Motion Control of Smart Material Based Actuators : Modeling , Controller De - sign and Experimental Evaluation

Motion Control of Smart Material Based Actuators: Modeling, Controller Design and Experimental Evaluation Sining Liu, Ph.D. Concordia University, 2013 Smart material based actuators, such as piezoelectric, magnetostrictive, and shape memory alloy actuators, are known to exhibit hysteresis e ects. When the smart actuators are preceded with plants, such non-smooth nonlinearities usually lead to poor tracking performance, undesired oscillation, or even potential instability in the control systems. The development of control strategies to control the plants preceded with hysteresis actuators has become to an important research topic and imposed a great challenge in the control society. In order to mitigate the hysteresis e ects, the most popular approach is to construct the inverse to compensate such e ects. In such a case, the mathematical descriptions are generally required. In the literature, several mathematical hysteresis models have been proposed. The most popular hysteresis models perhaps are Preisach model, Prandtl-Ishlinskii model, and Bouc-Wen model. Among the above mentioned models, the Prandtl-Ishlinskii model has an unique property, i.e., the inverse Prandtl-Ishlinskii model can be analytically obtained, which can be used as a feedforward compensator to mitigate the hysteresis e ect in the control systems. However, the shortcoming of the Prandtl-Ishlinskii model is also obvious because it can only describe a certain class of hysteresis shapes. Comparing to the Prandtl-Ishlinskii model, a generalized Prandtl-Ishlinskii model has been reported in the literature to describe a more general class of hysteresis shapes in the smart actuators. However, the inverse for the generalized Prandtl-Ishlinskii model has only been given without the strict proof due to the di culty of the initial loading curve construction though the analytic inverse of the Prandtl-Ishlinskii model is well documented in the literature. There-