D. Karnopp Department of Mechanical

and Aeronautical Engineering, University of California, Davis,

Davis, CA 95616

Active and Semi-Active Vibration Isolation In the five decades since the founding of the ASME Design Engineering Division, the important problem of vibration isolation has been attacked first through the design of passive spring-damper suspensions and later by the use of active and semi-active elements. This paper reviews the historical development of theoretical concepts necessary for the design of isolation systems and indicates how control theory began to influence vibration isolation in the last half of this period. Practical active and semi-active suspensions have only recently become possible with the advent of powerful but relatively inexpensive signal processors. To illustrate these developments for engineers who have not been intimately involved with active systems, only simple vibrational system models will be discussed, although some modern hardware will be shown which is now being applied to complex systems. Instead of attempting to review the many theoretical concepts which have been proposed for active systems, this article will focus on a relatively simple idea with which the author has been associated over the past thirty years; namely the "skyhook" damper. This idea came through purely theoretical studies but is now used in combination with other concepts in production suspension systems. Two quite different application areas will be discussed. The first involves stable platforms to provide extreme isolation for delicate manufacturing operations against seismic inputs and the second involves automotive suspensions. Although similar concepts are found in these two application areas, the widely varying requirements result in very different suspension hardware. The special case of the semi-active damper, which requires very little control power and is presently reaching production, will also be discussed.

1 Introduction The theory of vibrations is a triumph of classical analytical

mechanics. Whittaker (1904) traces the development of this theory from the study of small oscillations of a pendulum by Galileo through major contributions by Brook Taylor, D'Alembert, Euler and Daniel Bernoulli who in 1753 showed that compound vibrations could be resolved into motions of independent simple modes. Lagrange provided a general theory of the vibration of systems with finite degrees-of-free­dom in 1762-5.

In the face of this theoretical understanding, a mathemati­cal physicist might be excused for thinking that the job of engineering practical control measures to ameliorate the undesirable effects of vibration would be relatively trivial. In fact, apart from the usual problems associated with cost, reliability, and manufacturability, engineers initially were prevented from designing effective vibration isolation schemes by a lack of education in the field. It has been pointed out (Den Hartog, 1947) that prior to the middle 1930's, "the subject had not yet been introduced into the curriculum of our technical schools." Den Hartog, having been trained as an electrical engineer and familiar with the techniques used

Contributed by the Design Engineering Division for publication in the Special 50th Anniversary Design Issue. Manuscript received Oct. 1994. Technical Editor: D. J. Inman.

to describe alternating current electrical circuits, was a pio­neer in introducing mechanical engineers to vibration control means.

In the early days of vibration isolation, the emphasis was on the balancing of rotating machinery and the introduction of compliant suspension elements. Most of the time, spring rates for suspensions were chosen to avoid resonant response but in some cases the basic concepts were surprisingly vague. Den Hartog himself (Den Hartog, 1947, p. 149) answers his own question, " . . . how do we have to design the main springs [of an automobile] for maximum riding comfort... ? with the answer, "the springs have to be made as soft as possible... ." Since there was no discussion of any real limitations to the softness of suspension springs, it seems that design guides for isolation systems were not very well devel­oped at this time.

The importance of energy dissipation in suspension sys­tems was recognized early on but it was often not clear how much damping was desirable and, for that matter, there were few damping devices which produced the viscous type of damping forces assumed by the linear theory of vibrations. The relatively few special cases treatable by the mathemati­cal theory of nonlinear oscillations provided little help for practical vibration control and computers capable of simulat­ing nonlinear systems were not readily available until fairly recently. In many cases, what damping did exist came from

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sliding friction in linkages, bearings, or leaf springs or was inherent in visco-elastic materials used. After the second world war, hydraulic shock absorbers became common in vehicle suspensions but the amount and type of damping to be installed was decided more by trial and error than by any unified theory. Den Hartog's advice on the matter is typical: "The introduction of damping at these high road frequencies is undesirable. But the case of resonance is not excluded, and, from that standpoint, damping is very desirable." He goes on to discuss the difficulties of deciding on the proper amount of damping considering the wide variety of roadway disturbances which may be encountered but more than a few general words of advice to a suspension designer are not to be found.

