Adaptive Nonlinear Compensation Of Piezoelectric Actuators

Piezoelectric actuators are widely used in industrial and academia applications. However, the hysteresis is an inherent character of the piezoelectric material which leads to the nonlinear relationship between input voltage and piezoelectric actuator response. Hence, the nonlinear compensation is essential in the piezoelectric actuated systems.In this dissertation, important mathematical models are studied for a precise description of the hysteresis between voltage and displacement, namely Preisach model, Prandtl-Ishlinskii model and Bouc-Wen model.The Prandtl-Ishlinskii model is applied as an approach for the simultaneous modeling and compensation of the hysteretic characteristics because of its generalized description and an analytically obtained inverse. Both the hysteresis model and its inverse are formed by weighted superpositions of elementary operators which can be described mathematically and reflect the qualitative properties of the transfer characteristic. On the other hand, proof of the existence, uniqueness, Lipschitz continuity and thus input-output stability of the inverse operator are natural preconditions for the practical realization of the inverse operator using a numerical inversion procedure.Subsequently, the least mean square (LMS) algorithm is chosen for the adaptive parameter identification to ensure the modeling accuracy. A practical adaptive inverse control scheme is introduced for the fusion of LMS with the inverse compensation.The performances of the modeling and compensation scheme in reducing hysteresis are then verified with the aid of experimental results. Cases of low frequency and high frequency inputs are studied respectively.