Semi Active Comparison

8/10/2019 Semi Active Comparison

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Nader JaliliMem. ASME

Assistant Professor,

Robotics and Mechatronics Laboratory,

Department of Mechanical Engineering,

Clemson University,

Clemson, SC 29634-0921

e-mail: [email protected]

A Comparative Study and Analysisof Semi-Active Vibration-ControlSystemsSemi-active (SA) vibration-control systems are those which otherwise passively generated

damping or spring forces are modulated according to a parameter tuning policy with onlya small amount of control effort. SA units, as their name implies, fill the gap betweenpurely passive and fully active vibration-control systems and offer the reliability of pas-sive systems, yet maintain the versatility and adaptability of fully active devices. Duringrecent years there has been considerable interest towards practical implementation ofthese systems for their low energy requirement and cost. This paper briefly reviews thebasic theoretical concepts for SA vibration-control design and implementation, and sur-veys recent developments and control techniques for these systems. Some related practicalapplications in vehicle suspensions are also presented. DOI: 10.1115/1.1500336

1 Introduction

In most of todays mechatronic systems a number of possibledevices, such as reaction or momentum wheels, rotating devices

and electric motors are essential to the systems operation andperformance. These devices, however, can also be sources of det-rimental vibrations that may significantly influence the mission

performance, effectiveness and accuracy of operation. Severaltechniques are utilized to either limit or alter the vibration re-sponse of such systems. In vibration isolation either the source ofvibration is isolated from the system of concern also calledforce transmissibility, see Fig. 1a, or the device is protectedfrom vibration of its point of attachment also called displace-ment transmissibility, see Fig. 1b. Unlike the isolator, a vibra-tion absorber consists of a secondary system usually mass-spring-damper trio added to the primary device to protect it fromvibrating see Fig. 1c. By properly selecting absorber mass,stiffness, and damping, the vibration of the primary system can besuppressed 1.

A vibration-control system, either as an isolator or an absorber,is said to be active, passive, or semi-active depending on theamount of external power required for the system to perform itsfunction, see Fig. 2, 2. A passive vibration-control unit consistsof a resilient member stiffnessand an energy dissipatordamperto either absorb vibratory energy or load the transmission path ofthe disturbing vibration 3, Fig. 2a. This configuration has sig-nificant limitations in structural applications where broadband dis-turbances of highly uncertain nature are encountered. In order tocompensate for these limitations, active vibration-control systemsare utilized. With an additional active force introduced as a part of

a suspension unit, u( t) in Fig. 2b, the vibration-control systemis then controlled using different algorithms to make it more re-sponsive to sources of disturbance 2,46. A combination ofactive/passive treatment is intended to reduce the amount of

external power necessary to achieve the desired performancecharacteristics 7.

In view of these systems, it often occurs that the system isrequired to operate over a wide band load and frequency rangewhich is impossible to meet with a single choice of stiffness anddamping. If the desired response characteristics cannot be ob-tained, an active vibration-control system may provide an attrac-tive alternative for such broadband disturbances. However, suchactive configurations suffer from control-induced instability in ad-

dition to the large control effort requirement. This is a seriousconcern that prevents common usage in most industrial applica-tions. On the other hand, passive vibration-control systems espe-

cially vibration absorbers are often hampered by a phenomenonknown as de-tuning. This occurs due to deterioration of thestructural parameters and/or variations in the excitation frequency,and the passive system will no longer be effective.

Semi-active also known as adaptive-passive configuration ad-dresses these limitations by effectively integrating a tuning controlscheme with tunable passive devices. For this, active force gen-erators are replaced by modulated variable compartments such asvariable rate damper and stiffness, see Fig. 2c 810. Thesevariable components are referred to as tunable parameters ofthe vibration-control system, which are re-tailored via a tuningcontrol thus resulting in semi-actively inducing optimal operation.Much attention is being paid to these arrangements for their lowenergy requirement and cost. Recent advances in smart materialsand adjustable dampers and absorbers have significantly contrib-

uted to applicability of these systems 1113.The remainder of the paper is organized as follows. Section 2briefly reviews semi-active vibration-control system design as avibration absorber as well as an isolator. Adjustable suspensionelements including variable rate dampers and springs are pre-sented in Section 3. Section 4 overviews the fundamental prin-ciples of automotive semi-active suspensions, followed by recentadvances in this area. Application of control techniques to semi-active vibration-control systems is presented in Section 5 and fi-nally Section 6 concludes the study.

