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Application of a self-tuning fuzzy PI–PD
controller in an active anti-roll bar
system for a passenger car
V. Muniandy
a
, P.M. Samin
a
& H. Jamaluddin
a
a
Faculty of Mechanical Engineering, Universiti Teknologi, 81310
UTM Skudai, Malaysia
Published online: 26 Aug 2015.
To cite this article: V. Muniandy, P.M. Samin & H. Jamaluddin (2015): Application of a self-
tuning fuzzy PI–PD controller in an active anti-roll bar system for a passenger car, Vehicle System
Dynamics: International Journal of Vehicle Mechanics and Mobility
To link to this article: http://dx.doi.org/10.1080/00423114.2015.1073336
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Vehicle System Dynamics, 2015
http://dx.doi.org/10.1080/00423114.2015.1073336
Application of a self-tuning fuzzy PI–PD controller in an
active anti-roll bar system for a passenger car
V. Muniandy∗
, P.M. Samin and H. Jamaluddin
Faculty of Mechanical Engineering, Universiti Teknologi, 81310 UTM Skudai, Malaysia
(Received 13 January 2015; accepted 13 July 2015)
A fuzzy proportional-integral-derivative (PID) controller has not been widely investigated for active
anti-roll bar (AARB) application due to its unspecific mathematical analysis and the derivative kick
problem. This paper briefly explains how the derivative kick problem arises due to the nature of
the PID controller as well as the conventional fuzzy PID controller in association with an AARB.
There are two types of controllers proposed in this paper: self-tuning fuzzy proportional-integral–
proportional-derivative (STF PI–PD) and PI–PD-type fuzzy controller. Literature reveals that the
PI–PD configuration can avoid the derivative kick, unlike the standard PID configuration used in
fuzzy PID controllers. STF PI–PD is a new controller proposed and presented in this paper, while
the PI–PD-type fuzzy controller was developed by other researchers for robotics and automation
applications. Some modifications were made on these controllers in order to make them work with
an AARB system. The performances of these controllers were evaluated through a series of handling
tests using a full car model simulated in MATLAB Simulink. The simulation results were compared
with the performance of a passive anti-roll bar and the conventional fuzzy PID controller in order to
show improvements and practicality of the proposed controllers. Roll angle signal was used as input
for all the controllers. It is found that the STF PI–PD controller is able to suppress the derivative
kick problem but could not reduce the roll motion as much as the conventional fuzzy PID would.
However, the PI–PD-type fuzzy controller outperforms the rest by improving ride and handling of a
simulated passenger car significantly.
Keywords: active anti-roll bar; fuzzy PI–PD; derivative kick; handling simulation; passenger car
1. Introduction
An anti-roll bar (ARB) acts as an essential suspension component in most of passenger cars
and other types of ground vehicle to increase cornering stability. ARB’s function is to resist
vehicle’s roll motion without affecting pitch and vertical displacement of the vehicle. ARB is
also compatible with both independent (McPherson strut, double wishbone, etc.) and semi-
rigid (torsion beam) suspension systems. This allows manufacturers to use softer springs
(as opposed to harder springs to overcome excessive roll when there is no ARB) in their
vehicle to increase ride comfort without compromising handling up to a certain limit. Yaw
response can be influenced by utilising a different stiffness of an ARB employed at the front
in comparison with the one fitted at the rear of the car. By manipulating the front and rear
roll stiffness, lateral weight distribution of the car can be tuned, determining the amount
of grip exerted by front and rear wheels in the event of taking a corner with medium to
*Corresponding author. Email: vj_vallavan@yahoo.co.uk
c 2015 Taylor & Francis

2 V. Muniandy et al.
high lateral acceleration. For example, a car with a higher front roll stiffness compared to
its rear will tend to understeer because the rear wheels are allowed to maintain its contact
pressure to the road while the vehicle body rolls, hence maintaining the grip throughout the
corner. The front wheels, however, were restricted by the ARB, causing the inner wheel’s
vertical force towards the road reduced slightly due to the reaction of ARB that pushes the
inner wheel upwards as the after-effect of the outer wheel being displaced upwards during
the roll motion. This action causes the front axle to compromise its grip, hence reducing
the car’s overall steering effect. If the roll stiffness is too high, the vehicle will reduce its
suspension independencies, causing discomfort to passenger.[1] For example, in an event of
road irregularities, a stiff ARB will transfer the rebound movement of one wheel to the other
side of the axle, causing the whole vehicle to vibrate more than necessary. Therefore, with
the demand to improve vehicle performance in terms of comfort, speed, and functionality,
a more advanced suspension system is required. This is where an active suspension system
comes in, and converting an anti-roll bar into an active actuator is a possible solution. An
AARB enables roll stiffness to be adjusted according to the motion of a vehicle in real time,
thus improves handling and ride quality.
AARBs have been researched by many researchers using various types of controllers. Very
few used a semi-active controller because it is known to give poor results.[2] On the other
hand, others who used fully active controllers for their AARB systems have successfully
improved handling and ride comfort of the tested vehicles.[3–10] As other inventions, AARB
systems do have their disadvantages, which were discussed in earlier works. For example,
Cimba et al. [3] researched on an AARB which was installed by replacing the link rods with
hydraulic actuators. A bang-bang-type controller was used due to its minimal requirements
of computational resources. However, the bang-bang controller showed a poor performance
when introduced to uncertainty. An adaptive controller was mentioned in [3], but no further
analysis on the same was reported. By referring to Antsaklis and Chair [11], it is clear that
systems with high uncertainties could not be controlled efﬁciently by using a simple lin-
ear or feed-forward controller. Vehicle suspension system operates within high uncertainties
where a controller designer must take various factors into account, such as road irregularities,
vehicle speed, total weight, and weight distribution. All these factors can vary unexpectedly
and may not be expressed in an exact mathematical formula. Alternatively, complex con-
trollers may be feasible because these controllers exhibit a certain level of adaptation ability
that is able to cope and act appropriately in an uncertain environment to ensure a promising
performance.
As mentioned earlier, semi-active systems received least attention when it comes to anti-
roll bars due to its inability to introduce energy (in the form of resistance torque in the case
of an anti-roll bar) to the suspension system. An anti-roll bar needs to resist the vehicle body
roll by introducing resistant torque to the suspension system, which could not be achieved
by using a semi-active system alone. In layman terms, a semi-active system can only ‘stop’
the car’s body from further rolling but could not ‘push’ the body back to its original position.
A semi-active system utilising a ‘Lock-In’ controller was proposed in [2], which locks the
position of the vehicle at the roll state during cornering to reduce roll angle when opposite
corner is taken. However, this approach depends on the GPS system to pre-determine the
vehicle travel path. It was shown that the controller could not completely eliminate the roll
angle, but assists the vehicle to take the next corner with less roll. The effectiveness of the
system depends on the initial roll angle, thus causing the degradation of performance if a
pre-planned path is not followed. Also, the optimum operating range is lower compared to
a fully active system.[2] To overcome this problem, a secondary assist system called modal
control strategy was introduced. However, the overall improvement is still dependent heavily
on the ﬁrst corner’s lateral acceleration.

