Performance Investigation of H∞ Controller for Quarter Car Semi-active Suspension System using Simulink

This paper affords the design and improvement of a semi-active suspension system for an automobile. The main idea is to increase the semi-active suspension system damping vibration of the automobile body even as crossing the bump and sine pavement on the road. This system is modelled for 1 / 4 car system after which the entire system has been simulated using Mat lab/Simulink. It is used to physically simulate the quarter vehicle system of the automobile and have a look at the time domain response to the road disturbances. H infinity controllers is used to govern the damping properties of the semi-active suspension system mechanically. The system is designed in contrast to the most of the available suspension systems using a third order hydraulic actuator. The proposed system is compared with H2 optimal controller to test the performance of the system for the control targets suspension deflection, body acceleration and body travel for the bump and sine road disturbances. The simulation result of this studies reveal the efficiency of the advanced H∞ controller for the quarter car semi-active suspension system.


II.Mathematical MODELS A. Semi-active Suspension System Mathematical Model
The design of the semi-active suspension block diagram is shown in Figure 1  12 Where Zs is the position of the sprung mass, Zu is the position of the unsprung mass and Zr is the road displacement. These equations are solved numerically using MATLAB's dynamic system simulation software, SIMULINK.

B. Hydraulic System Transfer Function
The hydraulic actuator system is a third order system with transfer function of the form:

III.ROAD PROFILES
Four types of road disturbance input are used to simulate the semi-active suspension system road conditions.

A. Bump Road Disturbance:
The bump input road disturbance is shown in Figure 2.

B. Sine Pavement Road Disturbance:
The sine wave input road disturbance is shown in Figure 3.

A. H ∞ Contrller Design
A control system is robust if it remains stable and achieves certain performance criteria in the presence of possible uncertainties. The robust design is to find a controller, for a given system, such that the closed-loop system is robust. The objective is to find a stabilizing controller K to minimize the output z, in the sense of energy, over all w with energy less than or equal to 1. Thus, it is equivalent to minimizing the H infinity-norm of the transfer function from w to z as shown in

B. H2 Optimal Controller Design
There are many ways in which feedback design problems can be cast as H2 optimization problems. It is very useful therefore to have a standard problem formulation into which any particular problem may be manipulated. Such a general formulation is afforded by the general configuration shown in Figure 5.

V.Result and Discussion
The semi-active suspension system parameter is shown in

A. Simulation of the Proposed Controllers
The semi-active suspension system with H infinity and H2 optimal controllers are simulated using Matlab/Simulink for the control targets suspension deflection, body acceleration and body travel using bump and sine pavement road disturbances.

B. Simulation of a Bump Road Disturbance:
The Simulink model for a bump input road disturbance is shown in Figure 6. The simulation results for the control targets suspension deflection, body acceleration and body travel using bump road disturbances is shown in Figure 9, Figure 10 and Figure 11 respectively.

C. Simulation of a Sine Input Pavement Road Disturbance:
The Simulink model for a sine pavement input road disturbance is shown in Figure 12.

D. Numerical Comparison for Bump Road Disturbance:
The amplitude of the semi-active suspension system with H infinity and H2 optimal controllers for bump road disturbance is shown in Table II.

E. Comparison for Sine Pavement Road Disturbance:
The amplitude of the semi-active suspension system with H infinity and H2 optimal controllers for sine pavement road disturbance is shown in Table III.

VI.Conclusion
The H infinity controller successfully controlled the semi active suspension. When compared to the semi-active suspension system with H2 optimal controller, semi-active suspension system with H infinity controller substantially decreased the sprung mass displacement and therefore increased ride comfort of the automobile. Finally the simulation results prove the effectiveness of the semi-active suspension system with H infinity controller.

ACKNOWLEDGMENTS
First and formost, I would like to express my deepest thanks and gratitude to Dr.Parashante and Mr.Tesfabirhan for their invaluable advices, encouragement, continuous guidance and caring support during my journal preparation. Last but not least, I am always indebted to my brother, Taha Jibril, my sister, Nejat Jibril and my family members for their endless support and love throughout these years. They gave me additional motivation and determination during my journal preparation.