2 Semi-Active Vibration-Control System Design

SA vibration-control systems can achieve the majority of theperformance characteristics of fully active systems, thus allowing

for a wide class of applications. The idea of SA configuration isvery simple: to replace active force generators with continuallyadjustable elements which can vary and/or shift the rate of theenergy dissipation in response to instantaneous condition of mo-tion. This section presents the basic understanding, fundamentalprinciples and design issues for SA vibration-control systems.

2.1 Semi-Active Vibration Absorption Design. A vibra-tion absorber is elastically attached to the vibrating body to alle-viate detrimental oscillations from its point of attachmentsee Fig.2. The underlying proposition for SA absorber is to properly ad-

just the absorber parameters such that it becomes absorbent ofthe vibratory energy within the frequency interval of interest.

Contributed by the Technical Committee on Vibration and Sound for publication

in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 2001;

Revised April 2002. Associate Editor: R. L. Clark.

Copyright 2002 by ASMEJournal of Vibration and Acoustics OCTOBER 2002, Vol. 124 593


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In order to explain the SA absorber concept, a single-degree-of-freedom SDOF primary system with an SDOF absorber attach-ment is considered as shown in Fig. 3. It is easy to show that thetransfer function between the excitation force and primary systemdisplacement can be expressed as

TF s Xp s

F s mas

2caska

H s (1)

where

H s mps2 cpc askpka mas

2c aska

c aska2, (2)

xp(t) is the primary system displacement, f(t) is the externalforce, ka and c a are the adjustable absorber stiffness and damping

coefficients and Xp(s) and F(s) are the Laplace transformationsofxp(t) and f(t), respectively.

The steady state displacement of the primary system due to aharmonic excitation is then

XpjFj

kama2j ca

Hj (3)

where is the disturbance frequency and j1. Utilizing ad-justable properties of SA unit i.e., variable rate damper c a and

spring ka, an appropriate parameter tuning scheme is selected tominimize the vibration of the primary system subject to externaldisturbance f( t) .

2.1.1 Harmonic Excitation. When excitation is tonal, the ab-sorber is generally tuned at the disturbance frequency. For com-plete attenuation, the steady state Xp(j) must equal zero. Con-sequently from Eq.3, the ideal stiffness and damping of the SAabsorber are adjusted as

kama2, c a0 (4)

Notice this tuned condition is only a function of the absorberelements ma, ka , and c a. That is, the absorber tuning does notneed information from the primary system except the vibratingfrequency and hence its design is theoretically stand-alone. Fortonal application, ideally zero damping in the absorber subsectionresults in improved performance, for the damped or undampedprimary structure. In practice, however, damping is incorporatedin order to maintain a reasonable trade-off between the absorbermass and its displacement. Hence, the design effort for this classof application is focused on having precise tuning of absorber tothe disturbance frequency and controlling damping to an appro-priate level. Referring to Snowdon 14, it can be proven that theabsorber, in the presence of damping, can be most favorablytuned if adjustable stiffness and damping are selected as

Fig. 1 Schematic ofaforce transmissibility for foundation isolation, bdisplacement trans-missibility for protecting device from vibration of the base, and c application of vibrationabsorber for suppressing primary system vibration

Fig. 2 A typical primary structure equipped with three versions of vibration-control systems: a passive, b active, and c semi-active configuration

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kop tm amp

22

mamp2, c op tma 3kop t2 mamp (5)

