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Hardware-in-the-loop simulation of magnetorheological dampers for vehicle suspension systems


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Hardware-in-the-loop simulation of magnetorheological dampers for vehicle suspension systems
D C Batterbee and N D Sims* Department of Mecha

nical Engineering, The University of She?eld, She?eld, UK The manuscript was received on 22 May 2006 and was accepted after revision for publication on 9 October 2006. DOI: 10.1243/09596518JSCE304

Abstract: Magnetorheological (MR) ?uids provide an elegant means to enhance vibration control in primary vehicle suspensions. Such ?uids can rapidly modify their ?ow characteristics in response to a magnetic ?eld, so they can be used to create semi-active dampers. However, the behaviour of MR dampers is inherently non-linear and as a consequence, the choice of an e?ective control strategy remains an unresolved problem. Previous research has developed a method to linearize the damper’s force/velocity response, to allow implementation of classical control techniques. In the present study, this strategy is used to implement skyhook damping laws within primary automotive suspensions. To simulate the vehicle suspension, a two-degree-of-freedom quarter car model is used, which is excited by realistic road pro?les. The controller performance is investigated experimentally using the hardware-in-the-loop-simulation (HILS) method. This experimental method is described in detail and its performance is validated against numerical simulations for a simpli?ed problem. The present authors demonstrate that feedback linearization can provide signi?cant performance enhancements in terms of passenger comfort, road holding, and suspension working space compared with other control strategies. Furthermore, feedback linearization is shown to desensitize the controller to uncertainties in the input excitation such as changes in severity of the road surface roughness. Keywords: magnetorheological, HILS, feedback linearization, vehicle, suspension, control

1 INTRODUCTION It is well known that semi-active damping devices can o?er an attractive compromise between the simplicity of passive systems, and the cost of higher-performance fully active approaches [1]. Consequently, there has been a great deal of research to develop such dampers, along with suitable control strategies. An elegant method of creating a semi-active damper is to use a smart ?uid as the operating medium [2]. This ?uid can rapidly modify its ?ow characteristics when subjected to an electric or magnetic ?eld. In particular, magnetorheological (MR) ?uids, which respond to magnetic ?elds, have seen widespread commercial success in recent years [3].
* Corresponding author: Department of Mechanical Engineering, University of She?eld, Mappin Street, She?eld S1 3JD, UK. email: n.sims@she?eld.ac.uk

The con?guration of an MR damper is shown schematically in Fig. 1. As the damper piston moves, the MR ?uid is forced through an annular ori?ce (the ‘MR valve’), which is exposed to a magnetic ?eld generated by a coil. This leads to the formation of particle chains that increase the resistance to ?uid ?ow, thus enabling the development of a controllable damping force. A typical force–velocity relationship for an MR damper under di?erent magnetic ?elds is shown in Fig. 2. Various applications of MR dampers have been considered, such as the seismic control of bridges [4] or tall buildings [5], and suspension systems for vehicles [6], passenger seats [7], or washing machine drums [8]. One method that can be used to experimentally test such systems is the use of hardware-in-the-loopsimulation (HILS). This allows one aspect of the system to be physically tested, while the remainder of the structure is simulated in real time. For a vehicle suspension problem, the semi-active MR damper
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Fig. 1 MR damper design and operation

but the complex behaviour of the dampers means that the choice of control strategy remains an unsolved problem. Previous research by the present authors [6, 14, 17–19] has focussed on a control strategy that can enable the device to operate as a semi-active force generator, enabling the use of classical suspension control strategies. To date, the application of this approach has been investigated by HILS testing of single-degree-of-freedom (SDOF) structures [14]. In the present article, the work is extended to consider in detail the problem of automotive suspension systems, using a quarter-car model [20]. The paper is organized as follows: after introducing the theoretical approach with particular emphasis on controller design, the hardware and software con?guration is described. This experimental method is then validated by comparing model and experimental data for a simpli?ed problem. The experimental data for the suspension system problem are then presented, and performance comparisons are made between the di?erent control strategies. Finally, some conclusions are drawn regarding the relative performance of di?erent control systems, along with the suitability of HILS testing for this class of problem.

