Backstepping-Based Quasi-Sliding Mode Control and Observation for Electric Vehicle Systems: A Solution to Unmatched Load and Road Perturbations

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Abstract
The direct current (DC) motor is the core part of an electrical vehicle (EV). The unmatched perturbation of load torque is a challenging problem in the control of an EV system driven by a DC motor and hence a deep control concern is required. In this study, the proposed solution is to present two control approaches based on a backstepping control algorithm for speed trajectory tracking of EVs. The first control design is to develop the backstepping controller based on a quasi-sliding mode disturbance observer (BS-QSMDO), and the other controller is to combine the backstepping control with quasi-integral sliding mode control (BS-QISMC). In the sense of Lyapunov-based stability analysis, the ultimate boundedness of the proposed controllers has been detailedly analyzed, assessed, and evaluated in the presence of unmatched perturbation. A modified stability analysis has been presented to determine the ultimate bounds of disturbance estimation error for both controllers. The determination of ultimate bound and region-of-attraction for tracking and estimation errors is the contribution achieved by the proposed control design. The performances of the proposed controllers have been verified via computer simulations and the level of ultimate bounds for the estimation and tracking errors are the key measures for their evaluation. Compared to BS-QISMC, the results showed that a lower level of ultimate boundedness with a higher convergent rate can be reached based on BS-QSMO. However, a higher control effort can be exerted by the BS-QSMO controller as compared to BS-QISMC; and this is the price to be paid by the BS-QSMO controller to achieve lower ultimate boundedness with a faster convergence rate.

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