Modeling and Analysis of Active Full Vehicle

Suspension Model Optimized Using the Advanced

Fuzzy Logic Controller
Shailendra Kumar and Amit Medhavi
Mechanical Engineering Department, Kamla Nehru Institute of Technology, Sultanpur, Uttar Pradesh—228118,
India. E-mail: shailendra.kumar@knit.ac.in

Raghuvir Kumar
Director General at BN College of Engineering and Technology, Lucknow, Uttar Pradesh—226201, India.

P. K. Mall
Department of Mechanical Engineering, Babu Banarasi Das Engineering College, Lucknow, Uttar Pradesh—
226010, India.

(Received 11 August 2021; accepted 4 January 2022)

The suspension system plays a major role in automobiles to improve passenger comfort, passenger safety and
road handling. It isolates the body of a vehicle from road disturbances. The full vehicle would be subjected to
disturbances from all four wheels or a full suspension model of the vehicle and, thus, a full-suspension model of
the vehicle should be added to the idea of an enhanced control preview. The input data for the fuzzy logic controller
(FLC) is the velocity and acceleration of the front and rear wheels. Controller outputs are considered to be active
forces that improve driver comfort, safety and road handling characteristics. The objective of this work is to model
and analyse an active full vehicle suspension. The model is optimized using advanced FLC to improve driver
comfort, safety and road handling. The mathematical model for the active full vehicle suspension model has been
derived. The necessary background for the Simulink fuzzy logic and FLC has been presented. All the simulations
are carried out using MATLAB/SIMULINK, a high-performance numeric computation and visualization software
package. The fuzzy logic-controlled active values have been compared with ordinary passive simulated values
for road profiles. The result of the simulation show that the designed advanced FLC has improved ride comfort
by effectively reducing the vehicle body displacement. There is also an appreciable reduction in velocity and
acceleration with no increase in suspension travel.

1. INTRODUCTION studying the quarter-vehicle model, half-vehicle model4–9 and

full-vehicle model suspension system used to construct the ac-
The automotive industry is concentrating more on passenger tive suspension regulation rule.10, 11 The quarter vehicle sus-
safety and comfort as technology advances. The vehicle sus- pension model has the simplest construction and the degree
pension system plays an important part in providing passen- o freedom (DOF) is the full vehicle suspension model that
gers with riding comfort by separating the cabin from various can better explain the dynamics of the vehicle.11, 12 The half-
road disturbances. The suspension system is classified primar- vehicle suspension model is used to provide a balance between
ily into three groups: i) Semi-active suspension system (SASS) precision and effectiveness. The researchers suggested differ-
ii) Active suspension system (ASS) and iii) Passive suspension ent control systems to boost the efficiency of the ASS.13 The
system (PSS). Traditional springs and dampers are used in the control strategy is one of the most important characteristics of
PSS to absorb road disturbances.1 It also allows for a trade-off active suspensions and many control strategies have been stud-
between the comfort of the passenger ride and the control of ied in the literature, such as adaptive filtered-x,14 optimal con-
the vehicle on the road. The traditional spring and externally trol,8 sliding mode control,15, 16 H-infinity control,17–19 fuzzy
operated damper are used in the SASS. The damping coeffi- logic control (FLC),20–25 neural network control,26–28 model-
cient of this form can be managed based on the chassis accel- free fractional-order sliding mode control,29 based backstep-
eration sensor inputs that calculate the vertical acceleration of ping fast terminal sliding mode control30 and preview con-
the vehicle’s body. In addition to traditional passive suspen- trol.31–38 The idea of preview information in vehicle suspen-
sion systems, the ASS utilizes force actuator (Fa ) components sions was first proposed by bender,39 suggesting that the use of
in a closed-loop control system.2 Based on the feedback from preview information would effectively enhance the efficiency
the various sensors associated with it, the Fa provides suffi- of vehicles. In the control approach, preview information on
cient control force to the device. First, a vehicle model is re- road disturbances is used before road disturbances operate on
quired to regulate the suspension.3 Researchers are currently the vehicle body. This method will reduce the response time of

