A Unified Framework for Identification, Estimation, and Control of an Experimental Duffing–Holmes System

This paper presents a comprehensive framework for the identification, state estimation, and robust control of a bistable Duffing–Holmes oscillator, validated through an experimental setup. First, to address parametric uncertainty, a Recursive Least Squares Method (RLSM) with a forgetting factor is applied to a filtered model representation, enabling accurate parameter convergence from noisy measurements. Subsequently, a Nonlinear Integral Extended State Observer (NIESO) is designed to reconstruct unmeasured states and estimate total disturbances. A key theoretical contribution is the derivation of explicit gain conditions that guarantee the observer’s stability, overcoming limitations of previous designs. For trajectory tracking, an observer-based backstepping controller is synthesized. Crucially, to bridge the gap between theory and practice, a drift-free integration scheme is implemented to generate feasible position commands for the shake table, preventing actuator saturation. Experimental results confirm the framework’s effectiveness, achieving a 3.7-fold reduction in RMS tracking error compared to open-loop operation, with the tracking error rapidly converging to a small neighborhood within approximately 0.2 s. Furthermore, the closed-loop system demonstrates superior energy efficiency, requiring significantly lower actuator voltage to sustain stable interwell oscillations.