论迟滞与时滞
胡海岩，王在华
摘要:迟滞和时滞是自然科学、工程科学、乃至社会科学中常见的两种现象, 但在我国学术界常被混淆. 从两种现象的定义和本质出发, 阐述两者的共性、个性及其联系. 通过多个例子说明: 迟滞现象反映两个相关参变过程周期变化时彼此间的相位滞后关系; 而时滞现象则反映两个相关动态过程任意变化时彼此间的时间滞后关系. 在某些特定的情况下, 它们可以等同; 但在一般情况下, 它们是具有不同性质的两类现象, 尤其在描述记忆特性方面, 两者有本质的差异.
关键词：迟滞；时滞；黏弹性；受控系统
On hysteresis and retardation
Haiyan Hu, Zaihua Wang
Abstract：Hysteresis and retardation are two kinds of popular phenomena in natural sciences, engineering sciences and social sciences. However, they are often confused in both academic and technical circles. This paper, starting from the definition and the nature of two kinds of phenomena, presents their general and individual characteristics, as well as their relations. The illustrative examples in the paper show that the hysteresis implies the phase delay of two processes varying periodically with a physical parameter, while the retardation reflects the time delay of two dynamic processes varying arbitrarily in the time domain. In the case of both linear hysteresis and harmonically time-varying input, they look identical. The nonlinear hysteresis, however, will reduce their relevance even the harmonically time-varying input remains unchanged. In general, they are two kinds of quite different phenomena by nature. In the aspect of memory, for example, the hysteresis and retardation characterize local memory and global memory, respectively. As for their transfer property, a hysteretic system corresponds to the rational fractional and a delayed system corresponds to that with one or more exponential functions. Even though there is a closed hysteretic loop for the linear hysteretic system, the output of a nonlinear system under harmonic input may not behave periodically. The nature of hysteresis comes from the multiple branches of a hysteretic loop, instead of the closed loop. The nature of a delayed system defines a continuous mapping between two continuous functions in their corresponding closed intervals. Such a delayed system, hence, is infinitely dimensional, no matter how short the time delay is and how many degrees of freedom the system has. As a matter of fact, a linear dynamic system involving any time delays has to be modeled as a delay differential equation, which has infinite dimensions and infinite number of eigenvalues. Furthermore, nonlinear dynamic systems with time delays exhibit even more complicated dynamics. Time delays are usually very short in mechanical systems. However, the neglect of time delays in the dynamic analysis of a delayed system may result in essential mistakes.
Keyword：hysteresis; retardation; time delay; viscoelasticity; controlled system
原文链接：http://lxxb.cstam.org.cn/CN/abstract/abstract141972.shtml
