JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

43, 1, pp. 179-201, Warsaw 2005

FUZZY CONTROL FOR MR DAMPER IN A DRIVER’S

SEAT SUSPENSION

Bogdan Sapiński

Department of Process Control, University of Science and Technology

e-mail: deep@uci.agh.edu.pl

The paper concerns the application of fuzzy logic to the control of ama-
gnetorheological fluid damper (MR damper) employed in a driver’s seat
support. The seat is modeled as a 1DOF system to which a generalized
model of anMRdamper valid for fluctuatingmagnetic fields is attached.
The performance of the feedback systemwith a fuzzy controller is tested
in computer simulations and comparedwith the performance of an open
loop systemand the feedback systemwith anon-off controller.The obta-
ined results are verified in laboratory experiments. For this purpose, the
on-off and fuzzy real-time controllers for theMR damper are developed
in integrated design and control environment of MATLAB/Simulink.
The advantages of fuzzy control are proved in experimental investiga-
tions.

Keywords:MRdamper,driver’s seat,vibration, fuzzy, control, algorithm

1. Introduction

MR devices provide modern and elegant solutions for semi-active control
in a variety of applications, offering several advantages: simplicity of a struc-
ture, small number of mobile components, noise-free fast operation and low
power demands.They act as interfaces between electronic control systems and
mechanical systems. In recent years, several MR devices such as dampers and
brakes have been commercialized anddeveloped to themass production stage.
At present, MR dampers are successfully applied in machine engineering and
construction industry.
In the automotive field, new commercially available devices, in which

unique features of MR fluids are used, include: Delphi Automotive’s
MagneRideTM shock absorbers, Carrera’s MagneShockTM automotive racing



180 B.Sapiński

shocks and the Motion Master Ride Management System. MR dampers em-
ployed in those devices can be powered directly from common, low-voltage
sources such as batteries, 12-volt automotive supplies or inexpensive AC/DC
converters. Moreover, standard electrical connectors andwires can be reliably
used, even in mechanically aggressive and dirty environment, without fear of
dielectric break down.

Delphi shock absorbers and Carrera’s automotive racing shocks provide
the possibility for real-time control and optimization of suspension damping
characteristics that improve ride comfort andmaneuverability of a vehicle (all
four corners of the vehicle are independently controlled adjusting the damping
force in response to vehicle speed and road conditions).

The Motion Master system offers safety and comfort for drivers via auto-
matic adaptation to both driver’s bodyweight and continually changing levels
of shock and road vibration. In this way, driver’s responsiveness and control
while reducing fatigue and risk of injury can be improved.

The driver’s seat, whose suspension is equipped with a MR damper to
be controlled, requires that displacement, velocity or acceleration signals be
measured and processed in accordance with a specified control algorithm to
produce an input signal for the MR damper. The main task of the MR dam-
per is to quickly adjust the damping force to current operating conditions
in accordance with the predetermined objective function. The damping force
is controlled with the use of a controller programmed in accordance with an
algorithm which adjusts the current driver connected to the MR damper co-
il. That endows us with means to minimize the gain of amplitude vibrations
transmitted onto thedriver’s bodyat excitation frequencies near the resonance
frequency, while the efficiency of vibro-isolation at higher frequencies should
not deteriorate.

Inmanyalgorithms, velocity signals fromsuspensioncomponents aremade
use of.Generally, these algorithms fall in two categories: on-off and continuous
algorithms (Ahmadian, 1999). The already patented on-off algorithm (U.S.
Patent 5,712, 783, 1998) involves switching of the suspension system from the
minimal (on) tomaximal (off) positions which correspond to theminimal and
maximal damping states for theMRdamper.The continuous algorithmallows
us to enhance the number of switching levels of damping for the suspension
system such as a continuously variable damping coefficient may be achieved.

