PhD ceremony Ms. R. Ouyang: Stability analysis and controller design for a system with hysteresis

PhD ceremony: Ms. R. Ouyang, 14.30 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Stability analysis and controller design for a system with hysteresis

Promotor(s): prof. J.M.A. Scherpen

Faculty: Mathematics and Natural Sciences

This thesis provides an approach for stability analysis and controller design for a system with Duhem hysteresis nonlinearity. Different from other methodologies, we study a natural input-output property of Duhem hysteresis operator: counterclockwise input-output behavior (CCW I/O behavior) and clockwise input-output behavior (CW I/O behavior).

The sufficient conditions on the Duhem operator (CCW or CW) are provided and also the dissipativity properties of such operator are investigated. In particular, we show the dissipativity property of the CCW (or CW) Duhem hysteresis operator by constructing an explicit storage function satisfying the CCW (or CW) dissipation inequality. Based on the dissipativity property of the Duhem hysteresis operator and motivated by real applications, we investigate the stability of a feedback interconnection between a linear system and a Duhem hysteresis operator. This absolute stability problem is solved based on the CCW or CW I/O property of the linear system and the Duhem operator.

Furthermore, we have studied the robustness property of a second-order linear plant controlled by a proportional, integral and derivative (PID) controller with a hysteretic actuator. The hysteretic actuator is modeled by a Duhem model which exhibits: (i) CW I/O dynamics; (ii) CCW I/O dynamics. The robustness of the closed-loop system with respect to the measurement noise is also given, using the integral input-to-state stability (iISS) concept. Finally, experiments on a piezo-actuated stage has been conducted to validate our stability and controller design approach.