Simultaneous compensation of hysteresis and creep in a single piezoelectric actuator by open-loop control for quasi-static space active optics applications |
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| Affiliation: | 1. Université de Toulouse, ICA/ISAE, Toulouse 31055, France;2. Civil Aviation University of China, College of Aeronautical Engineering, Tianjin 300300, China;3. Université de Toulouse, ISAE/DMIA, Toulouse 31055, France;4. Université de Toulouse, ICA/INSA-Toulouse, Toulouse 31077, France;1. Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, 818 Fenghua Road, Ningbo, Zhejiang 315211, China;2. Department of Mechanics, School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei 430074, China;1. Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo 315211, PR China;2. Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, PR China;3. Department of Engineering Mechanics, Zhejiang University, Yuquan Campus, Hangzhou 310027, PR China;1. Biomechatronics, Faculty of Technology, Bielefeld University, PO-Box: 10 01 31, 33501 Bielefeld, Germany;2. Biological Cybernetics, Faculty of Biology, Bielefeld University, PO-Box: 10 01 31, 33501 Bielefeld, Germany;3. Faculty of Engineering and Mathematics, University of Applied Sciences, Wilhelm-Bertelsmann-Straße 10, 33602 Bielefeld, Germany |
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| Abstract: | Owing to their excellent properties piezoelectric actuators are studied as embedded elements for the quasi-statically active shape control of spatial optical mirrors. However, unwanted nonlinear effects in piezoelectric actuators, i.e., hysteresis and creep, severely limit their performance. This paper aims at developing a control methodology to compensate hysteresis and creep in a piezoelectric actuator simultaneously for quasi-static space active applications. In the methodology developed, hysteresis and creep behaviors are successively compensated by open-loop control. First, a derivative Preisach model is proposed to accurately portray the hysteresis while requiring relatively few measurements and describing the detachment between major and minor loops. The inverse derivative Preisach model is derived and inserted in open-loop to achieve hysteresis compensation. Then, the creep in the hysteresis compensated piezoelectric actuator is described by the use of a nonlinear viscoelastic model and a low pass filter is suggested to eliminate the effect of the inverse derivative Preisach model on the step reference input. To invert the creep model, the concept of “input relaxation” is implemented and an inverse multiplicative structure allows identifying the parameters of the inverse model while circumventing the difficulty of a mathematical computation. Finally, by cascading the low pass filter, the inverse model of creep and the inverse derivative Preisach model one after the other with the single piezoelectric actuator, the simultaneous compensation of hysteresis and creep is achieved. Experimental results show that in the case of step-like reference signals the hysteresis and the creep in a piezoelectric actuator can be significantly reduced at the same time. It implies that the developed methodology is effective and feasible in space active optics applications for which quasi-static distortions need to be compensated. |
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| Keywords: | Hysteresis Creep Relaxation Piezoelectric actuator Preisach model Nonlinear viscoelastic model |
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