By the time of the late 1950's and early 1960's random vibration had become a research topic due primarily to problems associated with rough burning of rocket engines and fatigue of aircraft parts due to turbulence excited vibra­tion. By this time most mechanical engineers had some exposure to sinusoidally excited vibration in their basic edu­cation and courses in random vibration were being intro­duced at the graduate level. An ASME Research Committee on Random Vibration formulated a program in 1959 to standardize and extend the techniques associated with noise in electronic communication networks to mechanical systems resulting in a monograph (Crandall, Mark, 1963). Since natu­ral frequency tuning is not effective for broadband random disturbances, the advent of random vibration analysis fo-cussed designers on finding the best set of spring and damp­ing rates for specific problems often by minimizing mean square response quantities. At about this time, optimal con­trol techniques were being developed and applied and there began to be a clear convergence of ideas about techniques to optimize the dynamics of control systems and mechanical vibrational systems (Karnopp and Trikha, 1969).

Although designers of vibration control systems began to use the same types of mathematics to describe their problems as control system designers, there remained an important difference. It was almost universally assumed in the vibration community that only passive devices such as springs, dampers or extra masses would be used to design isolation systems while control engineers almost always thought of active actu­ating devices responding to sensed variables for their sys­tems. During the decade of the 1960's the ideas of active control for vibration isolation began to be widely proposed but the widespread practical implementation of these con­cepts has only recently become practical.

Below, two specific areas of application of active and semi-active suspensions will be discussed in which one com­mon concept has played a role and in which commercial products have been designed and put into production. The first area involves seismic isolation platforms for sensitive experiments or for manufacturing processes requiring ex­tremely low levels of vibration. The second involves automo­tive suspensions which are subject to large and unpredictable roadway disturbances and maneuvering loads. The concept is the so-called "skyhook damper" which has been realized as part of a variety of active and semi-active isolation schemes. It is of interest that although common concepts may appear in two different applications of vibration isolation, entirely different actuator, sensor and signal processing hardware may be dictated by different excitation and response require­ments.

2 Basic Ideas of Active Vibration Isolation It is not possible here to review the many hundreds of

contributions to active vibration isolation over the past 50 years. See ElBeheiry et al. (1994) and Hrovat (1993) for two recent extensive bibliographies. Early examples of active sus-

Moving Base Fig. 1 Single degree-of-freedom active vibration isolator

INPUT VIBRATION

OPTIMUM TRANSFER

i

FUNCTION

W (S) Y

Bta f 'f- ' gun

M

" ' i IM/Y\

J k-f

RECEIVER VIBRATION

RELATIVE EXCURSION

<?

Fig. 2 Block diagram for Wiener filter design of active isolator

pensions in the 1950's and 60's tended to be concerned with specific hardware for the actuators and sensors, and con­troller signal processing was severely limited (Federspiel-Labrosse, 1954, 1955; Olson and Allen, 1965; Smith and Lum, 1968; Leatherwood and Dixon, 1968). Here we concen­trate on general studies of the theory of vibration isolation including active control forces which only later resulted in practical applications.

In the middle 1960's, the present author and a graduate student embarked on a research project attempting to apply the contemporary optimal control concepts to vehicle suspen­sions (Bender, 1967a,b; Bender, Karnopp and Paul, 1967). (This was part of a federal government sponsored program intended to revolutionize ground transportation.) The sim­plest possible vehicle suspension model is shown in Fig. 1 where V0 represents the vertical velocity due to roadway unevenness and the V is the velocity of the suspended mass. The innovation in the isolator conceptual design was to make no presumption about how the suspension forces were to be generated. The technique used to formulate an optimal sys­tem was based on the so-called Wiener filter which could, for example, find the transfer function between V and V0 which would minimize a weighted sum of mean square acceleration of the isolated mass and a mean square relative excursion or rattle space between the mass and the base for random base excitation. Figure 2 shows a block diagram used in setting up the Wiener filter process. A Wiener filter solution produces the optimal closed loop transfer function. State space tech­niques, which were developed subsequently, solve the same problem by producing a set of feedback gains relating the active force to the system state variables.