This paper is focused on fuzzy control for an MR seat damper which be-
longs to the category of continuous control algorithms. It iswell known that no
matterwhich system is considered, there are always three basic steps characte-
ristic for all fuzzy controllers, i.e. fuzzyfication of controller inputs, execution



Fuzzy control for MR damper... 181

of controller’s rules and defuzzyfication of outputs to a crisp value to be im-
plemented by the controller (Piegat, 1999). At any fuzzy controller output we
might get any value from the interval bounded by the minimal and maximal
damping states for the MR damper.
The paper reports a part of a research work (Sapiński, 2003) proceeding

the development andperformance testing of an autonomous control system for
an MR seat damper of the RD-1005 type, engineered by Lord Corporation.
This systemwas based on a microcontroller with a fuzzy set processing unit.

2. MR damper

The concept of MR damper operation is based on the MR effect which
involves quick changes in viscosity of anMRfluidunder the action ofmagnetic
field (Rabinow, 1948). In this study, we employ an MR damper operating in
the flowmode, whichmeans that the produced damping force is controlled by
the flow resistance of the MR fluid portion contained in the gap (Jolly et al.,
1999). A schematic diagram of theMR damper is depicted in Fig.1.

Fig. 1. Schematic diagram of anMR damper

Fig. 2. RD-1005 damper – general view

In this study, we used the RD-1005 damper that is recommended for dri-
ver’s seats in trucks, buses and agriculture tractors. A general view of amodel
of the RD-1005 damper is shown in Fig.2. Basic technical data of the RD-
1005 damper are as follows (Lord Corporation, 2003): it has ±25mm stroke,
208mm extended length and 155mm compressed length. The main cylinder
houses thepistonhead,magnetic circuit, accumulator andMRfluid.The input
voltage is 12VDC. The input current can be varied from 0A to 2A. The coil



182 B.Sapiński

resistance is 5Ω (at ambient temperature) and 7Ω (at 71◦C). The damping
forces (peak to peak) is 2224N (velocity 50 ·10−3m/s, current 1A) and 667N
(velocity 200 · 10−3m/s, current 0A). The maximum extension force should
be kept below 4448N, the maximum operating temperature of the outer cy-
linder should not exceed 71◦C, and the maximum continuous current should
not exceed 1A. The durability of the RD-1005 service life damper is about
2million cycles (±13 ·10−3m, 2Hzwith input current from 0A to 0.8A). Re-
sponse time (dependent on the amplifier and power supply) is less than 25ms
(time to reach 90% ofmaximum level during 0A to 1A step input at velocity
51 ·10−3m/s).

3. On-off and fuzzy control algorithms for the MR damper

It wasmentioned before that on-off algorithms and continuous algorithms
are particularly recommended to the MR damper control. Principles of these
algorithms are explained in Fig.3.

Fig. 3. Damping states in anMR damper

It appears that the benefit of the on-off algorithm lies in its simplicity.
This is because the switching function is utilized where the damping force
may assume the minimum Fmin or maximum values Fmax which correspond
to damping states of minimumdamping ratio c1l ormaximum damping coef-
ficient c1h (black bounded lines).

It is obvious that the benefit of the fuzzy algorithm is that the number of
switching levels of damping is increased such as the controllable characteristic
might become as effective as that of the continuously variable damping coef-



Fuzzy control for MR damper... 183

ficient. This means that the damping force may assume any value from the
interval bounded by Fmin and Fmax (cmin and cmax) (grey area). The above
shows a potential application of fuzzy logic that can be used in an MR dam-
per. Fuzzy logic works by executing rules that correlate controller inputswith
desired outputs thatmay exist anywhere between theminimumandmaximum
damping states. These rules, in this case relating to the damping levels in the
system, can be formulated intuitively or on the basis of an expert’s knowledge
about the system to be controlled. The switching criterionmight be based on
information from velocity sensors, however in practical applications it is usu-
ally based on information from either displacement or preferably acceleration
sensors. This is so these quantities have to be controlled in considerations of
comfort and loading gauge requirements.

4. Driver’s seat suspension with a controllable damper – case

study

Let us consider a simple passive suspension system equipped with a con-
trollable damper represented by a 1DOF model and compare the behaviour
of the system complete with a fixed viscous damper upon applying a fuzzy
algorithm and an on-off algorithm.

