2-DOF Robust $ H_{\infty }$ Control for Permanent Magnet Synchronous Motor With Disturbance Observer

This article presents a two-degree-of-freedom (2-DOF) <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> speed control structure for permanent magnet synchronous motors (PMSMs). This structure consists of three parts: an <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> disturbance observer (DOB), an <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> feedback controller, and an <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> feedforward controller. First, the <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> problem, and the feedback controller design method for PMSM are presented. The stability theory, and the solution are introduced. Second, the disturbance observer is designed as an <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> disturbance tracking problem to estimate the external load torque, and increase the robustness. The speed controller is redesigned, and regards the estimated torque as one of the input. Finally, based on the 2-DOF structure, an <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> feedforward controller is designed. The generalized plant takes the whole close-loop model into account. The proposed method has a fast dynamic, and strong robustness against the external disturbance, and parameter variation. Several simulations, and experiments of conventional proportional integral controller, standard <inline-formula><tex-math notation="LaTeX">$ H_{\infty }$</tex-math></inline-formula> speed controller, and proposed method are operated in a PMSM system, and compared to validate the accuracy of the disturbance observation, and the effectiveness of the proposed method.