please solve all part

Q3. (10 marks) Given a reactor in which the temperature is controlled by cooling water. The transfer function relating reactor temperature to cooling flow rate is given by: G(s)=Q(s)T(s)=10s+12e2s[F/GPM] Assuming the control valve linear. The valve is fully closed at controller output of 15psig and supplies 50GPM at a controller output of 3psig. Time constant and time delay have units of minutes. a) Find Gv of the valve. Is the valve air-to-open or air-to-close? Is this good choice (explain) (2 Marks) b) For Gm=1, find the tuning parameters of PID controller using the following tuning methods: - Direct Synthesis method with c equal to 1/3 process model dominant time constant. (2 Marks) - ITAE method (Disturbance) (2 Marks) c) Plot the closed loop response of both controllers for unit step change in the set point. Which controller setting gives conservative response? (4 Marks)