4.1. Fixed viscous damping

Aschematic diagramof a simplepassive suspensionof a driver’s seatwitha
fixed viscous damper is shown in Fig.4. The following designations are used in
Fig.4: m1 – seatmass, k1 – spring stiffness, c1 –damping factor of thedamper
to be controlled, x0(t) – displacement-input excitation (base displacement),
x1(t) – seat frame displacement.

Fig. 4. Schematic diagram of a passive suspension

Let us assume the initial conditions x1(0) = 0, ẋ1(0) = 0 and the base
harmonicmotion x0(t)=X0 sin(2πf0t).Thesystemresponsecanbeexpressed



184 B.Sapiński

as x1(t) = X1 sin(2πf0t−ϕ1). It is apparent that the output displacement
amplitude X1 depends on X0, f0 and c1. If m1 =100kg and k1 =36861Nm,
the undampednatural frequency of the suspension is f0s =3.06Hz and cross-
over frequency is f0c =

√
2f0s =4.31Hz (f0c is the frequency value such that

the transmissibility X1/X0 =1). Note that the fixed ”compromise” damping
coefficient c1m =1000Ns/mwill provide rapid damping of free vibrations.
Displacement transmissibility characteristics obtained for a suspension

with the fixed viscous damper c1m = 1000Ns/m and with controllable
(switched damper) for two values of the damping coefficient (c1 = 4c1m =
4000Ns/m and c1 = c1m/4 = 250Ns/m), showing the minimum attained di-
splacement transmissibility for a fixed spring (k1 =36861Ns/m) are provided
inFig.5. It is seen that the transmitteddisplacement amplitude is significantly
reduced as long as:

– the damping coefficient is increased to c1 =4c1m at a low frequency,

– the damping coefficient is decreased to c1 = c1m/4 at high frequency.

Fig. 5. Displacement transmissibility for the suspension with various damping levels

It implies also a certain trade-off between the resonance control and high-
frequency isolation associatedwith the passive suspension system; as the dam-
ping increases, the resonance peak is attenuated but the isolation is lost at hi-
gher frequencies. However, as the value of the damping coefficient is increased,
the location of the peak shifts towards smaller frequencies.

4.2. On-off controllable damping

Theon-off control algorithm, applied to theMRdamper involves switching
of themagnetic control field between two constant levels: the upper boundary
– maximum field excitation or the lower boundary – no field (or ”fail-safe”
condition). This produces a high or low level of damping ratio depending on



Fuzzy control for MR damper... 185

whether the acting disturbances are below or above the cross-over frequency
of the suspension transmissibility characteristic.
Let us consider the following input – displacement x0(t) applied to the

base (Fig.6):

– step of 10 · 10−3m, amplitude ±10 · 10−3m at frequency 2.8Hz, time
0-5s,

– step of −10 · 10−3m, an amplitude ±10 · 10−3m at frequency 3.06Hz,
time 10-15s,

– step of 10 ·10−3m, an amplitude ±10 ·10−3mat frequency 4.3Hz, time
20-25s,

– 0m in between.

Fig. 6. Displacement – input excitation

Now, let us assume the switching criterion applied to the damper thatwith
relation to the sprungmass acceleration ẍ1:

– if |ẍ1| ­ 3m/s2, then c1 =4000Ns/m,
– if |ẍ1|< 3m/s2, then c1 =250Ns/m.

Time patterns of displacement and acceleration responses obtained for the
suspension with fixed viscous damping (c1 = 1000Ns/m) and with on-off
damping (switchedbetween c1 =250Ns/mand c1 =4000Ns/m)areprovided
in Fig.7 and Fig.8. When analyzing time patterns of displacements in Fig.7,
the initial length of the spring with the stiffness k1 was assumed to be 0.4m.
The obtained results lead us to the following statements:

– acceleration response for individual components is reduced,

– acceleration response to simultaneously applied frequency components
is reduced, too,



186 B.Sapiński

Fig. 7. Displacement responses for a suspension with: (a) fixed viscous damping,
(b) on-off controllable damping

Fig. 8. Acceleration responses for a suspension with: (a) fixed viscous damping,
(b) on-off controllable damping



Fuzzy control for MR damper... 187

– displacement response to individual frequency components is reduced,

– displacement response to simultaneously applied frequency components
might increase – however, the higher frequency component is effective-
ly eliminated, so that this represents a kind of trade-off in eliminating
unwanted transmission of large high frequency accelerations.

