Active vibration isolation using an induced strain actuator with ... · 271 Active vibration isolation using an induced strain actuator with application to automotive seat suspensions

271

Active vibration isolation using an inducedstrain actuator with application to automotiveseat suspensions

Mark Malowicki and Donald J. Leo∗Center for Intelligent Material Systems andStructures, Mechanical Engineering Department,Virginia Polytechnic Institute and State University,Blacksburg, VA, USA

Active vibration isolation of automotive seats requires actu-ators that achieve millimeter-range displacements and forceson the order of 300 N. Recent developments in piezoceramicactuator technology provide a means for achieving these forceand displacement levels in a compact device. This workdemonstrates that prestressed, curved piezoceramic actuatorsachieve the force and displacement levels required for activeisolation of automotive seats. An estimate of the force anddisplacement requirements are obtained from numerical sim-ulations on a four-degree-of-freedom car and seat model thatutilize representive road accelerations as inputs. An actua-tor that meets these specifications is designed using piezoce-ramic materials. Free displacement of 4.4 mm and blockedforce greater than 300 N are measured. The actuator is inte-grated within a dead mass setup that simulates the isolationcharacteristics of an automotive seat. Control experimentsdemonstrate that active vibration is achievable with realisticroad disturbances. Feedback control is able to eliminate anyamplification due to mechanical resonance and reduce theisolation frequency from 9.5 Hz to 2 Hz.

1. Introduction

Vibration isolation in existing seat designs isachieved passively through foam padding placed be-neath the seat frame and the passenger. Recent tests ona passenger seat of a luxury sedan demonstrated thatthe foam padding was the primary mechanism for re-ducing the transmission of floor vibrations to the pas-

∗Corresponding author: 307 NEB, Mechanical Engineering De-partment, Virginia Tech, Blacksburg, VA, 24061-0261, USA. Tel.:+1 540 231 2917; Fax: +1 540 231 2903; E-mail: [email protected].

senger in both the translational and rotational degreesof freedom [12,13].

This paper investigates an alternative approach toproviding vibration isolation in automotive seats. Weinvestigate the use of a piezoelectric actuator to provideactive vibration isolation. It has been shown throughanalysis and experiment that active isolation overcomesmany of the inherent limitations of passive isolationsystems. Beard et al. [3] demonstrated that absolutevelocity feedback overcomes the constraint betweendamped response and high-frequency vibration isola-tion. More recently, Leo and Inman [11] demonstratedthat active-passive isolation can achieve significant im-provements over passive control when the input energyis concentrated near the break frequencyof the isolationsystem.

The advantages of active control approaches havelead to the experimental demonstration of the technol-ogy in several industries. Miller et al. [16] demon-strated the development of active-passive vibration iso-lation system consisting of a fluid mount and an elec-tromagnetic actuator sized for applications in jet air-craft. More recently, magneto-rheological fluids havebeen utilized to develop ‘semi-active’ mounts for vi-bration isolation [1]. Active-passive vibration isola-tion has been experimentally demonstrated using voicecoil actuators for precision pointing and steering sup-pression [19]. Anderson et al. [2] discuss the develop-ment of a hardmount vibration isolation system usingelectromagnetic actuators for precision instruments onspacecraft.

Applications of piezoceramic actuator technologyhave been limited to vibration isolation systems thatrequired sub-millimeter strokes. The primary area ofapplication has been micron-level vibration isolationsystems for space environments. Bohannan et al. [5]have demonstrated the use of piezopolymer films forspaceborne vibration isolation systems.

This work contributes to the field of active isola-tion by demonstrating the feasibility of using piezo-

Shock and Vibration 8 (2001) 271–285ISSN 1070-9622 / $8.00 2001, IOS Press. All rights reserved

272 M. Malowicki and D.J. Leo / Active vibration isolation using an induced strain actuator

electric actuators as control elements in automotive ap-plications. In contrast to space applications, vibra-tion isolation in automotive systems requires displace-ments on the order of 1–10 mm. Piezoelectric actuatorsare typically not considered for applications which re-quire millimeter-range displacements due to their lowachievable strain (≈ 0.1%), but recent work in the fieldof actuator development has overcome many of theselimitations. Several actuator designs have been de-veloped that achieve displacements on the order of 1–5 mm, including mechanically-amplified devices andprestressed curved actuators. Near [18] presents a clearsummary of the various actuator types and comparesthe tradeoffs between force and stroke for piezoelectricdevices. Other types of actuators have been developedsince Near’s overview, including recurve-type [6] andtelescoping designs [4],and frequency-rectified devicesusing piezohydraulic elements [14,15,17].

