International Conference on Emerging Research in Computing, Information, Communication and Applications, ERCICA 2014, held on 01-02 Aug 2014 in Nitte Meenakhsi Institute of Technology, Bangalore, India Paper ID: 600

1. Proceedings of
‘Second International Conference on Emerging Research in Computing, Information,
Communication and Applications’
(ERCICA-14)
Comparative Analysis of Multiple Controllers for Semi-Active Suspension System
a*Prashantkumar R., Surag R. Kulkarni, Deepak Sharma, Rakesh Sambrani, Varun V. Desai
M. Tech II Semester, Department of ECE, S.D.M.College of Engineering and Technology, Dharwad-580002, India
243
Abstract
The primary objective of this study is to model and simulate multiple controllers for vehicle suspension system and optimize the response of the
system for different driving modes and road profiles. The fundamental goals of a suspension system are to support the vehicle mass, to isolate
the vehicle body from road disturbances and to maintain the traction force between the tire and the road surface. The approach employed in this
work is to realize and simulate the mathematical model of the single wheel semi-active suspension system, with two degrees of freedom (2-
DOF). Multiple controller models are designed and are tuned to obtain optimal response for the system. Performances of PID, Skyhook and
Groundhook controllers are then analyzed in depth for different road profiles. Matlab Simulink provides a very good platform for modeling,
analyzing and optimizing the 2-DOF single wheel suspension system.
Keywords: Driving modes; Road profiles; 2-DOF; PID controller; Skyhook controller; Groundhook controller; Matlab Simulink.
1. Introduction
Basically, suspension system comprises of a coil spring, a damper and linkages that connects a vehicle to its wheels [1]. The
purpose of suspension system in automobiles is to improve ride comfort and road holding. Ride comfort literally indicates the
easiness experienced by the rider even on uneven terrains. Road holding points to the traction maintained between the tire and the
road surface. In normal road condition, ride comfort is the main concern but on sports track, road holding concerns the most.
Unfortunately, optimizing both parameters simultaneously has not been possible. Hence while designing the suspension systems
focus is on choosing the spring and damper coefficients, such that a perfect trade-off is achieved. With the recent advances in ride-by-
wire concept and damper technology, it is possible for the rider to switch between different modes, like comfort, city or sports
mode. Suspension system can be broadly categorized into three types: Passive suspension system, Active suspension system and
Semi-active suspension system. Semi-active system is particularly grabbing the attention of researchers for its sheer advantages
over the other two systems. Literature survey justifies that semi-active systems have less mechanical failure rate, less complexity,
and have much low power requirements compared to active systems [3]-[5]. Furthermore, as pointed out in [6] and [7] semi-active
systems have a very competitive performance and are good choice for overcoming system performance conflict. Controller is the
inevitable part of the semi-active system. Various controlling schemes have been proposed employing different principles in [8]-
[10]. In this paper few of the popular controller systems like PID controller, Skyhook controller [9] and Groundhook controller are
designed and compared.
2. Single Wheel Suspension Model
The model shown in Fig.1 represents a 2-DOF single wheel suspension model. The dynamic model, which can describe the
relationship between the input and output, enables one to understand the behaviour of the system. Equations of motion (1) and (2)
are used in building mathematical model of the system. As we have considered mass movements only on the vertical axis,
ignoring the other movements of the vehicle, this system is said to have 2-DOF. Since the distance (x1–w) is hard to measure and
the deformation of the tire (x2–w) is negligible, the displacement (x1–x2) is used to analyze the behaviour of the suspension system.
* Corresponding author. Tel.:+918123868668;
E-mail address:prashantkumar21@outlook.com.

