LINEAR EXTENDED STATE OBSERVER BASED BACK-STEPPING CONTROL FOR UNCERTAIN SISO NONLINEAR SYSTEMS

In this paper, a control scheme combining linear extended state observer (LESO) technique and back-stepping method is proposed for a class of single-input and single-output (SISO) nonlinear uncertain system with known linear dynamics, unknown nonlinear functions, internal uncertainties and external disturbance. And the system states are not available for measurement. An improved LESO was presented. Compared to the extended state in typical LESO structure, the one in this improved LESO does not contain the known linear terms. This handling approach can decrease control energy. This improved LESO can estimate simultaneously both the systems states and the total disturbances. Through the compensation function of the extended state, the original system can be changed into the linear system. Then we utilized the back-stepping method, which is different from nonlinear PID used during the typical ESO-based control design process, stabilizes the resulting linear system. Rigorous stability analysis shows that the system output asymptotically converges to zero. Finally, the numerical simulation results are given to illustrate the effectiveness of the proposed controller.