Robust Integral Backstepping Speed Control for TSR-Based MPPT in Variable-Speed PMSG Wind Energy Conversion Systems

Abstract

Efficient maximum power extraction in variable-speed wind energy conversion systems (WECSs) remains challenging because of nonlinear turbine dynamics, continuously varying wind conditions, measurement disturbances, and mechanical-parameter uncertainties. This study presents a robust nonlinear integral backstepping control (BC) strategy for generator-speed regulation within a Tip-Speed Ratio (TSR)-based Maximum Power Point Tracking (MPPT) framework. The proposed controller combines nonlinear backstepping stabilization with integral compensation to improve reference tracking and reduce persistent tracking errors. The turbine-generator mechanical inertia is explicitly incorporated into the control formulation, providing a physically consistent representation of the mechanical dynamics and enabling systematic evaluation of parameter uncertainty. A comprehensive comparative assessment is conducted in MATLAB/Simulink using four control strategies: proportional-integral (PI), integral-proportional (IP), sliding-mode control (SMC), and the proposed integral BC. The controllers are evaluated under five complementary scenarios: variable wind speed, measurement noise, abrupt stepwise wind-speed variations, ±20% mechanical-inertia uncertainty, and a 10-ms rotor-speed measurement delay. Performance is assessed using the Integral of Squared Error (ISE), Integral of Absolute Error (IAE), and Integral of Time-weighted Absolute Error (ITAE), together with statistical measures across the five scenarios. Under the baseline variable-wind condition, BC achieves ISE = 24.4164, IAE = 1.539, and ITAE = 0.716, outperforming PI, IP, and SMC in all three indices. Under abrupt stepwise wind-speed variations, BC further achieves ISE = 0.00110, IAE = 0.0056, and ITAE = 0.0529, demonstrating rapid transient error suppression. The proposed controller remains stable under ±20% mechanical-inertia variations and a 10-ms measurement delay. Across the five scenarios, BC achieves the lowest mean ISE, IAE, and ITAE values of 19.353, 1.231, and 2.642, respectively, as well as the lowest standard deviations for ISE and IAE. SMC exhibits particularly consistent performance under measurement noise and the lowest standard deviation for ITAE. Overall, the results demonstrate that the proposed integral BC provides the most favorable balance of tracking accuracy, transient performance, and robustness among the investigated strategies. The improved rotor-speed regulation supports operation near the optimal TSR and effective aerodynamic power extraction. The findings highlight the potential of the proposed approach for robust MPPT control of variable-speed WECSs.