PI Backstepping Control of a Surface-Mounted Permanent Magnet Synchronous Motors

Backstepping control is a systematic technique for stabilizing nonlinear systems, particularly Permanent Magnet Synchronous Motors (PMSMs), by addressing their coupled electrical and mechanical dynamics. This Lyapunov-based approach allows for the design of control laws in a step-by-step manner, enhancing stability and performance under uncertainties. This paper presents a comprehensive evaluation of the PI Backstepping (PI-BS) Controller for speed regulation of PMSMs, showing significant improvements in dynamic performance, stability, and disturbance rejection compared to the Gain-Scheduled PI (GSPI) Controller. The control design focuses on rotor speed regulation through q-axis current, ensuring global asymptotic stability via Lyapunov criteria. Simulation results demonstrate the PI-BS controller's superior performance: during a step change from 0.2 PU to 0.9 PU, it achieves a rise time of 19.26ms and minimal overshoot of 0.50%, outperforming the GSPI controller's 22.83ms rise time and 1.53% overshoot. Under nonlinear load disturbances at 1.0 second, the PI-BS controller recovers faster with fewer oscillations, and in a speed reversal from 0.9 PU to -0.8 PU, it outperforms the GSPI controller with a fall time of 17.92ms and an overshoot of 0.50%. By decoupling the electrical and mechanical subsystems, the PI-BS controller offers precise speed and torque regulation under varying conditions. Its Lyapunov-based stability analysis ensures global asymptotic stability, enhancing robustness against disturbances and parameter variations. The controller’s faster response times, reduced overshoot, and improved disturbance rejection make it a highly reliable solution for high-performance motor control, particularly in industrial and automotive applications.