MODELLING, IDENTIFICATION, AND COMPENSATION OF COMPLEX HYSTERETIC AND LOG(t)-TYPE CREEP NONLINEARITIES

摘要

Undesired complex hysteretic nonlinearities and complex log(t)-type creep dynamics are present to varying degrees in virtually all smart-material-based sensors and actuators provided that they are driven with sufficiently high amplitudes. In motion and active vibration control applications, for example, these nonlinearities can excite unwanted dynamics, which leads in the best case to reduced closed-loop system performance and in the worst case to unstable closed-loop system operation, This necessitates the development of purely phenomenological models that characterize these types of nonlinearities and dynamics in a way that is sufficiently accurate, robust, amenable to control design for compensation, and efficient enough for use in real-time applications. To fulfill these demanding requirements this article describes a new compensator design method for combined complex hysteretic nonlinearities and complex log(t)-type creep dynamics based on the so-called Prandtl-Ishlinskii approach. The underlying parameter identification problem, which has to be solved to obtain a suitable compensator, can be represented by a quadratic optimization problem that produces the best least-square approximation for the measured input-output data of the real combined hysteretic nonlinear ity and creep dynamics, Special linear inequality and equality constraints for the parameters guarantee the unique solvability of the identification problem, the invertability of the identified model, and thus a reliable compensator design procedure Finally, the compensator design method is used to generate an inverse feedforward controller for the simultaneous compensation of the hysteretic nonlinearities and the log(t)-type creep dynamics of a piezoelectric stack actuator. In comparison with the conventionally controlled micropositioning stage with a nonlinearity error of about 14%, the inverse controlled micropositioning stage exhibits only about 1.7% error.