Disturbance estimation and compensation controller based on cascade sliding mode observer containing multi-nonlinear-discontinuous functions

The sliding mode observer (SMO), characterised by nonlinear discontinuous functions, has demonstrated effectiveness in state estimation and unknown disturbance reconstruction. However, conventional single-layer SMOs remain susceptible to undesired oscillations (chattering phenomena) induced by output measurement noise, which critically degrades estimation fidelity. To address the limitation, this study proposes a novel observer architecture, the Sliding Mode Observer and Cascade Observer (SMO-CO), incorporating multiple nonlinear discontinuous components. The SMO-CO comprises two layers: a primary layer adopting the traditional SMO structure and a secondary layer designed to attenuate noise-induced perturbations. The system model systematically accounts for measurement noise through descriptor augment remodelling, establishing a robust synthesis framework for observer parameter selection. A systematic design methodology coordinates gain optimisation across both layers, accompanied by Lyapunov-based stability analysis to verify closed-loop compensator efficacy. Numerical simulations demonstrate the SMO-CO's superior performance in mitigating chattering and enhancing estimation smoothness. Furthermore, the proposed structure significantly reduces control consumption compared to other existing observers.