State-Estimator-Based Feedback Control for a Class of Piezoelectric Systems With Hysteretic Nonlinearity

Because the piezoceramic materials were ferroelectric, the inherent hysteretic nonlinearity always existed in the piezoelectric system (PES). Due to the existence of hysteresis and modeling error, the system performance by only PID control often deteriorated. Because not all of the states of the PES were measurable, a state estimator was required to obtain the unavailable state. To begin with, a feedback linearization using estimated state was employed to transform the PES to a new coordinate system. To track the trajectory with a primary frequency, the reference model with desired amplitude and phase features was also designed. In the mean while, a tracking error model was achieved for the system analysis. Then the feedback linearization with a sliding-mode control including equivalent control and switching control was established to enhance system performance. The equivalent control using the signals from state estimator and reference model was designed to gain the desired control behavior. The switching control was applied to ameliorate the robust performance. Finally, the stability of the overall system was verified by Lyapunov stability theory. The tracking result converged to a set in terms of system and control parameters. In summary, the state-estimator-based feedback control contained state estimator, feedback linearization, reference model, and sliding-model control. Experiments of the PES were also presented to verify the usefulness of the proposed control.