Vehicle System Dynamics 3
Road input control was used together with steering input control in an AARB system
designed by Mizuta et al. [5]. The road input controller was derived based on Skyhook
theory in the roll direction. The effectiveness of this AARB system was shown experi-
mentally. To implement the road input controller, a thorough study on human sensitivity
on vibration and typical real-world road proﬁles is very important. To increase both ride
comfort and handling capability, road input control must be combined with steering input
control. This increases the number of sensors and components, hence reducing system
reliability.
Cronje and Els [6] extended the work of Everett et al. [7] in designing a specialised AARB
system to improve off-road handling without compromising ride comfort. The controller used
for this system was simple, consisted of limiter and gains only. The vehicle roll angle can be
totally eliminated up to 0.4 G of lateral acceleration. The limit imposed at 0.4 G is to warn
drivers that the vehicle is about to reach its linearity limit. Due to this limit, this controller is
not suitable for cars driven at a high speed as the tyre forces at that point will be crucial and
hard to predict. Furthermore, a controller calculating actuator force with a single proportional
action is not suitable for mass production or to be used in different types of vehicle. Even if
it is used in a single vehicle model, the change in the vehicle’s weight, tyre pressure or other
external disturbances may cause unwanted results. The system does not affect the vehicle
in terms of vertical acceleration; hence, there is no effect on ride comfort. Although sim-
ulation results showed promising outcomes, the practicality of this controller in real-world
application needs further studies.
Sampson and Cebon [8] designed an AARB system for a single unit heavy vehicle which
adopts linear-quadratic-gaussian approach to design the controller. A partial-state feedback
controller was designed using linear quadratic Gaussian-loop transfer recovery technique.
This controller is capable of improving roll stability up to 46%; however, a complex mathe-
matical derivation is involved to derive the controller. Furthermore, steering disturbance has
to be estimated (measured if possible) to be feed into the feedback law for better control-
ling performance. Similarly, Kim and Park [9] used gain scheduled H∞ control, which also
needs secondary semi-active system to work optimally apart from its complex mathematical
derivation. A satisfactory result was obtained when the active system was incorporated with
variable damping system (which is a semi-active system) to work as a hybrid system for the
AARB. Yim and Yi [10] used the sliding mode control algorithm for a hybrid vehicle AARB
system, but it needs too many supplementary systems such as electronic stability control,
active front steering, and direct yaw moment control in order to work at its full potential.
These active controllers need a deeper mathematical analysis and the derivation may have
to be repeated if the type of vehicle in which the controllers being installed is changed. This
is because, when the vehicle parameters change, the controller’s parameters are no longer
optimal.
In this paper, fuzzy proportional-integral-derivative (PID) controller is the focus due to its
potential for further improvement in the future to beneﬁt the AARB system. A PID controller
is prone to create a sudden rise in output signal (which is known as ‘kick’) when introduced
to high noise input signals.[12] This phenomenon, also known as the derivative kick, occurs
because of the mathematical nature of PID where the derivative term tends to increase dras-
tically when there is a sudden change in the direction of error – from positive to negative and
vice versa. Other than that, a PID controller has limited optimal operating range compared
to those advanced controllers. Throughout history, PID controllers showed more convincing
results when controlling the main spring and damper rates rather than just controlling the roll
rate.[13] A simple PID controller was previously used in force and actuator displacement con-
trol in an AARB system designed by Sorniotti et al. [4]. The derivative kick problem was not
addressed in [4] because a PID controller was not used as the main controller to determine

desired active force for the AARB system. PID controllers have been used in conjunction
with other controllers to increase their performance significantly.
A Fuzzy PID controller was applied into an AARB system by Xinpeng and Duan,[14]
which was designed for sport-utility-vehicle (SUV). This controller is able to tune the basic
PID controller’s parameters by using fuzzy rules in real time according to the error signal
input. The system’s ability to significantly reduce roll angle and improve direction stability
were supported only by simulation results. This controller was chosen because of its ability
to self-tune for a better performance while retaining its classical advantages such as robust,
suitability for non-linear applications, and precise response.[15] Fuzzy logic controllers are
based on human knowledge, highly adoptable in non-linear systems and cost effective.[16]
There are two ways to incorporate a fuzzy logic into a classical PID controller[17,18]:
(a) Conventional fuzzy PID where PID controller’s gains are to be tuned in real time by
fuzzy logic controller according to fuzzy rules set by experienced personnel.
(b) PID-like fuzzy controller is a fuzzy logic controller designed as a set of heuristic con-
trol rules, and the control signal is directly deduced from the knowledge base and the
fuzzy inference as it is done in MacVicar-Whelan or diagonal rule-base generation
approaches.
The first category, conventional fuzzy PID, is also known as self-tuning fuzzy PID (STF-
PID) in some literature. The second category is known as PID-type fuzzy controllers, which
are considered equivalent to classical PID controllers from the viewpoint of input–output
relationships.[17,18] Conventional fuzzy PID controllers and PID-type fuzzy controllers
retain the same characteristics despite the difference in construction method. It is also known
that both fuzzy PID controllers always perform better than standard PID controllers.[16] On
the other hand, a fuzzy PID also retains its classical disadvantages, such as integrator windup,
the derivative kick, and incompatibility in a highly fluctuating system, such as a vehicle sus-
pension system.[19–22] The derivative kick phenomenon is often undesirable and usually
occurs when a system is highly oscillatory. Researchers found that by eliminating the deriva-
tive kick, better control can be achieved. To eliminate the derivative kick, derivative action is
suggested to be applied on the feedback measurement itself, and not at the error.[15] Since the
feedback form of the process is negative to the error, derivative term is always placed in the
feedback itself in commercial use.[12] A number of solutions requiring modification of PID-
type fuzzy controllers have been reported in the literature.[18,22–26] Furthermore, several
STFPID controllers have been improved over the years by various researchers.[17,27–31]
However, these controllers are being used in fields other than vehicle dynamics. STFPID
controllers are often tested in environment using step inputs, thus can perform satisfactorily.
The objective of this paper is to demonstrate the derivative kick phenomenon when con-
ventional/STFPID controller is exposed to experimental data with high fluctuation. The
derivative kick problem has not been discussed before when PID-based controllers imple-
mented in AARB systems.[3–10,14] In order to solve the derivative kick problem, a new
controller is designed by incorporating possible solutions discussed by previous researchers.
The new controller introduced in this paper is self-tuning fuzzy proportional-integral–
proportional-derivative (STFPI–PD). The new controller’s response will be compared with
that of an STFPID controller used in an AARB system, as reported in [14]. This paper
attempts to show that a PI–PD controller can be tuned by using the conventional fuzzy
PID method to overcome the derivative kick problem without eliminating the structure of
a classical PI–PD controller. This method enables the use of a larger number of membership
function to ensure a smooth transition between fuzzy rules and better freedom in customis-
ing fuzzy rules according to expert’s knowledge. In contrast, fuzzy rules in a PID-type fuzzy