The fundamental tradeoff in piezoelectric actuatordesign is between actuator stroke and actuator force.Increasing the displacement of piezoelectric actuatorsis accompanied by a reduction in force. Assessing thefeasibility of a piezoelectric actuator requires a modelof the system and an estimate of the force and displace-ment requirements for the actuator. To assess the fea-sibility of seat isolation, the inputs to the model mustbe realistic road disturbances such that the magnitudeof the critical parameters (i.e. force and displacement)reflect actual road conditions.

Our paper assesses the feasibility of piezoelectric ac-tuation by first determining an input excitation that re-flects realistic road conditions. These inputs are basedon the work by Gillespie in the analysis of vehicledynamics. Road inputs are combined with a state-space representation of the seat-suspension system of aquarter-car model to determine the force and displace-ment requirements for the piezoelectric actuator. Anactuator that meets these specifications is designed andtested on a dead-mass setup that represents the verticaltransmissibility of an existing automotive seat.

The first step in the actuator feasibility study is thedetermination of actuator requirements. The seat andpassenger are modeled in a vertical motion, four de-gree of freedom system which incorporates the seatsuspension, effects of the vehicle suspension, as wellas a representative input derived from measured roadinput data. The model output can then be compared topassenger comfort data which has been experimentallydetermined by various researchers.

2. Input excitation of the road disturbance

The input excitations to the seat and vehicle modelare modeled with power spectral densities (PSD) of theroad disturbances. The energy content in road distur-bances has been summarized by Gillespie and is shownin Fig. 1. The PSD amplitude falls with increasingfrequency, which is typical of all roads due to the factthat low wavenumber (high wavelength) surface dis-turbances have larger height variations than do highwavenumber (low wavelength) disturbances. Since ac-celeration is more commonly used in the measure ofride quality, the road surface elevation variation can beexpressed as an acceleration by differentiating twice.The differentiation involves multiplying by frequency,and so the acceleration spectrum now shows a char-acteristic increase in amplitude with increasing fre-quency.

Taking a quarter-car model, the road roughness istransmitted through the suspension as illustrated inFig. 1 [8]. The middle graph is the frequency responsefunction of a typical automotive suspension. Takingthe road acceleration input and multiplying it throughthe suspension response, we finally arrive at the accel-eration spectrum at the vehicle level. At the level of thevehicle floorboard, only lower frequency disturbanceswill be experienced. The vibration that has managedto survive the primary suspension’s filtering efforts isnow left as the input to the base of the automotive seat.The seat is the final level of isolation between roadroughness and the passenger.

2.1. Passenger comfort

The performance of the seat is quantified by relatingthe vibration levels to commonly-accepted indicatorsof passenger comfort. While there may be no absolutestandard of human comfort due to the fact that no twohuman beings are exactly alike,research has proven thatwe can define a zone or area in which people generallyexperience discomfort. Above this region the vibrationis certain to be intolerable, and below this region thevibration level is acceptable. In order to quantify thiszone, we can begin by simplifying our considerationsto a human being subjected to simple sinusoidal motionin one direction. An extensive research summary isgiven in Gillespie’s text, and is reproduced in Fig. 2.

Each line in the figure represents a line of constantcomfort above which a test subject will complain ofexcessive vibration. While the absolute level of vibra-tion at which a person will complain varies from study

M. Malowicki and D.J. Leo / Active vibration isolation using an induced strain actuator 273

Fig. 1. Power spectral density after seat suspension [8].

to study, the characteristic shape is seen to be similar.Human beings are especially sensitive to vibration inthe range of 4–10 Hz, where each curve dips to itsminimum. This is often attributed to resonances withinthe abdominal cavity. Above and below this 4–14 Hzrange, sensitivity decreases and humans are tolerant ofhigher acceleration levels. The variance seen betweenresearchers is due to differences in several factors, in-cluding seating position, compliance of the seat surfaceused, stated definition of discomfort, subject size, andso on.

