Simulation-Based Optimal Speed Control of PMSM Drives Using Discrete LQR with Integral Action: Design, Analysis, and Robustness Validation
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Abstract
This paper presents a discrete-time Linear Quadratic Regulator (LQR) augmented with integral action for high-performance speed control of Permanent Magnet Synchronous Motor (PMSM) drives. Integral augmentation is embedded directly into the discrete-time LQR framework to eliminate steady-state error in both reference speed tracking and load disturbance rejection. A discrete-time Lyapunov function is derived, with real-time evaluation under parameter uncertainty, to guarantee asymptotic stability of the closed-loop system. A MATLAB m-file implementation enables fine-grained tuning of sampling rates and seamless translation to embedded architectures. Robustness is assessed via a comprehensive simulation suite, comprising step changes in speed reference, load torque disturbances, ±10 % variations in stator resistance and inductance, and ±15 % variations in rotor inertia and viscous friction. Head-to-head benchmarking against a cascade PI controller and a standard discrete-time LQR (without integral action) under identical scenarios quantifies improvements in convergence speed, overshoot reduction, and disturbance rejection performance. Simulation results demonstrate rapid convergence, minimal overshoot, and zero steady-state error, confirming the proposed method as a reliable, implementation-ready alternative for robust PMSM speed control.
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