New fast dynamic terminal sliding mode backstepping control

For a class of nonlinear system with uncertainties and disturbance,a new fast dynamic terminal sliding mode Backstepping control scheme is proposed.The sliding mode control is combined with Backstepping control to obtain robustness for system with matched uncertainties and unmatched uncertainties.Dynamic sliding mode has perfectly avoided the chattering in sliding mode controller.New fast terminal sliding mode has faster convergence speed than normal fast terminal sliding mode at any points.Where after,nonlinear disturbance observer with relaxed conditions is used to approximate the compound disturbance and adaptive robust control term is added to improve control performance.The stability of system is proved by Lyapunov theorem.Finally,simulation has proved the validity and advantage under the control scheme.