2.1.2 Broadband Excitation. In broadband vibration control,the absorber subsection is generally designed to add damping toand change the resonant characteristics of the primary structure inorder to maximally dissipate vibrational energy over a range of

frequencies. The objective of SA absorption system design istherefore to adjust the absorber parameters to minimize the peakmagnitude of the frequency transfer function (FT F()TF(s) sj) over the absorber variable suspension parameters

pc akaT. That is, we seekp to

minp

supminmax

FF T (6)

Alternatively, one may select the mean square displacement re-sponse MSDR of the primary system for vibration suppressionperformance. That is, the absorber variable parameters vectorp isselected such that the MSDR

Exp2

0

FT F2Sd (7)

is minimized over a desired wide band frequency range. S() isthe power spectral density of the excitation force f( t), and FTFwas defined earlier.

This optimization is subjected to some constraints in p space,where only positive elements are acceptable. Once the optimalabsorber suspension properties, c a and ka, are determined, theycan be implemented using adjustment mechanisms on the springand the damper elements. The conceptual devices for such adjust-able suspension elements will be discussed later in Section 3.

2.1.3 Simulations. To better demonstrate the effectiveness ofthe SA absorber over the passive and optimum passive absorbersettings, the simple system shown in Fig. 3 with the followingnominal structural parameters marked by an overscore is taken.

mp5.77 kg, kp251.132106 N/m, cp197.92 kg/s

(8)

ma0.227 kg, ka9.81106 N/m, ca355.6 kg/s

These values are from an actual test setting for vibration controlof high-frequency disturbances in submarine hulls. As shown inFig. 4, the absorber is a piezoelectric actuator with reaction masswhere its operating frequencies are in the range of 60010,000 Hz15,16. That is, the peak of FTF is minimized see thin lines inFig. 5. When the primary stiffness and damping increase 5% forinstance during the operation, the FTF of the primary system

deteriorates considerablydashed line in Fig. 5, and the absorberis no longer an optimum one for the present primary. When theabsorber is optimized based on optimization problem 6, the re-tuned setting is reached as

ka10.29106 N/m, c a364.2 kg/s (9)

which yields a much better frequency response see thick line inFig. 5.

2.2 Semi-Active Vibration Isolation Design. The param-eter tuning control scheme for the SA isolator is similar to that ofthe SA vibration absorber, with the only difference being in thederivation of the transfer function. The classical isolator systemshown in Figs. 1a and 1b consists of a rigid body of mass m,linear springkand viscous dampingc. Conversely to the vibration

absorber, the function of the isolator is to reduce the amplitude ofmotion transmitted from a moving support to the body Fig. 1b,or to reduce the magnitude of the force transmitted from the bodyto the foundation to an acceptable level Fig. 1a.

The transfer functions between isolated mass displacement andbase displacementor transmitted force to foundation and exci-tation forceare expressed as

FT

F0

X s

Y s

2nsn2

s22nsn2 (10)

X s

F s

1/m

s22nsn2 (11)

where c/2km is the damping ratio, nk/m is the naturalfrequency, and FTis the amplitude of the transmitted force to thefoundation see Fig. 1a.

Figure 6 shows the transmissibility TA (TAFT/F0X/Y)as a function of the frequency ratio /n and the damping ratio ,where the low frequency range in which the mass displacementessentially follows the base excitation, XY, is separated fromthe high frequency range of isolation, XY. Near resonance, TAis controlled completely by the value of the damping ratio. Afundamental problem is that while a high value of damping ratiosuppresses the resonance, it also compromises the isolation forhigh frequency region (n). An optimal setting for isolatorcan be obtained similar to optimum vibration absorber problem6 except with the transfer function 10 17. The frequency

Fig. 3 Application of a semi-active absorber to SDOF primarysystem with adjustable stiffness kaand damping ca

Fig. 4 PCB series 712 PZT inertial actuatorleft, schematic of operation middle, and a simpleSDOF mathematical model right from 16

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response plot of this transfer function shown in Fig. 7 indicatesthat the damping values sufficient to control the resonance haveno adverse effect on high frequency isolation as opposed to Fig. 6.

