Trajectory control of a ball in a ball and plate system using cascaded pd controllers tuned by PSO

Abstract

This paper proposes design of proportional and derivative (PD) controllers in cascade control scheme to control trajectory of a ball in a ball and plate system. Ball and plate system, manufactured by Feedback instruments (Model No. 33-240), is realized in MATLAB–Simulink environment as a platform to test the performance of proposed controllers. Neglecting cross-coupling between motions along x- and y-axes, a decoupled nonlinear model of the system is realized in MATLAB–Simulink environment. A cascaded control strategy is adopted to make the ball follow a reference trajectory specified by user. PD controllers are used in both inner and outer loop of cascade control strategy. Parameters of PD controllers are tuned by particle swarm optimization (PSO) which does not require in-depth analysis of the nonlinear plant dynamics. Effectiveness of proposed controllers is tested by checking the ability of the ball to track reference trajectories like circle, spiral, square, and hexagon.