Abstract:

: Starting from the problem of studying the parametric robustness in the case of the control of a permanent magnet-synchronous motor (PMSM), although robust control systems correspond entirely to this problem, due to the complexity of the algorithms of the robust type, in this article the use of switched systems theory is proposed as a study option, given the fact that these types of systems are suitable both for the study of systems with variable structure and for systems with significant parametric variation under conditions of lower complexity of the control algorithms. The study begins by linearizing a PMSM model at a static operating point and continues with a systematic presentation of the basic elements and concepts concerning the stability of switched systems by applying these concepts to the control system of a PMSM based on the field-oriented control (FOC) strategy, which usually changes the value of its parameters during operation (stator resistance Rs, stator inductances Ld and Lq, but also combined inertia of PMSM rotor and load J). The numerical simulations performed in Simulink validate the fact that, for parametric variations of the PMSM structure, the PMSM control switched systems preserve qualitative performance in terms of its control. A series of Matlab programs are presented based on the YALMIP toolbox to obtain Pi matrices, by solving Lyapunov–Metzler type inequalities, and using dwell time to demonstrate stability, as well as the qualitative study of the performance of PMSM control switched systems by presenting in phase plane and state space analysis of the evolution of state vectors: ω PMSM rotor speed, iq current, and id current.

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