Hysteresis Observation in Smart Material Actuators with Unstructured Uncertainty

Hysteresis phenomenon, which is prevalent in smart material actuators can affect control of the actuator, and should be compensated in the controller. In this paper its value is formulated as an internal state of the actuator, that is modeled by the Bouc-Wen model. A state observer, based on the position measurement is presented to estimate the hysteresis, which is not measurable by commercial sensors. The observer and convergence proof are presented using Lyapunov theorem, and the necessary constraints on design parameters are extracted. To facilitate these constraints, a lower order observer using velocity measurement is presented. The latter observer shows better transient and faster response. Both of the proposed observers are robust against model uncertainty. The effect of uncertainty in the estimated value is quantified and validated. An experimental setup using a piezoelectric actuator and an integrated strain gauge sensor is used as the test setup. Simulation and experimental results verify the effectiveness of the proposed schemes.