Nonlinear H_∞ Control Of The Magnetic Levitation System

The magnetic levitation control is one of the key technologies for the magnetic suspension system.In this paper, the model of EMS is established. Because the gap of the electromagnetic suspension system is so small, that the dynamic equations of the electromagnetic suspension system can be replaced by the linearized equations. Therefore difficulty of the design is mainly on the performance, not the stability. Firstly, the HJI (Hamilton-Jacobi-Isaacs) inequality based on the dissipation theory is established, and then the nonlinear controller is designed with nonlinear H∞control theory, which is composed of two sections, including state's first-order and second-order of each state's multiplication. The second-order term of the controller is obtained recurrently from the first-order design. The first-order term is equivalent to a linear control law.This paper introduces the Bode's integral theorem and its application to a lab set of the electromagnetic suspension system. The restriction of the performance is often ignored in the general design. It shows that the electromagnetic suspension system is more difficult to control in practice, since the peak value of the sensitivity is restricted by Bode's integral theory.In this paper, a nonlinear controller is designed to ensure the performance of the electromagnetic suspension system. And the first-order control law is verified by simulation with linear and nonlinear plant separately. And their performances are analyzed comparatively each other. It shows that some characteristics is are lost as a result of linearization. And then the nonlinear controller is simulated, which shows that the performance is improved as expected. Furthermore, it also demonstrates the performance limitation imposed by the Bode's integral theorem.