Stability and Hopf Bifurcation in the Watt Governor System

The Watt centrifugal governor is a device that automatically controls the speed of an engine. Dating to 1788, it can be taken as the starting point for automatic control theory (see MacFarlane [5] and references therein). In this paper the system coupling the Watt-centrifugal-governor and the steamengine will be called simply the Watt Governor System (WGS). Landmarks for the study of the local stability of the WGS are the works of Maxwell [6] and Vyshnegradskii [8]. A simplified version of the WGS local stability based on the work of Vyshnegradskii is presented by Pontryagin [7]. A local stability study generalized to a more general Watt governor design was carried out by Denny [2]. Enlightening historical comments about the Watt governor local mathematical stability and oscillatory analysis can be found in MacFarlane [5] and Denny [2]. There, as well as in [7], we learn that toward the mid XIX century, improvements in the engineering design led to less reliable operations in