2 VEHICLE MODELLING AND CONTROL OBJECTIVES It is well known that the ride characteristics of passenger vehicles can be characterized by considering the so-called ‘quarter car’ model [20]. Here, the system is reduced to a 2DOF lumped parameter model that considers the tyre sti?ness and damping, unsprung mass, suspension sti?ness and damping, and the sprung mass. This method has been widely used to investigate the performance of passive [21], semi-active [9], and fully active [22] suspension systems. To excite the quarter car system, broadband random signals representative of typical roads can be used [23]. The road pro?les can be generated using the following displacement power spectral density function S(n) S(n)=Cn?w

Fig. 2 Typical force/velocity response of an MR damper. Sinusoidal excitation – amplitude= 6 mm, frequency=2 Hz

can be experimentally tested, while the dynamics of the vehicle are simulated. This enables the performance of the novel damper design to be characterized without building an actual suspension system. This technique was pioneered by Besinger, Cebon, and Cole in the 1990s, with particular emphasis on larger road vehicles [9, 10]. However, this work did not consider the use of MR dampers, which pose additional problems owing to their highly non-linear behaviour [11]. More recently, researchers from the smart materials community have considered the use of HILS techniques for MR dampers [12–16],
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A

m2 cycle/m

B

(1)

Here, n is the wavenumber (cycle/m), and C and w are ?tting constants describing the severity of road roughness. The wavenumber n is given by f /V, where f is the vibration frequency and V is the vehicle speed. Consequently, for a given vehicle speed,
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the inverse fast Fourier transform can be used to determine the road surface heights in the time domain [24]. In the present study, motorway and principal road excitations were generated with frequency content from 0 Hz to 20 Hz, and Table 1 shows the corresponding values of C, w, and V. Under these excitation conditions, the performance of the suspension system can be characterized in terms of the following signals [20]: (a) car body acceleration, which provides a measure of passenger comfort; (b) wheel contact force, which provides a measure of road holding; (c) suspension working space, which relates to the packaging space for the suspension system. These signals can be presented in the time domain, frequency domain, or more compactly as rootmean-square (RMS) values. An e?ective semi-active suspension system control strategy should minimize all three signals. Before introducing some candidate control strategies, however, it is necessary to tackle the non-linearity of the MR damper, which makes application of control more complex. 2.1 Feedback linearization MR dampers exhibit highly non-linear force/velocity characteristics, which makes the objective of achieving a desired force very di?cult. To overcome this problem, work by the current authors and their colleagues has shown how the force/velocity response can be linearized [17]. The linearized MR damper can e?ectively emulate a viscous dashpot with a controllable damping coe?cient. Thus the control problem is simpli?ed to the determination of the linear damping rate that provides the desired force. This control strategy is known as feedback linearization, which is brie?y summarized below. The fundamental controller associated with feedback linearization is illustrated in Fig. 3. Here, feedback control is being used to implement a semi-active force generator. Through the appropriate selection of the feedforward gain G, and the feedback gain B, it can be shown that the actual damping force F becomes equal to the desired set-point damping force F [25]. Consequently, if the set-point force is d

Fig. 3 Controller block diagram of the semi-active force generator

proportional to the piston velocity, then the MR damper response is linearized. For the present study, values of G equal to 0.001 A/N and B equal to 0.8 were found to provide a good response (further details regarding the choice of controller gain can be found in references [18] and [26]). For the values chosen, the performance is illustrated in Fig. 4, where the sinusoidal response of the MR damper has been linearized. Here the set-point force to the controller (Fig. 3) was F =Dv (2) d where D is the set-point gain or the desired damping rate and v is the piston velocity. As shown, when D=6 kNs/m the response becomes almost linear. Moreover, the actual damping rate correlates very well with the desired damping rate, thus demonstrating the controller’s force tracking capability. The responses

Table 1 Road pro?le parameters
Pro?le Motorway Principal road C (m1/2 cycle3/2) 7×10?8 50×10?8 w 2.5 2.5 V (miles/h) 70 60