controller are fixed to ensure the fuzzy controller behaves exactly like a PI or a PD controller.
A PID-type fuzzy controller also usually employs two or three membership functions only
for both input and output because the process of deriving the rules is tedious if it involves a
high number of membership functions.
Beside these controllers, another controller developed by previous researchers will be
adopted into the AARB system in order to show the adoptability and compatibility of the
controller in improving vehicle ride and handling. This controller is a modified PID-type
fuzzy controller, which is known as fuzzy PI–PD controller (renamed as PI–PD-type fuzzy
logic controller (FLC) to avoid confusion in this paper). Similarly for PI–PD-type FLC con-
trollers, the derivative action is placed at the process feedback itself just like the method used
in the classical PID controller. By changing the structure to a PI–PD-type FLC controller,
such as adopting series (interacting) PID and parallel PD structures, the derivative kick prob-
lem can be avoided. These approaches were investigated in [22–24,26], which showed that
these modified PID-type fuzzy controllers clearly outperform the conventional fuzzy PID as
well as eliminate the derivative kick. For conventional PID-type fuzzy controllers, creating
3D rule to simultaneously tune all three control gains is a tedious work and often avoided by
designers.[26] Due to the nature of PID-type fuzzy controller having complex architecture,
researchers were driven to develop two-term PID-type fuzzy controllers where each fuzzy
controller will only controls two terms, PI or PD.[23]
This concept triggers the innovation of the design of a STFPI–PD controller which is pre-
sented in this paper. Similarly, the derivative action’s placement is changed to the forward
path of the control process in order to test the possibility of the derivative kick problem caused
by the STFPID controller without totally changing the structure of the controller into a PID-
type fuzzy controller. Other than the ability to self-tune according to the input disturbance
and vehicle parameter changes, the proposed STFPI–PD controller is expected to outperform
the conventional fuzzy PID controller that has already been tested in the AARB system. PI–
PD-type FLC controller, on the other hand, was only reported as a concept for application in
robotic industry without any real-world applications.[21] This is the reason why a PI–PD-type
FLC controller is chosen and adopted by modifying the scale of the membership functions;
so performance comparison can be made with the only known fuzzy PID controller applied
in AARB reported by Xinpeng and Duan.[14] This study will show the significance of devel-
oping a general controller to be used in different types of vehicles’ AARB system without
the need of tuning the controllers’ parameters. It eases the process of adopting the system
in different types of ground vehicles to control roll motion effectively. By knowing that a
PI–PD-type FLC controller is a solution for the derivative kick problem beforehand, the simu-
lation results for this controller presented as a demonstration that the controller can effectively
avoid the derivative kick and be able to apply in AARB systems. It is also to compare the per-
formance with the newly developed STFPI–PD controller so that the solution of the derivative
kick problem can be justified. Introducing raw experimental data as input to the control
system will show that the new proposed controllers are able to perform in a real vehicle.
To meet the objective of this study, the results of a series of handling tests through simula-
tion will be presented to show the improvement made by the proposed controllers, STFPI–PD
and PI–PD-type FLC in comparison with an STFPID controller. These simulation handling
tests will use actual experimental steering input data obtained by Samin [32] as input to
the MATLAB Simulink 16 degree of freedom (DOF) full car model in order to introduce
real-world noise into the simulation process. Both vehicle model and controller will be mod-
elled in MATLAB Simulink software. The simulation tests consisted of double lane change
(DLC), slalom, and step steer manoeuvre tests performed on a flat road at the speed of 40 and
50 km/h. The rest of this paper is organised as follows. Ride and handling full car model will
be presented in Section 2. The controllers’ structures including related fuzzy rules will be

explained in Section 3. Computer simulation results will be presented in Section 4 together
with discussions. Finally, conclusion will be made in Section 5.
2. Ride and handling full car model
The full car model is consisted of a 7 DOF ride model combined with a 9 DOF handling
model. This model was adopted from Samin [32] and upgraded by adding a dedicated ARB
model into this 16 DOF full car model. The 7 DOF ride model represents bounce, pitch,
roll, and four wheels’ vertical motion of the car. The model is based on several assumptions,
which have been discussed thoroughly in [32]. The equations of the ride model and vehicle
parameters can be found in [32], as this paper focuses only on equations related to anti-roll
bar as it is newly added. The general equations for each unsprung mass at each corner are as
follows:
Ftij − Fsij − Fdij = Muij ¨Zuij, (1)
where Ftij, Fsij, Fdij, Muij, and ¨Zuij represent tyre force, spring force, damper force, unsprung
mass, and unsprung mass’ vertical motion acceleration, respectively. The notations i and
j indicate front (f) or rear (r) and left (l) or right (r), respectively. It should be noted that
jacking force is not taken into consideration due to assumptions made earlier by Samin.[32]
The model is assumed to have ﬁxed roll axis at the centre of gravity, and coincides with
roll centre. The centre of gravity remains at the middle of the vehicle’s width. Due to the
absence of lateral displacement of roll centre, jacking force does not exist in this model.[33]
However, as mentioned earlier, this model is veriﬁed and successfully validated using a real
test car. Anti-roll bar model will be a part of ride model for ease of integration. Figures 1 and
2 show the free body diagrams of the anti-roll bar.
When the car undergoes roll motion, one of the wheels on a same axle will move in the
opposite direction in relative to the other wheel along vertical axis. This causes vertical forces
acting on each end of the anti-roll bar are opposing each other. The couple will create torque
and the bar is twisted about its lateral axis, along the length of the bar. One end of the bar is
connected to the left unsprung mass and the other to the right unsprung mass via link rods. The
displacements of the left and right ends of the bar are equal to (Zuil − Zsil) and (Zuir − Zsir),
respectively. The terms Zuij and Zsij refer to vertical displacement of unsprung and sprung
masses, respectively. Twist motion of ARB will occur if the sprung mass rolls even when
Figure 1. Free body diagram with forces acting on the anti-roll bar.

