posted 1 years ago

(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.

posted 1 years ago

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.

posted 1 years ago

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)

posted 1 years ago

(a) Define the process variables and the manipulated variables, as well as possible disturbances.

(b)Propose feedback control loops by sketching a schematic diagram.

(c) Propose any additional features in order to assure the safe operation of the process. Illustrate these features using a schematic diagram.

posted 1 years ago

b. (15 points) What is the new steady-state position? That is, where willt - o ? Show this using the final-value theorem.the mass settle as

O What are the initial conditions for this system?

2. (65 points) Imagine the spring is vertical. The weight is held by a platform atx=0 initially. If m=0.1kg , b=0.1 kg/ s , and k=1.0 kg/s . The platformis removed at t=0

c. (15 points) What is the maximum distance the mass will move from itsinitial position? (Hint: what is the force applied to the weight?)(15 peints) Whatvalue vwill recuultming

m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=f(t)

f(t) . This leads to the ODE

Consider a weight held in place by a spring. Initially suspended at rest, the height ofThe spring constant is kThis represents how "stiff" the spring is and is constant. The frictional losses areisthe weight is x=0The mass of the weight ismcharacterized by the constant b . The force applied to the weight after t=0

e. (15 points) Imagine the spring system is now horizontal.represents how far the spring is from its resting position. If 1 N of forceis instantaneously transferred to the weight (in thedirection)described above att=0 ,what is the response? That is, what isx(t) when the weight is flicked with 1 N of force? Assume the weightis only free to move in one direction.

posted 1 years ago

posted 1 years ago

following figure?

1. (20 points) What is the input function and the Laplace transform of the