Position Control of a DC Motor Using PID and LQR Methods

Abstract

In this study, a control system is developed for positioning a DC motor using optimal control methods to improve performance in terms of settling time, rise time, and the design of feedback gain K to minimize the cost function. The control approaches implemented include the Proportional-Integral-Derivative (PID) method and the Linear Quadratic Regulator (LQR) algorithm. The PID controller is designed to manage the motor's position by calculating the gain K using the Routh-Hurwitz criterion. The specific parameters Kp​, Ki, and Kd are then determined using the Ziegler-Nichols (Z-N) Oscillation method. For the LQR approach, motor position control is achieved by tuning the values of matrices Q and R, which influence the resulting KLQR​ gain.Simulations are conducted using MATLAB Simulink to evaluate performance. At the conclusion of the study, the identified PID controller parameters are Kp=3.72, Ki=1.2031, and Kd=2.8751. For the LQR controller, the optimal Q matrix is [100000;0100;000] with an R value of 0.01.