Figure 2. Free body diagram of anti-roll bar for twist motion.
the both corresponding left and right unsprung masses remain stagnant. For example, when a
heavy load is placed at the front passenger seat, the sprung mass will lean to one side, causing
the ARB to twist and resist the roll motion. The ARB twist angle, α, can be calculated by
using trigonometry when the bar is viewed from its side.
Assuming that α is small,
tan α =
(Zuil − Zsil) − (Zuir − Zsir)
larb
≈ α, (2)
where larb is the anti-roll bar’s arm length. Anti-roll bar equations are integrated into Equation
(1), creating set of equations as follows:[34]
Ftfr − Fsfr − Fdfr −
Krf
Wf
α = Mufr ¨Zufr, (3)
Ftfl − Fsfl − Fdfl +
Krf
Wf
α = Mufl ¨Zufl, (4)
Ftrr − Fsrr − Fdrr −
Krr
Wr
α = Murr ¨Zurr, (5)
Ftrl − Fsrl − Fdrl +
Krr
Wr
α = Murl ¨Zurl, (6)
where Krf is the front anti-roll bar stiffness, Krr is the rear anti-roll bar stiffness in unit
Nm/radian and, Wf and Wr are the widths of the front and rear tracks, respectively. The
term (Kri/Wi)α is the passive anti-roll bar force. For a full car model, there are two anti-roll
bars, which are at the front and rear, depending on a vehicle model. The ARB torque, Tari,
can be calculated using
Tari = Kri · α (7)
due to torque created by the bar, which depends on how much the bar twisted.[34] The
anti-roll bar’s torque will be added into the equation that calculates roll motion in the ride

Figure 3. Fully AARB free body diagram.
model, thus
Ir
¨∅ = {0.5TFzﬂ − 0.5TFzfr + Tarf} + {0.5TFzrl − 0.5TFzrr + Tarr}, (8)
where Ir and ¨∅ represent roll axis moment of inertia and roll acceleration, respectively.
The term Fzij represents sum of spring and damper forces at each wheels, according to its
corresponding location.
The equations for fully AARB are similar to passive anti-roll bar too. The anti-roll bar
forces, P1 and P10 in Figure 2 are replaced by active forces, Fac1 and Fac2, respectively. Both
active forces are created by a linear electric actuator, which replaces the link rod at one side,
leaving the other side as it is. Link rods were the original member which transfers anti-roll bar
forces to unsprung mass. This electric actuator will create forces based on the signal given
by the controller. Figure 3 shows how these two actuators create the anti-roll bar torque.
A fully AARB torque is given by
Tari = Wi(Faci), (9)
where Faci represents active force, with i indicating front (f) or rear (r).
To ensure the validity of Equation (9), few assumptions were made. The anti-roll bar in
fully active conﬁguration is assumed to be rigid. Since the bar is fully rigid, the force created
at one end will be transferred fully to the other end. The torsional dynamics of the bar was
neglected in the simulation. Total torque created will be based on the total force created by
the electric actuator. Passive anti-roll bar force in Equations (3)–(6) will be replaced by fully
active forces. Limited by the scope of the study, the controller will determine the value of the
desired force for both front and rear AARB actuators simultaneously depending on the roll
signal received from a single sensor. It is possible to achieve better handling by manipulating
the active forces at the front and rear of the car as presented in [4]; however, the focus here
is to show the solution to the derivative kick problem.
There are four sub-models associated with handling model: tyre, handling, longitudinal
slip, and side-slip models. These sub-models are combined to represent a 9 DOF handling
model. The Pacejka tyre model (also known as Magic Tyre model) was used in this simulation
due to its ability to reproduce non-linear behaviour of a vehicle.[35] The inputs for the tyre
model are side-slip angle, α, and vertical force Fz. Meanwhile the outputs are self-aligning
moment, Mz, lateral force, Fy, and longitudinal force, Fx. The 9 DOF handling model con-
sists of longitudinal, lateral, yaw, roll, pitch motions, and four wheel rotational speeds. The
longitudinal and lateral accelerations generated by the tyre model were used as the inputs for
the handling model. Due to the steer effect in the handling model, the vehicle will experi-
ence motion in lateral and longitudinal axes. The lateral and longitudinal accelerations were

denoted as ay and ax, respectively, which are given by
ax =
Fxfl cos δ + Fyfl sin δ + Fxfr cos δ + Fyfr sin δ + Fxrl + Fxrr
m
+ vy ˙ϕ, (10)
ay =
Fyflcosδ − Fxflsinδ + Fyfrcosδ − Fxfrsinδ + Fyrl + Fyrr
m
− vx ˙ϕ, (11)
where δ, ˙ϕ, and m are the steer angle, yaw rate, and vehicle mass, respectively. The motion vx
and vy can be obtained by further integration of ax and ay. The yaw motion will follow:
¨ϕ =
1
Izz
[WfFxfl cos δ − WfFxfr cos δ + WrFxrl − WrFxrr + WfFyfl sin δ − WfFyfr sin δ − LrFyrl
− LrFyrr + LfFyfl cos δ + LfFyfr cos δ − LfFxfl sin δ − Lf Fxfr sin δ + Mzfl
+ Mzfr + Mzrl + Mzrr], (12)
with respect to each tyre’s lateral, longitudinal forces, and self-alignment moment, where
Izz is moment inertia at z-axis. The yaw acceleration will be integrated and substituted into
Equations (10) and (11). The equations of roll and pitch motions generated by this handling
model are based on
¨∅ =
−mshsay + ∅(msghs − kr) − ˙∅cr
Ixx
, (13)
¨θ =
−mshsax + θ(msghs − kp) − ˙θcp
Iyy
, (14)
where hs, Iyy, Ixx, g, ¨∅, and ¨θ are the vertical distance of sprung weight from centre of gravity,
moment of inertia of y- and x-axes, gravity acceleration constant, roll and pitch accelerations,
Figure 4. The 16 DOF ride and handling full car model.

