Hybrid model predictive control and double integral backstepping for speed control of permanent magnet synchronous motors

Abstract

A robust hybrid control approach integrating continuous control set model predictive control (CCS-MPC) with double integral backstepping (DIBC) is proposed for high-precision speed regulation of permanent magnet synchronous motors. The outer speed loop uses a DIBC controller that generates the reference q-axis current while achieving asymptotic ramp tracking (Type-2 servo performance) without requiring load torque observers. The inner current loop employs CCS-MPC with embedded integral action for optimal q-axis current tracking, while backstepping handles d-axis regulation. Stability is proven using Lyapunov theory, singular perturbation theory, and input-to-state stability arguments. Compared to conventional integral backstepping as baseline, MATLAB simulations (at 10 kHz sampling) demonstrate 79% reduction in speed overshoot, 30% improvement in load rejection, and 11.8× lower integrated absolute error under ramp disturbance, with a computational cost of only 52 FLOPs per sampling period. A quantitative comparison with PI-based field-oriented control and active disturbance rejection control under identical conditions, including random, periodic, and noise-corrupted load scenarios, shows that the proposed controller is the only one of the four that eliminates the steady-state speed error under ramp load disturbances, while requiring no disturbance observer.