Design of an Optimal Linear Quadratic Regulator (LQR) Controller for the Ball-On-Sphere System

摘要

Linear Quadratic Regulator (LQR) is one of the optimal control methods that continue to gain popularity. This paper designed an optimal LQR controller to control the system of the ball-on-sphere. System equations were derived and due to the nonlinearity of the system, the equations were linearized. After that, the coefficient matrices of the system dynamics were derived. Given some initial conditions, the response was simulated and controlled close to the desired values. An improvement of about 87% was achieved and the performance of the controller was observed to be good based on the simulation results. The results showed that LQR controller is one of the best optimal control methods because of its high performance improvement.