ABSTRACT

This thesis presents the dynamic modelling of a linear quadratic regulator based optimal direct current (DC) motor controller for improved performance. This study investigates the optimal use of a controller in the control of DC motor speed. This work also carried out a comparison of time response specification between conventional Proportional-Integral-Derivatives (PID) controller and Linear Quadratic Regulator (LQR) for a speed control of a separately excited DC motor. The goal is to determine which control strategy delivers better performance with respect to DC motor’s speed. The control method to be implemented in this work is the LQR which is a state space controller and the model of SEDM is presented in state space form. MATLAB/SIMULINK program was developed and used to solve the steady state and transient mathematical models of the machines. The test for both controllability and observability were carried out in the rank of matrix two. When the PID and LQR were compared, it was observed from the plots of speed against time at open loop with unity value of 1Volt and 1Ohm, the SEDM system with the LQR control stabilizes faster at the speed of 1rad/sec and after about 1seconds. This shows the superiority of the LQR to the PID that stabilizes at a speed of 41rad/sec after about 80seconds which is too long. The LQR responses were compared with PID, the LQR shows a rise time of 1.26seconds, settling time of 1.99seconds, overshoot of 0.525%, steady state of unity (1) and a peak amplitude of unity (1). While the PID also give a rise time of 0.0404seconds, settling time of 2.76seconds, overshoot of 84.8%, steady state of 1 and a peak amplitude of 1.85. The PID and LQR were also varied for different values of moment of inertia for J (J = 0.01), 0.5J and 2J.  The variation were also carried out for different values of Viscosity of b (b = 0.00003), 0.5b, and 0.2b. The LQR rises and settles in 1secs with a unity steady state value of 1 in almost all the variations. These performance makes the LQR more superior to the other types of conventional controllers. Simulation results shows that the proposed controller (Linear Quadratic Regulator) gives better performance when compared with the PID controller. Performance of these controllers have been verified through simulation using MATLAB/SIMULINK software application package. According to the simulation results, the LQR method gives the better performance, such as settling time, steady state and overshoot compared to conventional PID controller.