Fig. 4 Linearized sinusoidal force/velocity response. Amplitude=5 mm, frequency=4 Hz
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for D=2 kNs/m and D=10 kNs/m represent the control limits of the device. When D=2 kNs/m, the set-point damping force is lower than the minimum value that is governed by the viscosity of the MR ?uid. Consequently, the current is set to zero amps, and the desired force is not achieved. It should be noted that the yield force e?ect that can be observed in this response is attributable to friction in the damper seals. For D=10 kNs/m, the set-point force is accurately achieved between ±0.06 m/s. Beyond ±0.06 m/s, saturation occurs as the maximum yield stress in the ?uid has been reached, i.e. the current is at its maximum value. Consequently, the actual force falls short of the set-point value. In the above example, the set-point force is always a dissipative one, i.e. the direction of the desired force is always in the same direction as the actual force. However, in a real control system, the set-point damping force may require an energy input into the system. In this scenario, the force produced by the damper opposes the desired value, and the MR control current will be switched o? in order to minimize the energy dissipated. In summary, feedback linearization provides an excellent force tracking strategy for MR dampers. However, it is still necessary to choose an appropriate value of the desired force at each point in time, and so some possible approaches will now be described. 2.2 Vehicle suspension control strategies Four di?erent suspension control strategies were investigated in the present study. 2.2.1 Open-loop To provide a performance benchmark for the controlled MR systems, an open-loop controller was investigated. Here, the feedback linearization procedure that was described in the previous section was not used. Instead, the current supplied to the MR damper was maintained at a constant level I , OL where values between 0 and 0.2 A were investigated. 2.2.2 Linearized As a more realistic benchmark, the MR damper was linearised using the controller that was discussed in section 2.1, so that the set-point force to the semi-active force generator (Fig. 3) was F =D(x ?x ) (3) ˙ ˙ d c w where x is the velocity of the car body, and x is ˙ ˙ c w the velocity of the wheel/axle assembly. This system is more representative of a conventional passive suspension with a viscous damper. The set-point
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gain D was varied between 1 kNs/m and 5 kNs/m, which approximately corresponds to sprung mass damping ratios between 0.2 and 1. 2.2.3 Linearized modi?ed skyhook control Skyhook control is well known to provide optimal performance for SDOF vibration systems. Here, the damping force is proportional to the absolute velocity of the vibrating mass, so that F =D x (4) ˙ d sky c This is known as linearized skyhook control, where D is the skyhook set-point gain. For 2DOF sky systems such as the quarter car, pure skyhook control attenuates vibration at the natural frequency of the sprung mass, but has an adverse e?ect at the natural frequency of the wheel mass (wheel hop frequency). This has led to an alternative strategy known as modi?ed skyhook control, which augments skyhook damping with body to wheel relative motion damping as an attempt to gain the advantages of both [9]. In the present study, the MR damper is used to achieve the modi?ed skyhook damping force. This is known as linearized modi?ed skyhook control, and with reference to Fig. 3, the set-point control force F is d F =D [a(x ?x )+(1?a)x ] (5) ˙ ˙ ˙ d sky-m c w c Here, a is a weighting parameter between 0–1, and D is the modi?ed skyhook set-point gain. When sky-m a=1, the desired force corresponds to linear body to wheel relative motion damping (which is identical with the linearized system – equation (3)) and when a=0, the set-point force corresponds to pure skyhook control (equation (4)). It will be shown in section 5 that this set-point force can be accurately achieved within the dissipative control limits of the MR damper. 2.2.4 On/o? modi?ed skyhook control On/o? modi?ed skyhook control involves switching the input current to a predetermined and constant level when the set-point force is a dissipative one I=I max : [a(x ?x )+(1?a)x ](x ?x ) ˙ ˙ ˙ ˙ ˙ c w c c w >0 – energy dissipation required

(6)

I=0: [a(x ?x )+(1?a)x ](x ?x ) ˙ ˙ ˙ ˙ ˙ c w c c w ∏0 – energy input required

(7)

Here, the controller gain I dictates the current max applied in the ‘damper on’ condition, and this was varied between 0.05 A and 0.2 A. Since no force feedback is required, the need to measure or estimate
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the damping force is eliminated. On/o? control therefore represents a major simpli?cation over the linearised modi?ed skyhook controller. However, the performance may su?er.

3 EXPERIMENTAL SET-UP When certain aspects of the model have particularly complex behaviour, such as a semi-active damper, the gap between theory and practice can be bridged by performing hardware-in-the-loop simulations. In the present study, the HILS con?guration shown in Fig. 5 was used. Here, the non-physical quarter car parameters are modelled in a real-time simulation. Using digital-to-analogue conversion, outputs from this simulation (damper displacement and control current) are used to excite the MR damper. Simultaneously, an analogue-to-digital converter provides the simulation with damping force data in order to complete the solution of the equations of motion. A photograph of the experimental facility is shown in Fig. 6. With reference to Figs 5 and 6, a host PC running xPC target is used to both implement the damper control strategies, and model the non-physical system parameters. This model is then downloaded onto a target PC, which performs the real-time simulation by communicating to and from the hardware via a National Instruments data acquisition card. An

Instron servohydraulic actuator and controller was used to excite a Carrera MagneShock MR damper, with a controlled displacement commanded by the target PC’s quarter car simulation. To power the MR damper, a high performance Kepco BOP ampli?er was used, providing high bandwidth dynamic current control. The actuator instrumentation included a built-in inductive displacement transducer, which was used for position feedback control of the servohydraulic actuator. Also, a dynamic load cell provided the force data for linearization of the MR damper, and simulation of the quarter car model. At this stage, it is worth pausing to consider the practical issues concerned with implementing the various controllers within an actual vehicle. The skyhook controllers described in section 2.2 require measurements of the absolute car body velocity, and the relative car body to wheel velocity. Such measurements can be di?cult to obtain from displacement sensors, especially the absolute velocity due to the lack of an inertial reference. However, previous research has shown how these variables can be obtained by integrating accelerometer signals [27, 28]. For example, Simon and Ahmadian [28] implemented on/o? skyhook control onboard a heavy truck. The authors used eight accelerometers in order to calculate the absolute car body and wheel velocities at each corner of the vehicle. With regards more speci?cally to feedback linearization, a means to measure the damping force is also required. This

