the control of semi-active dampers using relative control

892483

The Control of Semi-Active Dampers Using Relative Feedback Signals

Mark R. Jolly and Lane R. Miller Lord Corp.

Reprinted from SP-802 — Advanced Truck Suspensions

Truck and Bus Meeting and Exposition

Charlotte, North Carolina November 6–9, 1989

Downloaded from SAE International by Li Sun, Tuesday, January 20, 2015

No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher.

ISSN 0148–7191 Copyright 1989 Society of Automotive Engineers, Inc.

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. For permission to publish this paper in full or in part, contact the SAE Publications Division.

Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Activity Board, SAE.

Printed in U.S.A.


892483

The Control of Semi-Active Dampers Using Relative Feedback Signals

Mark R. Jolly and Lane R. Miller Lord Corp.

Abstract

An algorithm has been developed for the control of semi-active dampers which uses the feedback of displacement and velocity signals measured across the damper. This algorithm has been called "relative control." Experimental and computer simulation data show that the performance achieved with relative control can be superior to that of passive dampers. The motivation for examining this approach is that relative control can be implemented without electronics. Thus, an all-mechanical damper device, which in appearance looks identical to a conventional shock absorber, can be designed to implement relative control.

Introduction

In recent years, controlled suspension systems have begun to evolve into the market place. Technologies ranging from manually adjustable to fully active suspensions have been introduced or are being developed [1]. Obviously, the cost of the suspension system varies greatly with its level of sophistication. Many automotive and trucking applications may require active suspension systems which are

composed of sensors, actuators, and microcontrollers. However, in some applications, cost, simplicity, and ease of installation may be overriding factors. For these applications, a semi-active control approach called "relative control" has been developed which may have the potential for eliminating sensors, electronics, and actuators [2]. This concept is principally based on improving vibration isolation. Thus, while it may be applied to primary suspensions, secondary suspensions such as truck cab isolators and equipment mounting may benefit the most.

Semi-active suspensions have been shown to provide superior vibration isolation over conventional suspensions [3,4,5,6,7,8]. The active damper, shown schematically in Figure 1, is the key element of a semi-active suspension system. An active damper is similar to a passive damper in that both are only capable of

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dissipat ing energy. However, the force/velocity characteristics of the active damper can be varied by modulation of a valve.

A conventional single-degree-of-freedom (SDOF) suspension model is shown in Figure 2. This system is capable of isolating the mass M from base inputs by a parallel combination of a spring K and

damper C. The transmissibility of this conventional system is shown with solid lines in Figure 3.

The transmissibility, in this case, is the ratio of the output motion to the input motion. This ratio can be of displacement, velocity or acceleration. Note that a family of curves is generated by varying the damping ratio, ζ.

As damping is increased, isolation improves at low frequencies, but degrades at high frequencies. This trade-off is an inherent disadvantage of conventional suspension systems.

While semi-active suspensions can be designed to eliminate this performance trade-off [5], they tend to be more complicated and costly. Typically, the semi-active suspension will include sensors, microprocessors and valves. Currently, semi-active control policies require absolute velocity of the suspended mass as a feedback signal. Because absolute velocity is impossible to measure directly, special filtering techniques [93 have been developed

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to produce estimates of the absolute velocity from accelerometer signals.

This paper will present a new control scheme, which has been called relative control, that lends itself to a simpler, less expensive suspension system. The performance of such a suspension system is predicted to fall between that of a passive system and that of current semi-active systems.

'Skyhook' Control

C u r r e n t l y , most semi-ac t ive suspension research efforts investigating real-time control use control schemes which are, in part, derived from what is often called skyhook control [5]. Because, in essence, relative control can be viewed as a derivative of skyhook control, it is appropriate to first review skyhook control theory.

Figure 2 shows a conventional base-excited SDOF system. The total force on the mass provided by the passive linear elements K and C is given by

where X1 is the velocity of the mass, X2 is the relative displacement between the mass and the base, and U is the base velocity input. Through the study of optimal control, it can be seen that the damper C should be located between the mass and an inertial reference such that the damper force is proportional to the absolute velocity of the mass [5]. The force on the mass becomes

This configuration, known as the 'skyhook' damper system, is shown in Figure 4.

Transmissibility curves for the 'skyhook' damper system are shown in dotted lines in Figure 3. It can be seen that, indeed, as damping increases, isolation improves at both high and low frequencies. The results of Figure 3 can be intuitively

reasoned. The 'skyhook' damper tends to resist the absolute velocity of the mass, while the conventional damper tends to resist the relative velocity between the mass and the base. Hence, for high frequency input, the conventional damper tends to stiffen the suspension where a soft suspension is desirable.

