity of the sprung mass, is,and the relative velocity of the sprung and unsprung masses & :See Section 3.1, where a modified skyhook control strategy isinvestigated. Both is and will be filtered from the onlyavailable signal zs: Recall that only one acceleration sensor isused in this work. However, during the development stage ofcontrol laws and for the simulations and HILS of the developedcontrol laws, the following formula, equation (5b) of [4], may beused.

= f ( e ,e).Finally, to complete the feedback control loop, a filtered outputeauation is defined as follows:

(7)

in which the estimation of is and & from Zs is emphasizedand the forms of 4 and F2 are given in Section 3.3.

Cd = D , 4 d =4,D2d =D2, and Tis he sampling time.3. A Modified Skyhook Control

In this paper, the use of only one acceleration sensor formeasuring the sprung mass vertical vibrations and a 16-bitmicroprocessor for implementing the designed control algorithm isassumed. Therefore, control law design focuses on the practicality,implementability, and robustness of the algorithm rather than theperfection of the algorithm.The two control objectives are the improvement of both the ridequality and the drive stability. If fixed control g ains are used, thesetwo conflicting objectives cannot be achieved. However, byadapting the road roughness, i.e., chan ging control gains at variousroad conditions, both objectives can be achieved.3.1 Controller StructureA number of papers investigating advanced control techniquessuch as nonlinear adaptive control, preview control, and robustcontrol have appeared in the literature [1,6,7,11]. However, if astate feedback control strategy is adopted, either sufficient sensorsfor the w hole state variables or an estimate of the state vector isrequired. In this paper, a simple modified skyhook control withgain scheduling, in the form o f an o utput feedback control whichrequires a minimal number of sensors, is investigated.1) Ideal Skyhook ControlAmong the many control methods developed for theimprovement of ride quality, the skyhook control introduced byKamopp et al. [5] is known most effective in terms of the numberof sensors and the simplicity of the control algorithm. Theiroriginal work used only one inertia damper between the sprungmass and the inertia frame. This control method is applicable forboth a semi-active system as well as an active system. However,this strategy does not pay attention to the unsprung mass vibrationsand therefore might deteriorate the maneuverability of the vehicledue to excessive vibrations of the unsprung mass. In order toovercome the demerits of the original skyhook control, variousmodified approaches have been proposed in the literature [8 , lo].2) Skyhook-Groundhook ControlThe groundhook control, which assumes an additional inertiadamper between the unsprung mass and the ground besides theskyhook damper, was proposed in ord er to decrease the dynamictire force. This strategy can compromise two conflicting criteria,the ride quality and th e drive stability.From Fig. 1, the control force of the skyhook-groundhookmodel becomes

U = -csky is - ~ A L gr 0 ( i ,+ice) (8 )where c s b is the damping coefficient of the skyhook damper,

984


4/6

c p is the damping coefficient of the passive damper, and cgrois the damping coefficient of the groundhook damper. However,because the value of 8, has to be estimated, this skyhook-groundhook strategy is not suitable in our case.3)Modification of Skyhook ControlA modified skyhook control, which proposes the inclusion of avariable damper besides the skyhook damper, can still achieveboth control objectives by as signing adequate dam ping coefficientsat different frequency ranges of road inputs to the skyhook damperand the variable damper. The following law is proposed:

cm E p +C&, q f cp C m mU = -cmm [q.if+ (1- 4 ) . is]. (9)

where q is a weighting factor with a value between 0 and 1. Ifq = 0 , he control input becomes U = - c s b . is and therefore theimprovement of ride quality is focused. On the other hand, ifq = 1 , he control input becomes U = -c p .A1 and therefore theimprovement of manipulability is focused. H ence, by varying q ,a compromising control strategy can be fulfilled. It is remarkedthat even though the control input is given by (9), its realization iscarried out by the variable damper. Hence the actual dampingforce made by the CV D is limited as follows:

