An Early and Significant Paper in the History of Information Theory: on the Theory of Governors

Wischnegradsky, J [Vyshnegradskii, I. A.] . Sur la theorie generale des regulateurs. In:  Comptes Rendus de l'Académie des Sciences de Paris, Vol. 83, 1876,  p.318-320,  (translated here:  On the General Theory of Governors).  Very nice copy, the weekly issue removed from the larger bound volume.  $225

In modelling a steam engine with a centrifugal governor, Vyshnegradskii neglected Coulomb friction and linearised the system about an operating point. Unaware of the work of Maxwell and Routh from 1868 onwards, he investigated the conditions for the onset of 'hunting' (instability). Treating the engine as an integrator, and the governor as a second-order system, he made an ingenious change of variables in order to transform the resulting third-order characteristic equation into the form

        φ³ + xφ² + yφ + 1 = 0

the nature of whose roots determines the general form of the system transient response.

The parameters x and y, which depend on such system characteristics as governor restoring-force constant, moment of inertia, and so on, became known in the Russian and German literature as the Vyshnegradskii parameters. The transformed equation lent itself perfectly to a graphical technique of stability analysis, which the Zürich-based engineer A. B. Stodola later used in his work on hydraulic turbine control; as a result he prompted Adolf Hurwitz to develop his celebrated version of a general stability criterion. --Classic Papers in Information Theory, the Open University, here.