Model Predictive Torque Control with PWM using fast gradient method

We propose Model Predictive Torque Control (MPTC) with pulse width modulation (PWM) for Permanent Magnet Synchronous Machine (PMSM) Voltage Source Inverter (VSI) drive systems. MP-TC requires solving a Constrained Finite-Time Optimal Control (CFTOC) problem in real-time on embedded computational hardware. We demonstrate that the CFTOC is locally convex, which allows us to use standard numerical optimization techniques. In particular we use the fast-gradient algorithm. It is combined with the warm-starting and early termination technique for being able to solve the CFTOC on conventional embedded control hardware in real-time. The main control objective is to track a reference torque. Moreover, a d-axis current reference is set for Maximum Torque Per Ampere (MTPA) tracking and can be extended to include field weakening. We empirically demonstrate that our fast-gradient algorithm can be executed in real-time on embedded hardware. Furthermore we show that the MP-TC controller provides superior performance to the standard proportional-integral torque control on an experimentally validated software-in-the-loop platform.