Research done by M.J. Griffin exhaustively analyzescomfort contour curves in all three translational direc-tions, as well as rotational excitations about all threeaxes. His research shows that vibration in the verticaldirection causes discomfort at lower vibrational levelsfor a greater frequency range than do other directionalinputs. Griffin’s experiments also involve vibrationalinputs through the backrest and footrest, with verticalmotion of the seat still seen as causing the most dis-comfort [9,10].

In summary, humans are most tolerant of high fre-quency vibration, yet the magnitude of road inputs fallsoff with increasing frequency. Also, vehicle suspen-sions adequately filter out high frequency inputs, whileallowing lower frequencies to pass through to the bodyof the vehicle. At the interface of the vehicle and theseated human at the seat surface, high frequency vi-

bration is of lesser concern than low frequency inputs.These factors are used to assess the performance of theactive isolation system.

3. Seat-car model

The road excitation PSDs are combined with alumped parameter model of the seat and car for the pur-pose of determining force and displacement require-ments for the actuator. The model is developed bycoupling a quarter-car model with a two-mass-spring-damper model of the seat. The resulting four-degree-of-freedom model is shown in Fig. 3. Two degrees offreedom exist due to the unsprung (wheel and tire) massand the sprung (vehicle frame, body, etc.) mass, andtwo additional degrees of freedom are added in orderto consider the presence of both foam cushion and anactive suspension between the passenger and the vehi-cle. The foam is modeled with a spring rate Kf anddamping rate Cf , while the actuator is represented bya spring rate Ka in parallel with the force generatingactuator. The terms Ks and Cs represent the springrateand damping of the primary vehicle suspension, andKt represents the tire springrate.

The model allows a great deal of flexibility in theanalysis, as various vehicle applications can be consid-ered by modifying the primary suspension spring rate


Fig. 2. Tolerance to vertical vibration [7].

Fig. 3. Four-degree-of-freedom quarter-car and seat model.

and damping ratio. Seat isolation can be evaluated forthe case of a foam seat only and a rigid connection inplace of the actuator (with Ka set very large to imitateinfinite stiffness) or a fully active seat with no foam (Kf

set to a very large value). Even when removing foam tosave weight in the vehicle, some foam will be required

beneath the seated passenger in order to comfortablyconform to the contours of the passenger’s body. Thus,the lightweight seat application under consideration inthis thesis maintains some amount of foam even in theactive case.

The pitch and roll modes of the vehicle are not in-cluded in the model. Not only is the vertical input thedominant excitation arising from a paved road (in mostcases), but in addition, human discomfort is known tobe most sensitive to vibration in the vertical direction.Roll excitation has a power spectral density that fallsoff with decreasing wavenumber, and thus is largelyfiltered out by the suspension [7]. Pitch may becomecritically important if the road contains a specific forc-ing frequency, such as would be present in a fixed slablength concrete road, which excites a pitch resonanceof the vehicle. Such a special case is not consideredhere.

The equations of motion for a position vector x1 aregiven by

x1 =

xh

xf

xveh

xwh

(1)


F =

0 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 1 00 0 0 0 0 0 0 1

−kf

Mh

kf

Mh0 0 −cf

Mh

cf

Mh0 0

kf

Mf

−(kf+ka)Mf

ka

Mf0 cf

Mf

−cf

Mf0 0

0 ka

Mveh

−(ks+ka)Mveh

ks

Mveh0 0 −cs

Mveh

cs

Mveh

0 0 ks

Mwh

−(ks+kt)Mwh

0 0 cs

Mwh

−(cs+ct)Mwh

(6)

Mh 0 0 00 Mf 0 00 0 Mveh 00 0 0 Mwh

x1

+

cf −cf 0 0−cf cf 0 00 0 cs −cs

0 0 −cs (cs + ct)

x1

(2)