2. Prashantkumar R. .et.al.
m1
m2
244
2 Equations of motion:
1 ′
푚′
1푥+ 푏1 푥1 "
− 푥+ 푘1 푥1−푥2 = 0 (1)
푚2푥2 "
+ 푏2 푥2 ′
− 푥1 ′
+ 푘1 푥2−푥1 + 푏2 푥2 ′
− 푤′ + 푘2 푥2 − 푤 = 0 (2)
k1
m1
m1
k2
m1
m1
b1
m1
m1
b2
m1
m1
x1
m1
m1
x2
m1
m1
w
m1
Fig. 1. 2-DOF Single Wheel Suspension Model.
Here: m1 - Sprung mass; m2 - Unsprung mass; k1 - Spring stiffness coefficient of the suspension; k2 - Spring stiffness coefficient
of the tire; b1 - Damping coefficient of the suspension; b2 - Damping coefficient of the tire; x1 - Vertical displacement of sprung
mass; x2 - Vertical displacement of unsprung mass; w - Road excitation.
3. Types of Suspension System
3.1 Passive Suspension System
In Passive Suspension system the characteristics of the suspension elements are constant, in other words it has fixed spring and
damping coefficient. In the design of these systems, there is an inherent compromise between good ride comfort and road holding.
The 2-DOF single wheel passive suspension system is shown in Fig 1. This system is modelled in Simulink, as shown in Fig 2.
Fig. 2. 2-DOF Passive suspension model in Simulink.
Fig. 3. 2-DOF Semi-active suspension model in Simulink.
3.2 Active Suspension System
Active suspension system retains the basic structure of passive system, but the damper is replaced by an actuator and the force it
exerts is determined by a controller with closed loop control. The controller uses sensory information as feedback and provides the
actuating signal. Actuator generates appropriate force depending on the instant condition of the suspension motion. Actuators
required to produce such force require a large power source and this very reason has made automotive industry to hunt for alternate
system. Fig 4(a) shows the 2-DOF single wheel active suspension system.
3.3 Semi-Active Suspension System
The Semi-active suspension system offers the same response as active suspension. The dampers that are required to realize it
consume less energy and are comparatively less expensive. In semi-active suspension, the actuator is replaced with an adjustable
damper. Fig 4(b) shows the 2-DOF single wheel semi-active suspension system. The input to this new damper block is the control

3. signal from the controller. Controllers with different controlling schemes are discussed in the next section. Fig 4 shows the
Simulink model of semi-active suspension system.
m1
m2
k1
m1
m1
k2
m1
m1
fa
m1
m1
x1
m1
m1
x2
m1
m1
w
m1
x1’
m1
m1
Controller
x2’
m1
m1
c(t)
b2
m1
m1
A
m1
m2
k1
m1
m1
k2
m1
m1
c(t)
fb
m1
m1
x1
m1
m1
x2
m1
m1
w
m1
x1’
m1
m1
Controller
x2’
m1
m1
b2
m1
m1
(a) (b)
Fig. 4. (a) 2-DOF Single wheel active suspension system. (b) 2-DOF Single wheel semi-active suspension system.
k1
m1
m1
k2
m1
m1
x1
m1
m1
x2
m1
m1
w
m1
(a) (b)
245
4. Controller Schemes
The response of active suspension system or semi-active suspension system depends on the type of the controller used. We
have designed three commonly used controller systems namely: PID, Skyhook and Groundhook.
4.1 PID Controller
The mathematical equation of the PID controller is:
푐 푡 = 푘푝 푒(푡) + 푘푖 푒 푡 푑푡 + 푘푑
푑푒 (푡)
푑푡
(3)
Fig. 5. PID controller Simulink model.
Where, c(t) is the control signal, kp is proportional coefficient, ki is integral coefficient, kd is derivative coefficient, e(t) is the
error signal (e=u-uref), u is the measured process variable and uref is the reference variable. The reference variable uref is set to 0.
The control signal c(t) is the input signal to the adjustable damper. The Simulink model of PID controller system is shown in Fig.
5. The input to the PID controller could be either x1 (vertical displacement of sprung mass) or x2 (vertical displacement of
unsprung mass)
4.2 Skyhook Controller
m1
m2
k1
m1
m1
k2
m1
m1
x1
m1
m1
x2
m1
m1
w
m1
b2
m1
m1
csky
m1
m1
m1
m2
b2
m1
Cgnd
m1
m1
Fig. 6. (a) 2-DOF Ideal Skyhook suspension system. (b) 2-DOF Ideal Groundhook suspension system.

