Process Control - Video Lectures
Topic outline
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Students mustMark as doneCouganowr3E-5-3A tank having a cross-sectional area of 2 ft2 is operating at steady state with an inlet flow rate of 2 ft3/min. The head-flow characteristics are shown in figure.
- Obtain the values of \(\tau_p\) and \(K_p\) of the transfer function of the system written as \[ \frac{H(s)}{Q_{\text{in}}(s)} = \frac{K_p}{\tau_p s + 1}\]
(i)\(\tau_p =\)________ min
(ii) \(K_p = \)_______ min/ft2 - If the flow to the tank increases from 2 to 2.2 ft3/min according to a step change, calculate the \(h\) two minutes after the change occurs. ______ ft
- Obtain the values of \(\tau_p\) and \(K_p\) of the transfer function of the system written as \[ \frac{H(s)}{Q_{\text{in}}(s)} = \frac{K_p}{\tau_p s + 1}\]
(i)\(\tau_p =\)________ min
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Transfer Function of CSTR with First Order Reaction PageCoughanowr3E-5-5Consider the stirred-tank reactor shown in figure. The reaction occurring is \(A \rightarrow B\) and it proceeds at a rate \(r = kC_o\) where \(r\) = (moles of \(A\) reacting)/(volume.time); \(k\) = reaction rate constant; \(C_o(t)\) = concentration of \(A\) in reactor at any time \(t\) (mol \(A\)/volume); \(V\) = volume of mixture in reactor. Further, let \(F\) = constant feed rate, volume/time; \(C_i(t)\) = concentration of \(A\) in feed stream, moles/volume.
Assuming constant density and constant volume \(V\), derive the transfer function relating the concentration of \(A\) in the reactor to the feed-stream concentration.
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Linearized Transfer Function of Level System Page2023-15-ctrlA liquid surge tank has \(F_\text{in}\) and \(F_\text{out}\) as the inlet and outlet flow rates respectively, as shown in the figure below.
\(F_{\text{out}}\) is proportional to the square root of the liquid level \(h\). The cross-sectional area of the tank is 20 cm2. Density of the liquid is constant everywhere in the system. At steady state, \(F_\text{in} = F_\text{out} = 10\) cm3/s and \(h = 16\) cm. The variation of \(h\) with \(F_\text{in}\) is approximated as a first order transfer function. Which one of the following is the CORRECT value of the time constant (in seconds) of this system? _____ (20 / 32 / 64 / 128)
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Response of Two-Tanks System for Impulse Input PageCoughanowr3E-7-2The two-tank system shown in figure is operating at steady state. At time \(t=0\), 10 ft3 of water is quickly added to the first tank.
Determine the maximum deviation in level (feet) in both tanks from the ultimate steady-state values and the time at which each maximum occurs. Data: \(A_1=A_2=10\) ft2; \(R_1=0.1\) min/ft2; \(R_2=0.35\) min/ft2.
- Maximum deviation in level of first tank = _____ ft
- Time at which maximum level occurs in first tank = _____ min
- Maximum deviation in level of second tank = _____ ft
- Time at which maximum level occurs in second tank = _____ min
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Linearization with Two Variables Page
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Linearized Transfer Function of Non-interacting Tanks Page2019-30-ctrlConsider two non-interacting tanks-in-series as shown in figure. Water enters Tank 1 at \(q\) cm3/s and drains down to Tank 2 by gravity at a rate \(k\sqrt{h_1}\) (cm3/s). Similarly, water drains from Tank 2 by gravity at a rate of \(k\sqrt{h_2}\) (cm3/s) where \(h_1\) and \(h_2\) represent levels of Tank 1 and Tank 2 respectively (see figure). Drain valve constant \(k=4\) cm2.5/s and cross-sectional areas of the two tanks are \(A_1=A_2=28\) cm2.
At steady state operation, the water inlet flow rate is \(q_{s}=16\) cm3/s. The transfer function relating the deviation variables \(H_2\) (cm) to flow rate \(Q\) (cm3/s) is,
- \(\dfrac{2}{(56s+1)^2}\)
- \(\dfrac{2}{(62s+1)^2}\)
- \(\dfrac{2}{(36s+1)^2}\)
- \(\dfrac{2}{(49s+1)^2}\)
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Time Constant of Thermocouple from Initial Rate of Response Page2001-17-ctrlThe hot junction of a thermocouple having a time constant \(\tau \) min is initially at room temperature of 30\(^\circ \)C. At time \(t=0\) min, it is placed in a bath held at 100\(^\circ \)C. The thermocouple is connected to a recorder which has fast dynamics. At \(t=2\) min, the hot junction is withdrawn from the bath and held in the air which is at 30\(^\circ \)C. From the recorded data, the value of \(dT/dt\) at \(t=2^+\) min is given to you. \(dT/dt = -2.5\)\(^\circ \)C/min at \(t=2^+\) min. Is this data sufficient to calculate the time constant of the thermocouple? If so, suggest a procedure for calculation of the time constant \(\tau \).
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