The classical textbook isolator system shown in Fig. 3 has the following well known transfer functions if the spring and damper are considered to be linear:

V _ 2£a>„s + co2

V0 s2 + 2ltoBs + a>l

V s/m

~F ~ s2 + 2l<oms + (o2

(1)

(2)

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10.0

Fig. 3 Conventional passive isolator

10.0

1.0

Ml

0.1

0.001 —l—r-

i

"/ 1

Y ,

C=1.0 ^

0 .707-

" 0.25 -

U . 1

0 0

. . .

S. s \ s

/

/

> •

I-W 0.1 1.0 10.0

ia/u>

Fig. 4 Frequency response plot for passive isolator

where 5 is the Laplace transform variable, f is the damping ratio, con is the natural circular frequency and m is the mass.

Figure 4 is a frequency response plot from Eq. (1) showing that con divides the low frequency range in which the mass velocity essentially follows the base velocity, V =V0, from the high frequency range of isolation, V < V0. A fundamental problem is that while a high value of damping ratio sup­presses the resonance—which is good—it also comprises the isolation for co > u>n. (This is the fundamental problem Den Hartog referred to in the quote about damping in automobile suspensions cited in the introduction.)

When the Wiener filter technique was applied, it was found that the optimal transfer function for the active isola­tor corresponding to Eq. (1) for the passive isolator became:

1.0

v/v«|

0.1

0.01

f\ ' • f Y

""s ~ X T T 1 < \ A \

- C - 0 . 1

- 0.Z5

- 0.5

- 0.707(opt1mai;

- 1 . 0 .,

j a \ i

V IA Sfc SK \8

0.1 1.0 u/u) 10.0

Fig. 5 Frequency response for the optimal active isolator

V

+ 2£cons + u>l (3)

where £ was always y2 / 2 but wn depended upon the weight­ing factor between mean square acceleration and mean square rattle space in the criterion function used for optimization. The frequency response plot of this transfer function shown in Fig. 5 shows that damping values sufficient to control the resonance have no adverse effect on high frequency isolation. The curve for the optimum damping ratio of £ = 0.707 in Fig. 5 shows that the optimum isolator forms an ideal low-pass filter with a cut off frequency of wn. Strictly speaking, the result is valid only for a white-noise velocity input, but intuitively one can imagine that low frequency input compo­nents of V0 must be followed by V in order to minimize the mean square relative deflection of the isolator while at high frequencies the isolator should apply only small forces to minimize mean square acceleration of the isolated mass. Thus the response of V falls off sharply for frequencies greater than con.

Clearly, a resonant peak is undesirable so it seems logical that f should be greater than about 0.5, but too high a value for I effectively lowers the response near a>/wn = 1.0, in­creasing deflection without changing the degree of isolation for o)/(i>n » 1.0. The optimum filter has just enough damping to provide a sharp low pass filter response with no resonance peak, and the tradeoff between suspension deflection and acceleration is adjusted entirely by changing the undamped natural frequency coir

The important point is that the passive isolator system represented by Eq. (1) and Fig. 4 is considerably different from the optimum active isolator system represented by Eq. (2) and Fig. 5. No parameter set for the passive system can result in an optimum system. The fundamental reason is that the placement of the damper in Fig. 3 results in high forces

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^ ^ v

V,

V

v„ Fig. 6 A skyhook damper system and a partially active system incorporating a spring

transmitted from the base to the isolated mass for input components at frequencies well above the natural frequency. This effect cannot be mitigated for a passive system by reducing the damping since then undesirable resonant re­sponse occurs for input components near the natural fre­quency.