4.3. Fuzzy control damping

Let us assume the switching criterion applied to the damper with respect
to the sprungmass acceleration ẍ1:

– if |ẍ1| ­ 2 m/s2, then c1 =4000Ns/m,
– if 2m/s2 > |ẍ1| ­ 1.5m/s2, then c1 =2000Ns/m,
– if 1.5m/s2 > |ẍ1| ­ 1m/s2, then c1 =1000Ns/m,
– if 1m/s2 > |ẍ1| ­ 0.5m/s2, then c1 =500Ns/m,
– if |ẍ1|< 0.5m/s2, then c1 =250Ns/m.

Time patterns of displacement and acceleration responses for the prede-
termined damping levels are provided in Fig.9 and Fig.10.

Fig. 9. Displacement response for a suspension with 5 levels of controllable damping

Apparently, in the case of fuzzy control damping more significant reduc-
tion of acceleration anddisplacement responses for individual components and
simultaneously applied frequency components can be achieved than it is in the
case of on-off control. The reduction in the acceleration response to the higher
frequency displacement input is appreciable, while no significant transients
are observed at switching of the damper rate. The increase of the acceleration
response at each switching point occurs before switching and is associated



188 B.Sapiński

Fig. 10. Acceleration response for a suspension with 5 levels of controllable damping

with the damping level during the delay period. Nevertheless, the accelera-
tion response for the switched damper remains within the overall limits of the
responses for both the fixed damper and on-off control.

5. Simulation of a driver’s seat suspension with the MR damper

In computer simulations we used the generalized model of anMRdamper
valid for fluctuatingmagnetic fields (Sapiński andPiłat, 2003). It captures real
behaviour of the MRD over a wide range of operating conditions and proves
adequate in control applications. This model was developed as amodification
of the Spencer model (Spencer et al., 1996).

5.1. Open loop system

We investigate responses of open loop systems (suspension with a fixed
viscous damper and suspensionwith anMRdamper for constant levels of the
applied current) under sine displacement-input excitations. Simulation results
are shown in Fig.11.

On that basis, the variability range of the applied current for the MR
damper can be found, which would guarantee such a level of seat damping as
would be achieved when viscous dampers were employed.

5.2. On-off and fuzzy controllers

Let us consider a feedback system inwhich theMRdamper in the suspen-
sion is adjusted by on-off and fuzzy controllers. The structure of an on-off



Fuzzy control for MR damper... 189

Fig. 11. Acceleration transmissibility for the suspension with fixed viscous
dampers (a) and theMR damper (b)

controller is shown in Fig.12, where the input signals are: ẋ0 – base velocity,
(ẋ1− ẋ0) – relative velocity between the seat frame and the base. The output
signal (control signal) is: I – current in theMR damper coil.

Fig. 12. Structure of an on-off controller

The on-off controller is governed by the formula

I =

{

c for ẋ1(ẋ1− ẋ0)­ 0
0 for ẋ1(ẋ1− ẋ0)< 0

(5.1)

A block diagram of fuzzy controller processing with three distinct stages (fuz-
zyfication, inference, defuzzyfication) is provided in Fig.13. The considered
fuzzy controller usesMamdami’s inference system.

Fig. 13. Block diagram of fuzzy controller processing

The on-off and fuzzy controllers were designed on the basis of experiments
on an open loop system (m1 = 100kg, k1 = 36861Nm) over the frequency
range 1-12Hz. The bounded values of output for the on-off controller were:
0.0A and 0.15A. The fuzzy controller has 5 rules (Table 1). The input mem-



190 B.Sapiński

bership functions for seat frame velocity and relative velocity are triangular-
shaped (Fig.14), while the output membership functions are of the singleton
type (Fig.15). The controller uses three linguistic variables for each input
and three linguistic variables for the output: Minimum, Medium, Maximum.
The linguistic variables for the output correspond to the values of the applied
current:Minimum – 0.000A,Medium – 0.075A,Maximum – 0.150A.

