Visual Servoing Based Model Reference Adaptive Control with Lyapunov Rule for a Ball on Plate Balancing System

Abstract

The 2 Degree of Freedom (DoF) ball balancer system is a highly nonlinear system where the position of the ball is controlled by controlling the two servo motors simultaneously. In general, conventional Proportional Integral Derivative (PID) controller and Proportional Velocity (PV) is used to control the location of the ball on a plate in $\pmb{X}$ and $\pmb{Y}$ axes. But the major concerns are both classic PID and PV fails to track the ball position accurately due to non-linearity, process parameters variations and uncertainties. The above demerits are overcome by implementing Model Reference Adaptive Controller (MRAC) based PID controller. The closed loop reference model is chosen based on desired time domain specifications and by dominant pole placement technique. The gain values of the PID controller are tuned by MRAC to obtain optimal performance. MRAC based PID controller with MIT rule, modified MRAC with MIT approach, and modified MRAC with the Lyapunov rule are implemented in Simulink. The controller's performance on the benchmark Quanser 2 Dof ball balancer system is evaluated in real-time and comparative analysis is made. From the comparison, it is found modified MRAC based Lyapunov approach suppress the overshoot, provides better stability and tracks the system set-point accurately. On the other hand modified MRAC offers less Root Mean Square (RMS) value and faster tracking with less adaptation gain.