New adaptive sliding mode control for a mismatched second-order system using an extended disturbance observer

An adaptive sliding mode control (ASMC) approach for a second-order system based on an extended disturbance observer (EDO) is proposed in this paper for systems with mismatched uncertainties. The EDO-based ASMC method is investigated to eliminate the effect of mismatched disturbance by using a novel adaptive sliding surface consisting of the disturbance estimation. The proposed method exhibits the following two attractive features: Firstly, the proposed adaptive sliding mode with disturbance estimation is insensitive to the mismatched disturbance; that is, the asymptotical stability of the adaptive sliding mode can be guaranteed in the presence of the disturbance estimation error of the EDO. Secondly, the chattering in traditional sliding mode control methods is eliminated by using an adaptive term the adaptive parameter. Compared with the disturbance-observer-based sliding mode control and the EDO-based modified sliding mode control method, numerical simulation results and application examples show that the proposed approach is robust, has the best dynamic performance and eliminates chattering.