Gain scheduling control for magnetic levitation device using redundant descriptor representation

This paper proposes Gain Scheduling (GS) control for magnetic levitation device using redundant descriptor representation. The purpose of this study is to stably float a steel ball and let the distance between a coil and a steel ball follow the reference without error. GS control has a potential not only to deal with large variation range but also to improve the control performance. In this study, designed controllers are able to let a steel ball float stably in not a one equilibrium point but some variation range by scheduling an equilibrium point. However, designing a GS controller is difficult in the framework of state space representation. The redundancy of descriptor representation is applied to this difficulty. It is shown that a GS controller can be easily designed by introducing redundant descriptor variables. The robust stability for the system with uncertain parameters is guaranteed theoretically by using matrix polytope representation. Then, the problem is formulated as solving a finite set of Linear Matrix Inequalities (LMI) based on previous research. Finally, the effectiveness of the proposed method is verified by comparing a GS controller and a robust LQ controller in some simulations and experiments.