4. Prashantkumar R. .et.al.
Force of the ideal Skyhook damper can be defined mathematically as:
퐹푠푘푦 = 푐푠푘푦 푥1 ′
However in ideal Skyhook system, the damper connection to the fixed point can be performed only in a stationary system. In
mobile systems like vehicle suspension, a force actuator between sprung and unsprung masses is used to simulate the Skyhook
damper force. In a semi-active suspension system, a controllable damper is used as the force actuator.
퐹푑 = 푐1(푥1 ′
246
− 푥2 ′
)
But, Fd must be equal to Fsky
∴ 푐1 =
푐푠푘푦 푥1 ′
푥1 ′
− 푥2 ′
Since the semi active damping force cannot possibly be applied in the same direction as the Skyhook damping force, the best
that can be achieved is to minimize the damping force.
∴ 푐1 =
2 1 ′
푐푠푘푦 ′
푥푥1 ′
−푥, 푥1 ′
푥1 ′
− 푥2 ′
≥ 0
0, 푥1 ′
푥1 ′
− 푥2 ′
< 0
(4)
The Simulink model of practical Skyhook controller is realized using (4) in a user defined Matlab function block. In the
Skyhook construction, the damper is connected to the sprung mass and the vibration is damped, so better ride comfort is achieved.
Whereas the unsprung mass vibration remains without damping force. To overcome this limitation we have designed a
Groundhook controller which provides better road holding.
4.3 Groundhook Controller
2 1 ′
′
Force of the ideal Groundhook 2 damper can be defined mathematically as: 퐹푔푛= 푐′
푑 푔푛푑 푥Similar to Skyhook controller: 퐹푑 = 푐2(푥− 푥)
But, Fd must be equal to Fgnd
∴ 푐2 =
푐푔푛푑 푥2 ′
푥1 ′
− 푥2 ′
Since the semi-active damping force cannot possibly be applied in the same direction as the Groundhook damping force, the
best that can be achieved is to minimize the damping force.
∴ 푐2 =
2 1 ′
푐푔푛푑 ′
푥푥2 ′
−푥, −푥2 ′
푥1 ′
− 푥2 ′
≥ 0
0, −푥2 ′
푥1 ′
− 푥2 ′
< 0
(5)
The Simulink model of practical Groundhook controller system is realized using (5) in a user defined Matlab function block.
Groundhook controller enhances the traction force between tire and road (better road holding). However, ride comfort degrades
considerably.
5. Optimizing Controllers
5.1 Saturation Limit
It is also important to note that practical dampers [2], [4], can only accept input in a specified range (depending on
manufacturer). As a result, a more limited range for the high and low level of damping should be defined as:
푏푎 =
푏푚푎푥 푐 > 푏푚푎푥
푏푚푖푛 푐 < 푏푚푖푛
푐 표푡ℎ푒푟푤푖푠푒
Here, bmax = 3000; bmin = -3000;
5.2 Tuning Controller Parameters
Tabulation I and II shows the coefficient of PID, Skyhook and Groundhook controllers, tuned to obtain the optimum response
from the system for respective modes.

5. 247
Table I: Model Coefficients for PID
Coefficients of optimized PID controller for different modes
Mode/Coeff kp ki kd
Comfort 0.552 5.52 0.5
Sports 50 5.52 0.5
City 50 100 -0.5
Table II: Model Coefficients for Skyhook and Groundhook
Coefficients of optimized Skyhook and Groundhook controller
Mode/Coeff bsky= csky bgnd= cgnd
Comfort 2450 -
Sports - 100,000
6. Road Profiles
6.1 Road Profile 1
This road profile represents edges of the roads. The simulation of the same is shown in Fig. 7. It is generated using a pulse
generator from Simulink library with following parameters: Amplitude = 0.1m; Period = 40s; Pulse width = 10s
Fig. 7. Simulation of Road Profile 1
Fig. 8. Simulation of Road Profile 2
6.2 Road Profile 2
This road profile represents irregular road surface [3]. Fig. 8 shows the simulation of the road profile 2. It is generated by
realizing (6) in a user defined Matlab function block included in Simulink library.
푤(푡) =
푢1(푡) 0.25 < 푡 ≤ 0.5
푢1(푡) 0.75 < 푡 ≤ 0.9
0 표푡ℎ푒푟푤푖푠푒
(6)
Where, 푢2 푡 = 0.05 1 − cos 8휋푡
푢1 푡 = 0.025 1 − cos 8휋푡
7. Simulation Results
Once the suspension system, controllers and road profiles are modelled in Simulink using necessary built-in and user defined
models from the library, they are subjected to simulation. Necessary parameters and coefficients have been listed in previous
sections. Note that the y-axis represents amplitude (in meter) and the x-axis represents time (in second). The simulation results for
all types of suspension system and controller schemes are presented in this section.
Fig. 9. Body displacement: Passive, Semi active (PID & Skyhook).
Fig. 10. Wheel displacement: Passive, Semi active (PID & Skyhook).