Although the original idea was to generate any force necessary using some form of actuator as shown in Fig. 1, it soon became apparent that an "almost passive" system as shown in Fig. 6 could be arranged to have the optimal transfer function. The problem with the conventional passive system of Fig. 3 was that the damper was in the wrong place, producing a force related to the relative velocity between the mass and the base rather than a force related to the absolute mass velocity. In many cases, and certainly for most vehicles, there is simply no place to attach the end of a physical damper which should have zero inertial velocity. We there­fore called the configuration on the right side of Fig. 6 a "skyhook damper" system. The actuator produces a force Fc equivalent to the force a physical damper connected to ground would produce. Although the skyhook damper con­cept was derived originally only for a single degree-of-free-dom system with a white noise input, isolators applying forces or moments to inertia elements related to their absolute linear and angular velocities by active or semi-active means are still often referred to as skyhook damper systems.

When state space techniques became better known, the Wiener filter approach was largely supplanted by state vari­able feedback methods. One could then see that for the single degree-of-freedom case, the spring and skyhook damper were providing forces proportional to two state vari­ables (Karnopp, 1973). The Wiener filter does, however, have an interesting advantage since it applies to more than finite state systems. For example, if vehicles travel along guideways which can be sensed ahead of the vehicle, a preview effect is possible and its benefit can be assessed. Figure 7 (Bender, 1968) shows optimal trade-off curves for active suspensions with zero and infinite preview as well as an approximate realization using a skyhook damper, a "real" spring of con­stant kv and an active component which could be realized by a spring of constant ks reacting to the roadway ahead of the vehicle. There was a proposal to achieve the effect of preview using sensed signals throughout a long train (Karnopp, 1968) and attempts to use roadway information sensed ahead of vehicles have continued to the present day.

Although studies of active and semi-active suspensions have gone far beyond the simple single degree-of-freedom discussed above, it is notable that the idea of the skyhook damper force reappears over and over again in isolation control strategies as engineers search for simple and effective means for vibration control with passive and active elements.

0.04 0.06 0.1 0.2 0.4 0.6 08 10 20 30 VEHICLE-ROADWAY RELATIVE DISPLACEMENT

(SEC1"^) \JZ r AV

Fig. 7 Vibration clearance trade-off for simple preview suspension for several values of preview time, T (seconds) (Bender, 1968)

We next discuss two areas in which active control ideas have resulted in viable products. In both cases, the idea of abso­lute velocity feedback has played an important although certainly not exclusive role.

3 Seismic Isolation Platforms Certain instruments and manufacturing systems are ex­

tremely sensitive to vibration and must be isolated from micro-seismic base motion. Typically such devices are mounted on massive blocks supported on soft suspensions. Because of the extreme levels of isolation required many practical difficulties arise in the design of the suspension elements. Limitations to isolation may be due to "spring surge," (the modal response of low spring constant steel springs), or due to small amounts of dry friction in the suspension. A partially active type of suspension involving self-leveling pneumatic isolators has been used since the 1960's (Kunica, 1965).

Damping of the type represented in Figs. 3 and 4 is not desirable and, since the relative motion between the isolated block and the support is small and the forces must also be small, it is quite feasible to consider applying active forces using voice-coil electromagnetic actuators to generate the force Fc shown in Fig. 6. While various types of sensors and control loop compensation schemes have been used (Broder-sen, 1974), it is interesting that a commercial system, the Electrodamp Active Vibration Control System (Anon, 1994c) uses as sensors geophones which, above a natural frequency, produce a signal proportional to the absolute velocity of the isolated mass. Thus, in simple terms, a geophone, a propor­tional amplifier and an electrodynamic actuator provide an active skyhook damper system. A recent patent (Schubert, 1992) uses this scheme with an electronic circuit to extend the geophone's ability to sense velocity below its mechanical natural frequency and this type of system has been available for a number of years in the Electrodamp product (see Fig. 8). Another system, the Neutralizer (Anon, 1993) also uses voice coil actuators, geophones, and pneumatic spring ele­ments to support a block and to provide isolation in up to six degrees-of-freedom using active force control.