+

kf −kf 0 0−kf (kf + ka) −ka 00 −ka (ks + ka) −ks

0 0 −ks (ks + kt)

x1

=

0−Fa

Fa

Froad

where vertical positions are given by xh for the humanpassenger, xf for the seat frame, xveh for the vehicle(sprung mass), and xwh for the wheels and axle (un-sprung mass). The equations can then be written in thestate space form according to

x = Fx + Gdud + Gcuc

yo = Hox + Jouc

ys = Hsx(3)

with variables defined as

x state vectoryo, ys observation or sensor output vectorud, uc disturbance or control inputF system matrixGd, Gc disturbance or control input matrixHo, Hs observation or sensor output matrixJo feedforward observation matrix

(4)

The input vector u contains both a defined road inputsignal, and an actuator input force as determined by thefeedback system. The state vector x is now defined as

x =

xh

xf

xveh

xwh

xh

xf

xveh

xwh

(5)

The state space matrices for the system, accordingto Eq. (3), become,

Gd =

0000000kt

Mwh

Gc =

00000−1Mf1

Mveh

0

(7)

Ho =

1 0 0 0 0 0 0 0

0 0 1 0 0 0 0 00 0 0 0 0 0 0 0

Hs =[1 0 −1 0 0 0 0 00 0 0 0 1 0 −1 0

]

Jo =

0

01

For these particular H and J matrices, the values inthe output vector y will be:

[yo

ys

]=

passenger displacementvehicle displacementactuator forcepassenger displacement

relative to vehiclepassenger velocity relative

to vehicle

(8)

The Jo matrix has been chosen to output the actuatorforce in the third row of yo. The Hs matrix as shown


*

*

* *

*

*

*

*

*

*

*

**

*

*

*

o

oo

o

o

oo o

oo

o

o

o

o

o

Fig. 4. Simulated time history for passive and active isolation.

here outputs the position difference and velocity differ-ence (of the attachment points of the actuator) in thefirst and second rows of ys, respectively.

With a complete model of the system in the freeresponse condition, the next step is to close the loop andapply a feedback which alters the system response asdesired. The feedback system can also be modeled instate space form, with the system matrix now reflectingthe actuator dynamics. The expression for feedbackcontrol is

uc = −Jfbys (9)

To simply apply feedback gains based upon the out-put of the model, gains are placed in the Jfb matrix.This provides a suitable estimate of required actuatorperformance.

4. Simulation results

Numerical analysis is performed with the parametersshown in Table 1. Known mass values are used for theseat, and the remaining mass values are approximatedfor a typical small to mid-size sedan type automobile.Spring and damper rates are chosen so as to have atypical primary suspension resonance at 1.5 Hz anda wheel hop mode at 12 Hz. Seat cushion damping

is based upon experimental measurement of an actualpassenger seat [13].

Three cases were examined: 1) the open loop, freeresponse of the baseline seat having full foam thick-ness, 2) the open loop free response of a seat with halfthe foam removed, and 3) the closed loop response ofa seat having half the foam removed which has an ac-tive seat suspension added in. Case 2 demonstratesthe degradation in vibration isolation that results fromremoving half of the foam out of the seat, and case 3represents the attempt at forcing case 2 back to at leastthe level seen in case 1. The goal of the active system isto recover the performance lost in removing foam andso case 1 is taken to be the desired level of isolation.

Feedback gains are applied to two outputs of thesystem – the position difference between the passengerand the vehicle, and the velocity difference between thepassenger and the vehicle.

A sample time history of the simulated output isgiven in Fig. 4, which shows the vertical displacementof the passenger (xh) for each of the three cases. It isobvious from the figure that removing foam from theseat causes larger excursions in xh, which will be expe-rienced by the passenger as a less comfortable ride. Theclosed loop case demonstrates a marked improvement,and more than recovers the performance lost with theremoval of foam from the seat.


* * * ** **

* ** * *

*

Fig. 5. Simulated frequency response demonstrating the effects of active control on the seat transmissibility.

Figure 5 shows the frequency response function forall three cases. With the decrease in foam thickness, theperformance loss is seen as a higher peak at both systemresonances. This is due to the loss of damping withthe decrease in foam thickness. Note that the resonantfrequencies remain constant, since in the half foam casethe spring in parallel with the actuator is assumed torecover the loss in spring rate with the removal of foam.The spring shown by Ka in Fig. 3 is necessary as itoffloads the actuator by supporting the static weight ofthe seat and passenger. The actuator then needs onlyto apply force for the dynamic movement of the mass,and not to support the mass in a static condition. Thisgreatly decreases actuator force requirements. With theactuator incorporated in feedback control of the system,a performance improvement is obvious in Fig. 5. Theisolation frequency of the system has been decreasedfrom 5 Hz to 2.5 Hz, and the transmissibility at bothresonant frequencies has been decreased.

