Operator- and Observer-Based Tracking Control Design for Nonlinear Plants and Its Application to a Flexible Arm Using Shape Memory Alloy Actuators

In this paper, an operator- and observer-based nonlinear tracking control scheme is proposed. Initially, the error-based extended state observer (eESO) is employed on the objective nonlinear plant, which addresses the compensation for perturbations like modeling uncertainty, unknown dynamics and external disturbance. Moreover, an additional feedback loop is constructed following the principle of the operator-based robust right coprime factorization (RRCF) feedback framework, which aims at further guaranteeing the robust stability of the proposed overall tracking scheme. Specifically, by interpreting each component as an operator and designing the controllers to satisfy the robust stability condition, the proposed scheme can be shown to be bounded-input bounded-output (BIBO) stable, while the satisfactory tracking performance is achieved simultaneously. The proposed nonlinear tracking control scheme is then applied into a flexible arm system that is driven by the shape memory alloy (SMA) actuator. Experimental validation demonstrates that the proposed method outperforms the selected benchmark methods in terms of mean RMSE, achieving values of 0.0692, 0.0653, and 0.0781 across three experimental scenarios, respectively. These findings confirm the effectiveness and practical feasibility of the proposed tracking control scheme.