Watt steam governor stability

Abstract

The physics of the fly-ball governor, introduced to regulate the speed of steam engines, is here analysed anew. The original analysis is generalized to arbitrary governor geometry. The well-known stability criterion for the linearized system breaks down for large excursions from equilibrium; we show approximately how this criterion changes.

Stability and Hopf bifurcation in an hexagonal governor system

“…Remark 3.4 The family (11) has been studied in Denny [2], focusing the Lyapunov stability of the equilibrium point (13), outside the bifurcation surface (14). The stability conditions in [7] and [2] have been extended in Theorem 2.2 to a more general WGS model given in (1). For this more general model, however, the study of the codimension one Hopf bifurcation involves much longer calculations.…”

“…The historical relevance of the Watt governor study as well as its importance for present day theoretical and technological control developments -going from steam to diesel and gasoline engines -have been widely discussed by MacFarlane [5], Denny [2] and Wellstead -Readman [9] among others. In this paper the original stability analysis due to Maxwell and Vyshnegradskii of the Watt Centrifugal Governor System -WGS-has been revisited and extended to the following situations: 3.…”

“…In this paper we present a simple way to understand the Hopf bifurcation in a WGS, which is more general than that presented by Pontryagin [7], Al-Humadi and Kazarinoff [1] and Denny [2]. We believe that our approach has the advantage of connecting the physical parameters of the system to the stability of the stationary equilibrium point and the bifurcating periodic orbit.…”

Understanding Pendulums

“…7.1). The main function of a Watt steam governor, and associated linkage, is to keep the steam engine speed reasonably constant, irrespective of the load (Lineham 1914;Denny 2002). The time of swing, T; for one revolution of the governor is given by Eq.…”

“…James Clerk Maxwell's theoretical analysis, published in 1868, showed why hunting occurred, and indicated how it could be avoided. Maxwell's analysis is reproduced by Denny (2002). Maxwell's analysis initiated the discipline now known as control engineering.…”