Optimal Control for Magnetic Levitation System Using H-J-B Equation Based LQR

This paper deals with the designing of linear optimal controller for Magnetic Levitation system (Maglev) in both simulation and real time. The Hamilton-Jacobi-Bellman (HJB) equation is employed to design the closed loop optimal control of infinite-time as well as finite-time Linear Quadratic Regulator (LQR) system with quadratic performance measure or index. The objective of the proposed controller is to stabilize the Maglev system and to control the ball position for tracking the desired ball position. The two different cases of weights of the LQR controller are selected on the trial and error basis for studying and improving the time response performance of the system. The performance comparison between infinite-time LQR and finite-time LQR is also investigated in both simulation and real time. To validate the effectiveness of proposed controller, it is compared with the classical PID controller between their relative time response and performance indices of the system. In the future, a detailed study of robustness in the presence of model uncertainties or external disturbance will be incorporated as a scope of further research.