Mechatronic semi-active and active vehicle suspensions

Control Engineering Practice 12 (2004) 1353–1367

ARTICLE IN PRESS

*Correspondi

167412.

E-mail addre

[email protected]

0967-0661/$ - see

doi:10.1016/j.con

Mechatronic semi-active and active vehicle suspensions

Daniel Fischer*, Rolf Isermann

Institute of Automatic Control, Darmstadt University of Technology, Landgraf-Georg-Str. 4, D-64283 Darmstadt, Germany

Received 14 February 2003; accepted 25 August 2003

Abstract

After discussing various principles of suspensions with variable dampers and springs as well as active components, mathematical

models of these systems are derived. It is shown how the unknown parameters can be obtained experimentally through parameter

estimation by using body accelerometers, wheel accelerometers, and suspension deflection sensors in different combinations.

Experimental results are described for suspensions on a test rig and in cars driving over road surfaces. Through recursive parameter

estimation these parameters can be obtained on-line in real time. Then, feedback principles are derived for controlling the damping

ratio of dampers with proportional magnetic valve actuators. The mathematical models are then used for fault detection and

diagnosis of the damper by combining parameter estimation and parity equation methods.

r 2003 Elsevier Ltd. All rights reserved.

Keywords: Mechatronic; Semi-active suspension; Control; Parameter estimation; Fault detection

1. Introduction

The vehicle suspension system is responsible fordriving comfort and safety as the suspension carriesthe vehicle-body and transmits all forces between bodyand road (Reimpell & Stoll, 1989). In order to positivelyinfluence these properties, semi-active or/and activecomponents are introduced, which enable the suspen-sion system to adapt to various driving conditions. Byadding a variable damper and/or spring, drivingcomfort and safety are considerably improved comparedto suspension setups with fixed properties. This strategyrequires that the control behavior of these componentsis known and that laws on how to adapt the freeparameters depending on the driving excitations areknown. This also complies the identification and faultdetection of the involved components resulting in amechatronic design. These elements of a mechatronicsuspension design are presented in the following.

1.1. Vehicle suspension system

The vehicle suspension systems basically consist ofwishbones, the spring, and the shock absorber to

ng author. Tel.: +49-6151-167407; fax: +49-6151-

sses: [email protected] (D. Fischer),

u-darmstadt.de (R. Isermann).

front matter r 2003 Elsevier Ltd. All rights reserved.

engprac.2003.08.003

transmit and also filter all forces between body androad. The task of the spring is to carry the body-massand to isolate the body from road disturbances and thuscontributes to drive comfort. The damper contributes toboth driving safety and comfort. Its task is the dampingof body and wheel oscillations, where the avoidance ofwheel oscillations directly refers to drive safety, as anon-bouncing wheel is the condition for transferringroad-contact forces.Considering the vertical dynamics and taking into

account the vehicle’s symmetry, a suspension can in afirst step be reduced to the so-called quarter-car modelas shown in Fig. 1. Here, elements for modeling theCoulomb friction and an additional force DFu resultingfrom active or semi-active components are added. Thetire is typically modeled by a single spring.Now, the terms of driving safety and comfort are

defined. Driving safety is the result of a harmonioussuspension design in terms of wheel suspension, spring-ing, steering and braking, and is reflected in an optimaldynamic behavior of the vehicle, whereas driving comfort

results from keeping the physiological stress that thevehicle occupants are subjected to by vibrations, noise,and climatic conditions down to as low a level aspossible. It is a significant factor in reducing thepossibility of misactions in traffic (Bosch, 1996).Typically, the acceleration of the body .zB as an obviousquantity for the motion and vibration of the car body

ARTICLE IN PRESS

mw

mB

z w-z

Br-

z w

cw

cB

r

zw

zB

FB

Fz

dB

FC

�Fu

Fig. 1. One-dimensional vertical vehicle representation—the quarter-

car model.

Fig. 2. Frequency response magnitude for normalized body accelera-

tion and tire load for a passive suspension system.

dB

mB

cB

cW

0.08 0.1 0.14 0.160.12

0.12

0.08

0.09

0.1

0.11

0.13

0.14

normalized tire load variation Fz,dyn/Fz,stat [1]

norm

aliz

ed b

ody

acce

lera

tion

zB

/g [

1]

safety

com

fort

spring

stiffness

body mass

tire stiffness

damping

coefficient

..

Fig. 3. Influence of vehicle parameters, quarter-car simulations.

D. Fischer, R. Isermann / Control Engineering Practice 12 (2004) 1353–13671354

and the tire load variation as indicator for the roadcontact are used for determining quantitative values fordriving comfort and safety, respectively. Therefore, theeffective values of these normalized values are applied

.zB;rel;eff ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

T

Z T

t¼0

.zB

g

� �2

dt

s;

Fzdyn;rel;eff ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

T

Z T

t¼0

Fz;dyn

Fz;stat

� �2

dt

s: ð1:1Þ

The typical transfer-functions of the quarter-carmodel for the normalized body acceleration and tireload in respect to the road excitation are shown inFig. 2. In order to improve the ride quality, it isimportant to isolate the body, also called sprung mass,from the road disturbances and to decrease theresonance peak of the sprung mass near 1Hz, which isknown to be a sensitive frequency to the human body. Inorder to improve the ride stability, it is important tokeep the tire in contact with the road surface andtherefore to decrease the resonance peak near 10Hz,which is the resonance frequency of the wheel also calledunsprung mass.For a given suspension spring, the better isolation of

the sprung mass from road disturbances can be achievedwith a soft damping by allowing a larger suspensiondeflection. However, better road contact can be achievedwith a hard damping preventing unnecessary suspensiondeflections. Therefore, the ride quality and the drivestability are two conflicting criteria. Fig. 3 illustrates thisconflict, showing the variation of drive safety andcomfort with the changing vehicle parameters bodymass, stiffness and damping in the ‘‘conflict diagram’’.The conflict diagram presents the vehicles proper-

