An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t=0, the set point is increased at the rate of 0.5 mA/min (equivalent to a rate of 2 deg F/min). If the current settings are:
Kc= 2 (dimensionless)
τI= 1.5 min
τD=0.5 min
a) Derive an expression for the controller output p(t).
b) Repeat (a) for a PI controller.
c) Plot the two controller outputs and qualitatively discuss their differences