respectively. The variables kp and cp represent pitch stiffness and pitch damping coefficient,
respectively. The variable cr is the roll damping coefficient and kr is the total roll stiffness,
where
kr = kts + ktr. (15)
Equation (15) shows that the vehicle’s total roll stiffness is consisted of the sum of roll
stiffness contributed by the spring, kts and the roll stiffness contributed by ARB, ktr.[36] The
term ktr will be equal to 0 if there is no ARB installed. For a passive full car model, the
term ktr is influenced by passive ARB; and for a full car model with active ARB, the term ktr
is influenced by the active actuators’ forces. All sub-models developed (which includes ride,
Pacejka tyre, handling, brake, side slip, and longitudinal slip models) are required to represent
the 16 DOF full vehicle model. Detailed explanation, vehicle parameters, and derivation of
this 16 DOF full car model can be found in [32]. Figure 4 shows the complete block diagram
of the 16 DOF full car model.
3. Controller structures
In this paper, a new approach is investigated for solving the derivative kick problem. All
tested controllers will receive roll angle as input signal. For a real car application, roll angle
can be measured by using tri-axial accelerometer or silicon sensing tri-axial gyroscopes
located at the CG of the car. A sensor with 250 Hz of maximum frequency response, ±2
G of acceleration range, and powered by 12 V DC power supply is sufficient for this appli-
cation. These kinds of sensors are widely available in the market. Lateral acceleration signal
can be also used as input signal since it is the direct cause of roll motion. However, lateral
acceleration is not influenced by active ARB because lateral acceleration is generated by a
centrifugal force. (It is impossible for anti-roll bar to affect this variable physically.)[37]
STFPID controllers were not often considered when it comes to controlling highly oscil-
latory systems as newer PID-type fuzzy controllers are available. This research opens up
a possibility where the classic PI–PD controller is adopted into a STFPID controller. The
concept is similar to that of the conventional fuzzy PID, but now instead of tuning three coef-
ficients (Kp, Ki, and Kd) for a PID controller, the fuzzy controller will tune four coefficients
for the PI–PD controller (Kp, Kp, Ki, and Kd) in real time. There will be two proportional
actions involved: one placed at the error signal together with integral action, and another
is placed at the feedback signal together with derivative action as the method to avoid the
derivative kick. The controller configuration is similar with PI–PD-type FLC, but the differ-
ence is the gain values are to be tuned by fuzzy controller without removing the core structure
of the actual PI–PD controller. Hence, this new controller will be known as STFPI–PD
controller. Basic algorithms of all controllers are explained in the next section.
3.1. PI–PD-type fuzzy controller
For PI–PD-type fuzzy controller (PI–PD-type FLC), the derivative action is placed at the
measurement of the process feedback but not after the feedback error.[22] The basic concept
of this controller is shown in Figure 5.
In order to improve the controller’s compatibility to non-linear system, Veeraiah et al. [22]
implemented fuzzy logic to design PI–PD-type FLC controller. The controller is designed to
preserve the linear structure of conventional PI–PD controller and substitute the coefficient
gains with non-linear fuzzy functions. The output of PI–PD-type FLC controller, uPI−PD(nT),

Figure 5. Basic layout of PI–PD controller.
is represented by
uPI−PD(nT) = uPI(nT) − uPD(nT) (16)
where uPI(nT) and uPD(nT) are the equivalent outputs from fuzzy PI and fuzzy PD con-
trollers, respectively. Prior to that, in Laplace domain, both conventional analogue PI and PD
controllers can be represented by
uPI(s) = Kc
p +
Kc
i
s
E(s), (17)
uPD(s) = (Kc
p + Kc
ds)Y(s), (18)
where uPI(s) and uPI(s) are outputs of analogue PI and PD controllers, respectively; Kc
p, Kc
i ,
and Kc
d are proportional, integral, and derivative gain, respectively. It can be seen that PI
controller is inﬂuenced by error signal E(s) and PD controller is inﬂuenced by process output
Y(s). By applying bilinear transformation, Equations (17) and (18) are transformed into a
discrete version. Hence, fuzzy PI controller output is written as
uPI(nT) = uPI(nT − T) + KuPI uPI(nT), (19)
where uPI(nT) is the fuzzy PI controller output, T is the sampling period and KuPI is the fuzzy
PI control gain. Similarly for fuzzy PD controller, the equation will be
uPD(nT) = −uPD(nT − T) + KuPD uPD(nT). (20)
By inserting Equations (19) and (20) into Equation (16), the output of PI–PD-type FLC
controller will be
uPI−PD(nT) = uPI(nT − T) + KuPI uPI(nT) + uPD(nT − T) − KuPD uPD(nT), (21)
where uPD(nT) is the fuzzy PD controller output and KuPD is the fuzzy PD control gain.
Both KuPI and KuPD will be determined by fuzzy rules. This controller’s layout applied in
active ARB is presented in Figure 6.
Similar to a standard fuzzy controller, membership functions and rules will be applied to
the fuzzy PI and fuzzy PD controllers. The inputs for both controllers will be in terms of roll
angle signal. As the derivative controller receives roll angle signal directly from the system
feedback itself, it is expected that the derivative kick phenomenon can be avoided. Earlier,
it has been stated that fuzzy PI controller has two inputs, which are roll angle error signal,
ep(nT) and rate of change of roll angle error signal, ev(nT). The fuzzy PI controller output
(also called as incremental control output) is denoted as uPI(nT). The inputs for fuzzy PD

Figure 6. PI–PD-type fuzzy logic controller layout.
Figure 7. PI–PD-type fuzzy logic controller Simulink model.
controllers are the roll angle, d(nT) and rate of change of roll angle, y(nT). Figure 7 shows
the actual construction of a PI–PD-type FLC controller in Simulink software with the indi-
cation of actual placement for each controller parameter, which are Kp, Ki, Kp, Kd, KuPD,
and KuPI. Despite the notations, these parameters act only as input sensitivity ratio in order to
avoid undesirable noise in the output. The proportional, derivative, and integral actions are
expressed in the form of non-linear fuzzy functions.
Figure 8(a) and 8(b) show the input membership functions for both PI and PD controllers.
The input unit in Figure 8(a) is in degree; while the input unit in Figure 8(b) is °/s. Figure 9
shows the output membership function for both PI and PD controllers since both outputs
are represented by the same membership functions. The output unit would be Newtons as
it represents the required force by the actuator. The range of each membership functions is
determined by typical operating range of a passenger car in a real application. The maximum
value for required force is bound by the hardware capability.
A set of control rule base is created for fuzzy PI control, which are as follows:
• RULE 1: IF ep negative AND ev negative, THEN PI-output = output negative.
• RULE 2: IF ep negative AND ev positive, THEN PI-output = output zero.
• RULE 3: IF ep positive AND ev negative, THEN PI-output = output zero.
• RULE 4: IF ep positive AND ev positive, THEN PI-output = output positive.

