  ### Question 40485  Verified

Process Dynamics And Control

(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)

### Question 40484  Verified

Process Dynamics And Control

A single-tank process has been operating with an inlet flow rate equal to29.4 m3 min-1. The operator increases the flow rate suddenly by 10%,resulting in a level change in the tank as recorded in Table Q3.

Assuming that the liquid-level dynamics follow a first-order model, determine:

(a) The Pl controller settings using the Ziegler-Nichols tuning relations.

(b) The process gain and time constant using Sundaresan and Krishnaswamy's method. Compare these values against the values from the graphical method.

### Question 40483  Verified

Process Dynamics And Control

Two liquid storage tanks are shown in Figure Q2. For System I, the valve acts with a resistance R = 580 s m-2, so that the relation between the flow (F)and liquid level in the tank (h) is given by F = hlR. For System II, a pump is used instead of the valve, meaning that variations in liquid level do not affect the exit flow rate. The diameter of each tank is the same, D = 1.1 m. For each system determine the following information and show all your workings:

(a) Process gain (Kp) and time constant (7).

(b) New steady-state liquid levels in both System I and System II, if the inlet flow rate suddenly changes from 3.0x10-3 m³ s-1 to4.5x10-3 m3 s-1. The initial steady-state level in both systems is 1.8 m.

(c) If each tank is 2.4 m tall, which tank overflows first? Calculate when this will happen.

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