Variable high-gain disturbance observer design with online adaption of observer gains embedded in numerical integration

In this paper, a variable gain design approach for the high-gain disturbance observer, called Proportional-Integral-Observer (PI-Observer), is proposed to solve the problem of choosing suitable observer gains. The high-gain PI-Observer is successfully applied to estimate unknown inputs of systems together with the system states. It is known that reasonable estimations of unknown inputs can only be derived using high observer gains. On the other hand, extremely large gains will cause serious problems with respect to measurements noise and unmodeled dynamics. According to the analysis of the estimation quality regarding to the factors which influence the estimation results, the optimal level of observer gains is changing during the estimation, an online adaption for the observer gains is therefore developed. The designed PI-Observer, called Advanced PI-Observer (API-Observer), will use changing observer gains from the adaption algorithm, which is proved to give stable estimation error dynamics. Simulation results from an elastic beam example are shown to illustrate the implementation of the API-Observer.