Modelling of ball and plate system based on first principle model and optimal control

Abstract

This paper presents modelling of ball and plate systems based on first principles by considering balance of forces and torques. A non-linear model is derived considering the dynamics of motors, gears, ball and plate. The non-linear model is linearized near the operating region to obtain a standard state space model. This linear model is used for discrete optimal control of the ball and plate system — the trajectory of the ball is controlled by control voltages to the motor.