Robust observer design for nonlinear strict feedback systems (Proposal of integral sliding mode observer)

In this paper, we present a new design of the robust observer called integral sliding mode observer (ISM observer) for nonlinear strict feedback systems. Many controllers that have been proposed in control engineering require full information of states. However, we may not be able to measure full states because of cost of sensors or physical constraints. Therefore, it is important to estimate the states of the systems. Many researchers proposed various observers for estimating the states. Luenberger observer is the most common observer in control engineering, and Luenberger observer applied to the nonlinear system is called nonlinear observer. However, nonlinear observer may not work well when it is applied to nonlinear systems with uncertainties. Therefore, the robustness of the observer is an important issue. In this research, we propose ISM observer by introducing some kind of auxiliary system to nonlinear observer. Even if the system has uncertainties, the proposed observer guarantees the stability and the robustness of the origin of estimation error system if the observer gains satisfy the conditions for generating sliding mode. We design sliding mode controller based on ISM observer and simulate van der pol oscillator and an unmanned airship with various uncertainties. The simulation results on the estimation errors and the control errors show the robustness of state estimation by ISM observer and the effectiveness of the controller based on ISM observer, respectively.