Micro Fluctuations Determine Control - Maxwell and Governor's Theory of Stability

Micro Fluctuations Determine Control - Maxwell and Governor's Theory of Stability

Although the importance of perturbations is not explicitly mentioned in Maxwell's "On Governors," the concept is essentially treated in the stability analysis of the system. In particular, it is closely related to the discussion on perturbations in that it mathematically analyzes the effects of small disturbances on the system and presents conditions for stability in feedback control.

Maxwell expressed the behavior of the governor in terms of differential equations and evaluated whether the system would return to its original equilibrium state or diverge when subjected to small perturbations. Within this theory, he analyzed how the system's response changes when given a disturbance and mathematically derived criteria for stability. He also noted that if the governor has a time delay, small perturbations can be amplified and eventually cause the system to oscillate. The mechanism by which this delay element amplifies the perturbation is an important concept in current control theory.

In addition, Maxwell examined how governors converge or diverge with respect to initial perturbations and analyzed how persistent small perturbations affect the behavior of the system. These discussions also serve as the basis for current linear systems theory and perturbation methods, providing an important framework for understanding under what conditions control systems operate stably.

As described above, although Maxwell's work did not explicitly use the term "perturbation," it was a pioneering attempt to analyze how small changes in a control system affect stability. As a result, he demonstrated the importance of designing control systems to account for the effects of perturbations and laid the foundation for modern feedback control theory.