International Journal of Computer Applications (0975 – 8887) Volume 103 – No 17, October 2014 13 Eigen Value Analysis of Optimal Controller Design of Wheeled Autonomous Mobile Robot Shahida Khatoon D/o Electrical Engineering F/o Engineering & Technology Jamia Millia Islamia New Delhi-110025 India Kaukab Naz, D/o Electrical Enggineering F/o Engineering & Technology Jamia Millia Islamia New Delhi-110025 India Ibraheem D/o Electrical Enggineering F/o Engineering & Technology. Jamia Millia Islamia .New Delhi-110025 India ABSTRACT The autonomous wheeled mobile robots (AWMR) are subjected to high demands concerning stability, controllability and safety. Therefore, it becomes very important to devise the effective and efficient control strategies for such system to get desired system dynamic performance. In this paper the state space model of the system has been developed, the dynamic behavior of the system has been studied and then optimal controllers are designed using full state feedback control strategy. The optimal controllers are designed for various operating conditions using pole placement technique. The dynamic response plots are obtained for various system states considering various operating conditions. The investigations of these reveal that the implementation of optimal controllers offer not only good dynamic performance, also ensure system dynamic stability. Keywords Autonomous wheeled mobile robot (AWMR), Linear quadratic regulator (LQR), Error weighting matrix Q, Control weighting matrix R, 1. INTRODUCTION Recently mobile robot has been one of the central subjects in the research and development arena in the field of autonomous agents. They have been extensively applied in service industry, surveillance, geographical survey, remote access of dangerous location around the world as well as in domestic needs some of the many aspects which are typically studied in mobile robotics are path planning, trajectory tracking and controller stabilization. Non-holonomic robot is a popular differential drive mobile robot which is used in research as well as industrial applications [12]. However, few problems are associated with this type of robot is its high speed motion and hence the difficulty in avoiding actuator velocity saturation[13]. This difficulty is overcome by modifying the trajectory tracking error appropriately[16,17]. According to the design criteria, the control law is defined such as to reduce the difference between future trajectory tracking error of the robot and the reference one. The other area of interest for researchers is to achieve the shortest path length of robot trajectory. In [11], a randomized planner is applied to surveillance robot to get optimal path. A differential drive mobile robot is applied to the area of defense and security patrolling [12,13] in which sensor signals are mapped into actuator response using behavioral architecture. This regulates both translational and rotational movements of the robot. A discussion of different steering controls where PWM is applied to control DC motor for stable navigation strategy is presented in[14]. The aim of this research is to investigate the suitability and examine the performance of linear control systems like the Linear Quadratic Regulator and Pole-placement controller in stabilizing the robotic system. The dynamic behavior of the robot needs to be described by a mathematical model in order to arrive at an efficient control strategy for the balancing of robot. In this work the equation of motion for a wheeled mobile robot and linear model for a DC motor is derived in detail. The robot is actually powered by two DC motors. First of all the state space model of the DC motor is derived. Then this model is used todrivethe dynamic model of the robot that provides a relationship between the input voltages to the actuators, in this case motors,and the control torque needed to control the mobile agent. 2. LITERATURE SURVEY Autonomous Mobile Robot (AWMR) system is a model of generally many variables, a non- linear system, which is inherently unstable which also provides an excellent platform for experimentation and research purposes because various strategies of control can be evaluated for stability of the system by the laboratory based experiments. Since the system is non-linear and unstable various useful and popular methods that are employed by the researchers for stability and control of the system , are self- tuned PID controllers, auto- tuned PID controllers Artificial neural network based controllers, fuzzy logic controllers, genetics algorithm, etc. [1- 3, 7, 9, 14] . In 1996, two researchers from the control system domain succeeded, using an analogue computer, in controlling an inverted pendulum in standing position on a cart, which was stabilized by horizontal force [18]. There are various types of inverted pendulum such as, the simple inverted pendulum, the rotary inverted pendulum, double inverted pendulum, the rotatory double inverted pendulum [17,19].The navigation characteristics of the robot, which are nonlinear, and other parameters which are time varying and statistically unstable, are analyzed by mathematical modeling to better understand the system [10].The Lagrange method, is usually employed to form the basis for better understanding of control problem. Dynamic model of the robot, is established which clearly has a physical relevance so that various strategies can be evolved for path planning and dynamic stability of the wheeled mobile agent[6,8,12,]. The research on such a complex system involves many important theory problems about system control, such as nonlinear problems, robustness, maneuverability and trajectory tracking problems [4,11,16]. Therefore, as an ideal example of the study, the inverted pendulum system in the control system has always attracted worldwide attention. And it has been recognized as control theory, especially the typical modern control theory research and test equipmentandthus various software platforms are