An SA isolator can also be utilized for disturbances with time-varying frequency. The variation of natural frequencywhich is afunction of suspension stiffness with the transmissibility TA, inthe absence of damping, is given as

nTA/ 1TA , 0TA1 (12)

With variable disturbance frequency, , and desired transmissibil-ity TA, the natural frequency n or the suspension stiffness kcan be changed in accordance with Eq. 12 to arrive at optimalperformance operation18. The conceptual devices for adjustablesuspension elements are briefly reviewed next.

Fig. 5 Frequency transfer functions

FTF

for nominal absorber

thin-solid; de-tuned absorber

thin-dashed; and re-tuned absorber thick-solid settings from 15

Fig. 6 Frequency response plot of transmissibility TA for the semi-active isolator as a function ofvariable damping ratio



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3 Adjustable Semi-Active Elements

Adjustable elements in semi-active vibration-control unit typi-cally comprised of variable rate damper and stiffness. Significantefforts have been devoted to the development and implementationof such devices for a variety of applications. Examples includeelectro-rheological ER 19,20, magneto-rheological MR 21fluid dampers, variable orifice dampers 22, controllable frictionbraces 23, controllable friction isolators 24, and variable stiff-

ness devices including pneumatic isolators 9,2528.3.1 Variable Rate Dampers. A common and very effective

way to reduce the transient and steady state vibration is to changethe amount of damping in the SA unit. Considerable design workof semi-active damping has been done in the 60s through 80s 29,and references therein for vibration control of civil structuressuch as buildings and bridges 30. Since then, SA dampers havebeen utilized in diverse applications ranging from trains 31,military tanks and other off-road vehicles 32,33 to machine tooloscillations 34. During recent years there has been considerableinterest in the SA concept in the industry for improvement andrefinements of the concept 35. Recent advances in smart mate-rials have led to the development of new SA dampers, which arewidely used in different applications.

In view of these SA dampers, the electro-rheological ER and

magneto-rheological MRfluids probably serve as the best poten-tial hardware alternatives for the more conventional variable-orifice hydraulic dampers36,37. From a practical standpoint, theMR concept appears more promising for suspension system sinceit can operate, for instance, on vehicle battery voltage, whereasthe ER damper is based on high voltage electric fields 36,37.Due to their importance in todays SA damper technology, webriefly review their operation and fundamental principles.

3.1.1 Electro-Rheological (ER) Fluid Dampers. Originally,the idea of applying an ER damper to vibration control has beeninitiated in automobile suspensions, followed by other applica-tions 38,39. ER fluids are materials which undergo significant

instantaneous reversible changes in material characteristics whensubjected to electric potentials Fig. 8. The most significantchange is associated with complex shear moduli of the material,and hence ER fluids can be usefully exploited in SA suspensionswhere variable rate dampers are utilized.

The rheological property of ER fluid is evaluated in shear modeand under the electrical potential, the constitutive equation of anER fluid damper has the form of Bingham plastic 40

yE, and yEE (13)

where is the shear stress, is the fluid viscosity, is shear rateandy(E) is yield stress of the ER fluid which is a function of the

Fig. 7 Frequency response plot of transmissibilityTAfor optimum semi-active suspension as a func-tion of variable damping ratio

Fig. 8 A schematic configuration of an ER damperfrom19



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electric field E. The coefficients and are intrinsic values,which are functions of particle size, concentration and polariza-tion factors.

Consequently, the variable damping force in shear mode can beobtained as

FER4rL d/hE sgn (14)

where h is the electrode gap, Ld is the electrode length of themoving cylinder,ris the mean radius of the moving cylinder, y isthe transverse velocity of the ER damper, and sgn() representssignum function see Fig. 8. As a result, the ER fluid damperprovides an adaptive viscous and frictional damping for use in anSA system 20,41.

3.1.2 Magneto-Rheological (MR) Fluid Dampers. MR fluidsare the magnetic analogs of ER fluid and typically consist ofmicron-sized, magnetically polarizable particles dispersed in acarrier medium such as mineral or silicon oil. When a magneticfield is applied, particle chains form and the fluid becomes a semi-solid, exhibiting plastic behavior similar to that of ER fluids Fig.9. Transition to rheological equilibrium can be achieved in a fewmilliseconds, providing devices with high bandwidth 21,42.

Similar to Bighams plasticity model of 13, the behavior ofcontrollable fluid is represented by

yH (15)

where H is the magnetic filed. In a manner like ER dampers, thevariable force developed by an MR damper is direct-shear mode is

FMRA/hyHA (16)

where y is the relative pole velocity, ALw is the shear polearea and the rest of the parameters are similar to those in ERnotations used in Eqs. 13 and 14.

3.2 Variable Rate Spring Elements. In contrast to variabledampers, studies of SA springs or time-varying stiffness havebeen also geared to vibration isolation applications, for structuralcontrols and vibration attenuation2 and references therein. Thevariable stiffness is a promising practical complement to SAdamping, since based on the discussion in Section 2 both thesuspension damping and stiffness should change to optimallyadopt to different conditions. Clearly, the stiffness has a signifi-cant influence on optimum operation even more over the damp-ing element 43.

Unlike the variable rate damper, changing the effective stiffnessrequires high energy25. Semi-active or low power implementa-tion of variable stiffness techniques suffers from limited frequency

range, complex implementation and high cost 9,44. Therefore, inpractice both absorber damping and stiffness are concurrently ad-

justed to reduce the required energy.

3.2.1 Variable Rate Stiffness (Direct Methods). The primaryobjective here is to directly change the spring stiffness to optimizea vibration suppression characteristic such as given in Eqs. 6 or7. Different techniques can be utilized ranging from traditionalvariable leaf spring to smart spring utilizing magnetostrictive ma-terials. A tunable stiffness vibration absorber was utilized for a4-DOF building Fig. 10, where a spring is threaded through acollar plate and attached to the absorber mass from one side and tothe driving gear from the other side 44. Thus, the effective num-ber of active coils,N, can be changed resulting in a variable springstiffness ka

kad4G

8D 3N (17)

where d is the spring wire diameter, D is the mean spring coildiameter and G is modulus of shear rigidity.

3.2.2 Variable Rate Effective Stiffness (Indirect Methods). Inmost SA applications, directly changing the stiffness might not bealways possible or may require a large amount of control effort.For such cases, alternatives methods are utilized to change the

effective tuning ratio (ka/ma/n1), thus resulting in a tun-able resonance frequency nl is the fundamental natural fre-quency of the primary system.

In Liu 45, a semi-active flutter suppression scheme was pro-posed using differential changes of external store stiffness. As

Fig. 9 A schematic configuration of an MR damper

Fig. 10 The application of a variable stiffness vibration ab-sorber to a 4DOF building from 44



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shown in Fig. 11, the motor drives the guide screw to rotate withslide block G moving along it, thus changing the restoring mo-ment and resulting in a change of store pitching stiffness. Using adouble ended cantilever beam carrying intermediate lumped

masses, a semi-active vibration absorber was recently introduced

in 46, where the position of moving masses was adjustableseeFig. 12. Figure 13 shows a SA absorber with an adjustable effec-

tive inertia mechanism 47. The SA absorber consists of a rod

carrying a moving block and a spring and damper which are

mounted on a casing. The position of the moving block, r,

on the rod is adjustable which provides a tunable resonance

frequency.

3.3 Other Variable Rate Elements. Recent advances in

smart materials have led to the development of new SA vibration-

control systems using indirect influence on the suspension ele-ments. A semi-active piezoelectric network was utilized in13forstructural vibration control see Fig. 14. The variable resistanceand inductance in an external RL circuit are used as real-time

adaptable control parameters.

