Folks no offence but I think you may be confusing the process requirement with the control loop.
PID is designed to control some external variable, be that a flow, level, position, whatever ...
Feedback from the thing you are controlling is generally referred to as the PV Process Variable.
The output which manipulates whatever is being controlled is called the MV Manipulated Variable
The PID loop is always attempting to get the PV to match the set-point ...
The difference between the two is the error term and drives the controller gain directly.
The integral term is about time and has a characteristic period, the average error within that period contributes to the MV.
The Derivative term is also about, more specifically rate of change, it to contributes the MV.
They are required when the PV is likely to change without an MV change.
If the PV is always directly proportional to the MV, like an RC Servo for example, you don't need a PID loop.
If you are driving a valve with the RC servo, controlling a fluid flow, then the flow is the PV and a PID loop is almost obligatory.
The PID loop its self should be set up so that it can accurately control its target with an acceptable level of oscillation, settling time and dead band, whilst remaining as responsive and accurate as possible.
Once you have a loop set up and your system, overall, can respond quickly and accurately you can then do whatever is required.
You have a requirement to change the position of a flap slowly and also not to move it at all for specific periods.
This should be done by ramping or fixing the set-point not by making the PID loop slow.
If you take this approach it will work in all circumstances other than you asking something to change faster than is physically possible.