(a)
(b)
Figure 8. . Membership functions: (a) for roll angle error (ep) and average change of roll angle (d) and (b) for rate
of change of roll angle error (ev) and roll rate ( y).
The membership functions have been kept simple in triangular form to reduce computing
memory usage. The structure of the membership functions for both input signals are the
same to avoid further memory allocations for the controller. The output signal for fuzzy PD
controller is denoted as uPD(nT).
Fuzzy PD controller’s rule set is as follows:
• RULE 5: IF d positive AND y positive, THEN PD-output = output zero.
• RULE 6: IF d positive AND y negative, THEN PD-output = output positive.
• RULE 7: IF d negative AND y positive, THEN PD-output = output negative.
• RULE 8: IF d negative AND y negative, THEN PD-output = output zero.
Defuzziﬁcation process is done based on ‘centre of mass’ approach. To optimise the con-
troller’s performance, a set of parameters for the controller was obtained using trial and

Figure 9. Membership functions for fuzzy PD and fuzzy PI output signals.
error method, which is simple. It is an initial step to determine the test parameters where
the parameters were chosen one by one while the changes occurring at the output were
tracked. Individual values often increased gradually until the desired plant output response
is achieved. Excessive amounts of actuator force and speed demands will also become the
limiting factor for this method. After extensive simulation tests, parameter value that satisﬁes
all simulation tests are as follows: Kp = 0.3140, Ki = 0.0971, Kp = 0.0576, Kd = 0.001,
KuPD = 0.4968 and KuPI = 0.4496. The sampling period is set to T = 0.01 second to cope
with the vehicle suspension system response. Integral windup problem is not expected from
this simulation because the simulation was executed in an ideal system assuming there is no
saturation or physical limitation on the actuators and other related hardware. In future, when
actual hardware implemented in this system, limiting the controller output according to the
physical limit of the actual actuator is strongly recommended.
3.2. Self-tuning fuzzy PID
STFPID controller was implemented in AARB by Xinpeng and Duan [14] in their attempt
to improve the ride and handling of a SUV. The controller algorithm uses conventional
approach, where the values of PID controller parameters are tuned online by fuzzy controller
depending on the feedback input received from the plant. This approach is more direct com-
pared to the approach used in PI–PD-type FLC controller. The general equation for the PID
controller is
Tac(t) = Kpe(t) + Ki
e
(t) + Kd e(t), (22)
where e(t) is the body roll error with respect to the desired roll angle, which is 0 at all time.
The corresponding desired active anti-roll torque is Tac. The body roll angle variety rate is
denoted by e(t) and the error sum is denoted by e
(t). The terms Ki, Kp, and Kd denote
integral, proportion, and derivatives coefﬁcients, respectively. The controller parameters Ki,
Kp, and Kd will be self-tuned by fuzzy controller according to the roll angle error, e and roll
angle error variety rate, e. The self-tuning ability is well known for its promising results.
Figure 10 shows the general block diagram for the controller.

Figure 10. Controller structure proposed by Xinpeng and Duan [14].
3.3. STF PI–PD controller
By incorporating the classical PI–PD conﬁguration into the STFPID method, the STFPI–PD
controller is expected to solve the derivative kick problem. This controller is designed as an
attempt to upgrade the currently available fuzzy PID controller used in an AARB system.
The general equation of PI–PD controller will be
Tac(t) = [Kpe(t) + Ki
e
(t)] − [Kp ∅(t) + Kd
˙∅(t)]. (23)
Note that there are two proportional actions; Kp and Kp, each for roll angle error, e(t) and
the direct measurement of roll angle input, ∅(t), respectively. The derivative action is applied
at the measurement of roll angle. The performance of AARB system can be adjusted by tun-
ing the parameter Kp, Kp, Ki, and Kd of PI–PD controller to inﬂuence the system’s rise time,
steady-state error, overshoot, and settling time. The tuning process of the controller param-
eters will be done by fuzzy controllers. These fuzzy controllers will receive roll angle error,
e(t) and error rate, ˙e(t) as inputs to tune the value of Kp and Ki; also, the fuzzy controllers
that receive roll angle value, ∅(t) and the roll rate value, ˙∅(t) as inputs will tune the values of
Kp and Kd. Figure 11 shows the general block diagram of the proposed controller.
Figure 11. General block diagram of STF PI–PD controller.

16V.Muniandyetal.
Figure 12. The membership functions of output Kp, Kp, Ki, and Kd.

Initially, the range of these parameters’ value was set by using trial and error method. The
parameter Kp is set at range of [0, 500], Kp is set at range of [0, 2000], Ki is set at range
of [0, 50] and finally Kd is set at range of [0, 100]. By having the basic knowledge of the
functions of each parameter, it is easier to set the range of each parameter with adequate
ratios. For example, it is known that Ki can remove steady-state error, but excessive integral
action may cause overshoot in the system (integral windup). Hence, the integral action is
limited to smaller magnitude compared to other actions in the controller. The ranges of each
parameter are shown in the form of fuzzy controller membership function in Figure 12.
The numbers of membership functions are limited by the hardware capability of the com-
puter to run the simulation in real time. Bell-shaped membership functions allow a smoother
transition between rules. The labels of membership functions for outputs are defined as Zero
(Z), Positive Small (PS), Positive Medium (PM), Positive Big (PB), and Positive Very Big
(PVB). Similarly, the labels for input membership functions are defined as Negative Big
(NB), Negative Small (NS), Zero (Z), Positive Small (PS), and Positive Big (PB). The range
of inputs is set to [ −1, 1] rad and [ −1, 1] rad/s for error and error rate, respectively (same
goes for roll angle and roll rate) using trial and error method. Figure 13 shows the membership
functions for inputs.
The fuzzy controller will tune each of PI–PD controller’s parameter based on rules set by
an expert. As for vehicle suspension system, it is recommended to have fast settling time
(a)
(b)
Figure 13. The membership functions of (a) inputs e(t) and ˙e(t) and (b) inputs ∅(t) and ˙∅(t).

Table 1. Fuzzy rules for Kp and Kp.
˙e(t), ˙∅(t)
e(t), ∅(t) Kp, Kp NB NS Z PS PB
NB PVB PVB PVB PB PM
NS PVB PVB PB PB PM
Z PB PB PM PS PS
PS PM PS PS PS PS
PB PS PS Z Z Z
Table 2. Fuzzy rules for (a) Ki and (b) Kd.
˙e(t)
e(t) Ki NB NS Z PS PB
NB PVB PB PM PM PM
NS PVB PB PB PM PS
Z PM PS Z Z Z
PS PM PM PS Z Z
PB PS Z Z Z Z
˙∅(t)
∅(t) Kd NB NS Z PS PB
NB Z Z PS PS PB
NS Z Z Z Z PS
Z Z Z Z PS PB
PS PS PS PS PB Z
PB Z Z Z PS PB
and less overshoot in order to reduce the motion of the vehicle body. The fuzzy rules were
adopted from Soyguder et al.,[17] which were designed for a system that requires precise
reactions with fast settling time without steady-state error. These criteria are also beneﬁcial
for vehicle suspension system. The fuzzy rules are presented in Tables 1 and 2.
The defuzziﬁcation process is carried out using the ‘centre of mass’ method, similar to the
method used for previous controllers discussed in this paper.
4. Computer simulation results
Computer simulation was performed using Matlab Simulink (version R2013a) software. Both
full car model and controller algorithm were modelled in the same software. Three types
of handling tests were carried out for the simulation process, which are DLC, slalom, and
step steer manoeuvre tests. The experimental procedures follow the guidelines of ISO 388
Part 2 and the speed was decided by the maximum speed allowable on that particular test
track. DLC test is chosen because it simulates a crash avoidance scenario. The second test is
a slalom test, which is the standard tests used to evaluate transient dynamic of the vehicle,
representing a real-world driving dynamics. Finally, step steer test was carried out to evaluate
driving dynamics during sudden input change. Recorded experimental data were used as the
input for this simulation process in the form of steering angle input. The input signal was
recorded from a passenger car travelling at the speed of 40 and 50 km/h for all mentioned
tests. Detailed experimental procedure was reported in [30].
The simulation results of STFPID, PI–PD-type FLC, and STFPI–PD controllers were com-
pared. The comparison is to show the occurrence of the derivative kick problem and to
demonstrate the effectiveness of the proposed controller. Xinpeng and Duan [14] did not

