Mixed-Sensitivity Controller Design for Repetitive Control in Hysteretic Systems

Smart actuators, like piezoceramic materials, have been increasingly used in many engineering fields. One such application of piezoceramic actuators is ultrahigh precision positioning and tracking. Applicability of these materials in high precision devices is hampered due to the presence of nonlinearities such as hysteresis. Tracking control of such hysteretic systems has received considerable attention in the past two decades. In this work, a systematic approach is developed to represent the hysteretic systems as time-invariant, parameter-dependent uncertain systems assuming variable stiffness and damping as uncertain parameters. And also, design of robust controller for tracking periodic signals by minimizing the mixed sensitivity H∞ norm of the closed loop system. The effectiveness of proposed method, in compensating hysteresis nonlinearities, is validated through experiments on Thunder actuator. The effectiveness of designed controller is demonstrated experimentally for tracking sinusoidal signals. Experimental results substantiated the improved tracking performance of closed loop system. Effective width of hysteresis loops is reduced to a great extent after incorporating the proposed controller. Robustness of the developed H∞ controller is demonstrated experimentally by verifying the performance of controller at different input amplitudes, input frequencies and change in physical properties of the system.