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

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