Control of a Ball and Plate System Using Model-Based Controllers

Abstract

A ball and plate system (BPS) is a benchmark system in control engineering. BPS is known to be nonlinear, a multivariable and an unstable system, has been widely used to investigate and demonstrate new control strategies that can deal with nonlinearities. The BPS consists of a metal ball, a plate which can be a resisitive touch screen and two servo motors with a linkage mechanism to move the plate. A resistive touch screen is placed over the plate, a plate is pivoted at its center such that the slope of the plate can be manipulated in two perpendicular directions with two servo motors to tilte the plate. In this thesis, the modeling of our BPS is based on the Euler-Lagrange approach, which is represented in the state space form with plate angles as inputs to the system. Then, the obtained model is linearized to be able to design linear controllers. Matlab and simulink programs are used for simulation tests to evaluate the closed loop system response and to determine the parameters and gains for different controllers. Moreover, the effect of the disturbances in the measurement is analyzed. Five control stratigies are selected for static and dynamic position tracking: model predictive control (MPC), proportional-integral-derivative (PID), state feedback, linear quadratic regulator (LQR) and linear quadratic tracker (LQT) controllers. These controllers have been implemented using the Arduino Uno ATmega328P. Therefore, the aim of this project can be summarized as to vi compare between the performance of the five different controllers for balancing a freely rolling ball in a specific position or to move it in a circle or square trajectory on the plate with the smallest settling time and the least possible error achieved for the dynamics of the real-time system.