Optimization of Energy for Tracking of the ‎Magnetic Levitation Ball Using the SDRE ‎Technique

This paper was dealt with the optimization of energy for tracking the magnetic levitation ball by using the technique of State-Dependent Riccati Equation. The magnetic levitation ball is widely used in various fields. This system includes a steel ball suspended by electromagnetic force. The differential equations of this system are nonlinear. Generally, first, these nonlinear equations are linearized around an equilibrium point. Then, a Linear Quadratic Tracker controller is designed for this system. Note that this system has a non-zero equilibrium point. However, in the technique of State-Dependent Riccati Equation, the nonlinear equations are linearized by using the method of State-Dependent Coefficients. If the system is pointwise stabilizable and detectable, the State-Dependent Riccati Equation has an answer. Then, an optimal control law is extracted so that the energy of tracking is minimized. In the end, it has been shown that four different trajectories are tracked appropriately using the proposed method.