Lyapunov-based constrained explicit current predictive control in permanent magnet synchronous machine drives

The current control problem of permanent magnet synchronous machine (PMSM) drives is a challenging problem which has to deal with quadratic and linear constraints and tight time constraint. The goal of this paper is to provide a controller synthesis method that can deal with these challenges effectively by developing an explicit predictive current control of PMSM drives. The objective is to adjust the stator voltages in order to obtain fast and monotonic transient current response while fulfilling the physical and computational constraints at all times. To this end, using a nonlinear model of the electrical subsystem of the PMSM in the rotor reference frame, an explicit one-step ahead model predictive controller (MPC) based on control Lyapunov functions is developed. A polytopic approximation of the states and control inputs is used in order to reduce the computational complexity. Then, the resulting MPC problem is reduced to a linear program. Furthermore, a piecewise affine explicit controller is obtained via multi-parametric linear programming. Comparative simulation results with the classical PI approach are reported showing significant improvement.