26 https://doi.org/10.20855/ijav.2022.27.11825 (pp. 26 36) International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022
 S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

the controller and actuator, thereby enhancing the suspension Table 1. Parameter values for full vehicle suspension.35
performance.34, 40 It is possible to model the vehicle suspen- Parameter Value
Mass of wheel (unsprung mass), Mu 59 kg
sion system as a half vehicle four-degree of freedom and to
Mass of vehicle body (sprung mass), Ms 1500 kg
evaluate the efficiency of the linear quadratic regulator (LQR) Tire spring stiffness, Ku 190000 N/m
and fuzzy control systems.41, 42 For the half vehicle, four- Roll axis moment of inertia, Ixx 460 kg m2
degree of freedom suspension system model,43 a proportional- Pitch axis moment of inertia, Iyy 2160 kg m2
integral sliding control system has been developed. On the half Rear spring stiffness, Ksr 38000 N/m
Front spring stiffness, Ksf 35000 N/m
vehicle four-degree of freedom suspension models, the linear
Distance between front of vehicle and C.G. of
and FLC system performance was analyzed.44 For the 2-DOF sprung mass, a
1.4 m
quarter vehicle suspension model, the fuzzy logic control sys- Distance between rear of vehicle and C.G. of
1.7 m
tem method was suggested and evaluated and a comparative sprung mass, b
C.G. height, h0 0.508
analysis was performed with a linear quadratic gaussian (LQG)
Width of sprung mass, w 1.524 m
controller.5 The researchers suggested to the ANFIS controller Distance between roll center and C.G., hroll 0.3 m
that the nonlinearity of the system should be controlled using Rear suspension damping, Csr 1100 N s/m
data from the full vehicle active suspension model proportional Front suspension damping, Csf 1000 N s/m
integral derivative (PID) control system.45 The half-vehicle
four-degree of freedom suspension system has been developed The researchers explored several control system techniques
with the LQR controller.46 The ANFIS design was evaluated to improve the efficiency of the suspension model. This paper
using the data-driven approach for half-vehicle six-degree of focused on the development and comparison of FLC for full
freedom suspension systems and its performance was com- vehicle model 7-DOF active suspension, providing insight into
pared with PSS.47 The proportional integral derivative con- the design and selection of suitable control algorithms for ve-
trol method has been created and studied for quarter vehicle hicle suspension systems by other researchers. The reaction of
two-DOF suspension systems.46 The design of the fuzzy quar- these controls has been studied using the road profile, pitch,
ter suspension control system has been addressed.15, 48, 49 The bumps, and rollover as road disturbances. Because of the ben-
development of the ANFIS for the SASS controller has been efits of the fuzzy control strategy and the effectiveness of the
discussed.50 The road profile can be simulated to measure preview results, this study suggests using the wheelbase pre-
the performance of the suspension system under different road view fuzzy control strategy to set up an active suspension con-
conditions based on ISO 8608.51, 52 The model of the LQR trol fuzzy preview to minimize chassis vibration to improve
control system was suggested for the active suspension sys- riding comfort. There is no current research that applies FLC
tem.42, 48, 53, 54 Fuzzy logic control rules optimization research system with preview information in the design of active full
has been discussed. A hybrid learning algorithm and the AN- vehicle suspension system, according to the best knowledge of
FIS architecture has been discussed.55 The ANFIS and propor- the authors.
tional integral derivative controllers were built and tested us-
ing LabVIEW software on an experimental active suspension 2. MATHEMATICAL MODELING
setup.56 The design, development and implementation of a
proportional integral derivative controller for auto-tuning have The model of the system for the full-vehicle suspension sys-
been discussed.57 Using the MATLAB proportional integral tem is given in Fig. 1. In contrast to the quarter-vehicle sus-
derivative auto-tuning tool,58 the PID controller was designed pension model, the full-vehicle suspension model is a more so-
for a two-degree of the freedom suspension system. The road phisticated model that represented the precise dynamics of the
profile classification model based on ANFIS was developed vehicle’s vertical motion. The full-vehicle suspension model
using semi-active suspension vehicles. An accurate model of is made up of a sprung mass and four unsprung masses linked
the actual system needs a full vehicle model with 7-DOF. A to it at four corners via the suspension system’s spring and
full vehicle model of ASS is developed by considering seven damper. The study’s model contained seven degrees of free-
degrees of freedom namely four vertical motions of the wheel, dom, including the sprung mass’s heave, roll, and pitch, as well
pitch, roll and heave motion of the vehicle body. A H infinity as the vertical displacement of four unsprung masses.
controller was introduced for the full vehicle model to sup- The suspensions were modeled as spring components and
press the effect of road disturbances and parameter uncertainty linear viscous dampers between sprung mass and unsprung
in actuator dynamics.17 A preview controller for full vehicle masses, whereas the tires were considered to be simple lin-
model-based active suspension was introduced with two con- ear springs without viscous damping. It was also expected that
trol approaches. The first controller optimizes the displace- the position of the sprung mass’s center of gravity (CG) did
ment of the actuator whereas the second controller controls the not vary over time and that the suspension system’s coordi-
pitch, heave and roll motion of the vehicle body.59 The com- nate system is linked to the vehicle’s CG and aligned with the
plexity of the mathematical model of the full vehicle and the vehicle’s major axes. The small-angle approximation is em-
nonlinear behavior of the actuator has increased the difficulties ployed to acquire the equations of motion, which added to the
of applying conventional control schemes to the active suspen- model’s restriction.19 The roll and pitch angles induced during
sion system.21, 60 Hence a model-free controller based on in- the operation were considered to be small, and the small-angle
telligent control schemes like fuzzy logic, neural networks are approximation was utilized to obtain the equations of motion.
gaining more importance in recent times and they are applied Table 1 lists the parameters utilized in this study.
successfully to control suspension systems in real time.3, 17, 42 Mathematical description of the study’s model was given as
International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022 27
S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

