A step by step adaptive super twisting controller for mismatched uncertain system

In this paper a step by step adaptive super twisting controller is designed for second order nonlinear strict feedback system with mismatched uncertainty. The design procedure is carried out by considering a virtual controller at each step. After obtaining the first step the desired dynamic model for each state is defined by the previous one and finally the actual control law is obtained. The design parameters of super twisting controller are estimated adaptively. The proposed method can be used for disturbance estimation also. The finite time convergence has been obtained by using a strict Lyapunov function. Simulation results demonstrate the efficacy of the proposed controller.