It is obvious that in most practical cases, such as vehicle suspensions, the 'skyhook' damper configuration is impossible to achieve. It is also impossible for a passive device located between the mass and the base to always mimick 'skyhook' damper force. For example, a conventional passive damper is only capable of resisting relative velocity, while a 'skyhook' damper generates forces independent of the relative velocity.

However, with the use of a semi-active damper, as shown in Figure 1, it may be possible to create any damping force Fd

between the mass and the base, as long as the power associated with that force is dissipated. In other words, it may be possible to vary damping C such that the force in Equation (1) looks like the force in Equation (2) when

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Since the semi-active damper cannot supply power to the system, the best it can do is to supply no damping force at all when Equation (3) is not satisfied. With the above considerations, a control policy can be constructed that will allow a semi-active damper located between the mass and the base to behave as close to a 'skyhook' damper as possible. This policy, given in Equations (4), will herein be referred to as skyhook control.

Assuming imperfect suspension devices, the in Equation (4) might imply "attempts to equal" or "ideally equals". It should be noted that the above considerations apply only to linear SDOF systems.

A version of skyhook control may also be implemented with an on/off type valve instead of a continuously variable valve. This means of control, often referred to as on/off control, is capable of creating a high relative velocity damping coefficient or a near zero damping coefficient, as dictated by the logic in Equations (4). On/off control generally performs worse than skyhook control, but is much easier to implement. Currently, most forthcoming semi-active suspension systems for automobiles use on/off control.

Relative Control

At the onset, the development of relative control was spurred by the desire to eliminate early difficulties in estimating the absolute velocity of the sprung mass. Further investigation and development uncovered more inherent advantages, one of which is the possibility of all-mechanical implementation [2]. The following development will outline the basic theory of relative control giving potential advantages and disadvantages as compared to skyhook control.

Relative control was developed by means of intuitive reasoning. Once again, semi-active control will be applied to a linear SDOF system as shown in Figure 2. The intuitive basis for relative control can be realized by considering the suspension force transmitted to the mass. In Equation (5), the suspension force FS is a combination of the spring force KX2 and the damper force C(X1-U).

Intuitively, for good isolation, we would like to minimize the suspension force FS on the mass. During oscillation, there are times when the spring force and damper force act in opposite directions. This situation occurs when the relative dynamic displacement X2 and the relative velocity X1-U act in opposite directions. Since the damper force opposes the spring force, the orifice area can be set such that the damper force and spring force tend to cancel each other. The spring force and the damper force act in the same direction when the relative dynamic displacement and the relative velocity act in the same direction. Since the spring force and damper force are additive in this case, the damping coefficient is set to zero to minimize the overall suspension force. Such control,

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which will herein be called relative control, is given by Equations (6)

Simulations have shown that optimal isolation is obtained when the gain α is near unity. Further investigation has shown that relative control is not too unlike skyhook control. Equations (6) differs from Equations (4) in that the damping force is varied between zero and some varying finite, value depending upon the sign of the product of relative velocity (X1-U) and relative displacement X2, rather than absolute velocity X1. For a broad frequency range, the relative displacement between the base and the mass X2 is in phase with and of proportional magnitude to the absolute velocity of the mass X1. The transfer function between the two states is given in Figure 5. Indeed, it can be seen that the two states behave similarly above the natural frequency of the SDOF system.

With the above considerations, a potential problem of relative control becomes evident from Figure 5. There is very poor correlation between relative displacement and absolute velocity at low frequencies. While this may have very little effect on the ability of relative control to isolate vibration, the system's performance may degrade at low frequency inputs.

Once again, the relative control logic may also be implemented with an on/off valve with a slight degradation in performance. It will become apparent that implementation of relative control with an on/off valve may only be easier in electromechanical systems, and not all-mechanical systems.

The Performance of Relative Control

Computer simulations were conducted of various types of suspension systems. To demonstrate the performance, simulation results of relative control will be compared

to the results of three other suspensions; 1) conventional, 2) skyhook controlled, and 3) fully active. Figure 6 gives a plot of the transmissibilities of the four different systems. It can be seen that the best performing system is the fully active, which essentially replaces the suspension spring and damper with an active force generator. With such a system, it is theoretically possible to mimick the forces that would be generated by a 'skyhook' damper. Relative control performs better than the conventional (passive) system, but slightly worse than skyhook control. Note that at

high frequencies, relative control performance is very similar to that of skyhook control. As predicted, at very low frequencies, relative control performs slightly worse than the passive system. In fact, Figure 6 suggests that the use of relative control may result in an amplitude ratio greater than 1.0 at 0.0 hz. Additional simulations were conducted at extremely low frequencies to study this effect. These simulations showed that the amplitude ratio approaches 1.0 at frequencies below 0.05 hz.