Figure 1. Active suspension model for full-vehicle system.

follows: Mu Z̈uf r − Csf Ż + Csf Żuf r + aCsf θ̇ + aKsf θ +

1 1
Ms Z̈ + (2Csf + 2Csr )Ż − Csf Żuf l − Csf Żuf r − wCsf ϕ̇ + wKsf ϕ + (Ksf + Ku )Zuf r − Ksf Z +
2 2
Csr Żurl − Csr Żurr + (2Ksf + 2Ksr )Z − Ksf Zuf l − Ku Zrf r + Ff r = 0; (5)
Ksf Zuf r − Ksr Zurl − Ksr Zurr − (2aCsf − 2bCsr )θ̇ −
(2aKsf − 2bKsr )θ − Ff l − Ff r − Frl − Frr = 0; (1) Mu Z̈url − Csr Ż + Csf Żurl − bCsr θ̇ − bKsr θ −
1 1
wCsr ϕ̇ − wKsr ϕ + (Ksr + Ku )Zurl − Ksr Z −
2 2
Iyy θ̈ + (2a2 Csf − 2b2 Csr )θ̇ + (2a2 Ksf − 2b2 Ksr )θ − Ku Zrrl + Frl = 0; (6)

(2aCsf − 2bCsr )Ż + aCsf Żuf l + aCsf Żuf r −

Mu Z̈urr − Csr Ż + Csf Żurr − bCsr θ̇ − bKsr θ +
bCsr Żurl − bCsr Żurr − (2aKsf − 2bKsr )Z +
1 1
aKsf Zuf l + aKsf Zuf r − bKsr Zurl − bKsr Zurr + wCsr ϕ̇ − wKsr ϕ + (Ksr + Ku )Zurr − Ksr Z −
2 2
aFf l + aFf r − bFrl − bFrr = 0; (2) Ku Zrrr + Frr = 0; (7)

1 1 MV 2
Ixx ϕ̈ + w2 (2Csf + 2Csr )ϕ̇ + w2 (2Ksf + 2Ksr )ϕ − Fc − = 0; (8)
4 4 R
1 1 1 M , Fc , and V represents total vehicle mass, centripetal
wCsf Żuf l + wCsf Żuf r − wCsr Żurl +
2 2 2 force, and vehicle speed, respectively. R is the road’s radius
1 1 1 of curvature. The car will rollover due to this centripetal force,
wCsr Żurr − wKsf Zuf l + wKsf Zuf r −
2 2 2 which should be avoided. To evaluate the rollover dynamics in
1 1 1 1 this investigation, an additional input to the vehicle was sup-
wKsr Zurl + wKsr Zurr − wFf l + wFf r −
2 2 2 2 plied in addition to the 4-wheel road input disturbances. To
1 1 simulate driving on a curved road and incorporate rollover, the
wFrl + wFrr = 0; (3)
2 2 system model was given a centripetal force as an input. The
equation gave the roll moment operating on the vehicle due to
this centripetal force:
Mu Z̈uf l − Csf Ż + Csf Żuf l + aCsf θ̇ + aKsf θ −
1 1 Mroll − Fc hroll = 0; (9)
wCsf ϕ̇ − wKsf ϕ + (Ksf + Ku )Zuf l − Ksf Z −
2 2 where Mroll is the vehicle’s rolling moment, and hroll was the
Ku Zrf l + Ff l = 0; (4) distance between the vehicle’s center of gravity and the roll

