Fractional-order command filtered backstepping sliding mode control with fractional-order nonlinear disturbance observer for nonlinear systems

Abstract

This study developed a fractional-order command filter-based backstepping control (BSC) combined with a fractional-order sliding mode surface and a fractional-order nonlinear disturbance observer. The fractional-order based command filter was introduced to obtain a much faster convergence time than the previous command filter and resolve an explosion of complexity of BSC. Next, the fractional-order sliding mode surface was combined directly with the recursive controller-design process of the BSC system to enforce robustness to a disturbance compared to the conventional BSC system. Finally, the fractional-order nonlinear disturbance observer was considered to obtain fast and improved disturbance estimation performance over the conventional integer-order based one. The proposed fractional-order BSC control system showed more straightforward controller structure and improved performance than the conventional integer-order based BSC system. This was proven by a comparative simulation of a nonlinear dynamic system.