Reduced ultimate-bound of tracking error convergence for ETV system with unknown upper-bound mismatched perturbation

The electronic throttle valve (ETV) is widely used in automobile engines to obtain efficient fuel combustion, improved fuel economy, and reduced emissions. The control of the ETV system is a challenging problem due to the unmatched structure of perturbation and its unknown upper bound. As such, deep control concerns are required. For such a system, recent control approaches could partially solve the ultimate boundedness of convergence error, but they have failed to find a solution in the presence of unknown upper-bound perturbation. The contribution of this study is to develop a novel backstepping-based barrier function integral sliding mode controller (BS-BFISMC) to find a solution for the ETV system without the pre-knowledge of the upper bound of perturbation. The proposed control scheme gets the benefits of the backstepping algorithm (BS) and barrier function integral sliding mode control (BFISMC), and the combined scheme could lead to reduced ultimate-bound convergence of tracking error and result in chattering-free control action. A rigorous stability analysis has been conducted to prove the finding reached by the proposed control approach. The efficacy and effectiveness of the proposed controller have been shown by conducting a comparison study with other existing control methods; namely, conventional backstepping controller, robust continuous backstepping (CRBS), and backstepping-based quasi-integral sliding mode controller (BS-QISMC). The numerical results showed that the proposed BS-BFISMC yields the lowest level of ultimate bound of tracking errors and the least control efforts as compared to other controllers. Also, it has been shown that the proposed controller does not require the upper bound of perturbation, which is a pre-requisition of all compared controllers.