28 International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022

 S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

center. The input of the rolling moment was applied to Eq. (3),
and the resulting equation is provided by Eq. (10):
1 1
Ixx ϕ̈ + w2 (2Csf + 2Csr )ϕ̇ + w2 (2Ksf + 2Ksr )ϕ −
4 4
1 1 1
wCsf Żuf l − wCsr Żurl + wCsf Żuf r +
2 2 2
1 1 1 Figure 2. Fuzzy Controller Overall Layout.
wCsr Żurr + wKsf Zuf r − wKsf Zuf l −
2 2 2 • An interface for fuzzification that changes the inputs of
1 1 1 1 the controller to linguistic variables that can be used in the
wKsr Zurl + wKsr Zurr − wFf l + wFf r −
2 2 2 2 inference mechanism. The fuzzy membership function
1 1
wFrl + wFrr − Mroll = 0; (10) can be described as follows:
2 2
2.1. State Space Formulation of the Full K = {(x, uk (x)) | x ∈ K, uk (x)[0, 1]} ; (12)
Vehicle Model where uk (x) is the membership function specifying the
The state-space variables for the full vehicle suspension grade of degree for any element in K which belongs to
model are assigned as in work of Senthilkumar et al.61 Nomen- the fuzzy set K. The lager values of uk (x) indicate the
clature: higher degrees of membership.
y1 = Ż velocity (payload speed of sprung mass)
• A rule-based (RB), a set of linguistic (“if-then”) rules
y2 = θ̇ angular velocity
that store the information of how the mechanism can be
y3 = ϕ̇ roll angular velocity
managed. An inference process that produces the control
y4 = Żuf l left-front wheel unsprung mass speed
judgment using the linguistic inputs and the RB.
y5 = Żuf r right-front wheel unsprung mass speed
y6 = Żurl left-rear wheel unsprung mass speed • An interface for defuzzification, which transforms lin-
y7 = Żurr right-rear wheel unsprung mass speed guistic outputs into crisp ones. The centroid defuzzifi-
y8 = Z heave position (ride height of sprung mass) cation technique can be expressed as:
y9 = θ pitch angle R
µA (Z)Z dz
y10 = ϕ roll angle ZCOG = RZ ; (13)
y11 = Zuf l left-front wheel unsprung mass displacement µ (Z) dz
Z A
y12 = Zuf r right-front wheel unsprung mass displacement
where ZCOG is the crisp output, µA (Z) is the aggregated
y13 = Zurl left-rear wheel unsprung mass displacement
membership function and Z is the output variable.
y14 = Zurr right-rear wheel unsprung mass displacement
The state-space equation is • The fuzzification stage converts the e(k) error and ec(k)
error change of suspension deflection into fuzzy values
{ẏ} = A{y} + B{f } + D{r}; (11)
using the membership function. Fuzzy rules based on ex-
where pert knowledge have been incorporated throughout the in-
{y} = [y1 , y2 , y3 , y4 , y5 , y6 , y7 , y8 , y9 , y10 , y11 , y12 , y13 , y14 ]T ference phase.
is the state vector; {r} = [Zrf l , Zrf r , Zrrl , Zrrr , Mroll ]T is
the road disturbance input vector; {f } = [Ff l , Ff r , Frl , Frr ]T With five linguistic variables described in Fig. 3, the trian-
is the control force input vector; A, B, and D are invariant gular membership functions. The actual input data is trans-
coefficients. formed into fuzzy values by this membership function. The
traditional basis was the classical understanding of Mamdani.
The range of the input variable and the output variable was
3. FUZZY LOGIC CONTROLLER DESIGN
calculated under different conditions by the results of the sim-
The FLC system provides an intuitive methodology to con- ulation. Table 2 shows the rules table for fuzzy logic control.
vert imprecise input into precise inputs. The FLC system nor- The justification for the creation of the fuzzy control rules is
mally involves 3 phases, i.e., fuzzification, control rule design to minimize the vertical displacement of the automobile body.
and defuzzification. The conversion of real-number (crisp) in- There are two inputs to the fuzzy logic controller used in the
put data to fuzzy data is involved in fuzzification. At this point, active suspension: velocity, acceleration, and one output: the
the membership functions (MF) used to fuzzy the suspension desired actuator force. For the five specified variables of the
model input and output data are chosen. Next, by providing ASS defined by a fuzzy set, a possible choice of the member-
the IF-THEN control rules, the fuzzy inference system is built. ship functions is as follows.56
The process of defuzzification transforms the output of the A two-dimensional fuzzy controller is constructed with two
controller from fuzzy values into real values. FLC system can inputs and a single output. The basic input and output uni-
handle complexity, nonlinearity and unpredictable behavior of verses are determined by the measured passive suspension ef-
actuator dynamics in active suspension system.2, 23, 62, 63 The fects and by trial and error. There are [−0.3, 0.3], [−1.5, 1.5]
actual suspension travel of each wheel act as a control param- and [−5000, 5000], respectively in the simple universes of e,
eter for the fuzzy controller. Generally, the fuzzy logic control ec and u. Three variables are differentiated between the MF of
system consists of four parts, as shown in Fig. 2: the input and output variables, i.e., NS: Negative Small; NB:
International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022 29
S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

