Control of hysteretic systems with Preisach representations

Abstract

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 materias 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 th e properties of the Preisach hysteresis model, as they pertain to controller design. The Preisach model is general in nature, and has been successful in modellin 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.

Experimentally, Preisach model identification is carried out for two shape memory alloy actuator configurations, including a differential actuator. For each actuator, models which are in the dissipativity class are identified. 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 identified for which the match was better. However, these better models were not in the dissipativity class, suggesting that this class is likely somewhat conservative.