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Abstract The dynamic behavior of a multiple-capacity passive system is compared to that of a single-capacity system of appropriate “time constant with a finite time delay.” Such a comparison indicates that the latter system reproduces the dynamic behavior of the multiple-capacity system with sufficient accuracy for most engineering purposes. This fact makes it possible to characterize such systems by a single parameter, the ratio of the time constant (L) of the single-capacity system to the delay (D). Values of the control constants for various degrees of stability are plotted against this ratio (L/D) for proportional, proportional-plus-integral, proportional-plus-integral-plus-derivative type regulators. An electronic analog computer was used in obtaining the data.
Chien et al. (1952) studied this question.