Active Unmatched Disturbance Rejection Quasi-Sliding Observer for Electronic Throttle Valve System Based on Backstepping Control

<div>This study addresses the control problem of the electronic throttle valve (ETV) system in the presence of unmatched perturbations. Most previous works have ignored the effect of actuating motor inductance, which results in an approximated model with a matched perturbation structure. However, if this assumption is not permitted, the ETV model turns into an exact model with unmatched perturbation and the control task becomes more challenging. In this article, a backstepping control design based on a quasi-sliding mode disturbance observer (BS-QSMDO) has been proposed to effectively reject the unmatched perturbation in the ETV system. A rigorous stability analysis has been conducted to prove the ultimate boundedness for disturbance estimation error and tracking error. The key to this proposed observer-based control design is to obtain a robust and chattering-free controller based on a quasi-sliding mode methodology. The proposed quasi-sliding mode observer works to estimate the unmatched perturbation to be then actively rejected by the backstepping controller. Moreover, the observer adds a boundary layer around the sliding manifold to confine the estimation errors within a non-zero layer at the sliding phase, which leads to a considerable reduction of the chattering effect. A comparison study of the proposed BS-QSMDO is made with another backstepping controller based on a nonlinear disturbance observer (BS-NLDO). The numerical results showed the superiority of BS-QSMDO over BS-NLDO in terms of the ultimate bound of estimation and tracking errors. The numerical results showed that the BS-QSMDO could improve the tracking position error, control effort, and estimation errors of unmatched uncertainty by percentages of 26.67%, 1.46% and 92.5%, respectively, as compared to BS-NLDO.</div>