Now that the Jfb matrix has been determined fora sufficient level of performance, actuator force andstroke can be extracted from the simulation results.Figure 6 shows a time history of both actuator force, inNewtons, and actuator stroke, in millimeters. Actuatorforce can be seen to reach peaks of approximately ±400 Newtons, with actuator stroke reaching ± 4 mil-limeters. RMS actuator force is 288 N, and RMS ac-tuator stroke is 2.9 mm. Results are summarized inTable 2.

5. Actuator design and testing

The actuator is designed using piezoelectric mate-rials because of their ability to achieve the force lev-els required of the isolation application. Piezoelectricactuators have only 0.1% maximum strain, thereforeone of the primary design considerations is determiningan actuator configuration that achieves the millimeter-range displacements estimated by the numerical sim-ulations. As discussed in Near [18], there are a num-ber of methods of increasing the stroke of piezoelec-tric actuators. For this work we have chosen to use aprestressed, curved piezoelectric actuator sold by FaceInternational Corporation. The rationale for this choiceis twofold:

1. A recent study by Berner and Brei [4] demon-strate that this type of actuator has a high energyoutput compared to other types of large-strokeconfigurations.

2. Their force and displacement ratings are in therange for this application and they are commer-cially available.

The key elements of the design and testing of theactuator are discussed in the following two sections.

5.1. Piezoceramic actuator implementation

While the prestressed piezoceramic devices exhibitforce and displacement levels near the requirements of


Fig. 6. Force and stroke levels computed from the car and seat simulations.

Fig. 7. Actuator endpoint movement under deflection.

the isolation application, the actual implementation intoa mechanical system is far from simple. Vertical dis-placement at the midpoint of the arch is developed by achange in radius of curvature, which also carries with ita corresponding horizontal movement of the endpoints.There are three distinct load – bearing points – one at thecenter and one at each end. In the horizontal direction,one of these must be constrained to keep the system inplace, but the other two must be allowed to slide freelyin order to accommodate the length change that accom-panies change in curvature. All three attachment pointsmust be constrained in the vertical direction, since thisis the direction in which force is to be applied to theseat system. Figure 7 demonstrates the situation, withthe arrows representing the free body reaction forces

required in the mounting scheme. In addition, the fixedend must allow rotational movement due to the smallangular change that accompanies deflection.

In this application, two stacked actuators will be usedin order to increase force level. A thin Teflon sheetplaced between the two devices serves to electricallyisolate the two oppositely charged surfaces, and alsoto permit the small amount of sliding that will occur.The midpoint of the actuator will be attached to theseat frame, while the endpoints will be attached to thefloorboard, with a static weight supporting spring inparallel with the actuator assembly. Figure 8 shows theincorporation of all necessary features into the actuatorcomponents and the assembled actuator. In the as-


Fig. 8. Actuator assembly.

tested configuration, the complete assembly weighs atotal of 488 grams.

Free displacement and blocked force measurements

Free displacement is measured by applying a voltagesignal to the actuator, in the absence of any externalload, and measuring displacement. A sinusoidal inputvoltage is applied at frequencies of 1 Hz, 5 Hz, and10 Hz. Since input voltage is limited to + 600 Vand − 300 V, a + 150 V offset is applied in order tomaximize peak to peak voltage range. A Polytech OFV303 laser vibrometer is used to measure displacement.Test setup and the measured results are shown in Fig. 9.Maximum stroke is 4.4 mm peak to peak for an input of900 V peak to peak. The data shows a reasonably linearresponse beyond 300 V, with a gain of 0.00625 mm/V.

At the other extreme of the operating envelope isthe case of zero displacement with maximum actuatorforce, or blocked force. The actuator is constrainedto prevent any displacement, energized, and blockedforce is measured (see Fig. 10) with a quartz forcetransducer is affixed between the actuator and the plate.Peak to peak input voltage is varied from 0 to 900 V,in increments of 50 V, with data taken for sinusoids of1 Hz, 5 Hz, and 10 Hz. Figure 10 shows a maximum of320 N peak to peak. Again, response is linear beyondthe 300 V level, with a gain of 0.41 N/V.