ties—driving comfort and safety—for a defined man-

euver as a point in the .zB-Fzdyn-diagram. Varying setupslead to curves, which elucidate the respective tendencies.As it can be seen from Fig. 3, the fixed setting of a

passive suspension system is always a compromisebetween comfort and safety for any given input set ofroad conditions and a specific stress. Semi-active/activesuspension systems try to solve or at least reduce thisconflict. In this regard, the mechanism of semi-active

suspension systems is the adaptation of the dampingand/or the stiffness of the spring to the actual demands.Active suspension systems in contrast provide an extraforce input in addition to possible existing passivesystems and therefore need much more energy.The illustration of Fig. 3 also clarifies the dependency

of a vehicle suspension setup on parameter changes as aresult of temperature, deflection, and wear and tear.These changes must be taken into account whendesigning a controller for an active or semi-active

ARTICLE IN PRESSD. Fischer, R. Isermann / Control Engineering Practice 12 (2004) 1353–1367 1355

suspension to avoid unnecessary performance loss. Inorder to prevent this, a robust or an adaptive controllerhas to be implemented. The latter results in a parameter-

adaptive suspension system that refers to a ‘controlsystem, which adapts its behavior to the changingsettings of the system to be controlled and its signals’(Isermann, 1992).

2. Semi-active and active suspension systems

Suspension systems are classified in the well-knownterms of passive, semi-active, active and various in-between systems. Typical features are the requiredenergy and the characteristic frequency of the actuatoras visualized by Fig. 4 according to Streiter (1996) andare summarized in Table 1.These representations point up the conflict that

automotive manufacturers face in their endeavor toimprove drive safety and comfort as high performingsuspension systems can only be achieved by high-energydemand and mostly expansive and complex actuationsystems. Actual solutions to this conflict are presented inthe following as basis for the subsequent design of amechatronic vehicle suspension.

2.1. Conventional semi-active dampers

The common function of conventional semi-activeshock absorbers is the variation of a bypass’ cross-sectional area that connects the two chambers of thedamper’s piston obtaining multiple performance curvesfrom a single shock absorber. Here, either variousthrottles or throttle systems are switched on or off or acontinuous valve controls the liquid resistance resultingin fixed step or continuous characteristics, respectively.

active

f [Hz]0.1 1 3 30passive

semi-active

slow

ly v

aria

ble

/ ada

ptiv

e

manipulation frequency

exte

rnal

ene

rgy

Fig. 4. Comparison between passive, adaptive, semi-active and active

systems.

The active throttle can either be integrated in thedamper or in an external bypass, which often isconstructed in the form of a ring channel. The throttle’sadjustment is achieved using an electric motor or bymeans of magnet valves. The latter provides highswitching times and a continuous adjustment (Reimpell& Stoll, 1996). In the past, a lot of innovativeapproaches has been developed to improve the func-tionality of the passive damper system such as manuallyadjustable dampers, load leveling by the self-pumpingdamper Hydromats and further concepts to positivelyinfluence the damper characteristics. For instance, astate of the art variable damper system is the Contin-uous-Damper-Control (CDC) system from Sachs (Cau-semann, 1999). This system consists of a proportionaldamping valve resulting in a continuous variabledamper adjustment and high switching times between11 and 40ms depending on the piston’s direction andvelocity and also on the direction of the damping ratiochanges (soft to stiff, stiff to soft).

2.2. Electro-rheological and magneto-rheological

dampers

In the last few years a new development has arisen inthe form of dampers taking advantage of the electro-rheological or magneto-rheological property of liquids.Both principles are based on the alteration of thedamping medium’s viscosity depending on an appliedelectric or magnetic field. Commonly, these fields areapplied in the duct connecting the upper and lowerchambers of a damper. One of the salient properties ofelectro-rheological fluid is that it has a fast response toan electric field and hence a wide control bandwidth(Choi, Lee, & Chang, 2001). Especially magneto-rheological shock absorbers have many attractivefeatures such as high yield strength and stable hystericbehavior over a broad temperature range (Yokoyama,Hedrick, & Toyama, 2001). In order to achieve thedamping forces required for a semi-active vehiclesuspensions a high electric field about 5 kV/mm andhigh voltages up to 6 kV (Kim & Choi, 2000) have to beapplied for electro-rheological shock absorbers. Formagneto-rheological shock absorbers a magnetic fieldabout 250 kA/m with a power supply of 2–25V and1–2A (Carlson & Jolly, 2000) is required. Obviously,these requirements and the long-term stability of thefluid properties are obstacles to the application incommon vehicle systems.Despite these unfavorable conditions for automotive

applications, a magneto-rheologic damper system is inserious production with the Magnetic Ride ControlSystem in the 2002 Cadillac Seville STS (Gilbert &Jackson, 2002). Here the fluid can react within 1msresulting in a 5 time faster reaction than previoussystems.

ARTIC

LEIN

PRES

S

Table 1

Classification of suspension systems. Natural frequencies: fB body and fW wheel

System System representation Force range Operation range Actuator/sensor demand Max. energy demand Improvements compared to passive system

Comfort Safety

Passive

∆z∆z

F

.

— — — — —

Slowly variable/adaptive

∆z∆z

F

.

ofB 4–8/X1 ca. 50W 15–20% 10–25%

Semi-active

∆z∆z

F

.

fB � fW 4–8/X8 ca. 50W 20–30% 10–25%

Active partially loaded

∆z∆z

F

.

0�fB 4–8/X12 1–2 kW > 30% —

Active fully loaded

∆z∆z

F

.

0�fW 4/X12 1.5–7 kW > 30% 25%

D.

