Generalized proportional–integral extended state observer-based controller design for fully actuated systems

In this paper, a feedback controller based on the extended state observer is proposed for fully actuated systems. First, a generalized proportional–integral observer is designed to estimate states and disturbances simultaneously. Using the linear parameter varying approach and the convexity principle, a linear matrix inequality condition is given to obtain the observer gains. Second, on the basis of the full-actuation property and the estimated states, a feedback controller, utilizing estimated disturbances to compensate for system disturbances, is designed to make all the states of the closed-loop system uniformly ultimately bounded. In addition, if disturbances are constant or slow time-varying, the observation errors and the states of closed-loop system are all exponentially convergent. Two illustrations are provided to show the validity and practicality of the proposed approach. Simulation results show that the estimated disturbances can follow the true values with relatively small errors, so compensating the system disturbances with estimated values can effectively reduce the ultimate bounds of states of the closed-loop system.