Modeling, analysis and control of flexible solid-state hysteretic actuators

A distributed parameters modeling and control framework for flexible solid-state hysteretic actuator is presented in this work. For the simplicity of analysis, the actuator dynamic behavior is decoupled and treated separately from the hysteresis nonlinearity. To include the effects of widely-used flexural mechanisms, a mass-spring-damper boundary condition is considered for system. Moreover, the effect of electromechanical actuation is included as a concentrate force at the boundary. The problem is then divided into two parts: first part deals with free motion analysis of system in order to obtain eigenvalues and eigenfunctions using the expansion theorem and a standard eigenvalue problem procedure. The effects of different boundary mass and spring values on the natural frequencies and mode shapes are demonstrated, which indicate their significant contribution to system performance.;In the second part, forced motion analysis of system and its state-space representation are presented. A frequency based control strategy utilizing widely used Lyapunov theorem is designed to obtain an accurate control over the actuator motion. A robust variable structure control is incorporated into the developed controller for compensation of ever-present plant structural uncertainties. A full order state feedback observer is designed to accurately mimic the states of an unobservable plant. An optimization algorithm is developed to compute the optimal observer gain matrix. Various frequency tracking simulations are performed using feedback controller-observer model to observe the effect of modes deficiency on the tracking frequency bandwidth of the controller.;Finally, for the accurate prediction of nonlinear multi-loop hysteresis effect, a major source of inaccuracies at quasi-static frequency, a recently developed hysteresis model based on three hysteric properties of piezoelectric material namely targeting of turning points, curve alignment and the wiping-out effect is used. Initially, the hysteresis nonlinearity is decoupled from the looping effect and modeled separately using an exponential function. The obtained exponential function is then utilized in a nonlinear mapping procedure, where it is mapped between consequent turning points recorded in model memory unit. This mapping also uses four constant shaping parameters - two for the ascending and two for the descending hysteresis trajectories. A proportional integral (PI) controller is used for the compensation of hysteresis nonlinearity. Performance of PI controller is validated using several numerical simulations. Finally, the method of combining robust feedback control strategy with the feedforward hysteresis compensation technique is presented to accomplish the precise control over actuator motion.