Another class of adjustable vibration-control systems is the so-

called hybrid treatment48. The hybrid design has two modes: anactive mode and a passive mode. With the aim of lowering the

control effort, relatively small vibrations are reduced in active

mode, while passive mode is used for large oscillations. Analo-

gous to hybrid treatment, semi-automated approach combines the

semi-active and active configurations to benefit from the advan-

tages of individual schemes while eliminating their shortfalls49.By altering the adjustable structural properties in semi-active

Fig. 12 A typical primary system equipped with the double-ended cantilever absorber with adjustable tuning ratio throughmoving masses m from 46.

Fig. 11 A semi-active flutter control using adjustable pitching stiffnessfrom 45

Fig. 13 Schematic of the adjustable effective inertia vibration absorberfrom 47



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unit and control parametersin active unit, a search is conductedto minimize an objective function subject to certain constraints,which may reflect performance characteristics.

4 Automotive Semi-Active Suspensions

Earlier studies on SA vibration-control systems have been fo-cused on automobile related application. One noticeable reason isthat the importance of energy dissipation in vibration-control sys-tems is recognized most in automotive suspensions, where ride

comfort and vehicle handling are encountered. For this reason, webriefly review the application of SA systems to automotive sus-pension and present some recent developments in this area.

4.1 An Overview of Automotive Suspensions. Advancedvehicle suspension systems such as adaptive, semi-active, and ac-tive have extensively been used in most conventional groundtransport fleets. Due to slow response time in adaptive systemsand high energy consumption and cost in active suspensions, theyare unlikely to survive in the future market 5052.

Due to large forces and velocities involved in suspension sys-tems, it is important to minimize the actuator power requirementfor practical and economical reasons. For the actuator in the semi-active suspension systems, multi-stage dampers and continuouslyvariable dampers, or variable lever ratio systems and modulatedtransformers are being utilized 29. These suspensions are calledlow bandwidth or fast load lever systems and often incorpo-rate semi-active dampers which produce high frequency control-lable forces with low power requirements.

In vehicle suspensions, physical actuator limitations or costconsiderations may render an elegant design concept totally im-practical. For this reason, there has been interest in exploring thepossibility of improving suspension performance by modulatingthe characteristics of essentially passive elements such as springsand dampers. SA suspensions represent a compromise betweenperformance improvement and simplicity of implementation.

4.2 Vehicle Models. The vehicle models range from thesimplest one as a single DOF quarter car model which allows foronly one-dimensional vertical or heave motion, to a very complexwith many DOF 5255. A quarter car model considers only one

wheel and sprung mass bounce motion in the vertical direction.For this model, more DOFs other than the basic two degrees offreedom could be considered. However, each mass will only haveDOF in the vertical direction, and pitch and roll are neglected seeFig. 15a. The next category of model incorporates the verticaloscillation of the vehicle as well as the pitch of the vehicle bodysee Fig. 15b. This is often referred to as a half-car or bicyclemodel 58. The next modeling option incorporates heave, pitchand roll as shown in Fig. 15c.

While these models are relatively simple, making use oflumped mass and linear spring characteristics, they will still pro-vide a reasonably accurate indication of vehicle behavior undernormal operating conditions. To illustrate the theoretical concepts

and avoid disturbing the focus of the subject, we briefly discuss,using a simple quarter carSQCmodel of Fig. 15awhat may beachieved by linear damping and spring stiffness variations. Al-though this is a simple model, it is quite suitable to study theperformance of a vehicle suspension in both the bounce motionand tire deflection 56.

The governing equations of motion for the sprung and unsprungmasses are:

m1z1z1z2 bz 1z20(18)

m2z2z2z1 bz 2z1k2z2z00

where m 1 is a quarter of the body mass sprung, m 2 is the massof the wheel, b and are the adjustable damping and stiffness ofthe suspension, and the rest of the parameters are defined in Fig.15a.

Figure 16 shows such adjustable damper whereby the checkvalves assure that for both directions of piston motion, the hydrau-lic fluid flows the same way through a solenoid controlled blow-off valve thus resulting in a variable damping 57. In order todemonstrate the effect of suspension element variations on theride comfort, the frequency response of body velocity as a mea-sure of ride comfortis shown in Fig. 17. These adjustable damperand stiffness are optimized with respect to ride comfort and sus-pension rattle space. A performance characteristic is then con-structed to perform this optimization.

