1). An electronic PID temperature controller is at steady state with an output of 10 mA. The set point equals the initial steady-state process temperature. At t = 0, the error signal is increased at the rate of 0. 4 mA/min, which is equivalent to a rate of 2°F/min. If the current settings are Kc = 3 (dimensionless), τI = 1. 5 min, τD = 0. 5 min, then (a) Derive an expression for the controller output p(t) (b) Repeat (a) for τD = 0 (a PI controller only) (c) Plot the two controller outputs and qualitatively discuss their differences. (d) What is the transmitter calibration of mA/°F? (e) Say after 1 min, the error signal went back to zero. What would p(t) be in that case?