(a) The control block diagram of a typical feed forward controller is presented in Figure Q4.1. Derive the closed-loop transfer function between that Y and Ysp(i)(Y/ Ysp), assuming that D = 0. \text { Show that } \frac{Y}{D}=\frac{G_{d}+G_{v} G_{p} G_{f} G_{t}}{1+G_{v} G_{c} G_{m} G_{p}} \text { when } Y_{\mathrm{sp}}=0 Maple syrup is evaporated to raise the sugar concentration of the syrup,making it suitable for food topping, as shown in Figure Q4.2. As a chemical engineer, you are asked to design a selective control system capable of controlling the level and exit flow rate of the concentrated syrup. Considering this information, answer the following: (i)Propose control loops by sketching a schematic diagram of theselective control system.(5 marks) (ii) Explain how the proposed selective control works during normaloperations. (iii) Discuss how the proposed selector operates when the flow rate of concentrated maple suddenly drops. (iv) Comment on the advantages of this selective control system in respect to a single loop system.(2 marks)

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