Abstract This paper investigates a composite control strategy combining an extended state observer (ESO) with sliding mode control (SMC) for mechanical systems subject to unknown disturbances and unmeasured velocity states. The main contribution is the development of an improved ESO with a time-varying gain mechanism that addresses the peaking phenomenon commonly associated with conventional high-gain observers while maintaining fast convergence. This time-varying gain is designed to start from a conservative value and smoothly transition to a high-gain regime, providing a quantitative trade-off between transient peaking and asymptotic accuracy. Based on the accurate disturbance estimates and reconstructed states from the proposed observer, a sliding mode controller is synthesized with active disturbance compensation, which significantly reduces chattering–a long-standing issue in conventional SMC. The second contribution lies in the theoretical analysis: using Lyapunov theory, we rigorously prove the uniform ultimate boundedness of all closed-loop signals and explicitly characterize how the observer and controller parameters influence the steady-state error bound. Unlike existing ESO-based methods that focus solely on observer structure optimization, the proposed framework integrates state estimation and robust control in a unified composite architecture with provable stability guarantees. Simulation results demonstrate that the proposed method achieves superior tracking accuracy and disturbance rejection compared to conventional PID and SMC without ESO, confirming its effectiveness under severe interference.
Li et al. (2026) studied this question.