The Bouc–Wen model has been widely adopted to describe hysteresis nonlinearity in many smart material-actuated systems, such as piezoelectric actuators, shape memory alloy actuators, and magnetorheological dampers. For effective control design, it is of interest to estimate the hysteresis state that is not measurable. In this paper, the design of a state observer for the Bouc–Wen model is presented. It is shown that, with sufficiently high observer gains, the state estimate error, including that for the hysteresis state, converges to zero exponentially fast. The utility of the proposed hysteresis observer is illustrated in the design of a high precision output-feedback position tracking controller, and the resulting tracking error is shown to decay exponentially via Lyapunov analysis. Simulation and experimental results show that the proposed hysteresis observer and the high precision position tracking controller outperform a traditional extended state observer and the corresponding tracking controller, respectively.
