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?