Fig. 5 Schematic diagram of the HILS experimental facility
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Fig. 6 Photograph of the HILS experimental facility (with no damper installed)

could be accomplished using a load cell at each corner of the vehicle, or the force could be derived from a state estimator used in conjunction with the accelerometer signals. Such considerations are outside the scope of the present research but would be an interesting topic for future research. In the HILS experimental system, the velocity measurements are calculated in the ‘virtual’ loop and so sensors are not required. However, a complication arises owing to the presence of the actuator dynamics, which causes the actual damper displacement to lag behind the desired displacement. For the actuator in the current study, the phase delay

was found to be 6 ms in the frequency range of interest [14]. This delay means that the ‘simulated’ velocity of the mass, which is used to compute the set-point skyhook force (and hence current), does not coincide with the force and displacement that is actually being measured. To correct for this, an additional time delay (6 ms in this case) must be incorporated into the controller. This is illustrated in Fig. 7 for a linearized skyhook controller, where the velocity of the mass has been delayed by 6 ms. Consequently, the velocity used to compute the setpoint force is brought back in phase with the actual velocity.

Fig. 7 Skyhook control implementation with the HILS quarter car system
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Fig. 8 A schematic diagram of the HILS system numerical model

The inclusion of the above delay compensates for the velocity lag in the controller, but there is still a 6 ms delay in the force signal received by the realtime simulation from the physical test rig. This will a?ect the accuracy of the HILS results, e.g. sprung mass velocity, and thus it is prudent to validate the experimental method, which is the subject of the next section.

4 HILS VALIDATION Previous work [14] by the present authors used the HILS test facility to investigate a SDOF vibration isolator using an MR damper. A comprehensive model of the damper, HILS test rig, and control system was developed that allowed a detailed comparison between modelled and experimental behaviour. This work will now be summarized to demonstrate the validity of the HILS testing approach. Using a previously validated model of the MR damper [29], along with a servohydraulic system model, a numerical simulation of the hardware-inthe-loop experiment was made possible. This will be referred to as the ‘HILS simulation’ and the corresponding numerical model is illustrated schematically in Fig. 8; by removing the model of the actuator, giving the ‘ideal simulation’, the e?ect of the actuator dynamics can be investigated. Figure 9 compares the HILS experiment with the HILS simulation for a linearized skyhook controller. The results are shown in terms of the transmissibility estimate, where a broadband displacement excitation was used. For both skyhook gains, good correlation exists between the HILS simulation and the HILS experiment, thus validating the numerical model of the HILS testing method.
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Fig. 9 Transmissibility estimates of the linearized skyhook SDOF systems [14]

By subsequently removing the actuator dynamics from the numerical model a good indication of the performance of the real system will result. Moreover, the e?ect of the servohydraulic system dynamics on control system performance will be evident. The result is also shown in Fig. 9 as the ‘ideal simulation’. It can be observed that the main e?ect of the actuator dynamics is to increase transmissibility thus degrading performance. This is particularly the case at higher frequencies (above 7–8 Hz), where the 6 ms delay results in a more
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signi?cant error in the force amplitude received by the simulation. Although this provides an inaccurate representation of the high-frequency response, it was previously shown that the relative performance between di?erent control strategies remains largely unchanged [14]. The HILS approach therefore serves as an e?ective prototyping tool, as a good assessment of the relative controller performance can still be determined. Owing to the large similarities between the SDOF isolator and the 2DOF quarter car system, this result serves to validate the use of the HILS method in the present study.

