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Design and analysis of a BELBIC controlled semi active suspension
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IOP Conf. Series: Journal of Physics: Conf. Series 1240 (2019) 012017
IOP Publishing
doi:10.1088/1742-6596/1240/1/012017
1
Design and analysis of a BELBIC controlled semi active
suspension system
P Sharma1, V Kumar2
1 PhD scholar, Department of Mechanical Engineering, NIT, Kurukshetra, India
2 Associate Professor, Department of Mechanical Engineering, NIT, Kurukshetra,
India
Email: ppankaj.ps@gmail.com
Abstract. The vehicle dynamics gives lot of consideration to quality of ride and the value of
comfort. These two are dependent on the suspension system of the vehicle. Researchers are
doing a lot of work in the field of improving these two parameters. A lot of approaches and
control systems like ANN, GA based system, fuzzy and hybrid control systems have been
formulated, simulated and tested. This paper deals with mathematical modeling and simulation
of passive and semi active system. The semi active system modeled here contains a new
approach of using intelligent controller based on Brain functioning with emotional signal,
known as BELBIC. The use of this controller has not been tested for suspension system as
identified through rigorous literature survey. The both systems are simulated for their response
to disturbance of road as step function and as profile of cosine shape. The results of passive and
proposed semi active system were analyzed to compare their performance in terms of
displacement of sprung mass and suspension travel as well as their settling time. The BEL
controlled system has performed very good. The displacement of sprung body has been
reduced in both the cases of road disturbances. The response against step input is better than
cosine. Similarly settling time has also shown in improvement for step and cosine function.
1. Introduction
From the time of inventions of the automobiles, quality of ride and the control of the vehicle are of
utmost importance for the engineers. The comfort of vehicle ride gets affected by transfer of vibrations
because of undulations in road e.g. bumps and humps. Engineers are putting lot of efforts right from
the beginning for developing better and better suspension systems for the vehicle. Initial suspension
design was the use of coil and leaf springs, further which were integrated with damper or shock
absorbers. It is the early eighties when with tremendous advancement in the field of electronics have
led the automotive design engineers to develop suspension system based on mechatronics approach.
Since then a lot of work has been performed for the continuous improvement in the design of
suspension by introducing semi active and active suspension using advanced control systems like
Fuzzy system, PI, PID etc. Now with the introduction of number of control techniques which are
nature or biological system inspired the more sophisticated and better performing suspension systems
are developed and are under the process of development.
A M Solovyov et al.[1] considered mechanical system dynamics under the effect of external force with
taking care of damper’s nature of hysteresis. Bouc-Wen model has been considered as mathematical
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expression for damper hysteresis. The work is simulated and results show that MR damper has very
good efficiency in resonance as well as outside resonance zone. Kareem Hassan et al. [2] worked on
simulation of passive and semi active suspension using LabView. The practical and theoretical results
were compared. The semi active suspension with PID controller performance was better than passive
in terms of parameters like settling time, peak overshoot, deflection of wheel and wheel position. Da
Shan Huang et al.[3] worked on simulation model of quarter car 2degree of freedom system. A PID
controlled semi active system is modeled and simulated and gains of PID are optimized by genetic
algorithm. The results shows drastic significant improvement in ride comfort. Mohamed Hassan et
al.[4] worked on study of the behavior of one fourth car active suspension in comparison to passive
suspension for road holding and ride quality. Two types of road disturbances were used for the
purpose of analysis, a random profile and a step function input. The result reveals that suspension with
twin accumulator gives significant improvements in ride quality in comparison to passive suspension.
The use of PI controller has shown improvement in displacement of wheel and vehicle body . Jiangbo
Wang [5] worked on mathematical modeling of roughness of road based on power spectral density.