6. Control experiment

The simplified case of a single actuator assem-bly controlling the vertical motion of a representative


Fig. 9. Experimental setup from free displacement measurement (top) and measured actuator free displacement versus voltage (bottom).

amount of dead mass can now be examined. A verticalmotion test stand driven by an electrodynamic shaker isemployed to analyze the system response. Since onlyone actuator assembly is being tested, one quarter ofthe total mass is used. This amounts to 24.4 kg, whichis one fourth of the 21 kg seat mass plus 77 kg of humanmass.

The setup is shown is Fig. 11. The steel mass isconstrained to vertical motion by means of the linearbearings sliding along the aluminum posts on eitherside, with the actuator assembly directly below the deadmass, situated on an adjustable height platform. The

two static weight supporting springs in parallel withthe actuator are readily visible in the picture, as are thetwo accelerometers (one on top of the mass, one on thetable surface directly below the actuator) used to mea-sure transmissibility. The calculated natural frequencyof the 24.4 kg dead mass with two 12.3 N/mm staticweight springs is 5.05 Hz. This does not account forthe added spring rate of the piezoceramic devices them-selves, which will raise the resonant frequency slightly.The stiffness of the springs in the test setup have beenchosen so that the natural frequency of the mass-springsystem is approximately equal to the resonance deter-


Fig. 10. Experimental setup for blocked force measurement (top) and measured blocked force versus voltage.

mined from transmissibility tests on the actual seat. Inan actual design, the springs also serve to offload thestatic weight of the passenger and the seat for the pur-pose of reducing the force requirements of the piezo-electric actuator. Over a range of weights (e.g. fordifferent passengers), the force capability of the actu-ator would be reduced due to the additional static loadplaced on the actuator. Although this is a practical de-sign consideration, this aspect of the problem was notstudied in our work.

To produce a shaker table noise signal that mimicsthe floor of a vehicle driving down the road, the dSpacedigital signal processing system is used for signal gen-eration and data acquisition. The representative road

input is simulated using a bandwidth – limited noisesignal filtered through two digital transfer functions.The first transfer function converts the noise from abroad spectrum noise to a signal that is representativeof an actual road surface. A second transfer function,representing the vehicle primary suspension, is used toconvert the road noise to a vehicle floorboard noise.The final signal is fed into the dSpace digital to analogconverter, and the actual output voltage signal is fed intothe amplifier driving the electrodynamic shaker. Theresulting input signal contains only lower frequencycontent, just as a typical road would. This signal isused to determine the effect of feedback control the seatvibration resulting from a representative road profile.


Fig. 11. Dead mass setup on test stand.

Fig. 12. Frequency response between the floor vibration and the mass motion: magnitude (top), phase (middle), and coherence (bottom).

Upon taking the frequency response function (FRF),the coherence in the higher end of the frequency rangeis very low. The filtering has done such a good jobscreening out all of the higher frequency content of thenoise signal that there is only negligible accelerationin the frequency range above 10 Hz to excite the sys-tem. When the input signal is so small, any noise inthe accelerometers, wires, or instrumentation becomeslarge in comparison, and results in low coherence. Toremedy this, a broadband input signal is used to excite

the shaker table during the frequency domain analysis.The broadband excitation allows us to determine thetransfer function between the floor vibration and themotion of the mass. The shaker table now has an ad-equate input signal throughout the analysis frequencyrange. The dips in the 6 Hz and 25 Hz range are at-tributable to the energy being absorbed by resonancesof the table and dead mass system.

With the broadband input signal, a suitable FRF ofthe system is obtained, as shown in Fig. 12. The res-


Fig. 13. Measured transmissibility plots illustrating the effects of feedback control.

onance of the system is at 6 Hz, with an isolation fre-quency of 9 Hz. The poor coherence at 25 Hz is due to aresonance of the surface of the shaker table itself, whichwas determined by moving the output accelerometerto various locations, and noting that the table surfaceitself resonates at 25 Hz.