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HL 21 —T1 K F u i f - ;^ 2 2

PAYLOAD MASS M ,X4«m_ i „, , I g ^

g j r 8 — ' 13 *IN SOUT j l r ^ ^ y a y _ r - f _ r ^ r ^ f _ y | l > , , f / r r r t 7 y y , —

"-yyTTrr-r-r-

7 6 . „C «G C

JguL

Fig. 8 Schematic diagram of an active isolator (Schubert, 1992). Upper figure indicates a velocity sensor (21), a compensation cir­cuit to extend the sensor frequency response (22 and middle fig­ure) and a voice coil force actuator (15 and bottom figure).

m „

i - = ^ _ I | -==1

m ,

R

_f

_J «.. Fig. 9 A "hard mount" active isolator (Beard, Schubert and von Flotow, 1994)

Although the skyhook damper scheme essentially changes the transfer function of Eq. (1) to the more desirable transfer function of Eq. (3) it leaves the transfer function due to'force disturbances of Eq. (2) unchanged. In some cases force disturbances on the mounting block or coupling to vibration modes of the equipment mounted on the block may degrade the isolation system performance and require complex tuning of the feedback paths to the actuators.

A proposed solution to the problem of force disturbance rejection using a "hard mount" concept is shown in Fig. 9 (Beard et al., 1994). In this system a stiff piezoelectric actua­tor supports an intermediate mass, m,, on which a conven­tional passive suspension rests supporting the isolated mass, mp. In this scheme, the passive suspension is stiffer than the pneumatic springs used in the two active systems discussed above thus rejecting force disturbances better but only pro­viding isolation at relatively high frequencies. Feedback con­trol of the piezoelectric actuator which basically controls the deflection 5C in Fig. 9, reduces the motion of m, to provide isolation at low frequencies. Interestingly enough, even for this very different active suspension it is found advantageous

0 1

«*-

T

1

Fig. 10 Schematic diagram of an active suspension constructed by Federspiel-Labrosse in 1954

to incorporate an "inertial damping" or skyhook damping effect for the isolated mass by means of an outer control loop. It is shown in Beard et al. (1994) that "Measuring passive mount load or deflection, the inertially damped trans-missibility of [Fig. 5] is realizable." Thus although this system uses a piezoelectric deflection actuator, it can be arranged to yield the same type of transfer function as a skyhook damper system.

In this application area, the physical requirements for relatively small forces and deflections are such that elec­tromechanical actuators of the voice-coil or piezoelectric type can be used and forces can be exerted directly on the moving ground as in Fig. 6. Problems arise mainly with the sensors and the control scheme. In the next application area the practical problems are associated more with the actuators and their power requirements and the actuators can only exert forces between two masses in the system and not on the moving ground itself. In this case the isolation problem is considerably more complex, but even here there is validity to the skyhook damper concept of inertial velocity feedback.

4 Automotive Active Suspensions The term "active suspension" is probably associated today

mainly with automobile suspensions and, indeed, interest in active vehicle suspensions goes back some 40 years (Federspiel-Labrosse, 1954, 1955). Figure 10 shows a schematic diagram of his system which was built and tested on the famous French car, the Citroen 2CV. His hydraulic system had valves controlled by a pendulum and was appar­ently inspired by his early work on television amplifiers. Other attempts at active suspensions also tended to used inertia effects both to sense acceleration and to actuate hydraulic valves (Obson and Allen, 1965).

There was a considerable time lag between the early active suspension systems using no electronics and the surge of prototype and limited production systems which began to appear in the 1980's. Toyota had a system for its Soarer in 1983 (Yokoya et al., 1984) and Group Lotus Car Companies attained a well known patent in 1984 (Williams and Wright, 1984). Lotus was an advocate of high bandwidth active sus­pensions and they have been particularly active in racing cars (Wright and Williams, 1989).

