Comparison of linear and nonlinear H∞ control for a permanent magnet synchronous motor

The objective of this paper is to design linear and nonlinear H_infin controllers, and compare them. For linear systems, the H_infin controller is obtained either by solving Riccati equations using iterative procedures or by linear matrix inequalities. However, for nonlinear systems, the task is more complicated. In the particular case of nonlinear affine-input systems, the solution of the H_infin control problem is derived from the Hamilton-Jacobi Equations (HJE). The exact explicit solutions of this type of equations are, in general, unknown or hard to compute. Approximate solutions are obtained from an iterative procedure. In this paper, we propose a nonlinear matrix inequalities approach to design a nonlinear H_infin controller. Simulations of the closed-loop synchronous motors responses for both nonlinear and linear H_infin controllers will be performed and compared. It is found that the nonlinear H_infin controller has better performances and robustness than the linear controller.