Abstract

The positioning and tracking performance of smart materials actuators is strongly limited due to the presence of hysteresis nonlinearity. The hysteresis of smart actuators, employed in micro-positioning tasks, is known to cause oscillations in the open-loop system's responses, and poor tracking performance and potential instabilities of the close-loop system. Considerable efforts are thus being made continuously to seek effective compensation of hysteresis effects in real-time applications. In this dissertation research, a stop operator-based-Prandtl-Ishlinskii model (SOPI) is proposed as a feedforward compensator for the hysteresis nonlinearities in smart actuators. The complementary properties of the proposed stop operator-based model in relation to the most widely used play operator-based Prandtl-Ishlinskii model are illustrated and applied to realize the desired compensation. It is shown that the stop operator-based model yields hysteresis loops in the clockwise direction, opposite to that of the piezoceramic micro-positioning actuators. It is further proven that the stop operator-based model exhibits concave initial loading behavior, while the play operator-based model, used to characterize the hysteresis behavior, follows a convex initial loading relation between the output and the input. On the basis of these complementary properties, it is hypothesized that a stop operator-based Prandtl-Ishlinskii model may serve as an effective compensator for known hysteresis nonlinearity that is described 'by a play operator-based model. The proposed stop operator-based model is subsequently implemented as a feedforward compensator in conjunction with the play operator-based model describing a known hysteresis nonlinearity. The effectiveness of the proposed compensator is demonstrated through simulation and experimental results attained with a piezoceramic micro-positioning stage. Both the simulation and the experimental results show that the proposed stop operator-based model can serve as an effective feedforward hysteresis compensator. A methodology for identifying the stop operator-based model parameters is proposed using those of a known play operator hysteresis model. Relations between the stop and play operator based-model parameters are also derived in the order to facilitate parameter identification. Furthermore, the relation between the stop operator based Prandtl-Ishlinskii model and the inverse Prandtl-Ishlinskii model, which has been proven effective hysteresis compensator, is demonstrated.