Fisch

er,R

.Iserm

an

n/

Co

ntro

lE

ng

ineerin

gP

ractice

12

(2

00

4)

13

53

–1

36

71356


2.3. Semi-active spring systems

The common concept of semi-active springs is basedon a system containing an air spring or hydro pneumaticsystem. The stiffness of an air spring can by approxi-mated according to Isermann (2003) by the followingequation:

c ¼ npA2

V: ð2:1Þ

As a result, the pneumatic systems are based on thealteration of the air volume V by adding or removing airand this results in a change of the stiffness. This leads toa continuously adjustable stiffness. Unfortunately, thisprocedure leads directly to a change in initial deflection.In order to prevent a varying initial deflection hydropneumatic systems can be implemented, which replacesthe removed air with hydraulic liquid.Switchable air volumes are another possibility. These

attempt to alter the total volume of air and thereby thestiffness without significant change in the mean deflec-tion. Cutting off or opening the pneumatic connectionbetween two volumes realizes two different stiffnessvalues (e.g. Electronic Air Suspension by Continetal-Teves, Sommer, 2003).

2.4. Active suspension systems

A variety of research projects and publications dealwith different types of active suspension systems.Typically discussed actuation systems are hydraulic(e.g. Williams, 1997), hydro pneumatic (e.g. Moreau,Noullant, & Oustaloup, 2001), and pneumatic systems.Also electro-mechanical systems are under research(Buckner, Schuetze, & Beno, 2000). Most of thesesystems also comprise passive elements such as conven-tional springs and dampers or hydro-pneumatic damp-ing and springing components involved in the actuationsystem. Due to the complexity, costs and energy demandof these systems, only few systems got to market.For example, the Active Body System of Mercedes

consists of a hydraulic piston in series with theconventional steel spring (Merker, Wirtz, Hiller, &Jeglitzka, 2001). This concept primarily aims at reducinglow frequent body motions ðfo2 HzÞ due to rolling,pitching, and stroking and also at reducing higherfrequent road excitations ðfo6 HzÞ:Another active suspension system in series production

is the Dynamic Drive system by BMW (Jurr et al.,2001). Here, a hydraulic rotation actuator is inserted inthe anti-roll-bar to reduce roll motions. Consequently,this actuation concept is not able to influence pitch andstroke movements of the body and reduce roadexcitations. However, this system is combined with asemi-active damper system to compensate for thesedisturbances within the bounds of semi-active systems.

Such concepts with an active roll bar combined withsemi-active damping are a promising trade-off betweencomplexity, costs and energy demand. The high,frequent road disturbances are handled by the fast andenergy uncritical semi-active damper system and the rollmotion, which cannot be inhibited by semi-activeconcepts, is reduced by the active anti-roll-bar. Due tothis application reduced demands result for the actua-tion system concerning its dynamics.

3. Dynamic models of a quarter car

Physical models for the investigation of verticaldynamics of suspension systems are most commonlybuilt on the quarter-car model. Greater accuracy isachieved by extensions to a half (e.g. Krtolica & Hrovat,1990) or full car model (e.g. Weispfenning, 1996). Thisaims to describe correctly the roll and pitch motion ofthe car and the connected inertia forces. The stabilizersalso can be involved in the modeling. In addition, thelever arm of the wishbones and the related forces can beconsidered (Streiter, 1996).In the following a quarter-car model is applied

according to Fig. 1. The sprung and unsprung massdisplacements are zB and zW ; respectively. The dampergenerates the force FD and the spring generates the forceFS: The dynamic tire load is Fzdyn: Fc describes thefriction of the damper and DFU the additional force ofthe active or semi-active components. Body mass mB;tire stiffness cW and damping coefficient dB arecommonly not constant. Apart from semi-activechanges of spring and damper, the wheel mass mW

and the body spring coefficient cB can be considered tobe constant. Using the road displacement r and the forceFB; which describes the body weight and the forcesresulting from driving maneuvers, as inputs and usingthe body acceleration .zB; the tire acceleration .zW and thesuspension deflection ðzW � zBÞ as outputs, the classicalquarter-car model can be derived

mB .zB ¼ cBðzW � zBÞ þ FD � FB þ DFu; ð3:1Þ

mW .zW ¼ cW ðr � zW Þ � cBðzW � zBÞ � FD � DFu: ð3:2Þ

The characteristic operating curve of steel springs showa smooth progressive relationship. However, theyusually are approximated by a linear curve in theiroperating point. Also, the tire is generally assumed tobehave as a linear spring. Whereas in the following, thestrongly degressive course of the damper’s characteristicis divided into a constant, a linear and a non-linearsquare component. Kraus and Dantele (1970) explainsthis fact by a complex hydraulic analysis of a damper:The non-linearity results from the opening of the pistonvalve and the stiffness of its spring. The dampercharacteristic can be approximated using linear and

ARTICLE IN PRESSD. Fischer, R. Isermann / Control Engineering Practice 12 (2004) 1353–13671358

non-linear damping parameters dl and dnl and aconstant force F0: These parameters reflect the con-structive parameters of the damper

FD ¼ dBlð’zW � ’zBÞ þ F0 signð’zW � ’zBÞ þ?

þ dBnl ’zW þ ’zBj j2=ð1þ2nÞ signð’zW � ’zBÞ: ð3:3Þ

The constant n is usually set to n ¼ 1; 5 (e.g. Majjad,1997). Another representation of FD is a piecewiselinearization of the curve into the segments i:

FDi ¼ dBið’zW � ’zBÞ þ Fgli; ð3:4Þ

where Fgli is a parameter needed for the bumplesssegmentation of the function.Another method of handling the non-linear charac-

teristic of the damper is the application of neuronalnetworks. For more details see, e.g. Halfmann (2001).However, this procedure does not comprise physicalparameters.