The dead mass setup allows us to perform active vi-bration isolation experiments with inputs that are rep-resentative of actual road profiles. Active control is im-plemented through feedback of the mass velocity to theinput of the piezoelectric actuator. A velocity signal isobtained by measuring the mass acceleration directlyand digitally-integrating the signal in the digital signalprocessor. The integrated signal is then amplified andoutput to the input of the actuator.

Figure 13 illustrates the effect of velocity feedbackon the transmissibility between the floor and the mass.The resonant peak is eliminated by even modest gains,and as gain is increased further, isolation frequenciesin the 2–3 Hz range are easily achievable. The gain isincreased up to a level showing significant clipping atthe maximum allowable actuator voltage of + 600 Vand − 300 V.

The experiments also demonstrate that low-frequencyvibration isolation is achieved without an increase in

the transmissibility at high frequencies. The frequencyat which the transmissibility falls below 1 is reducedfrom approximately 9.5 Hz in the uncontrolled systemto 2 Hz with maximum feedback gain. The decreasein the isolation frequency is not accompanied by anincrease in the transmissibility at high frequencies, aswould be the case for increasing the damping coeffi-cient of a purely passive isolation system.

The reduction in RMS acceleration produced by thecontrol used in Fig. 13 is given in Table 3. The tablealso shows the reduction in RMS acceleration achievedby the numerical simulation for the modeled foam seatverses the modeled active seat, which produced an 80%reduction in acceleration level. The dead mass ex-perimental setup did not include a test of actual seatfoam, and so a direct comparison cannot be made forthe passive cases, but the active cases can be compareddirectly. The input acceleration level was normalizedsuch that both the modeled and the experimental casesexperienced the same level of acceleration input. Amore than adequate level of isolation is achieved.

A typical automotive seat has a resonant peak at4 Hz with an isolation frequency at 6 Hz [13]. At4 Hz, the seat has a magnitude ratio of two, meaningany signal near 4 Hz that manages to pass through the


Fig. 14. Measured time history of the dead mass.

primary suspension will actually be amplified by thebaseline seat. This is one of the advantages of activesuspension systems – Fig. 13 clearly shows that it ispossible to actively control the system to eliminate anyamplification.

A time history of the dead mass setup being drivenwith a representative road input signal is shown inFig. 14. Both the open loop and closed loop responsesare shown, with the active case having an absolute ve-locity gain of 0.5. Identical random inputs are obtainedfor the two cases by using the exact same random sig-nal. The results are not as drastic as predicted by themodel, since greater effort was made to obtain a repre-sentative road signal in the dead mass experiment thanwas made in the simulation. The active system showsgreatest improvement over the baseline seat in the 4–10 Hz region, while the frequency content of the rep-resentative road signal begins to fall off above 3–4 Hz.

The representative road input does not incorporate dis-tinct road events such as potholes or railroad trackswhich might better emphasize the improvement of theactive system.

7. Conclusions

Prestressed, curved piezoceramic actuators are suc-cessfully applied to the problem of achieving vibrationisolation of an experimental setup representing one-quarter of a vehicle seat and passenger. The activesystem eliminates any amplification in the frequencyresponse function, whereas the baseline seat tested hasa magnitude ratio of two at its resonant frequency of4 Hz. Isolation frequency is reduced to 2–3 Hz, whilethe baseline seat does not begin isolation until 9.5 Hz.This was accomplished with the design of a piezoce-


ramic actuator that required millimeter-range displace-ments and forces on the order of 300 N.

The passenger comfort data suggests that a car seatwith a resonant peak in the 4–10 Hz region is direction-ally incorrect, since this is the frequency range in whichhuman beings are most sensitive to vertical vibration.By eliminating any amplification in this range, the po-tential for a passenger to experience discomfort is re-duced. This work demonstrates that velocity feedbackof the seat motion produces a highly damped systemthat exhibits no resonant amplification and maintainsdesirable high-frequency isolation characteristics.

Acknowledgements

The authors gratefully acknowledge the supportof DaimlerChrysler, program coordinator Mr. SteveBuckley.

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Active vibration isolation using an induced strain actuator with ... · 271 Active vibration isolation using an induced strain actuator with application to automotive seat suspensions