They worked on it by random method of integral white noise. A 2 DOF vehicle model was prepared in
Matlab/Simulink for the analysis. They studied the effect of road profile generated on vehicle
subjected to random road profile. Guoliang Hu et al.[6] worked on analyzing the MR damper
characteristics and modeling of quarter model of car. A hybrid fuzzy controller is designed for
analysis. The results showed that hybrid fuzzy controlled suspension has much better ride quality and
comfort. Shida Nie et al. [7] proposed a modified skyhook acceleration driven damping algorithm for
ride comfort. A two degree of freedom model of vehicle is simulated and results showed and
improvement up to eighteen percent. Fitri Yakub et al.[8] simulated a one fourth model of car to
analyse the effect of road disturbance on vehicle’s performance. A feedback controller of state type is
used for the work and showed reduction in vibration caused by road disturbance. Wentao Liu et al.[9]
carried research on different types of mechanical model of MR damper. The work was focused on
analyzing the characteristics of these various models to design a damper based on the results . Jumi
Bharali et al.[10] modeled three degree of freedom suspension system. Three controllers LQR, Fuzzy-
LQR and PID were designed for the analysis. The performance of semi active system comes out better
than passive system, and Fuzzy-LQR based system proves to be best among the three modeled
systems. Manuel Brazz Cesar et al. [11] worked on a single degree of freedom structure under the
excitation of earthquake. The designed a controller based on emotional learning of brain (BEL
controller). The system showed very improved results against the excitation when used with BEL
controller. Alvaro Vargas Clara et al.[12] developed a new controller known as Brain Emotional
Learning Based Intelligent Controller (BELBIC). Its effect on controlling the unmanned ground
vehicle is analyzed. The results shows that new controller is very robust and better than PID controller.
Jae Won Kim [13] worked on mathematical modeling of inverted pendulum system with rotary
motion. A novel intelligent controller based on brain learning was designed. The performance of
newly proposed BELBIC controller proved to be very robust and effective. Al Shahriar et al. [14]
modeled a passive suspension system in Matlab/Simulink environment. They simulated the bounce
and pitch response of the vehicle. They formulated a cosine road profile and simulated its effect on the
suspension system. Ehsan Lofti et al. [15] worked on new approach in Belbic controller known as
generalized belbic system. The proposed controller has proved to be very robust in controlling the
plant output. The proposed controller can be used for non-linear systems also and its use on other
control systems can be investigated. Reshma Ravi et al. [16] studied a brain emotional based
intelligent controller and design of this controller for spring mass system with damper. The model is
simulated and its performance is compared with PID controlled system. The performance of the belbic
controller comes out to be better than PID. Arpit Jain et al. [17] proposed a new intelligent controller
for tank reactor with continuous stirrer used in chemical field. The controller proposed is based on
emotional learning principle of brain known as BELBIC. The simulation is carried out in
Matlab/Simulink environment and proposed intelligent controlled system gives very good results.This
work also deals with the design of new biologically inspired controller based on learning of emotions
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by human brain. In rigorous literature survey not much work has been identified for the use of this
controller in semi active suspension system.
2. Mathematical Model of Suspension System
Mathematical model of suspension with passive configuration as well as semi active has been created
in this work. A one fourth model of car with degree of freedom two in number is taken for the
development of said model in mathematical form. For passive system configuration spring, damper
arrangement is taken whereas for semi active configuration an intelligent controller has been
introduced as a part for spring damper system to make it a closed loop system. Also the damper
considered is with smart fluid damper known as magneto rheological fluid. The figure 1 shows one
fourth passive model and figure 2 one fourth model of semi active suspension for vehicle[1]. Rigid
body consideration of vehicle with suspension for the purpose of analysis has been taken. The tire of
vehicle is modelled as to give combined effect of stiffness and damper, therefore represented as a
combination of damper and spring in the model[2].
Figure 1. Passive 1/4th suspension Figure 2. Semi Active 1/4th suspension
From proposed 2DOF (degree of freedom) configuration of vehicle suspension, equation of motion for
sprung and un-sprung mass are obtained using free body diagram as equation (1),equation (2).
(1)
(2)
Based on the above two equations state space modelling of the 1/4th car model is done. The matrix of
state space form in generalised form is represented by equation (3), equation (4).
(3)
(4)
Equation (3) and (4) deals with following matrix:
A = state space, B = input, C = output, D = transmission, V = System Input.
Let,
Therefore equation (1), (2) are rewritten as equation (5), equation (6).
