A Study of the Stability and Design of Shape Memory Alloy Actuators

I hereby declare that I am the sole author of this thesis. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. ii The University of Waterloo requires the signatures of all persons using or photocopying this thesis. Please sign below, and give address and date. iii A Study of the Stability and Design of Shape Memory Alloy Actuators Simple, light, and powerful, shape memory alloy actuators hold much promise for the future of lightweight robotics and miniaturization. As classic obstacles such as speed of operation are overcome, their widespread application may become a reality, and the eld of robotics will beneet from a truly novel actuator. Due to the lack of an adequate mathematical model, the stability of closed loop systems incorporating shape memory alloy actuators has been largely ignored. In this work, dissipativity-related stability theory is applied to a simple shape memory alloy-actuated position control system, using a recently-proposed model for a shape memory alloy wire under constant load. It is shown that, for a broad class of dissipative controllers, the system will be L 2 stable for some range of non-zero loop gains. This applies to the common P, PI, PD and PID controllers, among others, and is believed to be the rst result of its kind. Furthermore, methods are presented to determine the maximum stabilizing loop gain for a given controller. As well, a new design is proposed for the common rotary diierential shape memory alloy wire actuator. The new mechanism incorporates a mobile heat sink, providing a signiicant increase in operating frequency, without suuering the usual drawback of increased power consumption. iv Acknowledgements I would like to gratefully acknowledge the mentorship, support, and most importantly friendship, that my supervisor, Professor David Wang, has extended throughout the course of his tutelage. It would not be an overstatement to say that without his enthusiasm for teaching, and the excellent rapport he maintains with his students , I would not have begun this work. It is certainly true that without his guidance, I never would have nished it. I am also indebted to Professor Andrew Russell, without whom the apparatus for …