(a) Velocity (input) Table 2. The rules table for fuzzy logic control.
e / ec NB NS Z PS PB
NB NB NB NS NS Z
NS NB NS NS Z PS
Z NS NS Z PS PS
PS NS Z PS PS PB
PB Z PS PS PB PB

(b) Acceleration (input)

Figure 5. Bump road profile for the front and rear wheels.

bump height and non-uniform bump height, respectively:3

(c) Force (output)
(  
2πV tf

a0
1 − cos λ0 1 ≤ tf ≤ 1 + λV0 ;
Zrf = 2 (14)
0 otherwise;

(   
a0 2πV tr λ0
2 1 − cos λ0 tr0 ≤ tr ≤ tr0 + V ;
Zrr =
0 otherwise.
(15)

Figure 3. Membership function for input and output variables for fuzzy To investigate the behavior, two types of road input stimu-
controller. lation were used in this study: left wheel input and a speed
breaker. The front-left and rear tires got a single bump for the
left wheel input. Both or either of the front or rear tires con-
tacted the bump for the speed breaker input. Figure 5 shows
a graphical representation of the road profile. The road profile
bump inputs for the rear wheel and front wheel were calculated
using the formulae below. Where V is the vehicle forward ve-
locity, λ0 is the disturbance wavelength, a0 is the bump ampli-
tude, t is the simulation time and subscripts rr and rf denoted
the road-rear and road-front wheel inputs to the suspension, re-
spectively. tr0 = 1 + td , where td is the time delay between
the rear wheel and front wheel, written as:
a+b
td = ; (16)
Figure 4. Fuzzy controller surface viewer. V
where a is the distance between the vehicle’s front and rear
Negative Big; Z: Zero; PB: Positive Big; PS: Positive Small;
centers of gravity, and b is the distance between the vehi-
ec(k): error change; e(k): Error. Using the engineering con-
cle’s front and rear centers of gravity; a0 = 0.075 m, V =
text, the fuzzy rule base originally is given as follows: If (Ve-
15.50 m/s, and λ0 = 0.775 m.
locity is NB) and (Acceleration is NB) then (Force is NB), If
(Velocity is NB) and (Acceleration is NS) then (Force is NB)
etc. 5. RESULT AND DISCUSSION
5.1. Response of the Passive System
4. ROAD PROFILE The reactions of the passive vehicle suspension system for
the two inputs are compared. Figures 6 and 7 show that the
Road profile irregularities have been categorized as being amplitude of the response for the vehicle’s vertical bounce and
smooth, rough minor, or rough in nature. A smooth road pro- pitch motion is higher in the speed breaker input than in the left
file signifies a road disturbance with a single bump. The rough wheel input. Because both front-wheel tires contact the bump
minor and rough road profiles are characterized by uniform at the same time for the speed breaker input, the vertical height

30 International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022

 S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

Figure 6. Vertical bounce with a passive suspension system.

