A Stop Operator-Based Prandtl-Ishlinskii Model For Compensation Of Smart Actuator Hysteresis Effects

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.