4. Identification of a quarter-car model

The identification of mechanical systems is a widelyinvestigated field (Isermann, 1992). Meanwhile standardalgorithms and tools have been developed (e.g. Moseler,2001). In this paper the identification is used for thedevelopment of adaptive controllers, but it can also be abasis for fault detection and diagnosis (e.g. H .ofling,1996) as shown in Section 6. Applying these concepts tosuspension systems, the most important parameters arethe damping, body mass and the tire pressure or ratherstiffness. Weispfenning (1997) or BuXhardt (1995) usesignal analysis for the estimation of tire pressure. Thedamper can be identified using linear or non-linearmodels (Majjad, 1997; BuXhardt, 1995). The body massis often identified as being detached from suspensionsystems on the basis of the horizontal dynamics (e.g.DaiX, 1996; Holzmann, 2001) but can also be included inquarter-car identifications.

Table 2

Comparison of the various estimation equations for the quarter-car parame

Eqn. Measurable sensor signals Known parameters Parameter estim

(4.1) zW � zB; .zB cB dB, mB, Fgl

(4.2) zW � zB; .zW ; r � zW mW dB, cB, cW, Fgl

(4.3) zW � zB; r � zW cB, mW dB, mB, cW, Fg

(4.4) zW � zB; .zW cB dB, mB, Fgl

(4.5) (4.6) FF=FD; .zW — dB, mB, cB, Fgl

Because only very few measured variables will beavailable in suspensions, it is not possible to estimate allsix parameters of the quarter-car model. Hence, someparameters must be set as known fixed values. Throughsimple conversion of Eqs. (3.1) and (3.2), variousestimation equations and sensor setups can be found.The resulting arrangements for the different estimationequations are given below, see also Table 2

ðzW � zBÞ ¼ �dB

cB

ð’zW � ’zBÞ þmB

cB.zB �

1

cB

Fgl ; ð4:1Þ


cB

ð’zW � ’zBÞ �mW

cB.zW þ?

þcW

cB

ðr � zW Þ �1

cB

Fgl ; ð4:2Þ


cB

ð’zW � ’zBÞ �mW mB

cBðmW þ mBÞFgl þ?

�mW mB

cBðmW þ mBÞð.zW � .zBÞ þ?

þcW mB

cBðmW þ mBÞðr � zW Þ; ð4:3Þ


cB

ð’zW � ’zBÞ �mB

cB

ð.zW � .zBÞ þ?

þmB

cB.zW �

1

cB

Fgl ; ð4:4Þ

FS ¼ �dB

cB

’FS �mB

cB

ð.zW � .zBÞ þ mB .zW � Fgl ; ð4:5Þ

FD ¼ �dB

cB

’FD �mB

cB

.FD þmBdB

cB.zW � Fgl : ð4:6Þ

Practically, only the body acceleration and the deflectionare measured (Sommer, 2003). However, measuringinstruments for the road/wheel distance are meanwhilediscussed (e.g. Nomura & Takeshita, 1993) andmeasurement of wheel acceleration is expected to beused in the future. Therefore, (4.1) and eventually (4.4)are suitable for the identification, in particular as thevalues of the tire mass and the spring stiffness can be

ters

ation Properties

+ easy measurable quantities

+ cB is practically constant

+ cW is estimated

� road deflection is hardly measurable

l + cB and mW are practically constant

+ cW is estimatable

� road deflection is hardly measurable

+ easy measurable quantities

+ cB is practically constant

+ no a priori information is necessary

+ all parameters are measurable

� FS, FD are generally not measurable, except for air springs


assumed to be constant. In addition, the variable bodymass can be estimated using the static spring deflection.A reliable estimation requires an adequate excitation

of the system. So, the different results and requirementsfor the individual estimation equations suggest thecombination of these procedures controlled by an‘excitation-indicator’, in order to achieve a higher levelof performance and ensure a robust parameter estima-tion. Possible criteria for the various estimations are thevehicle velocity and the standard deviation of .zB; .zW andzW � zB: Also the eigenvalues of the estimation algo-rithms provide convincing information for the actualquality of estimation. (Kofahl, 1988; Knapp, 1993). Thebasic mechanism of the implemented indicator isillustrated by Fig. 5.In order to compensate for non-linearity of damper

characteristics, a piecewise estimation of the damperforce is assumed. This division is dependent on theactual values of ð’zW � ’zBÞ and results in a structure-variable system as shown in Fig. 6.For the valid range for each single model, a complete

set of parameters can be identified. This results inmultiple estimations for cB and mB; as these parameters

Fig. 5. Example for an excitation-indicator for the control of

parameter-estimation algorithms.

Fig. 6. Arrangement for the identification in sections.

are not dependent on the deflection velocity. Onepossibility of handling this fact is the calculation ofthe mean of these values in order to produce anunambiguous parameter set. Another possibility is toadmit only one value for each parameter, which is usedfor all identification models. The latter option enablesthe easy application of data-recursive algorithms such asRLS or DSFI.This concept is presented for the piecewise linearized

damper characteristic curve with N pieces. The estima-tion equation for each model arises in analogy to (4.1)and (3.4) to

ðzW � zBÞ ¼ �dBi

cB

ð’zW � ’zBÞ þ?

þmB

cB.zB �

1

cB

Fgli for i ¼ 1yN: ð4:7Þ

Or in a general form to

yðtÞ ¼ �a1i ’yðtÞ þ b0uðtÞ þ cgli for i ¼ 1yN

with yðtÞ ¼ zW ðtÞ � zBðtÞ and uðtÞ ¼ .zBðtÞ: ð4:8Þ

A possibility to bring these different equations into thesingle standard form

yðtÞ ¼ wTðtÞh ð4:9Þ

is to insert all coefficients a1i and cgli in one parametervector h.

