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Background:
PID (proportional-integral-derivative) control has been around for a long time.

It was in textbooks in the early 1900's. The Routh-Hurwitz stability criterion is from 1895. link Nyquist stability is from the 1930's. link

Question:
What is the oldest example of intentional PID control containing all the components (proportional, integral, and derivative)?

I would not be surprised to find something between 500 and 2500 years old.

More details:
PID control, also called PID, is defined (briefly) as the use of a weighted sum of the measured value (aka proportional), a sum (aka integral), and a difference (aka derivative) of some measured quantity, typically a distance from target, to control a system.

  • (P) A tax of 10% of the period-over-period increase could be considered derivative control, because if the period-over-period value acquired is constant then the increase is 0%.
  • (PD) If the tax were 1% of current value, and 10% of year-over-year increase, then it would be PD control, because it is taxing the measurement (proportional) and the change (derivative).
  • (PID) A tax of 10% on increase, 1% of total, and 1% times the sum of the last 2 years less a target, would be PID, because it would have all three components.

These sorts of things have been used (with varying degrees of success) for automobile cruise-control, guidance of heat-seeking missiles, electric coffee-pots, and control of investment portfolios. Because it is control-systems-engineering it applies to any "system" that meets the applicability criteria, whether electrical, mechanical, thermal, or economic.

Ongoing:
Antikythera mechanism was an extremely elaborate astronomical clock. I'm looking for PID indication there, perhaps in anti-backlash gearing.
An Embry-Riddle paper on the Ancient Control Systems

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  • $\begingroup$ Jokes aside, concerning your time estimation, I would call the development of modern calculus in 17th century a lower limit, before that I would not call the use intentional $\endgroup$
    – OpticalResonator
    May 29, 2018 at 13:57
  • $\begingroup$ @OpticalResonator - there exists a palimpcest that shows derivation of Riemann sums to integrate the volume of a function from ~300BC. That puts some basic calculus accessible at that time. I think the loss of the Library at Alexandria is still one of the most anti-intellectual acts of destruction in the history of the world. $\endgroup$ May 29, 2018 at 14:15
  • $\begingroup$ @SolarMike - there is 1830's for Routh's publication. I'm still looking. $\endgroup$ May 29, 2018 at 14:15
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    $\begingroup$ How far are you willing to abstract (as you already dropped a hard requirement for calculus)? Anything that looks at value, change of value and accumulation of value at the same time? Because that might land you with tax law... $\endgroup$
    – bukwyrm
    May 29, 2018 at 14:48
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    $\begingroup$ Have you read the english wikipedia article on PID control? The history section mentions a few early uses, where the steering of ships in 1922 by Nicolas Minorsky seems to have been the first use of a formal PID control law $\endgroup$
    – OpticalResonator
    May 29, 2018 at 15:16

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