Semilinear Duhem model for rate-independent and rate-dependent hysteresis
Semilinear Duhem model for rate-independent and rate-dependent hysteresis
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DOI：
10.1109/tac.2005.847035
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发表时间：
2005-05-01
影响因子：
6.8
通讯作者：
Bernstein, DS
中科院分区：
文献类型：
--
作者：
Oh, JH;Bernstein, DS
经典的Duem模型提供了一个有限维的磁滞微分模型。在这篇文章中，我们考虑了具有可证明性质的率无关和率相关半线性Duem模型。矢量场由输入率和线性动力学的乘积给出。如果输入速率函数是正齐次的，则模型的输入输出映射是速率无关的，从而在任意低的输入频率下产生持久的非平凡输入输出闭合曲线(即滞后)。如果输入速率函数不是正齐次的，则输入-输出映射是速率相关的，并且可以用低频输入的速率无关模型来近似。对于与速率无关和依赖于速率的模型，给出了收敛到极限输入输出映射的充分条件。最后，讨论了速率无关模型的反转行为和取向。
The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.