Dynamic output-feedback H_∞ control design for ball and plate system

Abstract

Ball and plate system is a nonlinear and unstable system, thus introducing great challenges to control scientists and it resembles many complicated real-time systems in several perspectives. There has been a good number of efforts to design a stabilizing controller for this system. This paper presents a dynamic output-feedback H_∞ control strategy for the plate and ball system based on the solution of linear matrix inequalities (LMIs). The discussion involves deriving the equations of motion of the system by using the Lagrange method, linearizing the nonlinear equations, and designing an H_∞ controller to achieve required tracking specifications on the position of the ball. The intent is to show the specified trajectory tracking performance outcomes in time domain via simulation studies conducted using MATLAB/Simulink. A circular and square trajectory following of the designed controller is compared with a baseline PID controller. It is revealed that the proposed controller exhibits an improved tracking performance to following the reference trajectories.