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Continuous hysteresis model using Duffing-like equation

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Abstract

Many material and mechanical systems, such as magnetorheological (MR) dampers used for reducing vibration in engineering systems, have long-standing modeling and control problems because of their nonlinear hysteresis behavior. Existing hysteresis models, including discontinuous and piecewise-continuous functions, are nonideal for numerical computation, stability analysis, and control design. This study links the hysteresis characteristics of a Duffing-like equation and an input–output system through a very subtle observation. Thus, the hysteresis dynamics are approximated using a traceable, second-order nonlinear ordinary differential equation with an inertial element. In addition, the hysteresis stability associated with energy dissipation can be analyzed using the Lyapunov method in a more deterministic and systematic manner than has previously been possible. Experimental work and hysteresis identification of a realistic MR damper device are presented to illustrate the proposed Duffing-like modeling techniques.

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Acknowledgments

The authors gratefully acknowledge the support of the Taiwan Ministry of Science and Technology, under grant 102-2625-M-007-001- ‘Development and Application of Model-Reference Semi-Active Control Methods for Magnetorheological Damper’, and National Center for Research on Earthquake Engineering, for the support in the pursuance of this work.

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Authors and Affiliations

  1. Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu City, 300, Taiwan, R.O.C.

    Jia-Ying Tu & Tsu-Yun Cheng

  2. National Center for Research on Earthquake Engineering, Taipei, 106, Taiwan, R.O.C.

    Pei-Yang Lin

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  1. Jia-Ying Tu
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Correspondence to Jia-Ying Tu.

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Tu, JY., Lin, PY. & Cheng, TY. Continuous hysteresis model using Duffing-like equation. Nonlinear Dyn 80, 1039–1049 (2015). https://doi.org/10.1007/s11071-015-1926-3

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