b) Question A1 a) A chemical process has inlet and outlet flows of the same volumetric flow rate q controlled by a flow control pump as shown in Fig.A1. The inlet flow compound includes chemical A and the concentration is measured as ci(t), while the concentration in the tank is stirred to be even and is c(t). The concentration of the liquid flowed into the tank, c(t), is seconds delay from the measured concentration ci(t). The volume of liquid in the tank is V and no chemical reaction takes place in the tank. 9.500) 'sa(1) to 9(1) Fig. Al i) Derive a mathematical, differential equation model for the process. [7 marks] ii) Express the model as a transfer function G,(s)=- C(s) assuming zero initial conditions. [5 marks] A controller is to be designed using the direct synthesis method. The process dynamics are described by the input-output transfer function Gp-5/(10s+1). i) Design a closed loop reference model G, to achieve: zero steady state error for a constant set point, a closed loop time constant one quarter of the process time constant. Explain any choices made. ii) Design the controller G, using the direct synthesis equation: G.(s)-- 6009ELE/SBC [7 marks] 1 G G, (1-G,) [6 marks]