Vol-6 Issue-2 2020 IJARIIE-ISSN(O)-2395-4396 11676 www.ijariie.com 1043 Optimal and Robust Controllers Based Design of Quarter Car Active Suspension System Mustefa Jibril 1 , Messay Tadese 2 , Eliyas Alemayehu Tadese 3 1 Msc, School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia 2 Msc, School of Electrical & Computer Engineering, Dire Dawa Institute of Technology, Dire Dawa, Ethiopia 3 Msc, Faculty of Electrical & Computer Engineering, Jimma Institute of Technology, Jimma, Ethiopia ABSTRACT This paper offers with the theoretical and computational evaluation of optimal & robust control problems, with the goal of providing answers to them with MATLAB simulation. For the robust control,  -synthesis controller and for the optimal control, LQR controller are designed for a quarter car active suspension system to maximize the ride comfort and road handling criteria’s of the vehicle. The proposed controllers are designed using Matlab script program using time domain analysis for the four road disturbances (bump, random sine pavement and white noise) for the control targets suspension deflection, body acceleration and body travel. Finally the simulation result prove the effectiveness of the active suspension system with  -synthesis controller. Keyword: - Quarter car active suspension system, optimal control, robust control, linear quadratic regulator 1. INTRODUCTION Active suspension system are designed to satisfy specific necessities. In suspension systems, normally two maximum vital capabilities are anticipated to be advanced – disturbance shocking up (i.e. Passenger consolation) and attenuation of the disturbance transfer to the road (i.e. Vehicle dealing with). The first requirement might be supplied as an attenuation of the damped mass acceleration or as a peak minimization of the damped mass vertical displacement. The second one is characterized as an attenuation of the pressure acting on the road or in simple vehicle model as an attenuation of the unsprung mass acceleration. It is apparent that there's a contradiction among those requirements. Effort devoted to passive suspension design is ineffective, due to the fact there is a contradiction among both requirements. The nice end result (in experience of necessities development) can be done by active suspension, this means that that a few additional force can act on system. The concept of optimal control has been nicely advanced for over forty years. With the advances of computer technique, optimal control is now widely used in multi-disciplinary applications which includes biological structures, conversation networks and socio-monetary systems and so forth. As an end result, increasingly people will benefit greatly via gaining knowledge of to resolve the optimal control problems numerically. Realizing such growing desires, books on optimum control put extra weight on numerical strategies. Necessary situations for diverse systems had been derived and specific solutions were given whilst possible. LQR is a control system that gives the pleasant viable performance with admire to some given degree of performance. The LQR design problem is to design a state feedback controller K such that the objective function J is minimized. In this approach a remarks advantage matrix is designed which minimizes the goal characteristic as a way to obtain some compromise among the use of control effort, the significance, and the speed of reaction so that it will assure a stable system. 2. MATHEMATICAL MODEL 2.1 Quarter Vehicle Active Suspension System Mathematical Model Let’s begin with the most effective active suspension system model as shown in Figure 1. It carries two springs (one in suspension and second representing vehicle tires), one dumper and source of energy as actuator. The model is described by way of the differential motion equations: