How Does a Machine Hold Its Own Speed? Let the Speed Move the Throttle

A steam engine driving a mill runs faster when the load falls away and slower when more machines are engaged, and a varying speed was unacceptable for spinning and weaving, where thread breaks if the rate changes. The obvious remedy was a person watching a gauge and adjusting the steam valve by hand, which is expensive, slow and inattentive. The alternative is to let the engine adjust its own valve. Building that requires a way of turning speed into a physical movement, and then connecting that movement to the valve in the direction that opposes the change rather than reinforcing it.

The classic arrangement is entirely mechanical and does the job in one linkage:

• •Two heavy balls hang from arms on a vertical shaft driven by the engine
• •Spinning the shaft throws the balls outwards and the arms rise
• •Rising arms lift a collar that slides on the shaft
• •The collar is linked to the steam admission valve
• •Rising speed therefore closes the valve, which slows the engine
• •Falling speed lowers the collar and admits more steam

The device is a working example of a general principle, that a system measuring its own output and feeding that measurement back to oppose a deviation will hold itself steady, and recognising that principle as general took a surprisingly long time. James Clerk Maxwell wrote a paper in 1868 analysing why these devices sometimes hunted, oscillating above and below the target speed instead of settling, and that paper is generally treated as the start of control theory as a mathematical subject. The same analysis applies to a heating system, an aircraft autopilot, a cruise control and a body regulating its own temperature. Understanding that the oscillation comes from delay in the loop, and that too strong a correction makes it worse, was the key insight.

Regulating a quantity by measuring it and acting against the deviation turns out to be a general solution, and examples predate the steam engine considerably. Float valves holding a constant water level are ancient and appear in Greek water clocks. Windmills used a device that adjusted the gap between the millstones according to the speed of the sails. Temperature regulators using the expansion of mercury to control a furnace damper were built in the seventeenth century for incubating eggs. Living bodies regulate temperature, blood sugar and dozens of other quantities the same way. The steam engine version mattered because it was ubiquitous, economically important and simple enough to be analysed mathematically.

The mechanical version has real weaknesses that explain why it was superseded. It cannot hold an exact speed, since the balls must sit at a different height to hold the valve at a different opening, which means the settled speed varies slightly with load, a residual error that is inherent to the design. It responds only after the speed has already changed. It is affected by friction and wear in the linkage. Later designs added mechanisms to remove the residual error, and modern equivalents measure speed electronically and compute the correction, which allows the response to be tuned precisely and to anticipate rather than merely react. The principle is unchanged.

Weights spun by the engine fly outwards as speed rises, lifting a collar linked to the steam valve so that going faster admits less steam, which holds the speed steady with nobody watching. Maxwell analysed why such devices oscillate in 1868, which began control theory. The mechanical form cannot hold an exact speed, since a different valve opening requires a different ball height.