(5)
(6)
For passive type of suspension the matrix for input and matrix for output data of state space model are
formed and given by equation (7), equation (8) respectively[3][4].
CS
KS
Ct
Kt
Sprung Mass, MSR
Un-sprung Mass, MUS
XSR
1
XUS
2
WRD
Controller
CS
KS
Ct
Kt
Sprung Mass,MSR
Un-sprung Mass, MUS
XS
R1
XU
S2
ZRD
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(7)
=
+
(8)
The state space model for suspension with intelligent controller is created from equation (9), equation
(10) obtained by free body diagram of figure 2.
(9)
(10)
Let,
The state space model for suspension semi active type is represented by equation (11), equation (12)
respectively[5][6].
(11)
=
+
(12)
3. Intelligent Controller BELBIC:
The intelligent controller based on biological behaviour of human brain in response to emotions has
been designed. The controller is known as BELBIC (Intelligent controller based on brain’s emotional
learning).Functioning of human brain’s ‘Limbic System’ is principle of its working. Significant
components of brain’s limbic system are Amygdala, Thalamus, Sensory cortex and Orbitofrontal
Cortex[11]. Generally the role of motivation and emotion are overlooked while studying the human
behaviour and performance. The driving force for us is Motivation, without which no one would do
anything. Emotions on the other hand are the indicators how good or bad is the course of action taken
due to motivation, whether further action is required or not. We can also say emotions are continuous
feedback to human system of learning. The BELBIC system receives one or more than one signal but
gives only one output. It is a system that generates action on the basis of sensory inputs resulted from
stimulus or external source and reward a signal generated internally also known as emotional cue [12].
Thalamus sends sensed input to amygdala and orbitofrontal cortex receives signal from amygdala, it
also receives emotional reward from unspecified source as till today its origin is unclear [13]. The
output of the limbic system is difference of outputs of orbitofrontal cortex and amygdala. Figure 3
shows the general structure for BEL intelligent controller.
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The mathematical expression for BELBIC system is described by equation (13) to equation (17)[14].
(13)
(14)
(15)
(16)
(17)
Here ISI is sensory input, OOFC is output of OFC, OModel is output of model, GAG and GOFC are the gains
of amygdala and OFC respectively. GAG always gets increased depicting the behaviour of emotional
learning increment against each input. The rates of learning in the system are given by alpha and beta.
Generally same value is assigned to them; otherwise a higher value to the alpha is assigned [15].
XS
Figure 3.BELBIC Structure
4. Simulink Model of Passive, BELBIC Controlled Suspension
The model for the purpose of simulation was prepared in the Matlab/Simulink environment [16]. For
our proposed model of BELBIC for control of suspension system sensory input (ISI) and emotional
signal or reward (IES) is given as:
ISI =
IES =
Where,
Er= Error signal
KS1, KE2 and KE3 = Gains for sensory input and emotional signal
Figure 4 and figure 5 shows the Simulink block structure of emotional signal and orbitofrontal cortex
respectively [17].
K2
Figure 4. Emotional Signal Simulink Structure
K3
U
+
-
+
-
0
Xs
ES
-
+
XS ES
XS SI
SI
A OC
ES
SI
A
ES
MO
Sensory Input
Emotional Signal
Amygdala
OFC
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Figure 5. Orbitofrontal Cortex Simulink Structure
The input parameters for the Simulink model are given as per table 1.
Table 1. Parameter values for input
S.No
Parameter
Value
S.No
Parameter
Value
1.
Sprung Mass , MSR
242 Kg
5.
Tire Damping Co-efficient, Ct
1510 N-s/m
2.
Unsprung Mass, MUS
42 Kg
6.
Suspension Spring Stiffness, Ks
6010 N/m
3.
Tire Stiffness, Kt
140000 N/m
7.
Suspension Damping Co-efficient, Cs
305 N-s/m
4.
Bump Height, WRD
10 cm
The model is simulated for the response of un-sprung and sprung mass displacement, their settling
time.