f,., if f , ' < uf, = U, if f,. < U .f,* (10)1s . if f,. > U

where f,* and f,. denote the maximum and the minimumdamping forces available at a given relative velocity.3.2Digital Filter DesignIn this section, two filters for estimating the absolute velocity o fthe sprung mass and the relative velocity of the sprung andunsprung masses are designed, which are needed to calculate theskyhook control law as derived in Section 3.1. It is also remarkedthat even though the measurement of B or 8, is possible, anestimation method is preferred considering the cost for extrasensors. A continuous filter which satisfies the designspecifications is first of all designed and then it is transformed toits discrete form. Because th e digital filters in this pap er are of thetype of high-pass filter, the bilinear transformation, which has nolimits on bandwidth, no aliasing, and preserves the stability, isused.1) Absolute Velocity of the Sprung MassThe filter to estimate the ab solute velocity from the accelerationdata of the sprung m ass is suggested as follows:

where < = 0 . 7 0 7 and w, =0.1 Hz. (12) functions as adifferentiator below 0.1 Hz and functions as an integrator above0.1 Hz. Consequently, this filter will provides a satisfactoryabsolute velocity of the sprung mass by excluding a DC offset.Before the discretization of (12), the frequency transformation isperformed to achieve the same frequency properties. Using thetransformation su ch thatw T 2 2 -1w, = - t a n n , s=--T 2 T z + l 'the following discrete transfer function is obtained.

~o i 2 T 2 + 4@kT +4 + 2 0 b 2 T -8)z-I +(on2 2 - & , T + 4 ) ~ - ~2) Relative velocity of the Sprung and Unsprung MassesThe relative velocity o f two masses is estimated using the modelof suspension dynamics. Assume that Bo = O and B is

sufficiently small. Then, the following approximations hold:1.V h o r P o , i U ~ i i , + i c e ,Z - - ( i , , - i , )ICand

i f S - I , 8 , = ' B ( 2 , - i u ) . (13)1,Therefore, the relative velocity o f the sprung and unsprung massesfrom measurement data is filtered as follows:

where ms , c p , nd k, are suspension parameters. It is notedthat a low pass filter l/(l+n) has been inserted fo r eliminatingnoises, where r = 1124wl ,


5/6

desired control force exceeds the maximum and the minimumdamping forces available, the actuator is saturated and only theavailable damping forces are provided. Therefore, the semi-activesuspension system, compared to the fully active one, may havealimited performance on a rough road. In order to generate thecontrol force required from the modified skyhook controller, thecurrent input for the desired damping force at a given relativevelocity.4.2 Current GenerationThe damping force generated in the actual damper depends ontwo things: the size of valve opening, i.e. the curren t input to thesolenoid valve, and the relative velocity of the rattle space. Todetermine the current input to the solenoid valve, it is necessary toknow the damping force characteristics o f the valve vs. the c urrentinput at given relative velocity. For this, two approaches can bepursued. One is an analytic approach, which investigates thedynamics of the entire hydraulic system including the cylinder andvalves. However, the mechanism of a semi-active system is verycomplicated and the damping force characteristics of expansionand compression strokes are different because of the one-sidedpiston rod. It is also difficult to measure the parameter values ofthe hydraulic system and furthermore these values are timevarying. Another approach is an experimental solution, which ismore or less straightforward. The damping forces for va rious inputcurrents at given relative velocity can be measured with a test rig.In this paper, the experimental approach is adopted.The experimental data can be either tabulated as a look-up tablefor the purpose of gain-scheduling or approximated as apolynomial equation by using the least squares method. Afterdividing the relative velocity range into four different sections, thepolynomial equations corresponding to individual sections aretabulated in Table 1.

2.5

Table 1Polynomial representation of damping force.

-.cl.- \

N=l1 8-- N= 5 1

solenoid valve used in this work is about 300Hz.

'3

4000 I. 4- M a Damplag (lookup)

Mm Dsmpmg @olynomld)2000 -5:I .

0 5 1 0 15-1000' ' ' ' '

-1 5 - 1 0 -0 5 0 0Velocity [dsec]

- 1.7033 sec.

Fig. 2 Damping force comparison: look up table and polynomial.

Maximum DampingForce Minimum DampingForce Fig. 3 Access time comparison: lookup table and polynomial.

10 20 30 40 501.0 IData Number (N)

0.2%o


6/6

transferred to the dynamic model in the com puter. By varying thecontrol parameters in real time, the procedures 3) -5 ) can berepeated.The sampling time is set to 0.001 sec. This time step should belarger than the combined time of the calculation time of plantdynamics and the input-output communication time between theexternal devices. In experiments when the actual calculation timewas larger than the step size, small oscillations had occurred in avalve of the hydraulic actuator. If these oscillations are deliveredto the CVD, it will be difficult to measure the exact damping forcefrom the loadcell. Hence it may affect the stability of the completecontrol system.Finally, the vertical accelerations of the sprung mass, whenpassing through a speed bump with 1 Hz frequency, for a passiveand a semi-active suspension are compared in Fig. 5 . The lowerplot of Fig. 5shows the current input applied to the CVD.