4.3 Semi-Active Suspension Performance Characteristics.It is important to recognize that automobile suspension must per-form several tasks in addition to isolating body from vibrationinduced by road unevenness 51. The vehicle body bounce, atti-tude of each wheel with respect to road surface, normal forcevariations at each wheel and many other criteria must be con-trolled. Although the focus here is on vibration isolation of sus-pension systems, a good design should allow for meeting severalconflicting requirements as explained next.

An optimal SA control problem is therefore formulated for theSQC model of Fig. 15 to briefly highlight the design procedure.For the performance index PI in the design of vehicle suspen-sion, sprung mass acceleration, suspension travel, and tire springexcursion can be incorporated. Sprung mass acceleration is a mea-

sure of body isolation, i.e., passenger ride comfort. Suspensiontravel or rattle space is typically a design constraint for limitingrigid body motion of the vehicle. Tire spring stroke or equiva-lently dynamic tire force is an indicator of road holding ability.Accordingly, a PI of the following form can be selected.

PI1

2TEz0

0

T

1z122z2z0

23z2z1

2dt

(19)

where E(z0) denotes the expectations of the random road distur-bance input z 0 , Tis a sufficient large endtime,1 , 2 , and3 areweighting factors for the penalized variables.

Given the linear system described by Eq. 18, a control se-quence U(t) can be chosen to minimize the PI given in Eq.19,

under the passivity constraint 10

U tz1 tz2 t0, 0tT (20)

In addition, since the vehicle structure can tolerate only boundedsuspension forces it is required that

U tUM, 0tT (21)

whereUM0 is the maximal allowed force. There are many exactnumericaland approximateanalyticalsolutions to this problemwhich we leave the details to 10,5758. To illustrate the effectof variable suspension damper b in Fig. 15, the dependence ofSA performance index on 2(b/2k1m1) is shown in Fig. 18.

Fig. 14 Schematic of a cantilever beam with SA piezoelectricRL network from 13



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4.4 Brief Overview of Recent Advances in AutomotiveSemi-Active Suspensions. The SA concept has been applied toa broad class of ground transport fleets, ranging from tractors andother farm vehicles to high-speed ground transportation vehicle.The SA suspension concept goes back to the early 1970s in theform of variable, controllable damping 59. Although the focus

here is on vibration isolation through vehicle suspension design, itmight be worthwhile mentioning that there have been a few ap-plications of vibration absorber with the aim of improving ridecomfort as shown in Fig. 19 60.

Some recent developments include: SA suspension with vari-able stiffness 61, electro-hydro-pneumatic slow-active suspen-

Fig. 15 a A SQC model of vehicle suspension system b half car modelincorporating the body pitchfrom58, andcwhole car model with heave,pitch, and roll motions from 58



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sion 62, SA suspension using ER fluid mount 63, fast loadlever suspension with variable lever rate 64, SA gas suspensionfor off-road vehicles 32, SA suspension for passenger trains31, and SA suspension using piston controlled disk valve 22.

5 Application of Control Techniques to Semi-Active

Suspensions

As discussed in the preceding sections, the SA suspension gen-erates forces passively but these forces are modulated continu-ously in accordance with some prescribed control law with only asmall amount of external power. In other words, the SA suspen-

sion is basically a device with time varying controllable dampingand spring.

The concept of SA control was first introduced by Karnopp in197429, and has since been developed and demonstrated to be aviable suspension alternative. Although not rigorously proven,damper and stiffness can be treated much like active force gen-erators for the purpose of controller design. That is, the SA

damper or spring is modulated according to the same controlpolicy and same sate measurement as its fully active force gen-erator counterpart. This section briefly reviews the control tech-niques for SA suspensions.

