Process Modelling and Dynamic Response - Instrumentation and Process Control - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2007

The dynamic model for a mixing tank open to atmosphere at its top as shown below is to be written. The objective of mixing is to cool the hot water stream entering the tank at a flow rate q₂ and feed temperature of T₂ with a cold water feed stream entering the tank at a flow rate q₁ and feed temperature of T₀. A water stream is drawn from the tank bottom at a flow rate of q₄ by a pump and the level in the tank is proposed to be controlled by drawing another water stream at a flow rate q₃. Neglect evaporation and other heat losses from the tank.
The dynamic model for the tank is given as

A

\(\frac{dV}{dt}=q_1+q_2-q_3\), \(V\frac{dT}{dt}=q_1T_0+q_2T_2-q_3T\)

B

\(\frac{dV}{dt}=q_1-q_4\), \(\frac{d(VT)}{dt}=q_1T_0-q_4T\)

C

\(\frac{dV}{dt}=q_1+q_2-q_4\), \(\frac{d(VT)}{dt}=q_1T_0+q_2T_2-q_4T\)

D

\(\frac{dV}{dt}=q_1+q_2-q_3-q_4\), \(V\frac{dT}{dt}=q_1(T_0-T)+q_2(T_2-T)\)

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2

2007 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2007

Match the transfer functions with the responses to a unit step input shown in the figure.
i. \(\frac{-2.5(-4s+1)}{4s^2+4s+1}\)
ii. \(\frac{-2e^{-10s}}{10s+1}\)
iii. \(\frac{-5}{-20s+1}\)
iv. \(\frac{-0.1}{s}\)
v. \(\frac{4s+3}{2s+1}\)

A

i-e, ii-c, iii-a, iv-d, v-b

B

i-a, ii-b, iii-c, iv-d, v-e

C

i-b, ii-a, iii-c, iv-e, v-d

D

i-e, ii-a, iii-c, iv-b, v-d

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3

2008 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2008

The unit impulse response of a first order process is given by \( 2 e^{-0.5t} \). The gain and time constant of the process are, respectively,

A

4 and 2

B

2 and 2

C

2 and 0.5

D

1 and 0.5

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4

2008 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2008

A unit step input is given to a process that is represented by the transfer function \( \frac{(s + 2)}{(s + 5)} \). The initial value (\( t = 0^+ \)) of the response of the process to the step input is

A

0

B

2/5

C

1

D

\(\infty \)

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5

2008 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2008

Which ONE of the following transfer functions corresponds to an inverse response process with a positive gain?

A

\(\frac{1}{2s + 1} - \frac{2}{3s + 1} \)

B

\(\frac{2}{s + 1} - \frac{5}{s + 10} \)

C

\(\frac{3(0.5s - 1)}{(2s + 1)(s + 1)} \)

D

\(\frac{5}{s + 1} - \frac{3}{2s + 1} \)

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6

2008 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2008

The time constant, \( \tau \) (in minutes) is

A

1.14

B

1.92

C

3.23

D

5.39

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7

2009 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2009

The roots of the characteristic equation of an underdamped second order system are

A

real, negative and equal

B

real, negative and unequal

C

real, positive and unequal

D

complex conjugates

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8

2009 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2009

For a tank of cross-sectional area 100 cm² and inlet flow rate (\(Q_i\) in cm³/s), the outlet flow rate (\(Q_o\) in cm³/s) is related to the liquid height (\(H\) in cm) as \(Q_o = 3\sqrt{H}\) (see figure below).
Then the transfer function \(\frac{\bar{H}(s)}{\bar{Q}_i(s)}\) (overbar indicates deviation variables) of the process around the steady-state point, \(Q_{i,s} = 18\) cm³/s and \(H_s = 36\) cm, is

A

\(\frac{1}{100s + 1}\)

B

\(\frac{2}{200s + 1}\)

C

\(\frac{3}{300s + 1}\)

D

\(\frac{4}{400s + 1}\)

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9

2010 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2010

Match the location of the poles/zeros in the s-plane, listed in GROUP I, with the system response characteristics in GROUP II.
GROUP I
P. Pole in the right half plane
Q. Pole at origin
R. Zero in the right half plane
GROUP II
I. Stable response
II. Integrating response
III. Unstable response
IV. Inverse response