5 EXPERIMENTAL RESULTS The HILS testing technique can now be used with con?dence to investigate the performance of the quarter car system, using the control strategies described in section 2.2. The non-physical system parameters used in this study are presented in Table 2, which were chosen to represent a small sized passenger car. For this vehicle con?guration, the Carrera MR damper provided a zero-?eld damping rate f approximately equal to 0.56. To maximize the min performance of a semi-active device, it is desirable for f to be small so that the energy dissipated min is minimized when an energy input is required. A scaling factor of 0.36 was therefore applied to the measured damping force F in order to lower f to min 0.2. In practice, this scaling could be achieved by modifying the damper’s internal geometry. To begin, Fig. 10 illustrates the e?ectiveness of the MR damper as a semi-active force generator. Here, the time history of the set point and actual damping forces is compared for the motorway excited linearized system. Clearly, the accuracy of the semi-active force generator is excellent, where the actual damping force tracks the commanded value very closely. This example serves to illustrate the usefulness of performing feedback linearization on MR dampers. In Fig. 11, the power spectral density (PSD) responses of the linearized modi?ed skyhook system are presented for the motorway excitation. Results
Table 2 Quarter car suspension parameters
Parameter Mass of car body Mass of wheel assembly Suspension sti?ness Tyre sti?ness Tyre damping rate Symbol (unit) M (kg) c M (kg) w K (N/m) K (N/m) w C (Ns/m) w Value 275 50 30 400 229 500 80

Fig. 10 Damping force–time history for the linearized quarter car systems. D=3 kNs/m. Motorway excitation

are shown for D =4 kNs/m where a is varied sky-m between zero and one. With reference to Fig. 11(a), skyhook control (a=0) is most superior in terms of passenger comfort, where signi?cantly lower PSD values are observed between 0 and 10 Hz. However, the disadvantage of pure skyhook control becomes apparent through observation of the wheel contact force prediction. As shown in Fig. 11(b), pure skyhook control minimizes the sprung mass resonant peak but the wheel hop vibrations become signi?cantly larger, as evidenced by the increased wheel force variation in the 9 to 14 Hz range. Figure 11(b) thus illustrates the advantages of using a modi?ed skyhook strategy (0<a<1), where by augmenting the skyhook system with linear body to wheel relative motion damping, the unsprung mass vibrations are improved. However, this improvement is at the expense of the sprung mass vibrations thus the suspension designer must tune a until a desirable trade-o? in performance is achieved. For the linearized modi?ed skyhook system, the desired force is not always dissipative, so it is interesting to investigate how e?ectively the MR damper can track the desired force. This is shown in Fig. 12, and the instants in time when an energy input is required are also indicated. During these instants, the set-point force is in the opposite
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Fig. 11 Frequency response of the linearized modi?ed skyhook system. D =4 kNs/m. sky-m Motorway excitation. (a) car body acceleration; (b) wheel contact force

Fig. 12 Damping force-time history for the linearized modi?ed skyhook quarter car system. D = sky-m 4 kNs/m, a=0.4. Motorway excitation

direction to the actual force, and so – as expected – the performance of the semi-active force generator deteriorates. Nonetheless, when the desired force is a dissipative one, the force tracking accuracy is very good as before. Furthermore, it was found that an energy input was only required for 20 per cent of the entire HILS test. This suggests that the performance of the semi-active MR system is likely to approach that of a fully active system. In conclusion, the semiJSCE304 ? IMechE 2007

active force generator performs extremely well in the face of broadband random excitations. This force tracking strategy could equally be applied to achieve force demands from other controllers, such as sliding mode or optimal controllers. The performance of the motorway excited on/o? modi?ed skyhook system is shown in Fig. 13. This is shown for I =0.15 A where a is varied between max zero and one. As with the linearized modi?ed skyhook system, pure skyhook control (a=0) provides the most superior response in terms of passenger comfort (Fig. 13(a)). However, with reference to Fig. 13(b), the on/o? system is unable to signi?cantly suppress the wheel hop vibrations when a is increased. Although some improvement can be observed for a>0, an analysis of the area under the PSD curves illustrates that there is no improvement in the RMS wheel contact force. Thus it is concluded that pure skyhook control is more suitable than modi?ed skyhook control, for an on/o? system. This result is in agreement with the present authors’ previous ?ndings in a recent numerical study of a quarter car MR suspension [6]. It is di?cult to ?nd optimal controller parameters based directly upon the frequency response of the system. An alternative approach is to compare the RMS value of one performance indicator against another, as a function of a control parameter. This is known as a con?ict diagram [9], and the optimal system will have its operating point closest to the origin where all of the performance indicators have been minimized. Figure 14 shows the con?ict diagram for the motorway excitation, where the RMS car body acceleration (Fig. 14(a)) and RMS wheel contact force
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Fig. 13 Frequency response of the on/o? modi?ed skyhook system. I =0.15 A. Motorway max excitation. (a) car body acceleration; (b) wheel contact force

Fig. 14 Con?ict diagrams for the motorway excitation. RMS suspension working space versus: (a) car body acceleration; (b) wheel contact force

