Additive-state-decomposition-based cascaded linear ADRC for nonlinear uncertain systems with application to PMSM speed regulation

Abstract

This paper investigates the tracking control problem for a class of nonlinear systems subject to time-varying total disturbance and proposes a cascaded linear active disturbance rejection control (CLADRC) approach based on additive state decomposition (ASD). By employing the ASD technique, the original system is equivalently decomposed into a nominal primary system and an uncertain secondary system. The primary system eliminates the estimated total disturbance to achieve precise reference tracking, while the secondary system suppresses the residual disturbance. Both subsystems are governed by state feedback controllers incorporating disturbance estimation and compensation. Compared to the standard linear active disturbance rejection control strategy, the proposed method fully decouples the tracking and robust components of the state feedback controller, enabling independent parameter tuning. Furthermore, by introducing a linear extended state observer for the secondary system, a secondary estimation of the residual disturbance is performed, thereby enhancing the robustness of the overall system. A criterion based on Lyapunov stability theory is provided to ensure that the closed-loop systems remain uniformly ultimately bounded. Finally, simulation and experimental results on permanent magnet synchronous motor (PMSM) speed regulation validate the effectiveness and superiority of the proposed approach.