Digital control of Ball & Plate model using LQ controller

Abstract

This paper proposes the design of linear quadratic (LQ) digital controller in Ball & Plate model in experimental environment. The non-linear mathematical model of Ball & Plate structure is presented and adequately linearized. Polynomial approach to controller design for two degrees of freedom (2DOF) controller structure is introduced as the main tool for determination of unknown parameters. This method requires placing poles of characteristic polynomial, which are semi-optimally determined using minimization of linear quadratic criterion. This criterion is minimized by spectral factorization with the aid of the Polynomial Toolbox for MATLAB. Experiments have proved that this type of controller is able to stabilize the ball in desired position on the plate, reject external disturbances and follow reference path without much effort. In addition, a simple maze was created on the plate to extend possibilities of the choice of reference signal. The algorithm is able to determine correct path through the maze and navigate the ball along this path.