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Note that in Figure 6, relative control might perform similarly to a passive system which is tuned to a lower natural frequency. This performance, of course, occurs without any reduction in the spring constant and wi thout the added problems of precompression and vehicle height control. From a vibration isolation standpoint, relative control allows the suspension system to have the vibration isolation quality of a system which is tuned to a lower n a t u r a l f requency w i t h o u t the disadvantages that a corresponding passive system would have.

While the simulation results of relative control may look promising, putting it to practice will be the ultimate judge of its worthiness. Inherent disadvantages of relative control may make it unsuitable for many suspension applications. For instance, a relative control system, optimally tuned for higher frequency isolation requires more suspension travel than competing means of control. Advantages of theoretical or actual vehicle implementation of vehicle primary suspensions, which generally require optimization of suspension travel, wheel dynamics and isolation, have yet to be demonstrated. Simulations have also shown that relative control does not respond favorably to disturbance forces applied directly to the suspended mass.

It is likely that relative control may perform better in applications where most of the disturbance energy is transmitted at higher frequencies. Such applications might include truck cab suspensions.

Electromechanical Realization of Relative Control

Figure 8 shows a schematic representation of how relative control might be implemented on a SDOF system. A relative velocity signal can be provided by a Linear Velocity Transducer (LVT) and a relative dynamic displacement signal can be provided by a Linear Variable Differential Transformer (LVDT). These two signals are

sent to a microprocessor which implements the control policy. In the case of relative control, the control policy given in Equations (6) would be implemented. The result of this control policy implementation would be a force command which would be conditioned and sent to the valve of an active damper similar to the one shown in Figure 1. Note that an accelerometer is not needed and that the feedback quantities are all measured in the rattle space volume between the base and the mass.

The term re la t ive dynamic displacement is used to describe the measure of deflection between the mass and the base which does not include static deflections. Therefore, the LVDT would

essentially have to be "zeroed" once installed into the suspension system while the car is at rest. If the mass M does not change, this procedure will work. However, if the mass M changes by fairly large amounts, then some scheme to "re-zero" the LVDT output may be necessary.

An alternative configuration may be used to implement relative control. In this configuration, the LVT and the LVDT would be replaced with load cells located in series with the damper and spring, respectively. Hence, load cells are used to produce signals of the actual spring and damper forces. According to the relative control policy of Equations (6), the direction of the relative velocity (damper force) is

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needed rather than the actual magnitude. So, even though the damping coefficient is constantly changing, the force transducer connected to the damper can still determine the direction of the relative velocity.

The system shown in Figure 8 was demonstrated in the laboratory. The laboratory configuration has an undamped natural frequency of 1.5 Hz. A hydraulic shaker provides random base input which is approximately flat in the frequency spectrum out to 10 hz and then decreases in magnitude. The active damper [10] uses a passive pressure relief valve in parallel with an adjustable bypass orifice. A stepper motor actuator is used to adjust the orifice to achieve the desired damping force. This arrangement essentially allows the damper to be a force generator when relative velocity is such that the desired force dissipates energy. Under any other condition, the bypass valve is commanded to a wide open position, such that the damping force is minimal.

Three experimentally generated transmissibility curves are shown in Figure 8. The three transmissibility curves are representative of systems using a soft passive damper, a stiff passive damper and an active damper using relative control. It can be seen that the stiff damper is very effective at attenuating the resonant peak,

but poor at attenuating higher frequency input. The soft damper effectively attenuates higher frequency noise, but is unable to attenuate the resonant peak. This results in excessive mass motion at the system's damped natural frequency. It can be seen that the use of relative control allows for the attenuation of both the resonant peak and high frequency input. Here again, it can be seen that the use of relative control shifts the resonant peak to a lower frequency.

All-Mechanical Implementation of Relative Control

One of the key aspects of relative control, which warrants some investigation, is the possibility of all-mechanical implementation. This aspect gives relative control the potential for being as inexpensive as a conventional shock absorber. In Figure 8, a basic schematic of an all-mechanical configuration which implements the relative control policy is shown [2]. This device uses direct mechanical feedback of relative position X2

and relative velocity X1-U to implement the relative control policy of Equations (6). With the system at rest, the relative dynamic displacement X2 is assumed to be zero. Two check valves are in place between the upper and lower chambers of the damper such that flow, resulting from relative motion, must pass through one of the two spring loaded poppets. The flow can then pass through a check valve into the opposite damper chamber. It is assumed that when the system is at rest no load is on either sprung poppet. When the mass is displaced up or down from the nominal position, the mechanical feedback linkage loads either the lower or upper poppet, respectively. The poppets behave like pressure relievers in that they produce a pressure drop that is approximately proportional to preload imposed on the poppet springs.