(Fig. 14(b)) are plotted against the RMS suspension working space. In Fig. 14, the variable parameter for each control system is as follows: (a) open-loop: I is varied between 0.05 and 0.2 A; OL (b) linearized: D is varied between 1 and 5 kNs/m; (c) linearized modi?ed skyhook: curves are plotted for D =3 kNs/m and 4 kNs/m, where a is sky-m varied between 0 and 1. (d) on/o? modi?ed skyhook: as skyhook control is optimal for this system (see Fig. 13), a=0 and I is varied between 0.05 A and 0.2 A. max With reference to Fig. 14, the open-loop system clearly has the worst performance. This is owing to
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the non-linear force/velocity characteristics, which creates a harsh response when the velocity changes direction. The linearized system, which better emulates a passive device, improves on this response but it is the skyhook-based controllers that provide the best performance. Moreover, the linearized modi?ed skyhook system is superior to the on/o? skyhook system, where lower levels of car body acceleration and wheel contact force can be achieved. Figure 14 also con?rms that pure skyhook control (a=0) is optimal in terms of minimizing car body acceleration. Furthermore, the linearized skyhook system provides superior wheel contact force levels to the linearized ‘passive’ con?guration.
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Fig. 15 Con?ict diagrams for the principal road excitation. RMS suspension working space versus: (a) car body acceleration; (b) wheel contact force

Similar conclusions can be drawn from Fig. 15, which presents the con?ict curves for the principal road excitation. However, a further advantage of linearized modi?ed skyhook control arises via a comparison of Fig. 14 with Fig. 15. Except for the linearized modi?ed skyhook system, the shape of the con?ict curve changes with the input excitation. This causes the optimum controller gain to change and performance su?ers, particularly for the on/o? and open-loop strategies. This point is better explained with the following example. An operating point for each control system was chosen such that the wheel contact force is minimized on the motorway. These operating points are highlighted on Fig. 14 by the circular markers, and the corresponding control parameters are given in Table 3. The performance of the same controller con?gurations is then shown on Fig. 15 for the principal road excitation. Clearly, wheel contact force levels are no longer optimal, except for the linearized systems. As the main di?erence between the two road inputs is the excitation amplitude, these changes in the optimum

Table 3 Controller parameters for the optimized control systems
Control strategy Linearized Open-loop MR linearized modi?ed skyhook On/o? modi?ed skyhook Controller gain D=2 kNs/m I=0.075 A D =4 kNs/m MRm I =0.125 A max a – – 0.4 0

controller gain are evidence of strong non-linearity in the on/o? skyhook and open-loop systems. Thus it is apparent that feedback linearization has desensitized the otherwise non-linear MR damper to variations in the input excitation. The latter result is summarized in Fig. 16, which shows the performance of the optimized controllers as a percentage improvement over the linearized system. As shown, linearized modi?ed skyhook control is superior for all performance indicators and input excitations. For the motorway excitation, improvements in car body acceleration (CBA), wheel contact force (WCF), and suspension working space (SWS) are 8.3, 4.5, and 18.7 per cent respectively. The motorway excited on/o? skyhook system also performs well where improvements are 6.2 per cent CBA, 1.7 per cent WCF, and 12.1 per cent SWS. However, when the input excitation changes, the on/o? system performance is degraded and no improvement in wheel contact force and suspension working space is o?ered. On the other hand, the linearized modi?ed skyhook system maintains superior performance, where improvements are 10.2 per cent CBA, 5.4 per cent WCF and 10 per cent SWS. It is also shown how the performance of the open-loop system is inferior to the linearized system for all but one of the performance indicators and excitation conditions. This indicates that the open-loop MR system is a poor benchmark for demonstrating the performance of a closed-loop MR system, since this still does not necessarily imply that the closed-loop behaviour is better than a passive system.
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Fig. 16 Percentage performance improvements over the linearized system. Optimum controller parameters are given in Table 3