Table 1.Base of rules for the fuzzy controller

No. Rule

1 IF (ẋ1− ẋ0) is Medium)) AND (ẋ1 is Medium)
THEN (current is Minimum)

2 IF (ẋ1− ẋ0) is Minimum)) AND (ẋ1 is Minimum)
THEN (current is Maximum)

3 IF (ẋ1− ẋ0) is Maximum)) AND (ẋ1 is Maximum)
THEN (current is Maximum)

4 IF (ẋ1− ẋ0) is Minimum)) AND (ẋ1 is Maximum)
THEN (current is Minimum)

5 IF (ẋ1− ẋ0) is Maximum)) AND (ẋ1 is Minimum)
THEN (current is Minimum)

Fig. 14. Triangular-shaped input membership function

The input-output graph for the fuzzy controller with 5 rules is shown in
Fig.16a. As the number of rules goes from 5 to 9, the input-output graph is
slightly changed (see Fig.16b).
Whilst comparing Fig.16a and Fig.16b we see that when the relative and

seat frame velocity have opposite signs, the current in the MR damper coil
controlled by the fuzzy controller with 9 rules will be zero, which will not
happen in the controller with 5 rules.



Fuzzy control for MR damper... 191

Fig. 15. Output membership function for the control signal

Fig. 16. Input-output graph for the fuzzy controller: (a) 5 rules, (b) 9 rules

5.3. Feedback system

The results obtained in computer simulations for the seat under sine
displacement-input excitations are presented in the frequency domain, and
in the time domain in Fig.17-Fig.19. In Fig.17, acceleration transmissibility
characteristics for the open loop system and feedback systemswith on-off and
fuzzy controllers (5 rules) are provided. In Fig.18 and Fig.19, time patterns
of the current in the coil and relevant control variables for feedback systems
with on-off and fuzzy controllers are shown.

It is seen in Fig.17 that the damping system with the MR damper and
on-off controller performs well at frequencies exciding 3Hz, and the system
with the fuzzy controller – above 4Hz. Time patterns in Fig.18 prove correct
performance of the implemented on-off controller that begins to functionwhen
the product ẋ1(ẋ1 − ẋ0) > 0 assumes a value above zero. Time patterns in
Fig.19 show that the fuzzy controller is responsible for an increase in the



192 B.Sapiński

Fig. 17. Acceleration transmissibility in open loop and feedback systems with on-off
and fuzzy controllers

Fig. 18. Time patterns of control, velocity product and frame velocity in the
feedback systemwith the on-off controller

Fig. 19. Time patterns of control and frame velocity in the feedback systemwith the
fuzzy controller



Fuzzy control for MR damper... 193

current in the coil when the seat velocity increases; at the same time, the
amplitude of the current is still below 0.150A.

Comparing the simulations results in the feedback systemwith fuzzy con-
trollers containing 5 and 9 rules, we see that no significant improvement of
system performance was achieved.

6. Laboratory testing of a driver’s seat suspension with an MR

damper

In this stagewe investigate a feedback system(driver’s seat suspensionwith
anMRdamper) with a fuzzy controller and compare its performance with an
open loop and feedback system with an on-off controller. For this purpose,
on-off and fuzzy real-time controllers were developed in an integrated design
and control environment utilizing a PC computer.

6.1. Experimental setup

A schematic diagram of the experimental setup for a driver’s seat is provi-
ded inFig.20. The power supply circuit consists of an electro-hydraulic shaker
(EHS) with a hydraulic pump (P) and a control cubicle (CB). Input-output
data was acquired using a data acquisition and control system based on a PC
withamultipurpose I/Oboard (RT-DAC4), operating in the software environ-
ment of Windows 2000, MATLAB/Simulink and Real TimeWindows Target
(RTWT).

The displacements x0 and x1 were measured with linear displacement
transducers (LVDT0 andLVDT1withmeasuring range ±0.01m).The output
signal from the controllers passes to the current driver and then to the MR
damper coil.

A general viewof the driver’s seatwith theMRdamper is shown inFig.21.
Potential damping states for the RD-1005 damper in the controllable range of
0.0-0.20A are shown in Fig.22.

