Performance Analysis of Linear Quadratic Regulator (LQR) Controller for D.C.Motor

Abstract

Control engineering is one subject which is perceived as being the most theoretical and most difficult to understand. In industries, application of motor control system is important to operation some process. An average home in Malaysia uses a dozen or more electric motors. In some application the DC motor is required to maintain its desired speed when load is applied or disturbances occur. This kind of system can be controlled using PID, Fuzzy, LQR and other more. Direct current (DC) motors have been widely used in many industrial applications such as electric vehicles, steel rolling mills, electric cranes, and robotic manipulators due to precise, wide, simple, and continuous control characteristics. Traditionally rheostatic armature control method was widely used for the speed control of low power dc motors. However the controllability, cheapness, higher efficiency, and higher current carrying capabilities of static power converters brought a major change in the performance of electrical drives. The desired torque-speed characteristics could be achieved by the use of conventional proportional integral-derivative (PID) controllers. As PID controllers require exact mathematical modeling, the performance of the system is questionable if there is parameter variation. In recent years neural network controllers (NNC) were effectively introduced to improve the performance of nonlinear systems. The application of NNC is very promising in system identification and control due to learning ability, massive parallelism, fast adaptation, inherent approximation capability, and high degree of tolerance. The outer speed and inner current control loops are designed as PD or PI controllers. However, the cascaded control structure assumes that the inner loop dynamics are substantially faster than the outer one. The electrical and mechanical parameters of the 2 DC motor, i.e., resistance, inertia, back-EMF, damping are identified from observations of the open loop response. Coulomb friction is considered as the main cause of the nonlinear motor behavior and is adequately compensated by a feed forward control signal. The residual steady state error caused by minor nonlinearities and uncertainties in the model is compensated by an integral error feedback signal. The proposed controller is evaluated for high and low velocity reference profiles including velocity reversal to demonstrate its efficiency for high-performance servo applications. The proposed scheme attempts to bridge the current gap between the advance of control theory and the practice of DC actuator systems. In this work, Linear Quadratic Regulator (LQR) controller is used in order to control the DC motor speed as we required. This techniques is used for tracking setpoint commands and reducing sensitivity to load disturbances. MATLAB is used to design and tune the LQR controller and be simulated to mathematical model of the DC motor. The Linear Quadratic Regulator (LQR) controller is a new method of controlling the motor. Linear Quadratic Regulator (LQR) is theory of optimal control concerned with operating a dynamic system at minimum cost.