Design and Implementation of GA Tuned PID Controller for Desired Interaction and Trajectory Tracking of Wheeled Mobile Robot

Abstract

The paper presents the design and implementation of a PID control based trajectory tracking of a nonholonomic wheeled mobile robot (WMR) with the objective of matching desired time domain specification and specified interaction. The desired time domain specification of output Y(s) is represented as a step response of a second order system with designer specific desired damping ratio (ζ) and natural frequency (ωn). The problem of finding the unknown parameters of PID controllers is formulated in a genetic algorithm (GA) based optimization frame in which the objective is to minimize the difference between the response of the designed closed-loop system and that of the desired closed-loop system. This procedure has been illustrated for achieving the desired time domain specification for WMR, taking different settling time of output response. The interaction analyses are carried out using the concept of Relative Gain Array (RGA). The RGA for both the desired and designed closed-loop systems are found to be matching. It has shown that interaction parameter λ controls both the steady-state and transient response of the desired closed-loop system. The interaction parameter also acts as a parameter which controls the coupling and is chosen by the designer as a specification to be met by the designed closed-loop system with PID controller.