Figure 14. Roll angle response for 40 km/h DLC test.
consider the controller in real-world application or by simulation using actual experimental
data. The lack of noise and fluctuations in the simulation input fails to point out the derivative
kick problem, thus the problem was left undetected. Here, with the usage of experimental
data as input, it can be shown that the derivative kick is prone to be a problem in vehicle
suspension system resulting negative impact in real-world applications.
Following are discussions on the response of the vehicle in terms of roll angle and roll
rate when given the steering angle input. Note that lateral acceleration and yaw rate are not
discussed in this section because ARB does not affect those variables physically. Figure 14
shows roll angle response when the vehicle subjected to 40 km/h DLC test.
By observing Figure 14, it can be said that all three controllers succeeded to reduce the roll
angle compared to a passive ARB. The maximum roll angle values are indicated in the figure.
It is clear that PI–PD-type FLC controller is able to reduce roll angle significantly, indicating
that PI–PD-type FLC is the most effective controller in reducing roll angle within these tested
manoeuvres. Due to lower roll angle, less oscillation is found in PI–PD-type FLC controller
response, hence improves ride comfort. STFPI–PD controller creates the highest roll angle
among active systems; although in some instances, when the vehicle body rolls towards its
original position, STFPI–PD controller is able to reduce roll motion faster compared to STF-
PID controller. Same DLC test was carried out for vehicle speed of 50 km/h and the results
hardly differ from what been obtained in Figure 14. Comparison in terms of RMS value and
percentage of improvement will be discussed later in this section.
In order to demonstrate the derivative kick phenomena, roll rate variables are presented in
Figure 15. Figure 15 shows roll rate response of the vehicle for 40 km/h DLC tests.
It can be seen in Figure 15, approximately at 6th, 11th, and 13th second, the STFPID
controller’s magnitude exceeds the passive ARB’s magnitude. Sudden transition in roll angle
direction causes the derivative term in STFPID to increase rapidly, causing this unwanted
rise in roll rate. It can be inferred that the derivative kick is prone to occur when the roll
angle changes sign or when the steering angle changes direction rapidly, causing large rate of
change in the error. This situation will cause passengers to feel a sudden jerk in split second,
hence causing annoyance and discomfort. When derivative gain acts on the error input, it will
create an undesired result; which is why the other two controllers use different approaches

Figure 15. Roll rate response for 40 km/h DLC test.
in placement of derivative terms. Similar results with different magnitude were found when
DLC test was carried out at 50 km/h. However, STFPI–PD successfully solved this problem
by reducing the roll rate in comparison with the STFPID controller and passive ARB. This
shows that the proposed method is able to avoid the derivative kick while reducing roll rate
and increasing comfort. STFPI–PD also improved the roll motion compared to passive ARB,
thus showing the potential of implementing in an AARB system.
Similarly, PI–PD-type FLC also managed to eliminate the derivative kick because the
derivative term receives signal from the feedback of the process directly. PI–PD-type FLC
performs better in reducing both roll angle and roll rate, by creating the least amount of
roll angle and rate. The roll rate of PI–PD-type FLC controller is always lower than passive
controller, hence improving comfort for both 40 and 50 km/h test. This is due to smooth
transition in roll angle provided by the controller. Overall, both proposed controller could
perform better than the STFPID controller. Lateral acceleration and yaw rate values do not
show signiﬁcant difference; hence, these responses will not be shown.
Slalom test was conducted and Figures 16 and 17 show the results of roll angle and roll
rate responses respectively for 40 km/h slalom test.
From Figure 16, it can be seen that all active controllers reduce roll angle in comparison
with passive ARB. The effect of each controller on the vehicle roll motion remains the same
despite different tests were carried out. The effectiveness of each controller shown in both
Figures 16 and 17 is in agreement with the discussion on DLC test section. Similar results
are observed when carrying out slalom test at 50 km/h and step steer test at 40 km/h; hence,
corresponding graphs are not presented in this paper. However, 50 km/h step steer test needs
further explanation where roll angle and roll rate for this test is shown in Figures 18 and 19.
For this test, the steering angle was not maintained at zero position before step steer
manoeuvre being applied.[32] This is known as stabilising period where the driver attempted
to set the car to its proper path. The steering angle was kept constant at 20° within the margin
of error for the ﬁrst 4 seconds, which can be referred in [32]. This error caused the vehicle
to experience slight roll motion along the way. But this error also provides a good argument
point to show that both proposed controllers perform better in eliminating steady-state error
compared to the fuzzy PID. In Figure 18, PI–PD-type FLC controller returns the vehicle body
back to almost zero position, reducing roll to negligible state within 4 seconds of the test. The

Figure 16. Roll angle response for 40 km/h Slalom test.
Figure 17. Roll rate response for 40 km/h Slalom test.
STFPI–PD controller is able to keep the roll angle lower than STFPID controller but could not
return back to zero position as the PI–PD-type FLC did. This is because the core structure of
construction of both STFPID and STFPI–PD controller is almost identical, hence sharing the
key behaviour. As for the roll rate response, STFPID still shows signs of the derivative kick
but the magnitude did not surpass the magnitude produced by the passive ARB. In order to
justify the required actuator force by the proposed system, the force required by each actuator
to actuate the AARB system is presented in Figure 20.
DLC test at 40 km/h was chosen to showcase the required force for each AARB systems.
The amount of force exerted by passive ARB seems non-existence as the stock ARB installed
in the test car is too small and may be built using low-quality material. The desired forces of
AARB systems follow the trend of passive ARB system, except for the AARB system which
utilises an STFPID controller. As can be seen from Figure 20, the output pattern of the desired
force by the STFPID controller has a signiﬁcantly different trend compared to other presented

