Cascaded extended state observers -based recursive sliding -mode dynamic surface control with nonlinear gains for uncertain nonlinear systems

In this paper, a recursive sliding -mode dynamic surface controller using an adaptive cascaded extended state observer (RSCESO) is proposed for the single-input-single-output (SISO) nonlinear systems in the presence of matched uncertainties and mismatched uncertainties, including parametric uncertainties and unknown time varying disturbances. Firstly, a series of cascaded extended state observers (CESO) are proposed to estimate the disturbances and the parametric uncertainties are handled by adaptation law in controller, which guarantees the mostly uncertainties are attenuated by the robust adaptive controller in the feedback, and avoiding high-gain feedback control. Secondly, the improved nonlinear gain functions are developed and incorporated into the control design to compensate for the input saturation limitation caused by the large control gain effectively. Finally, both a recursive sliding-mode surface and the nonlinear gain functions are introduced to deal with drawbacks in dynamic surface control approach. It is theoretically revealed that the proposed control strategy can make the tracking error arbitrarily small. Extensive comparative simulation results showed that the proposed RSCESO method has superiorities in terms of high-precision tracking accuracy and robustness to unknown time varying disturbances.