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
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.
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.
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