6.2. Environment for real-time controllers development

The integrated design and control environment makes use of the state-
of the art tools for simulation and modelling. Real-time control for an MR
damper employed in the seat was developed using the toolbox RTW (Real



194 B.Sapiński

Fig. 20. Experimental setup for testing the driver’s seat with the RD-1005 damper

Fig. 21. General view of the driver’s seat – ready for tests

Time Workshop) with the extension RTWT in the MATLAB/Simulink envi-
ronment. A diagram of real-time task creation in this environment is shown
in Fig.23.

The device driver blocks close the feedback loop while moving from simu-
lations to experiments. They include procedures in the language C. Real-time
controllers were developed through compilation and linking stages, in a form
of a dynamic link library (DLL), which was to be downloaded into memory
and started-up inMSWindows 2000.



Fuzzy control for MR damper... 195

Fig. 22. Damping states for the RD-1005 damper

Fig. 23. Diagram of real-time task creation in theMATLAB/Simulink environment

6.3. Experiments in open loop and feedback systems

Thefirst stage involved experiments in the open loop system configuration
to determine the characteristic of acceleration transmissibility vs. frequency.
Tests performed for base excitations with sine signals of the frequency 1-12Hz
and amplitude 1.5×10−3mrevealed that the resonance frequency of the seat
is about 5Hz (see Fig.24).



196 B.Sapiński

Fig. 24. Acceleration transmissibility in the open loop system

Similar experiments were conducted for feedback system configurations.
These tests followed an experimental program to check the operation of real
time on-off and fuzzy controllers. The seat framevelocity, and relative ẋ1 velo-
city, (ẋ1− ẋ0) were the input signals which, like the acceleration signals, were
reproduced by using derivative blocks of MATALB/Simulink. The sampling
rate for real-time tasks was 1000Hz. The constant c1 for the on-off controller
was taken as 0.10 and the base of rules for the fuzzy controller was assumed as
that given in Table 1. Selected time patterns of control, velocity product and
frame velocity for a sine displacement-input with the frequency 8Hz, provi-
ded in Fig.25 and Fig.26, bespeak correct operation of both feedback system
configurations.

Fig. 25. Time patterns of control, velocity product, frame velocity in the feedback
systemwith the on-off controller

Note that in the case of the on-off controller there are only two control
values (i.e. levels of the applied current): 0.000A and 0.100A, while in the
case of the fuzzy controller, the level of the applied current may assume any
value from the range 0.000-0.060A.



Fuzzy control for MR damper... 197

Fig. 26. Time patterns of control, velocity product, frame velocity in the feedback
systemwith the fuzzy controller

In the second stage, frequency characteristics of acceleration transmissibi-
lity vs. frequency in feedback systems containing on-off and fuzzy controllers
were determined (see Fig.27).

Fig. 27. Acceleration transmissibility in the open loop and feedback systemwith
on-off and fuzzy controllers

When comparing these characteristics with that obtained in the open loop
system, it is apparent that better performance is achieved in feedback system
configurations. That was also proved in the time domain; see Fig.28, where
time patterns of acceleration for the seat frame at a near-resonance frequency
(about 5Hz) are provided.

Figures 27 and 28 donot adequately capture the better performance achie-
ved thanks to application of the feedback systemwith the fuzzy controller. To
demonstrate that, zoomed sections of time acceleration patterns for open lo-
op and feedback systems with on-off and fuzzy controllers are compared in
Fig.29.



198 B.Sapiński

Fig. 28. Time patterns of frame acceleration in the open loop system and feedback
systems with on-off and fuzzy controllers

Fig. 29. Time patterns of frame acceleration – zoomed sections

Experimentsperformed in the feedback systemwith fuzzycontrollers,when
the number of rules went up from 5 to 9, revealed no significant improvement
of system performance, which is in agreement with the statement given in
Subsection 5.3.

To estimate the performance of feedback system configurations, the follo-
wing factors were introduced: f1, f2, ∆f,DP , S1 and S1+S2, (see Fig.30).
The computed values of performance factors are compared in Table 2.

