Nonlinear optimal control of magnetic levitation system based on HJB equation approximate solution

Magnetic levitation system is a highly nonlinear and open-loop unstable system. So, control of this system is a challenging problem. In this paper a nonlinear optimal controller based on Hamilton-Jacobi-Bellman Partial Differential Equation (HJB PDE) is designed for this system. Goal of proposed controller is stabilizing the system around a desired point. At first, a measure performance based on energy consumption is selected and then HJB PDE is formed. Finally an approximate solution method is used to solve the HJB PDE. Results show effectiveness of the utilized controller.