Ultimate bounded observer-based control of electrical vehicle driven by DC motor system with unmatched load torque

The unmatched perturbation of load torque is the essential problem in the Electrical Vehicle (EV) based DC motor which requires deep control concern for solution. In this study, the proposed solution to such a control problem is to design three observer-backstepping control schemes for speed trajectory tracking of EVs. The backstepping control algorithm has been developed based on three observers: Adaptive Disturbance Estimator (ADE), Nonlinear Disturbance Observer (NDO), and Quasi-Sliding Mode disturbance Observer (QSMO). Based on Lyapunov stability analysis, the ultimate boundedness of proposed controllers has been detailedly analyzed, assessed, and evaluated in the presence of unmatched perturbation. In the case of backstepping control based on ADE, the stability analysis has been conducted in the presence of stationary and time-varying disturbances to take into account the real load at the EV system. Moreover, a novel mathematical analysis has been conducted to determine the ultimate bound of disturbance estimation error in the case of backstepping based on QSMO. For the NDO-based backstepping controller, the design has been developed by proposing a new structure of nonlinear disturbance observer. The evaluation of proposed controllers has been verified with numerical simulations.