Figure 18. Roll angle response for 50 km/h step steer test.
Figure 19. Roll rate response for 50 km/h step steer test.
controllers. For the STFPID controller, the desired force overshoots every time when the roll
angle changes direction (refer Figure 14 for roll angle graph). This is due to the occurrence of
sudden kick in roll rate output. The exact mathematical analysis explaining this phenomenon
may be included in future works because currently, it is a tedious process to represent fuzzy
algorithms in pure mathematical form. Figure 20 shows that sudden change of input signal
direction causes STFPID controller output signal to increase rapidly. The PI–PD-type FLC
controller utilises the highest amount of force, considering the amount of roll motion that
the system could signiﬁcantly reduce. The proposed controller, STFPI–PD, follows the same
trend as the PI–PD-type FLC controller with a slightly lesser magnitude. It is found that the
required actuation forces for all the tested controllers do not exceed 1600 N for all tested
manoeuvres. A linear electric actuator with a dynamic speed of 200 mm/s at 1600 N with
200 mm stroke is sufﬁcient for optimal operating performance. The actuation requirements

Figure 20. Desired force required for each controller for DLC test at 40 km/h.
Table 3. RMS values of roll angle and roll rate for all tests.
40 km/h 50 km/h
RMS Roll angle (°) Roll rate (°/s) Roll angle (°) Roll rate (°/s)
DLC test Passive 2.1072 3.6380 2.7252 3.9845
STFPID 0.9190 2.1012 1.1214 2.3508
STFPI–PD 1.0184 1.9285 1.3085 2.1006
PI–PD-type FLC 0.3357 0.8277 0.4320 1.0317
Slalom test Passive 0.9709 1.4990 1.5395 2.5550
STFPID 0.5234 1.2479 0.7015 1.7567
STFPI–PD 0.4623 1.1322 0.7377 1.4697
PI–PD-type FLC 0.1544 0.8768 0.2500 0.8499
Step steer test Passive 0.5492 3.0882 0.9604 2.7619
STFPID 0.2937 2.0686 0.6208 1.8567
STFPI–PD 0.3231 2.3698 0.4777 2.0440
PI–PD-type FLC 0.1143 1.0897 0.1409 1.0256
are within the operating range of other AARB systems reported in [6,9,14], considering their
effective anti-roll moment.
In order to quantitatively justify the improvement made by all the active controllers com-
pared to the passive ARB, root mean square (RMS) values were calculated for all the
variables and presented in Table 3.
By observing Table 3, it can be seen that AARB reduces roll angle and roll rate for all
tests. STFPI–PD controller successfully eliminates the derivative kick caused by the nature
of STFPID, and performs better than STFPID in all tests. The performance of the STFPI–
PD controller is almost consistent in all tests by achieving about 50% of improvement in
reducing roll angle. This shows that the proposed STFPI–PD controller has the potential to
be used for AARB application and will perform effectively in a real-world driving scenario.
Unlike STFPI–PD, the performance of PI–PD-type FLC varies depending on the tests, but
still able to achieve the best performance among all tested controllers. The PI–PD-type FLC

Figure 21. Overall improvements made by each controller.
controller can be adopted for use in AARB systems. On the other hand, STFPID performs the
least favourable in all tests, especially by causing discomfort to passengers by introducing a
sudden rise in roll rate, higher than a passive ARB would do. For each test conducted, PI–
PD-type FLC performs the best by having the largest percentage of improvement, followed
by STFPI–PD and ﬁnally STFPID controller.
Average in improvement was calculated for both roll angle and roll rate improvements (all
tests included) to show the average improvement obtained from each controller compared
to the passive ARB. It is found that STFPID improves roll angle response of the vehicle
at about 49.61% in average and 32.83% in average for roll rate. Similarly for the proposed
new controller, STFPI–PD is able to improve roll angle response in average of 49.93%, and
roll rate reduced in average of 35.07%. The difference in average improvement between
STFPI–PD and STFPID controllers is not signiﬁcant, but the consistency of performance
and ability to reduce roll rate without any derivative kick made STFPI–PD controller more
promising. Finally for PI–PD-type FLC controller, it is found that on average, roll angle
response improved by 83.43% and roll rate response improved by 64.53%. So, it can be said
that PI–PD-type FLC controller is the best among the presented controllers. PI–PD-type FLC
controller improves the performance of AARB systems by outperforming STFPID in all tests
and variables presented. Figure 21 shows the overall improvements made by each controller
for each variable in a graphical form.
5. Conclusion
A new proposed controller, STFPI–PD controller, has been presented in this paper. This con-
troller has been successfully implemented into an AARB system and shown to improve
vehicle’s ride and handling characteristics. Also, the PI–PD-type FLC controller has been
successfully implemented in an AARB system, and is able to improve the vehicle’s roll
motion drastically. The reason for implementing these controllers into an AARB bar is to
overcome the derivative kick problem, which has been shown to occur when STFPID system
is exposed to real data. The derivative kick problem is shown to be solved by the proposed
controller, STFPI–PD controller, by eliminating the occurrence of sudden peaks in roll rate
variable of the vehicle in comparison to an STFPID controller. It is found that by adopting

self-tuning fuzzy controller into classic PI–PD controllers instead of a conventional PID con-
troller, one can further improve the system performance and allow its usage in high noise
application without having the derivative kick problem. In addition to that, PI–PD-type FLC
controller is found to be the best-performing controller among the tested controllers, which is
able to improve vehicle’s roll motion up to 85.33% and with an average of 83.43% in all tests
without introducing the derivative kick into system’s output. Roll rate response reduced by
PI–PD-type FLC controller up to 77.25% and with an average of 64.53% in all tests. ***Thus
it can be concluded that PI–PD-type FLC controller improves vehicle’s ride and handling and
performs better than conventional STFPID controller without initiating the derivative kick
problem.
The system’s effect on yaw rate and controllers’ parameters sensitivity study are not inves-
tigated and may become a future research objective. It is also recommended to use a more
complex vehicle model, namely commercially available vehicle simulation package to study
detailed effects of the controllers in various driving scenarios. Furthermore, all presented
tests are recommended to be carried out again at a higher speed to further extract the actual
performance of the new AARB system. A proper experimental test in the form of hardware-
in-loop experiment is being planned so that the presented results can be validated. Finally,
future work on implementing this system to other types of land vehicles which will benefit
from active roll control system is strongly encouraged.
Acknowledgement
The authors wish to thank the Ministry of Higher Education (MOHE) and the Universiti Teknologi Malaysia (UTM)
for providing the research facilities and support, especially all staffs of Faculty of Mechanical Engineering, Universiti
Teknologi Malaysia.
Disclosure statement
No potential conflict of interest was reported by the authors.
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