hT ¼ ½a11 y a1N b0 cgl1 y cglN �: ð4:10Þ

This ends up in an enlarged data vector w, whichcontains the control task for the different validity rangesfor the models. The coefficients, which are actuallyactive, receive the correct input signals, while the inputsof the currently inactive coefficients are weighted withzero. In the case of an active model i the followingscenario arises:

wTðtÞ ¼ ½0 y 0 � ’yðtÞ 0 y 0 ’zW ðtÞ � ’zBðtÞ

0 y 0 1 0 y 0�: ð4:11Þ

Thus, the DSFI or RLS algorithm is directly applicable.The large number of coefficients ð2N þ 1Þ is reducedconsidering a bumpless segmentation. Decreasing thenumber of the DC-component cgli to two representingthe offsets of the damping force in the origin ofcoordinates results in N þ 3 coefficients.Finally, the application of this procedure to a six-part

characteristic curve based on (4.1) results in thefollowing scheme:

ð’zW ðtÞ � ’zBðtÞÞ ¼ wTðtÞh; ð4:12Þ

hT ¼1

cB

½dB1 y dB6 Fgl1 Fgl2 mB�; ð4:13Þ

ARTICLE IN PRESS

wTðtÞ ¼

� ’D 0 0 0 0 0 �1 0 .zB 0p ’Dpv13

�v13 0 �ð ’D� v13Þ 0 0 0 �1 0 .zB v13p ’Dpv35

�v13 0 �ðv35 � v13Þ 0 �ð ’D� v35Þ 0 �1 0 .zB’D > v35

0 � ’D 0 0 0 0 0 �1 .zB v24 > ’D > 0

0 �v24 0 �ð ’D� v24Þ 0 0 0 �1 .zB v46 > ’D > v24

0 �v24 0 �ðv46 � v24Þ 0 �ð ’D� v46Þ 0 �1 .zB’Dpv24

8>>>>>>>>>><>>>>>>>>>>:

with ’D ¼ ’zW ðtÞ � ’zBðtÞ: ð4:14Þ

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-800

-600

-400

-200

0

200

400

600

800

1000

1200

(zW – zB)· [m/s]

d B [

Ns/

m]

referencepiecewise linearnonlinear

Fgl

v13

v35

piecewiselinear

nonlinear

Fig. 7. Identification of the damper’s characteristic curve with

piecewise linear and non-linear models, quarter-car simulation,

PRBS-excitation, DSFI with l ¼ 0:99:

Fig. 8. Quarter-car test rig.


Alternatively, the identification can be based on thenon-linear equation (3.3):

FD ¼ dBlð’zW � ’zBÞ þ?

þ dBnl

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi’zW � ’zBj j

psignð’zW � ’zBÞ þ?

þ F0 signð’zW � ’zBÞ: ð4:15Þ

Accordingly, only the differentiation between compres-sion and decompression motion is required. Thecorresponding procedure to the six-part characteristiccurve results in the equivalent scheme below:

’zW ðtÞ � ’zBðtÞð Þ ¼ wTðtÞh; ð4:16Þ

hT ¼1

cB

½dBl1 dBnl1 dBl2 dBnl2 Fgl1 Fgl2 mB�; ð4:17Þ

wTðtÞ ¼� ’D �

ffiffiffiffi’D

p0 0 �1 0 .zB for ’DX0;

0 0 � ’D þffiffiffiffi’D

p0 �1 .zB for ’Do0

8<:

with ’D ¼ ’zW ðtÞ � ’zBðtÞ: ð4:18Þ

For the visualization of these approaches, Fig. 7 showsthe results for the identification of the damper’scharacteristic curve with the DSFI algorithm with l ¼0:99 for PRBS-road excitation. The simulation is basedon a quarter-car model. The Coulomb friction is Fgl1 ¼þ100 Ns=m and Fgl2 ¼ �50 Ns=m: The identification isexecuted using the non-linear square function and a six-segment linear curve both considering the Coulombfriction. Both formulations approximate the real char-acteristic curve well.The identification methods were applied to a test rig,

shown in Fig. 8, which is equipped with a continuouslyadjustable damper. The damping is controlled by amagnetic valve, which opens or closes a bypasscontinuously. The test rig was constructed primarilyfor investigations on semi-active, parameter-adaptivesuspension control (BuXhardt, 1995).Fig. 9 shows the estimated damping curve for

different damper magnetic valve currents. Because risingdamper current opens the bypass the damping sinks.The damping curve was divided into four sections, twofor each direction of motion. It can be seen that thedamping curves at different damper currents can be

clearly distinguished. Application of parameter estima-tion with the non-linear equations led to approximatelythe same results.

ARTICLE IN PRESS

(zW – zB)· [m/s]

d B [

Ns/

m]

-1 -0.5 0 0.5 1

3000

2000

1000

0

-2000

-1000

0.40.6

0.81.01.2

Damper current [A] 0.2

Fig. 9. Estimated damping characteristics.

D. Fischer, R. Isermann / Control Engineering Practice 12 (2004) 1353–1367 1361

5. Suspension control

The objective of a control design for a vehicle’ssuspension is the maximization of drive safety and

driving comfort. Fundamental research (Mitschke,1994; Darenberg, Gall, & Acker, 1984) shows that onthe one hand a complete zero-regulation of the dynamictire load, or on the other hand a complete zero-regulation of the body acceleration, is only attainableusing an optimal force generator ðcB ¼ dB ¼ 0Þ: How-ever, both are not feasible simultaneously. A completeuncoupling of the body from the road disturbanceswould lead to a wheel springing on the road. Corre-spondingly, the complete minimization of the dynamictire loads would result in an unacceptable loss ofcomfort. Thus a compromise of these properties has tobe found.Suspension feedback control has been investigated

extensively in the last decade for active and semi-activesuspension concepts. At this, active control concepts canalso be partly transferred to semi-active systems leadingto a suboptimal solution compared to the active system(Butsuen, 1989). There exists various control conceptslike the linear-quadratic (LQ) state-vector feedback (e.g.Ursu, Ursu, & Vladimirescu, 1997) or the minimal-variance (MV) principle (BuXhardt, 1995). Non-linearrobust control techniques such as sliding mode controlare also applied (Alleyne & Hedrick, 1995), mostly as aconsequence of non-linear actuators. In regard tovarying parameters and conditions for suspensionsystems many robust controller approaches are devel-oped such as HN controllers, which are increasinglyapplied to this problem (Wang, Wilson, & Halikias,2001). Most controller designs require a linear system.In consequence, the non-linearity of the damper orspring can be compensated, e.g. using the principle of‘feedback linearization’ (Slotine, 1991) or can becomprised by a then non-linear controller design.Finally, all control concepts aim at introducing