A

P – I, Q – II, R – III

B

P – III, Q – IV, R – I

C

P – III, Q – II, R – IV

D

P – I, Q – IV, R – III

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10

2010 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2010

The transfer function, G(s), whose asymptotic Bode diagram is shown below, is

A

10s + 1

B

s - 10

C

s + 10

D

10s - 1

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11

2010 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2010

Consider the process as shown below:
A constant head pump transfers a liquid from a tank maintained at 20 psi to a reactor operating at 100 psi, through a heat exchanger and a control valve. At the design conditions, the liquid flow rate is 1000 litres/min, while the pressure drop across the heat exchanger is 40 psi, and that across the control valve is 20 psi. Assume that the pressure drop across the heat exchanger varies as the square of the flow rate. If the flow is reduced to 500 litres/min, then the pressure drop across the control valve is

A

30 psi

B

50 psi

C

80 psi

D

150 psi

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12

2012 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2012

A thermometer initially at 100°C is dipped at \( t = 0 \) into an oil bath, maintained at 150°C. If the recorded temperature is 130°C after 1 minute, then the time constant of thermometer (in min) is

A

1.98

B

1.35

C

1.26

D

1.09

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13

2013 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2013

A unit gain 2nd order underdamped process has a period of oscillation 1 second and decay ratio 0.25. The transfer function of the process is

A

\(\frac{1}{0.024 s^2 + 0.067 s +1}\)

B

\(\frac{1}{0.067 s^2 + 0.024 s +1}\)

C

\(\frac{1}{0.021 s^2 + 0.1176 s +1}\)

D

\(\frac{1}{0.1176 s^2 + 0.021 s +1}\)

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14

2013 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2013

Consider the following transfer function G_p(s) = \frac{5}{(2s+1)^4} (Note: The unit of the process time constant is in seconds.) The crossover frequency (in rad/s) of the process is

A

20

B

0.1

C

0.5

D

0.05

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15

2014 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2014

A unit IMPULSE response of a first order system with time constant \(\tau\) and steady state gain \(K_p\) is given by

A

\(\frac{1}{K_p \tau} e^{t/\tau}\)

B

\(K_p e^{-t/\tau}\)

C

\(\tau K_p e^{-t/\tau}\)

D

\(\frac{K_p}{\tau} e^{-t/\tau}\)

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16

2014 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2014

Assume that an ordinary mercury-in-glass thermometer follows first order dynamics with a time constant of 10 s. It is at a steady state temperature of 0 \(^{\circ}C\). At time \(t = 0\), the thermometer is suddenly immersed in a constant temperature bath at 100 \(^{\circ}C\). The time required (in s) for the thermometer to read 95 \(^{\circ}C\), approximately is

A

60

B

40

C

30

D

20

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17

2014 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2014

A step change of magnitude 2 is introduced into a system having the following transfer function
\(G(s) = \frac{2}{s^2 + 2s + 4}\)
The percent overshoot is __________

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18

2016 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2016

A system exhibits inverse response for a unit step change in the input. Which one of the following statement must necessarily be satisfied?

A

The transfer function of the system has at least one negative pole

B

The transfer function of the system has at least one positive pole

C

The transfer function of the system has at least one negative zero

D

The transfer function of the system has at least one positive zero

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19

2016 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2016

For a unit step input, the response of a second order system is
\[y(t) = K_p \left[ 1 - \frac{1}{\sqrt{1-\zeta^2}} e^{-\frac{\zeta t}{\tau}} \sin \left( \frac{\sqrt{1-\zeta^2}}{\tau} t + \phi \right) \right]\]
where, K_p is the steady state gain, ζ is the damping coefficient, τ is the natural period of oscillation and φ is the phase lag. The overshoot of the system is exp(−πζ/√(1−ζ²)). For a unit step input, the response of the system from an initial steady state condition at t = 0 is shown in the figure below.
What is the natural period of oscillation (in seconds) of the system?

A

15.9

B

50

C

63.2

D

100

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20

2017 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2017

The transfer function of a system is
\[ \frac{1}{4s^2 + 1.2s + 1} \]
For a unit step increase in the input, the fractional overshoot, rounded to 2 decimal places, is ______.

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