Publication: A modular port based model and passivity based control approach for a class of piezoelectric actuators
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Date
2023-10
Authors
Díaz Alastuey, Ignacio Nicolás
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Abstract
The focus of this thesis is modeling and controlling piezoelectric benders, with a primary emphasis on the control of displacement. Piezoelectric benders exhibit hysteresis between the driving voltage and the displacement, characterized by high non-linearity and a noticeable phase shift as the frequency increases. The proposed model leverages the elemental hysteresis component known as a ‘hysteron’ and integrates it with established electro-mechanical models found in prior works. The modeling framework combines port-Hamiltonian systems and Bond-Graph methodologies to ensure the creation of an energy-preserving port-based model.
Furthermore, the proposed model is identified using the ‘System Identification Toolbox’ in Matlab and compared to the classical Bouc-Wen model, which is a widely used modeling approach.
The comparison reveals that the proposed model offers an effective alternative, presenting over 96.5& fit percent as the driving voltage frequency increases and smaller RMSE than the identified Bouc-Wen model. Subsequently, the proposed model is employed to design two controllers, one utilizing a passivity-based approach, and the other employing the traditional Lyapunov stability approach.
In summary, an alternative approach to modeling piezoelectric benders is introduced in this thesis, along with the presentation of two simplified controllers designed for the piezoelectric bender model. These contributions offer valuable alternatives to existing methods for modeling and controlling piezoelectric benders.
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Keywords
Port-Hamiltonian systems , Non-linear systems , Lyapunov