Smallest Control Invariant Set and Error Boundaries of FCS-MPC for PMSM

This paper studies the steady-state behavior of Finite Control Set (FCS) Model Predictive Control (MPC) for permanent-magnet synchronous machine (PMSM). The control actuation is formulated as a trajectory tracking problem in the alpha beta stator flux space. The concept of set stability and Control Invariant Set (CIS) is used to determine the smallest possible current, i.e. flux ripple. The best achievable steady state region of the control error is proposed and validated, revealing the maximum switching performance of FCS-MPC. The upper bound of the control error is achieved by constructing a CIS with respect to any reference defined on the equilibrium operating points. The proposed analysis has direct applications since it can be used to predict and optimize the current ripple in real time. Another application is the variation of the sampling frequency to achieve maximum ripple requirements at minimum switching losses.