摘要：Piezoelectric actuators fundamentally possess hysteresis behavior. Estimation of the hysteresis is usually demanded for enhancing the performance of piezo-actuated systems. This paper presents an observer-based scheme to estimate the hysteresis in piezo—actuated flexible beams. The observer is based on a nonlinearity observer method. The discrete-time Kalman-filter algorithm is adopted for determination of the observer gains. The major advantages of the presented scheme include ease of implementation and robustness to uncertainty of hysteresis parameters. Simulation results demonstrate that the observer is able to estimate the hysteresis efficiently and has better robustness compared to the previous scheme existing in the literature. The present scheme was also successfully applied to a real-life system. Moreover, a control application example is included to demonstrate the effectiveness of the scheme.

摘要：Recently, the conditions of observers that can estimate directly Kx（t） for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, because of the equivalence in formulation, the existing conditions for unknown input observers can be used to establish directly a new set of sufficient conditions for that recent observer. This new set of sufficient conditions is much simpler, and therefore much more useful and significant, than the sufficient conditions derived in that recent paper. This new set of sufficient conditions also reveals some basic mistakes of that recent paper. In addition, this paper reveals the severe restrictiveness of this new set of conditions and proposes a fundamentally new observer design formulation that can relax that set of conditions significantly.