Auto-Zone Control Systems Auto-Zone CV-C Controller Installation Guide (Version 01A) - Manual (Page 39)

Auto-Zone CV-C Section 2
Sequence of Operation 2-29
The Integral ( I ) is added to itself each time through the loop. This prevents the valve
from stopping at a point of equilibrium where the proportional error is not changing,
therefore the valve position would be changing. The amount of effect the Integral can
have is limited by the Ki constant.
The Derivative ( D ) is used to track the rate of change in temperature error from
setpoint. If the last change was small, the derivative would have very little affect since the
( Error - OldError ) subtraction would yield a small value. In this case, the derivative
would not affect on the final valve position calculation.
If the last error was large, indicating the temperature was rapidly moving toward or away
from the setpoint, the valve position calculation could make a large adjustment due to the
proportional error. This could have the affect of causing hunting or overshoot in the
temperature control. To limit the proportional effect during rapid temperature changes,
the derivative becomes the brakes of the system if we are approaching setpoint or the
accelerator if we are moving away from the setpoint. If the temperature error had
increased from the last calculation, the derivative would create a positive value that
would be added to the proportional and integral values to create an even greater valve
position:
Accelerator Example:
OldError = 2°
Error = 4°
( Error - OldError ) = 2
P + I + 2 = Increased valve position
Brakes Example:
OldError = 2°
Error = 0°
( Error - OldError ) = -2
P + I + ( -2 ) = No Change in valve position
Since the Proportional Error was also reduced the derivative had the effect of canceling
any change in the valve position until it detects another movement down in the
temperature error. If the effect of remaining unchanged causes the temperature error to
increase again, then the valve position would again increase without ever having
experienced an unneeded or undesired decrease.
If the temperature had continued to drop, then the derivative would add to the
proportional error in an attempt to catch the temperature before it went too far below
setpoint.