6. Prashantkumar R. .et.al.
248
Fig. 11. Body displacement (Road Profile 1): PID & Skyhook.
Fig. 12. Wheel displacement (Road Profile 1): PID & Skyhook.
Fig. 13. Body displacement (Road Profile 2): PID & Skyhook.
Fig. 14. Wheel displacement (Road Profile 2): PID & Skyhook.
Fig. 15. Body displacement (Road Profile 1): PID & Groundhook.
Fig. 16. Wheel displacement (Road Profile 1): PID & Groundhook.
Fig. 17. Body displacement (Road Profile 2): PID & Groundhook.
Fig. 18. Wheel displacement (Road Profile 2): PID & Groundhook.
Fig. 19. City mode (Road Profile 1): PID controller
Fig. 20. City mode (Road Profile 2): PID controller

7. Fig. 9 and Fig. 10 are the simulation results of body and wheel displacement for passive and semi-active system (PID and
Skyhook controller). Passive system has overshoot and it requires larger settling time. It neither provides good ride comfort nor
road holding. For body displacement, the system with PID settles down quickly and for system with Skyhook, response is smoother.
For wheel displacement, system with PID has less overshoot than the system with Skyhook.
Fig. 11 - Fig. 14 are the simulation results of body and wheel displacement for semi-active system with PID (with x1 as
reference) and Skyhook controller with two different road profiles. Road profile 1: In terms of body displacement, PID system has
higher overshoot than Skyhook. In terms of body displacement Skyhook system has higher overshoot than PID system. Road
profile 2: Both in terms of body and wheel displacement, Skyhook system offers slightly better performance. Hence Skyhook
controller is ideal for Comfort mode.
Fig. 15 - Fig. 18 are the simulation results of body and wheel displacement for semi-active system with PID (with x2 as
reference) and Groundhook controller with two different road profiles. Road profile 1: In terms of body displacement, PID system
has lesser overshoot and requires lesser settling time than the Groundhook. In terms of wheel displacement, Groundhook offers
quicker road contact than PID but it oscillates for a while before settling. Road profile 2: Both in terms of body and wheel
displacement, PID system have lesser overshoot and require lesser settling time than the Groundhook system. Hence Groundhook
controller is ideal for Sports mode.
It is evident from the above simulation results that the Skyhook controller is ideal for comfort mode, whereas Groundhook
controller is ideal for sports mode. The PID controller indeed offers reasonable performance for both comfort mode and sports
mode. This very reason has encouraged us to employ PID controller for city mode by taking the average displacement value of
sprung mass and unsprung mass of the vehicle. Fig. 19 - Fig. 20 are the simulation results of body and wheel displacement for
semi-active system (PID controller) with two different road profiles for City mode. PID controller is tuned to obtain perfect trade-off
249
between ride comfort and road holding.
8. Conclusion
This paper has outlined the improvements in performance of semi-active suspension system over passive suspension system.
We have presented the response of different controllers for various road profiles and driving modes. It is evident from the
simulation results that no control scheme offers best response for all conditions. Skyhook controller offers better performance for
Comfort mode, where better ride quality is desired. Groundhook controller offers better performance for Sports mode, where
better road holding is desired. Lastly, PID controller provides optimal response for city mode where both better ride quality and
road holding are desired.
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