5. Simulation
The model for both suspension i.e. passive type and one with controller is simulated in Simulink. The
models are simulated for road disturbance as input to the system. Step and Cosine function inputs are
given to the system for analysis. The gain coefficient in the proposed controller based on emotional
learning of brain was identified by trial and error method [16]. The model is tested for its response
under different values of gain, and the gains obtained are KS1 = 300, KE2 = 200, KE3 = 2000. The
simulation results for the bounce, suspension travel and time to settle down for sprung body in case of
input as step function is shown in figure 6 and figure 7. The Sprung mass displacement is very high in
comparison to BEL system.
Figure 6.Sprung Mass Displacement (Step Input)
0 2 4 6 8 10
0
0.05
0.1
0.15
0.2
Time, t (sec)
Sprung Mass Displacement (m)
Passive
BEL Controlled
×
×
OC
Integrator
_
_
+
SI
ES
A
Beta
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Suspension travel response of BEL controlled suspension system is given by figure 7, the response
obtained shows significant improvement in case of BEL controlled system.
Figure 7.Suspension Travel (Step Input)
Figure 8 represents the response of both types of suspension system for cosine profile cleat. It can be
observed that there is significant reduction in overshoot as well as settling time for intelligent
controlled system.
Figure 8. Sprung Mass Displacement
Suspension travel is also improved for cosine input to the system in case of BEL system as shown by
figure 9. The settling time has also improved very significantly in this case.
Figure 9. Suspension Travel
0 2 4 6 8 10
-0.15
-0.1
-0.05
0
0.05
0.1
Time, t (sec)
Suspension Travel (m)
Passive
BEL Controlled
0 2 4 6 8 10
-0.04
-0.02
0
0.02
0.04
0.06
Time, t (sec)
Sprung Mass Displacement (m)
Passive
BEL Controlled
0 2 4 6 8 10
-0.1
-0.05
0
0.05
0.1
Time, t (sec)
Suspension Travel (m)
Passive
BEL Controlled
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6. Result and Discussion
The BELBIC controlled suspension system response when compared with passive type has shown
much improved performance. The percentage reduction in bounce and time for settle down has shown
significant improvement and are shown in tabulated form in table 2 and table 3 respectively.
This shows that newly adapted approach of emotional learning of mind for creating the controller for
suspension has significant scope for further work in this field.
Table 2 Overshoot Response
Type of Suspension
Passive
BELBIC
% overshoot reduction for BELBIC
Type of Input
Step
Cosine
Step
Cosine
Step
Cosine
Sprung Mass
Displacement
0.1713
0.0521
0.1008
0.0357
41
31
Suspension Travel
0.0683
0.0506
0.0128
0.0237
81
53
Table 3 Settling Time Response
Type of Suspension
Passive
BELBIC
% settling time reduction for BELBIC
Type of Input
Step
Cosine
Step
Cosine
Step
Cosine
Sprung Mass
Displacement
8
9
1.5
5
81
44
Suspension Travel
8
8
1.5
4
81
50
7. Conclusion
The simulation result of semi active suspension system with novel approach of BELBIC controller
shows improvement in ride comfort when compared with passive system. The following observations
are obtained:
For step input a significant improvement is shown in sprung mass displacement and suspension
travel. The improvement is 41% and 81% respectively for BELBIC controlled system.
For step input a significant improvement is shown in settling time of sprung mass displacement
and suspension travel. The improvement is 81% and 81% respectively for BELBIC controlled
system.
For cosine input improvement in sprung mass displacement and suspension travel is 31% and 53%
respectively for BELBIC controlled system.
For cosine input a significant improvement is shown in settling time of sprung mass displacement
and suspension travel. The improvement is 44% and 50% respectively for BELBIC controlled
system.
The overall result of simulation work shows that BELBIC controlled semi active suspension system
performance is significantly improved. The response against step input is better than cosine because
step input is a Heaviside function. In this function value clips between zero to highest magnitude
directly, therefore the error signal to BEL controller will be very high resulting in high value of
damping force generated by the system. This will result in sharp reduction in sprung mass
displacement. In case of cosine input, the profile of bump is smooth semi-circular type where error
signal change is not as high as for step, correspondingly damping force generated will also be low in
comparison to step input response.
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