additional forces to the suspension system to reduceroll, pitch, and stroke movements, as well as body and

wheel vibrations. So, the basic control approach issimilar for all actuation systems. Then, the physicalstructure of the considered system determines thefurther controller design and also directly limits theachievable system’s performance according to Table 1.According to this, many publications design a separatelydecoupled controller for the vehicle dynamics consider-ing a general force generator with a specific dynamicsand a separate inner actuator controller to control thedesired forces (e.g. Lakehl-Ayat, Dip, & Fenaux, 2002).In principle, each controller is hardly dependent on

the available sensor signals, which are typically thesuspension displacement and the body acceleration foreach suspension system (Sommer, 2003). The mainobjective in general is to find the optimal feedback rulesfor this sensor configuration in the face of an optimalactuator control. In the following a basic mechatroniccontrol algorithm for a semi-active suspension system isdeveloped.

5.1. Control concept

The presented control concept starts with the activeforce DFu between body and wheel, which can beintroduced by a semi-active or active system. Accordingto Eqs. (3.1) and (3.2) the following quarter-car model isassumed for the ensuing controller design considering alinearized damper and spring

mB .zB ¼ cBðzW � zBÞ þ dBð’zW � ’zBÞ þ DFu � FB; ð5:1Þ

mW .zW ¼ cW ðr � zW Þ � cBðzW � zBÞ þ?

� dBð’zW � ’zBÞ � DFu: ð5:2Þ

Eqs. (5.1) and (5.2) directly enable the transformation toa state-space representation. As input quantities themeasurable body wheel deflection zW � zB and itsderivative ’zW � ’zB estimated by numerical differentia-tion or using a State Variable Filter are suitable. Also,the absolute values of the body and wheel position zB

and r are also suitable. These quantities can be estimatedusing a Kalman filter (e.g. Karlson, Dableh, & Hrovat,2001). The body acceleration and the dynamic tire loadsare chosen as outputs to describe the drive safety anddriving quality. Starting from this a general LQ, HN;LMI, etc. approach results in a feedback law for theforce DFu which is controlled by separate controller asexplained in the following.Especially considering variable dampers and springs,

two different control concepts can be applied (Sommer,2003). For a more comfortable ride, softer shockabsorber characteristics than with conventional chassisare controlled. Where improved handling is required,the shock absorber characteristic is set to the situationby operating a solenoid valve, referring to a hard set up.These setups are distinguished and controlled on the

ARTICLE IN PRESS

FSpring

F

zW - zB

. .zW - zB

zW - zB

zW - zB

. .FDamper

Active Systems

+

Fig. 10. Force ranges of variable spring, damper and the combination

of both, comparison to active systems.


basis of the speed yawing moment and steering wheelangle as well as longitudinal and lateral acceleration.The second means of modulating the damping force isby using ‘‘Skyhook mode’’, which can be applied also toactive suspension systems (e.g. Lakehal-Ayat et al.,2002). Designed to modulate the body movementsdetected by the vertical acceleration sensors, Skyhookmode is based on the notion of an additional virtualshock absorber, attached to an imaginary point in thesky, in order to maintain the position of the body asconstant as possible. The Skyhook concept draws on thecinematic energy of the axles to absorb vertical bodymovement by modulating the damping force in thedirection required. While the damper controller onlyworks with the stated dynamic values, the variablespring control processes information on the staticcondition of the vehicle (weight, weight distribution)due to the slow dynamics of spring systems.

5.2. Spring and damper as semi-active force generators

In case of semi-active systems, the force DFu has to begenerated by the adjustment of the suspension para-meters. For the linearized system the following expres-sions can be determined by splitting the parameters cB

and dB in a constant (cB0 and dB0) and semi-active part:

cBðkÞ ¼FSðkÞ

zW ðkÞ � zBðkÞ¼ cB0 þ

DFSuðkÞzW ðkÞ � zBðkÞ

; ð5:3Þ

dBðkÞ ¼FDðkÞ

’zW ðkÞ � ’zBðkÞð Þ¼ dB0 þ

DFDuðkÞ’zW ðkÞ � ’zBðkÞð Þ

: ð5:4Þ

Now, the force DFu consists of the additive parts DFSu

and DFDu for the spring and damper, respectively. Onepossibility for this division bases on the physical natureof the semi-active elements: Deflection-dependent forcecomponents are assigned to the spring and velocitydependent components to the damper. This fact isillustrated in Fig. 10.The missing spaces represent the gap to active

systems, as active systems can produce forces for thesesituations, too. Another possibility for the division ofthe activating force to damper and spring is thedifferentiation between sprung and unsprung massforces. Independent of the control scheme, the highfrequent motion of the unsprung mass results in highfrequent manipulating forces, while the low frequentbody motion results in low frequent manipulatingforces. As real semi-active dampers provide higherswitching times than semi-active springs, the unsprungmass forces are assigned to the damper and the sprungmass forces, to the spring.For the control point of view Eqs. (5.3) and (5.4) are

problematically, as the suspension displacement and itsderivatives are in the denumerator. To compensate fordivisions by zero, these conversions can be preset in a

characteristic map or extended with an approach, wherethese cases are intercepted with holding the actualdamping or spring value.Experiments on the test rig showed the immense

dependency of the damper’s time constant, the remain-ing time delay of the low-pass filter and the micro-processor’s dead-time for the achievable performance ofa semi-active suspension system. Therefore, simulationswith various time constants and filter cut-off frequenciesare carried out with a minimal variance (MV) feedbackcontroller and a variable damper in case of roadexcitation. The curve progressions of the controlledcases result from different controller setups dependingon the weighting factors of the MV controller. AsFig. 11(a) shows, a larger sum time constant TS