It was apparent by the 1980's that electronic sensors and computers had reached a state such that sophisticated sus­pension systems were at least possible but the question of which type of actuator to use was vexing. Automotive suspen­sions deal with large forces, velocities, and deflections and there are questions about how to generate forces efficiently, reliably, and at acceptable financial and energy costs.

By the 1990's there were commercially available automo­tive active suspensions. Figure 11 shows a typical pressure

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Skyhook damper

I Manosuvering I loads

® Manosuvering loads ,

A m—i

Broadband actuator Control

Fig. 12 and Heess.

Roadway disturbances Roadway disturbances

Two contrasting versions of active suspensions (Karnopp 1991)

Fig. 11 Schematic diagram of electrohydraulic pressure control system (Hkatsu et al., 1990)

controlled strut actuator available on Toyota and Nissan vehicles in Japan and other countries (Yokoya et al., 1990; Akatsu et al., 1990). Such systems had some clear advantages over passive suspensions but also some disadvantages. A 1991 Nissan Infinity with active suspension when compared to the same car with a passive suspension cost more ($5500), weighed more (202 lbs.) and the suspension absorbed three to five horsepower. The result was a decrease in fuel economy from 16/22 city/highway mpg estimates to 14/19 (Cere, 1991).

It is important to recognize that automobile suspensions must perform several tasks in addition to isolating the body from vibrations induced by roadway unevenness (Karnopp and Heess, 1991). The body attitude must be controlled against maneuvering loads from cornering, braking and accel­erating and the attitude of each wheel with respect to the road surface (in particular the camber angle) must be con­trolled by the suspension. Furthermore, it is desirable to limit the dynamic normal force variations at each wheel to aid in longitudinal and lateral force generation by the tires and to limit the suspension deflection. Many of these requirements lead to design conflicts which can only be imperfectly re­solved with passive suspensions. Sports cars tends to have stiff, harsh suspensions with poor ride quality while luxury limousines may have a smooth ride on straight roads but poorly controlled body motions on curves or rough roads. Although we are focussing here on the vibration isolation aspects of automotive suspensions, it is clear that active suspensions should allow more flexibility in meeting the several conflicting requirements than suspensions restricted to the use of only passive elements.

Although there are arguments in favor of high bandwidth, fully active suspensions (Tillback and Brod, 1989; Wright and Williams, 1989), most commercial systems can be classified as low bandwidth systems which attempt to control body modes in the 1 Hz frequency range actively but control wheel hop modes in the 10 Hz frequency range mainly by passive means. The active systems have proved effective in control­ling body motions better than passive suspensions but gener­ally have not been as successful in improving high frequency isolation (reducing "harshness" in automotive terminology) compared to passive suspensions. A comparison of two types of active suspensions with a standard passive suspension on the same model automobile (Hillebrecht et al., 1992) using

Rood Surface

r-CHJL essure Control | |

Equivalent Model Propagation Character.siics

^ FN Frequency

o Resonant Frequency or Spring

Conventional Suspensions

Resonant Freauency ol Soting

Fig. 13 Schematic diagrams showing the skyhook damper force as a component of the control strategy for the Nissan hydraulic active suspension (Anon., 1989)

customers' subjective opinions showed that only certain as­pects of body control by the active systems were considered to be noticeable improvements.

The number of patents in the field of active suspensions is very large (Wallentowitz, 1991) but there continues to be a need for concepts which solve important motion control and isolation problems without requiring unrealistic hardware performance or costs which outweigh benefits.

There are many attempts in recent years to sort out the essential and realizable functions which active suspensions can be expected to perform, (Hrovat, 1993; Karnopp and Heess, 1991; Karnopp, 1992) and there are a number of proposed versions of active suspensions which use different hardware configurations to reduce power, increase reliability and reduce cost. Figure 12 shows two contrasting concepts. Fast load leveling (or "slow active" or "low bandwidth") active systems combined with semi-active controlled shock absorbers for higher frequency force generation could result in more practical systems than the high frequency actuator approach (Karnopp, 1987).

