Technical Brief

Constructive Proof of Preisach Right Inverse With Applications to Inverse Compensation of Smart Actuators With Hysteresis

[+] Author and Article Information
Yangyang Dong

Department of Mechanical Engineering, D403H,
Harbin Institute of Technology,
Shenzhen Graduate School,
Shenzhen 518055, China
e-mail: dongyang1314@126.com

Hong Hu

Department of Mechanical Engineering, D403H,
Harbin Institute of Technology,
Shenzhen Graduate School,
Shenzhen 518055, China
e-mail: honghu@hit.edu.cn

Zijian Zhang

State Key Laboratory of Robotics and Systems,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: zhangzijian999@163.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 20, 2012; final manuscript received June 24, 2014; published online August 8, 2014. Assoc. Editor: Eric J. Barth.

J. Dyn. Sys., Meas., Control 136(6), 064502 (Aug 08, 2014) (7 pages) Paper No: DS-12-1350; doi: 10.1115/1.4027922 History: Received October 20, 2012; Revised June 24, 2014

Hysteresis poses a significant challenge for control of smart material actuators. If unaccommodated, the hysteresis can result in oscillation, poor tracking performance, and potential instability when the actuators are incorporated in control design. To overcome these problems, a fundamental idea in coping with hysteresis is inverse compensation based on the Preisach model. In this paper, we address systematically the problem of Preisach model inversion and its properties, employing the technique of three-step composition mapping and geometric interpretation of the Preisach model. A Preisach right inverse is achieved via the iterative algorithm proposed, which possesses same properties with the Preisach model. Finally, comparative experiments are performed on a piezoelectric stack actuator (PEA) to test the efficacy of the compensation scheme based on the Preisach right inverse.

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Fig. 1

Basic hysteresis operator

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Fig. 2

Preisach plane with limiting triangle P0

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Fig. 3

Dividing functions (a) Hu(t) and Hd(t), (b) Vu(t) and Vd(t)

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Fig. 4

Relationships between spaces

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Fig. 5

Two different input signals with same RMS

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Fig. 6

Division of the limiting triangle P0 in a finite number of squares and triangles

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Fig. 7

Linearization of smart actuators with hysteresis

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Fig. 8

Iterative search procedure to calculate the compensated input signal uc(nT0) in the case when uc(nT0) > uc((n − 1)T0)

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Fig. 9

Experimental rig and block program of the data acquisition system

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Fig. 10

An attenuate sinusoidal trajectory. (a) The comparative results between the desired, two compensated and noncompensated voltage-to-displacement curves. (b) Error plot.

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Fig. 11

An arbitrary signal in the case when PEA subject to a small load of 440 g. (a) The comparative results between the desired, two compensated and noncompensated voltage-to-displacement curves. (b) Error plot.




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