Repetitive control of hysteretic systems using robust H-infinity controller
Pasala, Dharma Theja Reddy
Master of Science thesis
Unique properties of smart materials have enabled them to successfully replace conventional actuators and sensors. However, their effectiveness and applicability in control is hindered due to the presence of inherent hysteresis. In this thesis a systematic approach is developed to model this hysteresis in order to design a robust Hinfinity controller for tracking applications in one such smart material based actuator called Thunder actuator. The main objective of this work is to develop a controller to get rid of the delay, caused by the inherent hysteresis of the system, while following a commanded reference signal. To this end a mathematical model of the hysteretic system is developed and robust Hinfinity controller is developed for micro-position tracking control of the Thunder actuator. Tracking performance of compensated system is compared with open loop system for triangular and sinusoidal reference signals. Robustness of the developed Hinfinity controller is demonstrated and validated using experimental results. The first half of the thesis deals with the modeling of the Thunder actuator. Classical Preisach model is used to capture the hysteresis of the Thunder actuator. Congruency property and wiping-out property are verified and a classical Preisach model is developed for Thunder actuator using experimental data from first-order reversal curves. The Preisach model developed has been experimentally validated. Using Preisach model an equivalent time-invariant uncertain second order model is developed for Thunder actuator assuming variable stiffness and damping coefficients. The second half of the thesis involves designing a robust Hinfinity controller for the uncertain Thunder actuator model and validating the designed controller experimentally. Design of the controller is posed as a linear matrix inequality (LMI) problem and a mixed sensitivity optimal controller is calculated by minimizing the Hinfinity norm of the closed-loop system. Minimal tracking error is the performance criteria and noise rejection along with stability of the controller to time-invariant uncertainties are the robustness criteria in mixed sensitivity Hinfinity design. Full state robust controller is calculated for the nominal plant of the Thunder actuator. Robustness of the Hinfinity controller is verified through simulation and experimental studies. Experimental results demonstrate that the hysteresis loop-width of the Thunder actuator, in tracking sinusoidal and triangular signals, can be significantly reduced by using a robust- Hinfinity controller: this clearly demonstrates the effectiveness of the proposed control algorithm.
Mechanical engineering; Civil engineering