Naturally, there are a wide variety of control systems for the many proposed or realized active systems. It is interesting however that many contain a "skyhook damping" component (Tillback and Brod, 1989; Anon., 1989; Yokoya et al., 1984; Yokoya et al., 1990; Akatsu et al, 1990). Figure 13 shows how the Nisson Hydraulic Active Suspension incorporates a skyhook damper effect. The incorporation of absolute body velocity feedback in addition to other feedback terms and forces that could be generated by passive elements allows a close approach to an optimal state variable feedback system. This type of control policy is even more prominent when we consider high frequency control of dampers as a means to

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Fig. 14 Electro-hydraulic active damper schematic (Karnopp, Crosby and Harwood, 1974)

generate suspension forces with negligible power supply re­quirements.

5 Semi-Active Damper Suspensions For some vibration control problems such as those dis­

cussed in Section 3, the force level, frequency response, and deflection magnitude requirements are such that actuator and power supply limitations are not crucial to the introduc­tion of actively controlled forces. In other cases, such as the case of vehicle suspensions physical actuator limitations or cost considerations may render an elegant design concept totally impractical. For this reason there has been interest in exploring the possibility of improving isolator performance by modulating the characteristics of essentially passive elements such as springs and dampers.

Some early automobiles had provisions for the driver to adjust the shock absorbers but drivers of the time were not able to see enough advantage to such systems to warrant the extra expense and complexity. Many present-day automobiles have adjustable shock absorbers but most of these switch damping characteristics in response to sensed variables such as vehicle speed, lateral and longitudinal acceleration or other important variables.

Here we discuss quite another concept—a semi-active damper considered as an unpowered actuator which attempts to generate control forces similar to those that could be generated by a servo-actuator with a power supply. The original idea goes back to the early 1970's (Crosby and Karnopp, 1973; Karnopp, Crosby and Harwood, 1974) and resulted in the first of a series of patents (Karnopp and Crosby, 1974). At the time, the motivation was to generate skyhook damping forces using a controlled shock absorber. The patent was filed September 19, 1972 and many years later an English patent was discovered which was filed four days earlier (but granted later) which contained very similar ideas (Witt, 1976). Later a number of patents were filed which proposed a variety of hardware and control concepts for actively controlled dampers. Figure 14 shows the original concept which involved electrically controlled blow-off valves to control piston pressure separately in the tension and

Fig. 15 Schematic diagram of the electrohydraulic valve in the piston of a semi-active damper (Anon., 1992)

compression directions. A decade later shock absorbers based on this principle were designed and constructed in California and tested on an American vehicle in Germany. In the succeeding years many versions of semi-active dampers have been devised (Anon, 1992; Ohlin, 1988; Emura et al„ 1994; Decker et al., 1988). See for example Fig. 15. In this example, check valves assure that for both directions of piston motion, the hydraulic fluid flows the same way through a solenoid controlled blow-off valve. Electrical control power is supplied by wires in the hollow piston rod.

From the beginning, it was recognized that dampers can only dissipate mechanical power and thus the sign of the damper force (tension or compression) is always constrained by the sign of the relative velocity across the damper. Thus, it is not possible in principle for a semi-active damper to produce an arbitrary feedback control force at all times. This seemed to be a significant limitation in the first experiments on single degree-of-freedom systems but, as computer simu­lation studies showed, for more complex systems and for certain types of feedback strategies, the limitation was often not serious (Karnopp and Allen, 1975; Allen and Karnopp, 1975; Karnopp, 1988).

A study of a quarter car vehicle model (a two degree-of-freedom body, wheel model) showed that a combination of relative velocity damping forces and skyhook components in the damper was very effective in damping the body reso­nances without detrimental effects on isolation for frequen­cies between the body resonance frequency and the wheel hop frequency (Karnopp, 1983). See Figs. 16 and 17 and compare with the single degree-of-freedom case of Figs. 4 and 5. The generation of a combination of skyhook forces and conventional passive damping forces in an active damper means that the control force usually would dissipate power so that a semi-active damper is a nearly ideal actuator for this type of control law.

