Defence M.A. Vasquez Beltran: "Multi-loop Hysteresis and Recursive Remnant Control"

promotors: Bayu Jayawardhana, Reynier Peletier, Robert Huisman

Abstract: Many advanced instrumentation and high-tech systems have relied on the use of smart materials, such as smart memory alloys and piezoelectric material. The inherent non-linear memory behaviour, generally known as hysteresis, has become a defining characteristic that dictates and influences their function as actuators or sensors. In a recent development of piezoelectric material for a novel hysteretic deformable mirror (HDM) system, which is jointly developed by University of Groningen and Netherlands Institute for Space Research (SRON), an asymmetric butterfly hysteresis loop is exhibited; a phenomenon that was, until recently, not well-studied.

As a basis of this thesis, we study and characterise mathematical models of hysteresis exhibiting such asymmetric butterfly loops. In particular, we present classes of Preisach and Duhem hysteresis operators that are not only capable of displaying butterfly loops but also exotic multi-loop behavior.

Subsequently, we study systems and control properties in an interconnected system that contains hysteresis operators. Firstly, we analyze a Lur'e system whose feedback non-linearity is given by a Preisach butterfly operator. Secondly, we introduce the remnant control problem that corresponds to the working principle of the aforementioned HDM where the memory effect of hysteresis is exploited to hold a particular output configuration. In this problem, the remnant value refers to the retained output value when the input value is set to zero after the application of a certain control input signal and correspondingly, the remnant control problem pertains to the problem of designing this control input signal such that the remnant value can be driven to a desired reference value. We propose a recursive algorithm that can solve this remnant control problem and is applicable to both Preisach butterfly hysteresis operator and a class of Duhem hysteresis operators. Finally, we present numerical validation of the proposed remnant iterative control method to the shape control of HDM. These results can pace the way for the deployment of exoplanet imaging missions, next-generation photolithography machines, and high-tech systems.

Dissertation