In article ,
Stealth Pilot wrote:



in control system parlance PID is proportion, integral and derivative.

they are used when the state of the process being monitored cant be
directly measured but must be inferred or calculated as the integral
of some calculation. one that comes to mind is the inference of a flow
rate from the upstream pressure and downstream pressure differential
of a fluid flow through a known diameter aperture plate.

Stealth Pilot

PID control algorithms may well be used in conjunction with indirect
process monitoring, but that isn't my understanding of what PID means.

PROPORTIONAL --

You want to heat a pot of water to 170 degrees F with an electric
heating element. If you turn off the burner at 170, the water temp will
coast to 200. So you decide to scale back the power, beginning at 150.
The difference between target temperature ("set point") and the
beginning of scaling back power is called the "proportioning band."
Typically, the power to the burner is cycled off and on. 9 seconds on, 1
second off. Then 8 seconds on, 2 seconds off, etc. Even when the
temperature is above the target, you still get a couple of seconds of ON
time and 8 seconds of OFF time, just to minimize PIO -- Pilot Induced
Oscillation.

Now, you've got less initial overshoot, and smaller oscillations around
the set point. (An ON/OFF controller is always shutting off too late and
coming back on too late, because it can't anticipate and correct for lag
time in the system.)

INTEGRAL --

But, proportioning controllers tend to stabilize below set point. How do
you fix that? With manual reset, or, automatic reset, calculated
mathematically as an integral. Integral compensates for droop before it
exists.

DERIVATIVE --

We're still stuck with that pesky initial overshoot, the largest
magnitude deviation from set point, before the oscillations dampen out
to an acceptable level. (Tempering of chocolate requires very minimal
deviation, and the process requires many hours. Overheating and then
cooling a chocolate bar destroys the temper, and thereby the texture, so
don't do it!) The derivative function, obviously, watches the RATE of
change as the process temperature enters the proportioning band and
begins to approach the set point. To anthropomorphize, "where am I,
where am I going, and how fast am I getting there, and how quickly can I
react?" You start pulling the power back on downwind, at the latest,
planning a carefully controlled deceleration to stall speed two inches
off the ground. As things change, you keep fine tuning things.

Sorry for waxing pedantic on this one.