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.

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.

A proportional controller operated pneumatically is used to control temperature within the range of 65°F to 100°F.The measured temperature goes for 71°F to 78°F with the set point held constant when he controller is adjusted so that the output pressure goes from 3 psi (valve fully open) to 15psi (valve fully closed). Find the Proportional band.

In the process presented in Figure Q1, tomato pulp is heated as it passes through a steam heat exchanger and then enters an evaporator where the water boils off. The purpose of this process is to produce tomato paste, which has a lower water content than the pulp. As a chemical engineer, you are tasked to control the liquid level and temperature in the evaporator.Considering this information, answer the following: (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.

Question 1 An engineer uses a temperature sensor mounted in a thermowell to measure the temperature in a CSTR. The temperature sensor behaves as a first-order process with a time constant of 3 seconds, and the thermowell behaves as a first order process with a time constant of 9 seconds. Using Matlab: (a) Plot the open-loop response of the system to a step-change in the CSTR temperature. Comment on whether the response in under or over damped (b) Plot the closed-loop response of the system for proportional only control with a controller gain of unity. (c) The engineer notes that the measured temperature has been varying sinusoidally between 180 and 186°C with a period of 20 seconds for at least 10 minutes. Determine the likely temperature fluctuation in the CSTR contents to the nearest degree.

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 f(t) . This leads to the ODE m \frac{d^{2} x}{d t^{2}}+b \frac{d x}{d t}+k x=f(t) 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 O What are the initial conditions for this system? 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 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 d. (15 points) What spring constant value will result in the system comingto (and remaining within) 1% of its new steady-state position withoutovershooting that value as quickly as possible? 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.

The process described by the transfer function GP(S) Kp (T₁S+1) e-TDS (T₂S + 1)(T3S + 1) Gp(s) = is controlled by a P controller with an arbitrary gain of Kc. a) If Kc = 2; Kp = 5; T₁ = 2; Td = 1; T₂ = 2; T3 = 3 determine whether the closed-loop response will be stable using frequency response techniques. What is the limiting value of the controller gain to ensure stability? b) For the following scenarios, generate the Bode plots for the open- loop behavior using Excel. Comment on the effect of the parameter changes on plots 2, 3 and 4 using plot 1 as the reference. 1. 2. 3. 4. Kc = 2; Kp = 5; t₁ = 0; TD = 0; T₂ = 2; T3 = 3 Kc = 2; Kp = 5; t₁ = 0; TD = 5; T2 = 2; T3 = 3 Kc = 4; Kp = 5; T₁ = 0; TD = 0; T₂ = 2; T3 = 3 Kc = 2; Kp = 5; T₁ = 0; TD = 10; T₂ = 2; T3 = 3 c) Using the same general transfer function, plot the Nyquist plots using Excel for the following parameters. Comment on the behavior. 1. Kc = 2; Kp = 5; T₁ = 1; TD = 0; T₂ = 2; T3 = 3 2. Kc = 2; Kp = 5; T₁ = 3; TD = 0; T2 = 2; T3 = 3

Question 5 Determine the controller gain (Kc) for a proportional-only feedback controller for the system comprising the following elements that ensures a gain margin of at least 2 and a phase margin of at least 30°. Plot the controlled and uncontrolled closed-loop response of the system to a unit-step change in set- point. Gc= Kc; Gp = 50 30s +1' G₂ = 0.016 3s +1' Gm = 1 10s + 1

Q.4 An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t=0, the set point is increased at the rate of 0.5 mA/min. If the current settings are K₂= 2, t=1.5 min, Tp=0.5 min. (a) Generate the controller response in Simulink. (b) Repeat part (a) for a PI controller

Question #4 A system of three cylindrical tanks holding liquid is arranged as shown in Figure 1. Fint Fina Tank #1 R₁ F₁ h₁ h3 h₂ h₁ F₁ = R₁ Tank #2 R₂ F₂ Tank #3 Figure 1- Schematic showing layout of tanks. For all three tanks you can assume that the outlet flow rate is equal to the height in the tank divided by the valve resistance, i.e.: h3 hz F₂= F3: R₂ R3 a. Clearly derive the transfer function that relates the height in tank #1 (hi) to the inlet flow to the tank (Fin). [4 marks] b. Tank #1 is 0.5 m in diameter and the value of R₁ is 200 s m². At steady state the liquid height is 1 m. What is the flow rate of liquid entering the tank (i.c. what is Fin,1)? [1 mark] c. Calculate the gain and time constants for tank #1. [2 marks] d. Derive the transfer function that relates the height in tank # 3 (ha) to the flow entering the system (i.e. to Flis and F2.in). [5 marks] c. Tank #2 has the same diameter as Tank #1, but R₂ = 0.5R₁. Tank #3 has double the diameter of Tank #1 (i.e. it is 1 m in diameter), and R3= R₁. Fin1 = Fin2 = 0.01 m³ s¹. If the system is at steady state what is the liquid level in each of the tanks? [3 marks]