5.1 Semi-Active Control Concept. The elementary SAcontroller design is the so-called on-off SA strategy, which wasfirst proposed in65. It switches the damper off whenever sprungand unsprung masses move in the same direction and unsprungmass has a larger velocity. In any other situations the damper is setto the ON state. The schematic of the conceptual control law isshown in Fig. 20.

A somewhat more sophisticated approach is to change thedamping from soft to firm and vice versa through a manual orslow adaptive control. This is referred to as on-off skyhook

Fig. 16 Schematic design of the electro-hydraulic valve in thepiston of a semi-active damper from 57

Fig. 17 Variations in frequency response of body velocity forSQC model with variable damper from 17

Fig. 18 Variation of normalized PI as a function of variablesuspension damping ratio from 10

Fig. 19 A 2DOF vehicle model with dynamic vibrationabsorber



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control policy, whereby the damper is configured as shown in Fig.21. Mathematically, the on-off skyhook control policy can be de-scribed as

z1z1z20, chigh damping(22)

z1z1z20, clow damping

The combination of relative velocity damping forces and sky-hook components is very effective in damping the body responsewithout detrimental effects refer to Fig. 17 on isolation for thefrequencies between the body resonance frequency and the wheelhop frequency 10. The frequency response is demonstrated inFig. 22, where significant improvement is attained over the con-ventional variable damping configuration of Fig. 17.

During recent years there has been considerable interest in theon-off SA concept. Further improvements and refinements of theconcept were reported 52 and references therein. Recent devel-opments in multi-variable control design methodology and micro-processor implementation of modern control algorithms haveopened a new era for the design of externally controlled passivesystems for use in SA suspensions.

5.2 Optimal Semi-Active Suspension. The continuously-variable SA policy represents the next step up in the sophistica-tion. It requires that the SA actuator continuously reproduce alinear quadratic LQ optimal control skyhook damping forcewhenever this is possible in view of the passivity constraint 10.

When this is not possible, the damper is simply turned off. Thecontinuously-variable SA policy was subsequently extended tomore complex model, which led to so-called clipped SA control

52. The optimal SA control law was first studied in 66. It waslater proved that the clipped SA policy may often be very close tobeing optimal but not always 10.

The fundamental concepts in optimum SA are similar to opti-mum automotive suspension systems discussed in Section 4.3.Simple, mostly LQ-based optimal control concepts give usefulinsights about the performance characteristics and other require-ments 52,66.

-

Fig. 20 On-off semi-active control decision

Fig. 21 Schematic of Skyhook damper arrangement

Fig. 22 Variations in frequency response of body velocity for SQC model with combination of variable damper and skyhookdampingfrom 17



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5.3 Other Control Techniques. As a result of the substan-tial ongoing theoretical advances in the areas of adaptive and non-linear controls 67, it is expected that the future will bring appli-cations of these techniques in advanced suspension design. Forpractical implementation, however, it is preferable to simplifythese strategies thus leading to simpler software implementations.For instance, suboptimal policy neglecting some performance re-quirements can serve as example of such simplifications. Somerecent developments in control techniques for SA suspensions in-clude: fuzzy reasoning, adaptive SA, SA suspension with observerdesign and many others 50 and references therein.

6 Conclusions

The fundamental principles of SA suspension were formulatedhere. There are many important areas directly or indirectly relatedto the main theme of this paper such as practical implementationof SA suspensions, nonlinear control schemes, actual hardwareimplementation, actuator bandwidth requirements, reliability andcost. Furthermore, in the process of designing a SA suspension, inpractice, several critical criteria must be considered, which werenot discussed here. These include weight, size, shape, center-of-gravity, types of dynamic disturbances, allowable system re-sponse, ambient environment and service life.

SA suspensions provide vibration suppression solutions fortonal and broadband applications with small amount of controland relatively low cost. However, it is quite a design challenge by

using conventional technologies to build a practical SA suspen-sion under the constraints of weight, size and cost. Furthermore,the design of SA suspension involves many mechanical and elec-trical components that puts limit on the tuning range of the reso-nance frequency of the device.

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