The following discussion is intended to show how the device of Figure 9

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implements the relative control policy of Equations (6). For this argument, extended/ extending will be considered to be positive and compressed/compressing will be considered to be negative.

First suppose that the relative dynamic displacement X2 is positive and the relative velocity X1-U is positive. In this case, the feedback linkage loads the lower sprung

poppet and unloads the upper sprung poppet. Since flow must pass from the upper chamber to the lower chamber, it must pass through the unloaded poppet. This results in relatively free flow and minimal damping force is created. When the relative displacement and the relative velocity are both negative, the opposite flow situation is created and, again, free flow

results. These two situations correspond to the second equation of Equations (6).

When the re la t ive dynamic displacement and the relative velocity have opposite signs, the flow will be such that it must pass through a sprung poppet which has been loaded by the feedback linkage. In this situation, substantial flow restriction occurs and high damping force is created. It can be seen that as relative displacement increases, the feedback linkage provides increasing load on one of the sprung poppets. Hence, the flow resistance and the damping force increase as the magnitude of relative displacement increases. In fact, if the poppet areas and the poppet springs are designed correctly, damping forces as described by the first equation of Equations (6) can be approximated.

Practical designs for mechanically implementing relative control are being pursued. Most of the ways investigated involve integrating the necessary valving into the shock absorber piston head.

Conclusion

The performance of semi-active relative control falls between the conventional passive suspension and the semi-active suspension which utilizes skyhook control. Because of its inherent lower cost, when implemented in a mechanical design, relative control has the potential for quick market introduction.

To be marketable, semi-active relative control has to be less expensive than semi-active skyhook control and, at the same, time it must perform better than a conventional system. This report demonstrates that these two criteria are possible. In fact, the cost of a semi-active relative control suspension may rival that of a conventional suspension. This possibility may lead to a sizeable retrofit market. While superior vibration isolation has been demonstrated, semi-active relative control may require more suspension travel. This requirement may limit the use of relative control to vehicles that can

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accommodate larger suspension travel. Other vehicle dynamics, such as handling and wheel hop, have not been investigated thoroughly. Also, the use of relative control in secondary suspensions, such as truck cab suspensions, should be investigated. Semi-active relative control warrants continuing development effort.

REFERENCES

[1] Wright, P. G. and D. A. Williams, "The Application of Active Suspension to High Performance Road Vehicles," Paper No. C239/84, IMechE, 1984.

[2] Miller, L.R., "Control Method and Means for Vibration Attenuating Damper," U.S. Patent 4,821,849," April 1989.

[3] Crosby, M. J. and D. C. Karnopp, "The Active Damper," The Shock and Vibration B u l l e t i n , Vol. 43, Naval Research Laboratory, Washington, D. C , 1973.

[4] Sharp, R. S. and S. A. Hassan, "The Relative Performance Capabilities of Passive, Active and Semi-Active Car Suspension Systems," Proc. IMechE, Vol. 200, No. D3,1986.

[5] Miller, L. R. and Nobles, C. M., "The Design and Development of a Semi-active Suspension for a Military Tank," Proc. SAE, No. 881133, Aug. 1988.

[6] Margolis, D. L., J. L. Tylee, and D. Hrovat, "Heave Mode Dynamics of a Tracked Air Cushion Vehicle with Semi-active Airbag Secondary Suspension," Journal of Dynamic Systems, Measurement, and Control, ASME Publication, Dec. 1975.

[7] Krasnicki, E. J., "Comparison of Analytical and Experimental Results for a Semi-Active Vibration Isolator," Shock and Vibration Bulletin, Vol. 50, Sept. 1980.

[8] Krasnicki, E. J., "The Experimental Performance of an 'ON-OFF' Active

Damper," Shock and Vibration Bulletin, Vol. 51, May 1981.

[9] Miller, L. R., "The Effect of Hardware Limitations on an On/Off Semi-active Suspension," Proc. IMechE, Paper No. C367-020, Oct. 1988.

[10] Ivers , D.E. , Miller, L.R., "Experimental Comparison of Passive, Semi-active On/Off, and Semi-active Continuous Suspensions", 1989 SAE Truck and Bus Meeting and Exposition, Nov. 1989.

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Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. For permission to publish this paper in full or in part, contact the SAE Publications Division.

Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Activity Board, SAE.

Printed in U.S.A.


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