Finite-Time Robust Speed Control of PMSM Drives Using Arbitrary-Order Sliding Mode Control With Data-Driven Gain Adaptation and Differentiation

Abstract

Permanent magnet synchronous motors have found wide application in high-performance systems, including electric cars and aerospace applications. Nevertheless, it is difficult to achieve accurate speed control due to the system’s nonlinearities, parameter uncertainty, and external perturbations. Traditional control approaches, such as proportional-integral (PI) and linear-quadratic regulator (LQR) controllers, are not particularly robust in such situations. Although classical sliding mode control provides enhanced robustness, it is commonly known to cause chattering and be sensitive to the choice of gain. More recent higher-order and observer-based sliding mode control methods ease some of these constraints, but they often require a priori knowledge of disturbance bounds, a low-order disturbance estimate, or complicated adaptive control. Such conditions can limit their ability to ensure convergence in finite time and discourage their application to real-time systems. To address these difficulties, this paper proposes an Arbitrary-Order Sliding Mode Controller (AOSMC), an Adaptive Arbitrary-Order Sliding Mode Differentiator (AOSMD), and a Genetic-Algorithm (GA)-based offline gain-optimization scheme. Throughout, a clear division of roles is maintained: the GA performs offline optimization of the fixed design parameters prior to deployment, whereas all online gain adaptation is performed exclusively by the projected dead-zone adaptive laws of the AOSMD. The AOSMC provides flexible, arbitrary-order sliding surfaces, whereas the AOSMD delivers accurate real-time estimates of high-order derivatives and lumped disturbances without prior knowledge of their bounds. The GA optimizes the fixed control and differentiator design parameters offline, prior to deployment, improving performance under varying operating conditions and reducing gain overestimation. A Lyapunov-based analysis establishes finite-time convergence of the tracking and estimation errors to a small residual set whose size is determined by the measurement-noise dead zones and the a priori gain ceilings of the adaptation, and exact finite-time convergence to zero under an explicitly stated sufficient condition on those ceilings. Simulation and experimental results show that the proposed method achieves better tracking accuracy, faster convergence, and greater robustness, with less chattering, compared with traditional SMC and higher-order SMC schemes, demonstrating the effectiveness of the proposed control scheme for a practical PMSM drive.