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101

5

2

10°

5

2

icr1

5

V/VO (BP: BPN/4 TO BPNX4]

10"

l = j

*gsd -*«

: : : =fi= / \

M A 4 1 rv-^ \ \ \ \ V \

• N

s S, \ \

"V \ \ \

V ^

Is

\ ^

' / \ " 7~m.

\ \

\ \ s \ 10" 10° 2 5 101 2

FREQUENCY [HZ] 10c

Fig. 16 Variations in frequency response of the body velocity due to roadway velocity input for quarter car model as passive damping is varied (dark line represents conventional suspension)

101

5

2

10°

5

2

io-i

5

V/VO [BA: BPNXO TO BPN*4]

10"

~*s~ k. • ^ \

-. V ' s \ V

".— N\^

10" 10° 2 5 101

FREQUENCY [HZ] 102

Fig. 17 Variations in frequency response of body velocity due to roadway velocity input for quarter car model as skyhook damping is introduced (dark line represents conventional suspension)

As far as body isolation goes, a skyhook damping force applied between body and wheel produces results not much different from full state feedback using an unrealistically ideal force generator (Chalisani, 1986). See Fig. 18. One reason is that any linear feedback force applied between wheel and body results in a fixed frequency response for the body transfer function at a specific frequency near the wheel hop frequency (Hedrick and Butsuen, 1988). Thus active control forces have major effects on isolation near the body resonant frequency but little effect near the wheel hop reso­nant frequency. This can be seen in Figs. 16, 17, and 18, and reinforces the idea that skyhook damping of the body abso­lute velocity is a good place to start in developing a control law for semi-active suspension vehicles. Semi-active dampers can also be controlled to emphasize reduction in pitch and roll motions using either pitch and roll rate sensors or through the use of absolute velocity sensors at three or more points on the body. Some semi-active shock absorbers incor­porate accelerometers to measure body acceleration at the

- -4B0O X | .1524 X2 » 1348 Xg + &M X«

_l_ _L_ 0.1 1 10 100 1000

Frequency (rad/sec)

Fig. 18 Acceleration frequency response curves for reference passive suspension and an ideal complete state variable feedback active suspension (Chalasani, 1986)

mounting point and to electronically convert to body velocity at each of the four mounting points.

Recently there has been indication that semi-active sus­pension systems will be commercially available (Anon., 1992; Anon., 1994a,b). It may be that a system using low power active elements for vehicle attitude control and semi-active dampers for resonance control and intermediate frequency isolation will finally prove to be commercially more success­ful than the low band with hydraulic active systems presently on the market (Karnopp, 1987). One must keep in mind that while a semi-active damper can improve isolation against roadway unevenness, it cannot react effectively to reduce roll in a steady corner or pitch due to severe braking or accelera­tion. In these cases, it seems necessary to be able to supply energy as well as to dissipate it.

6 Conclusions It is probably no surprise in retrospect that progress on

practical active or semi-active vibration control systems has been relatively slow. The design of such systems requires a clear concept, related not only to the mechanics of the system but also to automatic control and system dynamics. Sensors and actuators must be available and their limitations considered and finally cost effective signal processing devices must be available. Only relatively recently has progress in all these aspects come to the point at which practical designs are possible. The reason why so much effort has been expended in the field of automobile active suspensions no doubt has to do with a potential mass market, but there are many other potential areas for active control. Active noise control tech­niques are well advanced, active motor mounts are in the prototype stage and there are even proposals for actively isolating buildings from earthquakes. Although each applica­tion area has its own specific problems, some of which may prove practically insurmountable, the future will certainly see an increasing use of active means for vibration and noise isolation.

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Special 50th Anniversary Design Issue JUNE 1995, Vol. 117/185

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