generally deteriorates the performance. For example,the available reductions of the mean body accelerationwith TS ¼ 30; 20; 10; 0 ms are 11%, 14%, 20%, 32%.According to these results, the sum time constant TS

should be less than 10ms. Nowadays the time constantis of the order of 40ms. Here, electro-rheological ormagneto-rheological dampers can tap the full potentialof semi-active suspension systems.Another limiting aspect for the performance of a

semi-active damper is the regulation range. The pre-sented simulations are based on a damper with100 Ns=modBo2000 Ns=m: While smaller dampingrates are not achievable, higher damping rates arepossible with an adequate damper design. In order toinvestigate the extension of the regulation range adamping of 100Ns/modBo5000Ns/m is assumed. Theresults obtained are shown in Fig. 11(b).The extension of the regulation range leads to a

significant increase in performance. While the smallregulation range reduces body acceleration and tire loadvariation by about 25% and 10%, the large regulationrange achieves a reduction of about 35% and 17%,respectively. This clearly shows the potential of anextension of the dampers regulation range.

ARTICLE IN PRESS

1234

1: T = 0 2: T = 0 3: T = 0 4: T = 0

0

0.02

0.04

0.06

0.08

0.10

0.12

dBmin

100Ns/m < dB < 2000Ns/m

100Ns/m < dB < 5000Ns/m

normalized tire load variation Fz,dyn/Fz,stat [1]

..no

rmal

ized

bod

y ac

cele

rati

on z

B/g

[1]

d Bmaxd Bmax

com

fort

safetysafety

com

fort

0.090

0.085

0.080

0.075

0.070

0.065

0.060

0.055

0.0500.06 0.07 0.08 0.09 0.05 0.1 0.15

(a) (b)

Fig. 11. (a) Comparison between different sum time constants, simulation and variable damper with relative MV state feedback and (b) comparison

between passive and semi-active damper with various regulation ranges, simulations and relative state-vector feedback.

vehicle

systemexcitation

r, FB

verticalmovement

controller

parameterestimation

computationof

coefficients

u

performanceindex I x

processsignals

cB, cw, dB, mB, FCˆˆˆˆˆ

feed

back

leve

l "fa

st"

adap

tatio

nle

vel "

slow

"

vehicle

(a)

(b)

systemexcitation

r, FB

verticalmovement

ZB, ZB, Zw, Zw

controller

parameterestimation

computationof

coefficients

u

performanceindex I

processsignals

ai, biˆˆ

ai, biˆˆ

cB, cw, dB, mB, FCˆˆˆˆˆ

adap

tatio

n an

d co

ntro

lle

vel "

slow

"

computationof desireddamping

x

performanceindex I

_

dB,refˆ

dB,actˆ

..

ZB, ZB, Zw, Zw

..

Fig. 12. (a) Feedback of estimated parameters (parameter feedback)

and (b) adaptive suspension feedback control (state feedback).


5.3. Parameter adaptive suspension system

Mechatronic concepts often comply adaptive con-cepts on tribute with changing parameters due to wear,fading, temperature influences, etc. For suspensionsystems two different control approaches are proposed,as demonstrated in Fig. 12. Firstly, the suspension

feedback control is characterized by the feedback ofprocess signals using, for example, a state vectorcontroller. This aims at controlling the states of thevehicle such as body and wheel acceleration to specificvalues. This ‘‘fast’’ feedback level is extended by a‘‘slow’’ adaptation level, in order to adapt the controllerto the actual system parameters. This enables an optimalcontrol performance despite altering parameters. Sec-ondly, the feedback of estimated parameters via aparameter controller intends to maintain the suspen-sion’s parameters to specific values, in order tocompensate fading effects of the damper or to adjustdifferent set points, so that a certain performance of thesuspension system is controlled.

5.4. Suspension feedback control results

Applying a minimal variance approach to the statespace system (Eqs. (5.1) and (5.2)) with zWB and ’zWB asrelative states, a quadratic performance criterion includ-ing zWB; ’zWB; .zB;Fz;dyn led to the results presented inTable 3. The percent quantities refer to the referencepoint of the underlying passive suspension and a specificexcitation. The application of an ideal variable damperand spring results in a reduction of the mean bodyacceleration up to about 46%. This is nearly the samedimension as an active suspension system (60%). The

ARTICLE IN PRESS

Table 4

Influence of faults on the parameter estimates: +: increase;� decrease;

0: no influence

Fault cB dB,dec dB,com Fgl,dec Fgl,com

Process faults + Friction 0 0 0 + �+ Damping 0 + + 0 0

+ Spring stiffness + 0 0 0 0

Sensor faults + Offset z00B 0 0 0 + +

+ Offset zWB 0 0 0 � �+ Gain z00B + + + + +

+ Gain zWB � � � 0 0

Table 3

Comparison of active/semi-active suspension systems compared to a

standard passive system, simulations

Road excitation

(%)

Body excitation

(%)

Variable damper 23 20

Variable spring 30 12

Variable spring and damper 46 22

Active 60 55


sole application of a variable damper provides only areduction of up to 23% for the mean body acceleration.This elucidates the effect of the combination of avariable damper and a variable spring.In case of body acceleration a reduction of nearly

20% is achievable. This smaller result compared to theroad excitation is explained by the restricted operationrange of the semi-active elements.Applying this control scheme to the test rig causes a

reduction of the body acceleration, of about approxi-mately 10%. This smaller value compared to thesimulations is explainable by the information loss onaccount of low-pass filtering and the time constants ofthe real setting elements.