Figure 9. Vertical displacement of front and rear wheels.

Figure 7. Pitching response with a passive suspension system.

and pitch angle are higher. Figure 8 illustrates that when a

speed breaker is applied, there is no roll motion since both the Figure 10. Vertical displacement of front and rear wheels.
front and rear suspension wheels contact the bump at the same
time, but when the bump is delivered solely to the left wheels, reduced, resulting in an enhancement in ride comfort. Fig-
the car is raised and a rolling motion is visible, as predicted. ure 12 shows the body bounce response; we can see that when
Figure 9 depicts the response of the front and rear wheels the controller is applied, there is nearly 81% in vertical bounce
in terms of vertical displacement. Because the rear suspension and 60% in settling time of the passive response.
is more difficult, the vertical amplitude of motion of the rear
wheel is greater than that of the front wheel. The wheel dis- Pitching is one of the most uncomfortable body positions in
placement plot is used to examine the contact between the tire a car, and it should be avoided if you want to be comfortable.
and the road surface. When the road bump input is supplied Figure 13 depicts the suspension model’s pitching motion re-
exclusively to the left tires, Figs. 10 and 11 demonstrate the sponse. With the controller, the pitch angle of the passive sus-
difference between the vertical motion of the wheels and the pension system is lowered by about 40%, and the settling time
road irregularities for the front and rear suspensions. A posi- is cut by 50%.
tive number shows that there is a gap between the tire and the Figure 14 depicts the rolling motion reaction. Roll is a very
road surface, while a negative value indicates that the tire has risky attitude that causes the majority of accidents when cor-
been “bitten” by the road surface. The contact should be con- nering or maneuvering. Rollover should be avoided at all costs
tinuous and the difference should be as near to zero as possible by decreasing the roll angle to the smallest amount feasible.
for optimal vehicle control. Based on the roll reaction, we can observe that there is a nearly
50% reduction in roll and an almost equal reduction in set-
5.2. Body Attitude tling time. Based on the foregoing study, an active suspension
Body bounce, pitch, and roll are the three primary attitudes system can significantly increase comfort and safety at high
of an automobile’s body that are crucial for ride comfort and speeds.
safety. The vehicle’s vertical displacement (body bounce) is

Figure 8. Rolling response with a passive suspension system. Figure 11. Vertical displacement of front and rear wheels.

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S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

(a) Left wheel

Figure 12. Vehicle body bounce vs. time.

(b) Right wheel

Figure 15. Vertical displacement of vehicle wheels vs. time.

Figure 13. Vehicle body pitch angle vs. time.

5.3. Vertical Wheel Displacement

The tire-to-road-surface contact is evaluated using vertical
wheel displacement. The decrease in overshoot in Fig. 15 in-
dicates that the active system has enhanced tire-to-road sur-
face contact. When the automobile hits a bump or cornering,
the ASS should be built to prevent the car from skidding or
drifting. A positive indication shows that there is a space be-
tween the tire and the road surface, while a negative sign in-
dicates that the tire has been bitten by the road surface. Fig-
ure 15(a) depicts the vertical wheel displacement for the left
Figure 16. Vehicle body vertical amplitude vs. time during cornering.
wheel, whereas Fig. 15(b) depicts the vertical wheel displace-
ment for the right wheel. The data show that the active suspen- The study uses a curving road with a radius of 40 meters
sion system improves surface contact between the tire and the and a vehicle speed of 25 meters per second as the road input.
road, resulting in a smoother ride. The length of the curved portion is such that the car enters the
curved path in 2 seconds, travels 250 meters, and exits on the
5.4. Response to Cornering straight road in 2 seconds.
Our research had been limited to straight road driving, Figures 16 and 17(a) depict the vehicle’s vertical displace-
rolling is a highly dangerous body position for a vehicle while ment and pitching reaction, respectively. Because the car is
cornering or maneuvering, and it is the cause of many road ac- traveling on a flat curving road, the active and passive reac-
cidents. As a result, from a safety standpoint, this should be tions are almost identical, and the response is practically nil.
removed or reduced. The roll response of the active and PSS during cornering is
seen in Fig. 17(b). The active system has a maximum roll an-
gle of 0.00174533 rad (0.10◦ ), which is virtually insignificant,
but the PSS has a maximum roll angle of 0.1019 rad (5.84◦ ).
The roll angle has been reduced by about 98 percent, allowing
the rollover to be avoided.
The vertical displacement of the left and right wheels with
the passive and active suspension types is shown in Fig. 18(a)
and (b). When the car turns to the left, the left wheel is raised
a few millimeters, and there is no longer any contact between
the left tires and the road, which is dangerous and should be
avoided. The active suspension’s response demonstrates that
this issue has been resolved and that a greater tire-to-road grip
Figure 14. Vehicle body roll angle vs. time. has been obtained. The findings show that ASS is safer for

