short paper read to the Royal Society in March 1868 by James Clerk Maxwell, then thirty-six and already the author of the equations of the electromagnetic field. It asked a practical question about steam engines and answered it with a method that became control theory.

the document

Maxwell, "On Governors", Proceedings of the Royal Society of London. It is in the public domain and transcribed at Wikisource. It opens with a definition:

“A GOVERNOR is a part of a machine by means of which the velocity of the machine is kept nearly uniform, notwithstanding variations in the driving-power or the resistance.”
— Maxwell 1868, first sentence

what it does

Maxwell wrote down the equations of motion of an engine with its regulator, assumed the disturbances were small so that the equations could be linearised, and asked when the motion settles rather than oscillating or running away. Stability, he showed, depends on the roots of the system's characteristic equation: every root must have a negative real part. He worked out the conditions for the simpler cases and left the general problem open. He also drew a distinction engineers still use: a moderator reduces a speed error in proportion to it but leaves some error standing; a governor in his strict sense keeps acting until the error is gone, the property now called integral action [paraphrase, not a quotation].

what's contested

Priority and influence. Maxwell was not alone. In 1876 the Russian engineer Ivan Vyshnegradskii published an analysis of the governor (Vyshnegradskii, 1876) that appears to have been independent and was more directly taken up by engineers; the stability problem for general polynomials was solved by Routh in his Adams Prize essay of 1877 and again, independently, by Hurwitz in 1895, at the prompting of the turbine engineer Aurel Stodola. Bissell (1989) reconstructs that second line and its translations [paraphrase, not a quotation]. Whether Maxwell's paper founded control theory or is the best-remembered of several starts depends on whether one is writing a history of ideas or of engineering practice.

Feedback before the word. Mayr (1970) traces feedback devices back to the water clocks of Hellenistic Alexandria, through Drebbel's thermostat and the windmill fantail to Watt's centrifugal governor (Mayr, 1970). Calling all of these "feedback" is a retrospective unification; the people who built them did not think of them as one kind of thing.

methodological critiques

The method's power and its limit are the same step: linearisation. The conclusions hold for small departures from steady running. Real governors had friction, backlash and dead zones, which produce effects (sticking, "hunting" between limits) that a linear analysis cannot represent; much of later control engineering is about what happens outside the linear regime.

later reception

The Routh–Hurwitz criterion is still taught in every control course. And when Norbert Wiener named a new field in 1948, he pointed to this paper as the first significant work on feedback mechanisms, and to "governor" as descended, through Latin, from the Greek word for a steersman, which is where cybernetics comes from (Wiener, 1948) [paraphrase, not a quotation].

Why it lasts. The paper turned a mechanic's problem (why does my engine hunt?) into a question about the roots of an equation, and so made regulation something one could reason about before building it. The same shape of question, will this loop settle?, is asked of thermostats, autopilots, economies and learning systems. See purpose in the reading room.

in the tour: the room called "Governors and feedback" has a placard called "The governor, before the word" ···

References

1. Maxwell (1868). On governors. Proceedings of the Royal Society of London. doi:10.1098/rspl.1867.0055
2. Vyshnegradskii (1876). Sur la théorie générale des régulateurs. Comptes Rendus de l'Académie des Sciences (Paris). English translation in Bissell (1989).
3. Routh (1877). A Treatise on the Stability of a Given State of Motion, Particularly Steady Motion. London: Macmillan. Scanned at the Internet Archive. archive.org/details/treatiseonstabil00routuoft
4. Hurwitz (1895). Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt. Mathematische Annalen. doi:10.1007/BF01446812
5. Bissell (1989). Stodola, Hurwitz and the genesis of the stability criterion. International Journal of Control. doi:10.1080/00207178908953500
6. Mayr (1970). The Origins of Feedback Control. Scientific American. doi:10.1038/scientificamerican1070-110
7. Mayr (1970). The Origins of Feedback Control. Cambridge, MA: MIT Press.
8. Wiener (1948). Cybernetics: Or Control and Communication in the Animal and the Machine. Paris: Hermann; Cambridge, MA: Technology Press; New York: Wiley.

see also