6. Fault diagnosis

6.1. Fault diagnosis with parameter estimation (test rig)

As many faults influence the parameter estimation,different faults can be distinguished (i.e. Ball!e &Isermann, 1997; Leonhardt, BuXhardt, Rajamani,Hedrick, & Isermann, 1993; Weispfenning, 1996).Table 4 gives an overview. In the first left column thechanges in the process or sensor variables are given. In theother columns, the influence on the estimated variables isshown. Table 4 reveals that there is a different pattern ofparameter estimates for nearly every fault. Only offsetfaults in the sensors cannot be distinguished.

6.2. Sensor fault detection with parity equations

(test rig)

Parity equations do not need permanent excitationand require less computational effort than parameterestimation, but do not give the same deep insight intothe process as parameter estimation. To combine theadvantages of parameter estimation and parity equa-tions it is proposed to supervise the process on-line withparity equations and to perform parameter estimationafter a fault is detected (Weispfenning, 1996). In thefollowing, an example of the use of parity equations fordetection of sensor faults is described.

With the abbreviation

DzWB ¼ ½zW � zB� ð6:1Þ

the z-domain transfer function of equations (4.1) can becalculated

GBðzÞ ¼DzWBðzÞ.zBðzÞ

¼b1z

�1

1þ a1z�1ð6:2Þ

which leads to the residual equation

rðkÞ ¼ DzWBðkÞ � b1 .zBðk � 1Þ þ a1DzWBðk � 1Þ: ð6:3Þ

Parameters a1 and b1 can be calculated applying the z-transform to Eqs. (3.1), (3.2) and (3.4) or using discrete-time parameter estimation in a fault-free process state.Fig. 13a shows the result with an offset of 0.1V (which isequal to approx. 3% of the maximum value) added tothe output of the acceleration sensor at the time t¼ 5 s:Fig. 13b gives the result with a sensor gain fault of 20%starting at t¼ 5 s: In both cases, the residuals are dividedby their thresholds. It is clearly visible that the offsetfault violates the threshold immediately. However, itcannot be distinguished which sensor, zW � zB or .zB;leads to threshold violation. A sensor gain faultobviously only affects the variance of the residual.Hence, the results show that in both cases a detection ofthe sensor fault is possible in principle, if the parametersof the process remain constant.

6.3. Fault detection in a driving car

To test various methods in a driving car, a mediumclass car, an Opel Omega, Fig. 14, was equipped withsensors to measure the vertical accelerations of bodyand wheel, as well as the suspension deflections. Torealize different damping coefficients the car is equippedwith an adjustable shock absorber, which can be variedin three steps. In Fig. 15 the course of the estimateddamping coefficients at different damper settings is givenfor driving over boards of height 2 cm, Fig. 14.After approximately 2.5 s the estimated values con-

verge to their final values. The estimated damping

ARTICLE IN PRESS

Time [s]

est.

dam

ping

coe

f. [N

s/m

] stiff

medium

soft

5000

4000

3000

2000

1000

0

-10000 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Fig. 15. Estimated damping coefficients for different damper settings

(speed about 30 km/h).

Fig. 14. Driving experiment for model validation and parameter

estimation.

..measured signals ZB, ZWB

cB

dB

mB

Fgl

Identi-fication

Kalman

Filter

VehicleModel

Parity

Equations

active/semi-activeforce �FU

FaultDetection

Fault

Indicator

ZB

ZB

ZB

ZWZWB

ZW

.. .

.

Fig. 16. Mechatronic vehicle suspension concept.

Fig. 13. Parity equation residual r(t) for: (a) acceleration sensor offset 0.1V at 5 s and (b) acceleration sensor gain offset of 20% at 5 s.


coefficients differ approximately 10% from the mea-sured ones.

7. Mechatronic vehicle suspension concept

Suspension systems with adjustable dampers andsprings or active components are often given asexamples of mechatronic systems, as they perfectlyembody the involvement of mechanic, electronic andcomputational systems by means of the integration ofcomponents and information processing. The integra-tion of components comprises electromagnets andvalves as well as sensors for deflection, pressure, and

acceleration. Integration by information processingenables a parameter-adaptive suspension and faultdiagnosis. Here, changing vehicle properties and faultsare detectable and by means of model-based concepts,the variable damper and spring are optimally influenced.In conclusion, the schematic diagram in Fig. 16

summarizes the presented algorithms for identification,control and fault detection for a semi-active or activevehicle suspension.

8. Conclusions

Methods and algorithms were developed to identify,control and diagnose faults in case of suspensionsystems proposing a mechatronic vehicle suspensiondesign concept for active and semi-active suspensions.The possibilities of such a mechatronic concept andthe general conditions for a mechatronic suspensiondesign due to the actual technical developments arepresented.In the beginning, models of the suspension system are

developed, which parameters are identified applying theRLS algorithm. These models and identified parameters

ARTICLE IN PRESSD. Fischer, R. Isermann / Control Engineering Practice 12 (2004) 1353–13671366

are the basis for the subsequent control and faultdetection design.After discussing the general conditions of suspension

control and various control concepts, a parameter-adaptive suspension control design is presented. In thisconnection, the potential of improvements for statespace feedback in the case of road and body excitation isdemonstrated by means of simulations and experiments.The different combinations of a sole variable damper orspring or both are performed. Here, the combination ofa variable damper and spring obtains the best results innearly the same size as an active suspension system.These results were principally proofed experimentally onthe test rig. However, the improvements were influencedconsiderably by the time constant of the magneticbypass valve. Investigations show that a semi-activesuspension’s sum time constant should be less than10ms.The model-based fault detection of vehicle suspen-

sions was done using a test-rig and a driving test vehicle.It was shown that an estimation of the characteristiccurve of a shock absorber is possible. By a classificationof the symptoms generated with parameter estimationand parity equations, an automated fault detectiondiagnosis is possible.

Acknowledgements

The described results were obtained in several projectswithin the DFG-Sonderforschungsbereich 241 (IMES:Integrated mechatronic systems). The authors highlyappreciate the continuous support over several years.

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