Fig. 30. Performance factors



Fuzzy control for MR damper... 199

Table 2. Performance factors of feedback systems with on-off and fuzzy
controllers

Performance On-off Fuzzy
factor controller controller

f1 [Hz] 4.07 4.02

f2 [Hz] 5.14 5.25

∆f [Hz] 1.07 1.23

DP 1.076 1.043

S1 8.170 8.080

S1+S2 11.086 11.627

Note that the fuzzy controller has better features (wider frequency control
range and smaller values of DP , S1) than the on-off controller.

7. Conclusions

The paper reports research on fuzzy control applied to an MR damper
employed in a driver’s seat support. It also indicates a potential application of
fuzzy logic that can be used in semi-active dampers. The criterion for estima-
tion of the system performance was based on the sprungmass acceleration.

The fuzzy controller was developed on the expert knowledge acquired in
the course of experiments. It appears to beflexible as its parametersmay easily
be altered through changes of membership functions and rules. The number
of 5 rules for the fuzzy controller was established as that giving satisfactory
improvement of the feedback system performance in comparison with that
containing an on-off controller.

The vibration control of the seat (with no cushion) for both feedback sys-
tem configurations was effective throughout a frequency range of 3-5Hz. Ad-
vantages of the fuzzy algorithm in comparison to the on-off algorithm are
revealed basing on the performance factors provided in Table 2.

In the experiments on the feedback system with the on-off controller, the
presence of the chattering effect was observed. As a result, the control signal
could be produced in the states when velocity product oscillated round the
zero value (the effect of non-zero off state damping).When assuming the dead
zone, the chattering effect could be eliminated (Sapiński and Rosół, 2003).



200 B.Sapiński

The research work is now focused:

• on fuzzy control for an MR damper in the seat with a cushion (2 DOF
system),

• introducing two switching criteria for the MR damper (one principle
based on the sprungmass acceleration and the second on relative displa-
cement of the seat frame and shaker base).

Acknowledgement

The research work has been supported by the State Committee for Scientific

Research as a part of the research programNo. 5T07B02422.

References

1. Ahmadian M., 1999, On the isolation properties of semi-active dampers,
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3. Piegat A., 1999,Modelowanie i sterowanie rozmyte, PLJ,Warszawa

4. Rabinow J., 1948, Themagnetic fluid clutch,AIEE Trans., 67, 13081315

5. Sapiński B., 2003,Autonomous control systemwith fuzzy capabilities forMR
seat damper,Archives of Control Sciences, 13, 115-136

6. Sapiński B., Pilat A., 2003, Generalizedmodel of a magnetorheological flu-
id damper for fluctuating magnetic fields, Journal of Theoretical and Applied
Mechanics, 41, 805-822

7. SapińskiB.,RosółM., 2003,Real-timecontrollers forMRseatdamper,Proc.
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Workshop, Warszawa-Jadwisin.

8. SpencerB.,Dyke S., SainM.,Carlson J., 1996,Phenomenologicalmodel
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10. United States Patent, 5,712, 783,Controlmethod for semi-active damper, 1998



Fuzzy control for MR damper... 201

Sterowanie rozmyte tłumikiem MR w zawieszeniu fotela kierowcy

Streszczenie

W artykule przedstawiono zastosowanie logiki rozmytej do sterowania tłumika
magnetoreologicznego (tłumika MR) w zawieszeniu fotela kierowcy. Fotel zamodelo-
wano jako układ o jednym stopniu swobody, do którego dołączono uogólnionymodel
tłumikaMR uwzględniający fluktuacje pola magnetycznego.W symulacjach kompu-
terowychporównanodziałanieukładuze sprzężeniemzwrotnymz regulatoremrozmy-
tym i regulatorem dwupołożeniowym.Wyniki symulacji zweryfikowanow badaniach
laboratoryjnych. W tym celu zrealizowano regulatory czasu rzeczywistego (rozmy-
ty i dwupołożeniowy) w środowisku projektowania i sterowaniaMATLAB/Simulink.
Zalety regulatora sprawdzono eksperymentalnie.

Manuscript received May 20, 2004, accepted for print June 22, 2004