6 CONCLUSIONS The current paper has described the performance assessment of semi-active suspension systems using hardware-in-the-loop simulation and a magnetorheological damper. Despite the dynamics of the servohydraulic actuation system, and the complex behaviour of the MR damper, the experimental method has been shown to enable a comprehensive comparison between di?erent control strategies. Before drawing speci?c conclusions, it is worthwhile to compare this paper with previous contributions in the ?eld. The use of HILS testing for semi-active vehicle suspension was described in detail by Cebon and his colleagues [9, 10]. However, at that time MR dampers were relatively undeveloped and so these earlier studies did not investigate the control problems associated with them. More recently MR dampers have been used in HILS testing [12, 16], but to the current authors’ knowledge none of these contributions accurately modelled the roadway excitation conditions, while considering the con?ict diagram to interpret performance. Since MR dampers are particularly non-linear, their performance can be especially sensitive to the excitation. Consequently, this study has intentionally focused on two di?erent, but physically realistic excitation conditions, unlike previous work. At the same time, the present study has included a novel technique to linearize the otherwise non-linear behaviour of the MR damper, thus enabling the use of classical semi-active control strategies. With regards to the HILS testing method in general, it was shown that the e?ect of the servohydraulic
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system dynamics is to degrade performance, particularly at higher frequencies. For a vehicle suspension, the wheel hop response may therefore be particularly inaccurate. Nonetheless, the relative performance between di?erent control strategies should remain unchanged [14], which serves to validate the e?cacy of the HILS method for controller prototyping. The speci?c conclusions of this work are therefore as follows. 1. The open-loop control response is worse than the linearized ‘passive’ system in terms of all performance indicators. Therefore, this is a poor benchmark system for MR vibration control studies, since a semi-active performance better than the open-loop case is not necessarily better than a simple passive system. 2. Feedback linearization desensitises the controller to uncertainties in the input excitation. Unlike the equivalent on/o? system, the performance remains optimal despite a change in severity of the road surface roughness. 3. Feedback linearization permits very accurate force tracking in the face of broadband random excitations. In the present study, this was demonstrated for skyhook-based controllers, although the control concept is equally applicable to other controller techniques such as optimal control.

ACKNOWLEDGEMENT The authors are grateful for the support of the Engineering and Physical Sciences Research Council (EPSRC) through a Doctoral Training Accounts (DTA)
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studentship (D Batterbee) and an Advanced Research Fellowship (N D Sims – r/S49841/01).

