Suspension system for automobiles

SUSPENSION SYSTEM FOR 
AUTOMOBILES
Instructor: Assoc. Dr. Huỳnh Thái Hoàng
GROUP 6:
1. Trần Đạo Long
2 Lê T Hữ. rọng u
3. Nguyễn Thái Việt
4. Nguyễn Thanh Bình
CONTENTS
MATHEMATICAL MODELING
INTRODUCTION
PID CONTROLLER
SIMULATE THE SYSTEM USING MATLAB
CONCLUDING REMARKS
INTRODUCTION
 Suspension systems have been widely applied to vehicles, right 
from the horse-drawn carriage with flexible leaf springs fixed at 
h f h d bil i h lt e our corners, to t e mo ern automo e w t comp ex 
control algorithms.
INTRODUCTION
 The main task of a vehicle suspension is to ensure ride 
comfort and road holding for a variety of road conditions.
INTRODUCTION
Suspension system
Passive Active
Suspension 
System: Can not 
be controlled
Suspension 
System: Can be 
controlled
INTRODUCTION
A typical suspension system used in automobiles
MATHEMATICAL MODELING
PASSIVE ACTIVE
Text Text
Suspension
Text
Text
Text
Text
system
MATHEMATICAL MODELING
Active Suspension System 
B : damping coefficient, N s/m 
F : actuator force, kN
K spring stiffness kN/m1 : , 
K2 : tire stiffness, kN/m 
m1 : quarter car sprung mass, kg
m : unsprung mass kg2 , 
R : road profile, m 
X1 : sprung mass vertical displacement, m 
X2 : unsprung mass vertical displacement, m 
X1-x2 : suspension travel, m 
x2-r : tire deflection, m 
MATHEMATICAL MODELING
1 1 1 2 1 1 2( ) ( ) 0m x B x x K x x F       For sprung mass m1:
2 2 2 1 1 2 1 2 2( ) ( ) ( ) 0m x B x x K x x K x r F         For unsprung mass m2
MATHEMATICAL MODELING
 Taking Laplace transform for the equations of active 
suspension:
2
1 1 1 2 1 1 2
2
2 2 2 1 1 2 1 2 2
. . ( . . ) ( ) ( ) 0
. . ( . . ) ( ) ( ( )) ( ) 0
m s X B s X s X K X X F s
m s X B s X s X K X X K X R s F s
     
       
2
11 1 1
2
21 2 1 2
( ) ( ). ( )
( ) ( )( ) .
X s F sm s Bs K Bs K
X s F sBs K m s Bs K K
                     
2 2 2
1 1 2 1 2 1det ( . )( . ) ( )m s Bs K m s Bs K K Bs K       
2
1 2 2( ) ( . )
( ) det
X s m s K
F s

2
2 1( ) .
( ) det
X s m s
F s

2
www.themegallery.com Company Logo
1 2 1 2 2( ) ( ) ( ).
( ) det
X s X s m m s K
F s
  
MATHEMATICAL MODELING
2
11 1 1
2
( ) 0. ( )
( ) ( )( )
X sm s Bs K Bs K
X K R
                2 21 2 1 2 .. s sBs K m s Bs K K     
1 2 1( ) ( . )
( ) det
X s K B s K
R s

2
2 2 1 1( ) ( . . )
( ) det
X s K m s B s K
R s
 
2( ) ( )X X K1 2 2 1. .
( ) det
s s m s
R s
 
www.themegallery.com Company Logo
MATHEMATICAL MODELING
Finding 
suspension travel 
( car body 
displacement):
1 2( ) ( ) ( ) ( )F s F s X s X s
1 2
2 9 2
2 1
.
( ) ( ) ( ) ( )
. . 4 6 .1 0 .
R s X s X s R s
K m s s
 
 
2 2
1 2 2( ) . 3 0 0 . 1 9 6 0 0 0m m s K s
   
MATHEMATICAL MODELING
Finding the sprung mass 
displacement:
1 2 1
2
1 2 2
( ) ( ) ( ) de t .( . ). .
( ) ( ) ( ) . de t
F s F s X s K B s K
R s X s R s m s K
  
6 5
2 1
2 2
2 2
.( . ) 196 .10 . 36456 .10
. 50 . 196000
K B s K s
m s K s
   
PID CONTROLLER
 PID controller involves 3 separate controllers: proportional, integral 
and derivative. 
PID CONTROLLER
 Effects of PID controller :
 Speed up response of the system
 Eliminate steady – state error to step input
PID CONTROLLER
Zeigler‐Nichols rules for tuning PID controllers:
( ). ( ) ( )
t
PID P I D
de tG K e t K e t dt K
d
  
( )
O
t
P
t
K de t. ( ) ( ) .P P D
I O
K e t e t dt K T
T dt
  
PID CONTROLLER
 Zeigler and Nichols suggested that we set the values of the
parameter KP , TI, and TD according to the formula shown in Table
We choose : KP= 3055; KD= 32060 and KI=0.7 for 
suspension system
S O SIMULATI N AND RE ULT
SIMULATION AND RESULT
 Pot holes
www.themegallery.com Company Logo
S O S
 RESULTS FOR STEP INPUT:
IMULATI N AND RE ULT
 Sprung mass displacement (Pot hole)
S O SIMULATI N AND RE ULT
 Sprung mass acceleration Vs time (Pot hole)
S O SIMULATI N AND RE ULT
 Suspension travel Vs time (Pot hole)
www.themegallery.com Company Logo
2 Bumpy road (sinusoidal input).       
www.themegallery.com Company Logo
 Sprung mass displacement 
www.themegallery.com Company Logo
 Sprung mass acceleration Vs time 
www.themegallery.com Company Logo
 Suspension travel Vs time
www.themegallery.com Company Logo
www.themegallery.com Company Logo
3.Random road 
 Sprung mass displacement
 Sprung mass acceleration Vs time 
www.themegallery.com Company Logo
 Suspension travel Vs time
www.themegallery.com Company Logo
CONCLUDING REMARKS
 The PID controller is designed for active suspension 
system. A quarter car vehicle model with two-degrees-of-
f d h b d l d Zi l Ni h l t i lree om as een mo e e . eg er- c o s un ng ru es 
are used to determine proportional gain, reset ate and 
derivative time of PID controllers. The system is 
developed for bumpy road, pot hole and random road 
inputs. The simulated results prove that, active suspension 
t ith PID t l i id f tsys em w con ro mproves r e com or
REFERENCES
 Development of Active Suspension System for Automobiles using PID Controller-
Mouleeswaran Senthil kumar, Member, IAENG.
 Design and Development of PID Controller-Based Active Suspension System for 
Automobiles- Senthilkumar Mouleeswaran- Department of Mechanical Engineering 
PSG College of Technology Coimbatore,India.
 Constructing Control System for Active Suspension System - Sayel M. Fayyad-
Department of Mechanical Engineering Faculty of Engineering Technology PO Box 
15008, Al Balqa Applied University Amman, Jordan.
 Vib ti C t l f B S i S t i PI d PID C t ll Sh ilra on on ro o us uspens on ys em us ng an on ro er- e za
Jain-Assistant Professor, Electronics Department YMCA University of Science and 
Technology Faridabad, India.
 Electromagnetic Suspension System: Circuit and Simulation SuleimanAbu Ein and - - 
Sayel M. Fayyad