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