3 53 02 52 0

1 00500-0-3 0-1 5-2 0-2 5

0 1 2 3 4 5 6t i me (sec)

1 8 1

- 0 2 1 . I . , . I . , . , .0 1 2 3 4 5 6

time (sec)Fig. 5 Vertical acceleration comparison: a passive damper and aCVD w ith the skyhook control (1 Hz speed bump).

5.ConclusionsIn this paper, a new control-oriented model for the semi-activeMacpherson suspension system, which incorporates the rotationalmotion of the unsprung mass, was investigated. Upon therequirement that only one acceleration sensor for the sprung massvibrations should be used, a modified skyhook control, whichutilizes a filtered absolute velocity of the sprung mass and afiltered relative velocity of th e sprung and unsprung masses, wasdesigned. The performance of the proposed controller wasevaluated by means of hardware-in-the-loop simulations. It was

demonstrated that the semi-active suspension system can stillachieve competitive performance by using road adaptive controllaws.References

[ I] Alleyne, A. and H edrick, J.K., 1995, Nonlinear AdaptiveControl of Active Suspensions, IEEE Transaction onControl Systems Techno loD, Vo1.3, No . 1, pp.94-101 .[2] Besinger, EH., Cebon, D. and Co le, D.J., 1995, ForceControl of a Semi-Active Damper, Vehicle System Dynamics,[3] Hanselmann, H., 1996, Hardware-in-the-loop SimulationTesting and its Integration into aCACSD Toolset, The IEEEInternational Symposium onComputer Aided C ontrol SystemDesign, Dearbom, MI, USA, pp.152-156.[4] Hong, K.S., Jeon, D.S., Yoo, W.S., Sunwoo, H., Shin, S.Y.,Kim, C.M. and Park, B.S., 1999, A New Model and anOptimal Pole-placement Control of the MacphersonSuspension System, SAE International Congress andExposition, Detroit, MI, S A E paper No. 1999-01-1331,[ 5 ] Kamop p, D.C., Crosby, M.J. and Hanvood, R.A., 1974,Vibration Control Using Semi-Active Force Generators,ASME Journal of Engineering fo r Industry, V01.96, No.2,[6] Kim, H. and Yoon, Y.S., 1995, Semi-Active Suspensionwith Preview Using a Frequency-Shaped PerformanceIndex, Vehicle System D ynam ics,Vo1.24, pp.7 59-780 .[7] Lin, J.S. and Kanellakopoulos, I., 1997, Nonlinear Designof Active Suspensions, IEEE Control System Magazine,[8] Novak, M. and Valasek, M., 1996, A New Concept of Semi-Active Control of Trucks Suspension, Proc. of AVEC 96,International Symposium on Advanced Vehicle Control,Aachen Un iversity of Technology, pp.141-151.[9] Stensson, A., Asplund, C. and Karlsson, L., 1994, The

Nonlinear Behaviour of a Macpherson Strut WheelSuspension, Vehicle System Dyn amics , Vol. 23, pp.85-106.[IO] Valasek, M., Babic, M., Sika, Z. and Magdolen, L., 1997,Development of Semi-Active Truck Suspension, Proc. ofthe 8th ZFAC/IFIP/IFORS Symposium on TransportationSystems, Chania, Greece, pp.470-475.[ I l l Yi, K., and Hedrick, J. K., 1993, Dynamic Tire ForceControl by Semi-Active Suspension, ASME Transactions,Journal of Dynamic Systems, Measurement, and Control,Vol.[I21 onsson, M., 1991, Simulation of Dynamical Behavior o f aFront Wheel Suspension, Vehicle System Dyn amics, V01.20,

V01.24, pp.695-723.

pp.267-276.

pp.6 19-626.

V01.17, No.3, pp.45-59.

115, NO .3, pp. 465-474.

pp.269-28 1 .

987

Documents

Sohn_00_Semi-Active Control of the Macpherson Suspension System HIL