This study investigates a parametric approach to design the proportional-integral (PI) controller for a permanent magnet synchronous motor (PMSM). Based on the solutions of the generalized Sylvester equation, the generally parametric expressions of PI controller and right eigenvector matrix are obtained. By using the parametric approach, the closed-loop system is converted into a linear time-invariant system with an expected eigenstructure. Further, a numerical example is put forward to illustrate the effectiveness and feasibility of the proposed parametric approach.
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