Control of hysteretic systems with Preisach representations

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. The last decade has seen a growing interest in the application of so-called \smart materials" as sensors and actuators. Transducers made from these materials are self-contained and scalable, and are well-adapted for use in distributed sensing and actuation. However, many of these smart materials display a highly non-linear input-output behaviour known as hysteresis, which can introduce delays and cause errors in position control tasks. This thesis examines some of the properties of the Preisach hysteresis model, as they pertain to controller design. The Preisach model is general in nature, and has been successful in modelling the hysteresis in several smart materials: magnetostrictives, piezoelectrics, and shape memory alloys. A novel state-space framework for the model is introduced, and a class of Preisach model is shown to be dissipative. This allows the application of energy-based controller design techniques to these non-linear systems. The Passivity Theorem is applied to determine a set of stabilizing controllers for velocity feedback of this dissipative class of Preisach models. iv Experimentally, Preisach model identiication is carried out for two shape memory alloy actuator conngurations, including a diierential actuator. For each ac-tuator, models which are in the dissipativity class are identiied. Applying the aforementioned theoretical results, this immediately provides a stability result for velocity feedback control of these actuators. While simulations using these models provide a good qualitative match with experimental data, other models were iden-tiied for which the match was better. However, these better models were not in the dissipativity class, suggesting that this class is likely somewhat conservative. v Acknowledgements In the three years during which this research was undertaken, I have had the pleasure and privilege of working with some wonderful people, each of whom deserves more thanks than this page allows. My supervisors, Professors Kirsten Morris and David Wang, provided support, guidance, and friendship over the years, and I would particularly …