REFERENCES
1 Karnopp, D., Crosby, M. J., and Harwood, R. A. Vibration control using semi-active force generators. J. Engng Industry, 1974, 96, 619–626. 2 Sims, N. D., Peel, D. J., Stanway, R., Johnson, A. R., and Bullough, W. A. The electrorheological longstroke damper: A new modelling technique with experimental validation. J. Sound Vibration, 2000, 229(2), 207–227. 3 Carlson, J. D. Magnetorheological ?uids – engineering applications today and tomorrow. 2nd ECCOMAS Thematic Conference on Smart structures and materials, Lisbon, Portugal, 18–21 July 2005. 4 Gordaninejad, F., Saiidi, M., Hansen, B. C., Ericksen, E. O., and Chang, F.-K. Magnetorheological ?uid dampers for control of bridges. J. Intell. Mater. Systems Structs, 2002, 13(2–3), 167–180. 5 Dyke, S. J., Spencer, B. F. Jr., Sain, M. K., and Carlson, J. D. Modelling and control of magnetorheological dampers for seismic response reduction. Smart Mater. Structs, 1996, 5, 565–575. 6 Batterbee, D. C. and Sims, N. D. Vibration isolation using smart ?uid dampers: a benchmarking study. Smart Structs Systems, 2005, 1(3), 235–256. 7 McManus, S. J. and St Clair, K. A. Evaluation of vibration and shock attenuation performance of a suspension seat with a semi-active magnetorheological ?uid damper. J. Sound Vibration, 2002, 253(1), 313–327. 8 Chrzan, M. J. and Carlson, J. D. MR ?uid sponge devices and their use in vibration control of washing machines. 8th SPIE Symposium on Smart structures and materials: damping and isolation, 2001, 4331, 370–378. 9 Cebon, D., Besinger, F. H., and Cole, D. J., Control strategies for semi-active lorry suspensions. Proc. Inst. Mech. Engrs, Part D: J. Automobile Engineering, 1996, 210, 161–178. 10 Besinger, F. H., Cebon, D., and Cole, D. J., Experimental investigation into the use of semiactive dampers on heavy lorries. Vehicle System Dynamics Proceedings of 12th IAVSD Symposium on Dynamics of vehicles on roads, 1991, pp. 57–71. 11 Yi, F., Dyke, S. J., Caicedo, J. M., and Carlson, J. D. Experimental veri?cation of multi-input seismic control strategies for smart dampers. J. Engng Mech., 2001, 127(11), 1152–1164. 12 Lee, H.-S. and Choi, S.-B. Control and response characteristics of a magneto-rheological ?uid damper for passenger vehicles. J. Intell. Mater. Systems Structs, 2000, 11(1), 80–87. 13 Choi, S.-B. and Han, Y.-M. MR seat suspension for vibration control of a commercial vehicle. Int. J. Veh. Des., 2003, 31(2), 202–215.
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14 Batterbee, D. C., Sims, N. D., and Plummer, A. Hardware-in-the-loop-simulation of a vibration isolator incorporating magnetorheological ?uid damping. 2nd ECCOMAS Thematic Conference on Smart structures and materials, Lisbon, Portugal, 2005. 15 Choi, S.-B., Song, H. J., Lee, H. H., Lim, S. C., Kim, J. H., and Choi, H. J. Vibration control of a passenger vehicle featuring magnetorheological engine mounts. Int. J. Veh. Des., 2003, 33(1–3), 2–16. 16 Lam, A. H. F. and Liao, W. H. Semi-active control of automotive suspension systems with magnetorheological dampers. Int. J. Veh. Des., 2003, 33(1–3), 50–75. 17 Sims, N. D., Peel, D. J., Stanway, R., Bullough, W. A., and Johnson, A. R. Controllable viscous damping: an experimental study of an electrorheological long stroke damper under proportional feedback control. Smart Materials Structs, 1999, 8, 601–605. 18 Sims, N. D., Stanway, R., Peel, D. J., Bullough, W. A., and Johnson, A. R. Smart ?uid damping: shaping the force/velocity response through feedback control. J. Intell. Mater. Systems Structures, 2000, 11, 945–949. 19 Sims, N. D. and Stanway, R. Semi-active vehicle suspension using smart ?uid dampers: a modelling and control study. Int. J. Veh. Des., 2003, 33(1–3), 76–102. 20 Crolla, D. A. Vehicle dynamics: theory into practice. Proc. Inst. Mech. Engrs, Part D: J. Automobile Engineering, 1996, 210, 83–94. 21 Sharp, R. S. and Hassan, S. A. Evaluation of passive automotive suspension systems with variable sti?ness and damping parameters. Veh. System Dynamics, 1986, 15(6), 335–350. 22 Wilson, D. A., Sharp, R. S., and Hassan, S. A. The application of linear optimal control theory to the design of active automotive suspension. Veh. System Dynamics, 1986, 15, 105–118. 23 Robson, J. D. Road surface description and vehicle response. Int. J. Veh. Des., 1979, 1(1), 25–35. 24 Cebon, D. and Newland, D. E. The arti?cial generation of road surface topography by the inverse FFT method. Proceedings of the 8th IAVSD Symposium on the Dynamics of vehicles on roads and railway tracks, Cambridge, Massachussets, Swets and Zeitlinger, 1994, pp. 29–42. 25 Sims, N. D., Stanway, R., and Beck, S. B. M. Proportional feedback control of an electrotheological vibration damper. J. Intell. Material Systems Structs, 1997, 8(5), 426–433. 26 Sims, N. D. Limit cycle behaviour of smart ?uid dampers under closed-loop control. J. Vibr. Acoustics, 2006, 128, 413–428. 27 Ahmadian, M. and Gravatt, J. A comparative analysis of passive twin tube and skyhook MRF dampers for motorcycle front suspensions. Smart structures and materials 2004 – damping and isolation, pp. 238–249 (International Society for Optical Engineering, Bellingham).
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28 Simon, D. and Ahmadian, M. Vehicle evaluation of the performance of magnetorheological dampers for heavy truck suspensions. J. Vibr. Acoustics, 2001, 123, 365–375. 29 Sims, N. D., Holmes, N. J., and Stanway, R. A uni?ed modelling and model updating procedure for electrorheological and magnetorheological dampers. Smart Mater. Structs, 2004, 13, 100–121.

I I

max OL

K K w M M c M w n S v V w x c x r x w a f ˙ min

APPENDIX Notation B C C w D D D sky sky-m feedback gain required for linearization road roughness constant (m1/2 cycle3/2) damping constant of the tyre (Ns/m) set-point gain for the linearized system (Ns/m) set-point gain for the linearized skyhook system (Ns/m) set-point gain for the linearized modi?ed skyhook system (Ns/m) frequency (Hz) actual damping force (N) set-point or desired damping force (N) feedforward gain required for linearization (A/N) current supplied to the MR damper (A)

switching current for on/o? skyhook control (A) constant current supplied to the openloop system (A) sti?ness of the primary suspension (N/m) sti?ness of the tyre (N/m) mass of the single-degree-of-freedom isolator (kg) mass of the car body (sprung mass) (kg) mass of the wheel/axle assembly (unsprung mass) (kg) wavenumber (cycle/m) power spectral density function of the road surface (m3/cycle) piston velocity (m/s) vehicle speed (mile/h) road roughness exponent displacement of the car body (m) displacement of the road input (m) displacement of the wheel/axle assembly (m) weighting parameter for the modi?ed skyhook systems zero-?eld damping rate of the MR damper over-dot represents di?erentiation with respect to time

f F F d G I

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