32 International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022

 S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

(a) (a) Heave

(b)

(b) Pitch

Figure 17. (a) Vehicle body pitch angle vs time, (b) Vehicle body roll angle
vs. time, respectively during cornering.
(c) Roll

(a) Left wheel

(b) Right wheel Figure 19. Response with the feed-forward system.

Figure 19 depicts the response with feed-forward control,

which has a smaller amplitude but a longer settling time than
the feedback response. This is undesirable because body mass,
or spring-mass, connects the front and rear suspensions; when
the front suspension is disturbed, the bodyweight is behind the
suspension; when the rear suspension is disturbed, the body-
weight is in front, but the applied control, which is taken from
the front suspension, assumes the body weight behind.

Figure 18. Vertical wheel Displacement vs. time during cornering. 6. CONCLUSION
rollover during turning and maneuvering, and is especially de- This study simulates the active suspension of a full vehicle
sired for high-speed cars. model and develops a fuzzy logic controller for the suspen-
sion system. The study proposes a fuzzy-logic-controlled ac-
tive suspension system for the passenger vehicle. The use of
5.5. Feed-Forward Control System
a fuzzy logic-based dynamic suspension controller improves
If the excitation is known ahead of time, the control signal ride comfort for cars traveling on varied road profiles while
can be delivered sooner to conduct the needed remedial ac- also reducing body acceleration. The reaction is investigated
tion, according to the feed-forward control approach. When it for disturbances such as road excitation and those generated by
comes to the vehicle suspension system, the road profile en- the vehicle itself. From the results obtained while investigating
countered by the front wheel will be the same as the distur- the performance of a vehicle running on a straight road and that
bance experienced by the rear wheels, but with a time delay subjected to bump disturbances, it has been found that when an
that is dependent on the vehicle’s speed. The control signals active suspension system is used an 81% reduction in vertical
applied to the front suspension are supplied after a time delay, amplitude is obtained while the settling time of the vertical dis-
which is determined by the controller’s reaction time and the turbances due to the bump is reduced by 60%. Furthermore, it
vehicle’s speed, to regulate the rear suspension’s disturbances. is evident from the results that the pitch angle is reduced by
International Journal of Acoustics and Vibration, Vol. 27, No. 1, 2022 33
S. Kumar, et al.: MODELING AND ANALYSIS OF ACTIVE FULL VEHICLE SUSPENSION MODEL OPTIMIZED USING THE ADVANCED. . .

9
40% followed by a reduction of 50% in settling time during Mustafa, G. I. Y., Wang, H., and Tian, Y. Model-free adap-
pitching. A 50% reduction in roll angle as well as for settling tive fuzzy logic control for a half-car active suspension sys-
time during rolling motion is achieved by the use of an active tem, Studies in Informatics and Control, 28, 13–24 (2019).
suspension system. The results obtained also help to conclude https://dx.doi.org/10.24846/v28i1y201902
that a 98% reduction in roll angle is also achieved during the
10
cornering of the vehicle. The current study shows that, during Kumar, S., Medhavi, A., and Kumar, R. Modeling of an
the simulation of an active suspension system with sensing and active suspension system with different suspension param-
actuating constraints, the performances of components of the eters for full vehicle, Indian Journal of Engineering & Ma-
system have a significant impact on the results obtained. The terials Science, 28, 55–63, (2021).
controller should be tuned carefully, failing in which the over- 11
shoot of the system rises rapidly and affects the results. The Kumar, S., Medhavi, A., and Kumar, R. Active
simulation results showed that the suggested active suspension and passive suspension system performance under ran-
system is highly successful in isolating the vehicle body from dom road profile excitations, International Journal
vibrations. of Acoustics and Vibration, 25, 532–541, (2021).
https://dx.doi.org/10.20855/ijav.2020.25.41702
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