2. An electronic parallel form of 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 0.5mA/min (equivalent to a rate of 2F/min ). If the current settings are Kc=2(dimensionless)I=1.5minD=0.5min (a) Write down the transfer function of a parallel form of PID controller without a derivative filter. (5%) (b) Derive an expression for the controller output p(t). (15%) [Hint: Laplace transform: F(s)=L[f(t)]=0f(t)e11dt ] 2. An electronic parallel form of 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 0.5mA/min (equivalent to a rate of 2F/min ). If the current settings are Kc=2(dimensionless)I=1.5minD=0.5min (a) Write down the transfer function of a parallel form of PID controller without a derivative filter. (5%) (b) Derive an expression for the controller output p(t). (15%) [Hint: Laplace transform: F(s)=L[f(t)]=0f(t)e11dt ]