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An infinite‐dimensional control concept for piezoelectric structures with complex hysteresis
Author(s) -
Kugi A.,
Thull D.,
Kuhnen K.
Publication year - 2006
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.96
Subject(s) - flatness (cosmology) , control theory (sociology) , piezoelectricity , cantilever , nonlinear system , controller (irrigation) , hysteresis , engineering , computer science , physics , structural engineering , control (management) , artificial intelligence , agronomy , cosmology , quantum mechanics , electrical engineering , biology
This paper is devoted to the infinite‐dimensional control design of a composite piezoelectric cantilever with complex hysteresis. The control concept being proposed comprises a flatness‐based trajectory planning in combination with a passivity‐based controller which guarantees the exponential stability of the resulting closed‐loop error system. Furthermore, in the course of the controller design we will exploit the additional degree‐of‐freedom provided by piezoelectric structures by designing the spatial distribution of the actuator and sensor layers, also referred to as the static shape control problem. It is well known that at higher electric field strengths the polarization of the piezoelectric material saturates and hence significant complex hysteretic nonlinearities appear. The mathematical model of the piezoelectric cantilever is approximated in form of a Hammerstein‐like model with the hysteretic nonlinearity at the input connected in series with a linear infinite‐dimensional beam model. Based on a modified Prandtl–Ishlinskii theory a systematic calculation of an inverse operator for compensating the hysteresis is presented. Measurement results on a commercially available parallel trimorph bender show the feasibility of the proposed control strategy, in particular for the case of large displacements. Copyright © 2005 John Wiley & Sons, Ltd.