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

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

2018 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2018

The decay ratio for a system having complex conjugate poles as \( \left(-\frac{1}{10} + j\frac{2}{15} \right) \) and \( \left(-\frac{1}{10} - j\frac{2}{15} \right) \) is

A

\(7 \times 10^{-1} \)

B

\(8 \times 10^{-2} \)

C

\(9 \times 10^{-3} \)

D

\(10 \times 10^{-4} \)

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15

2018 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2018

Consider the following transfer function: \( G(s) = \frac{3}{(5s + 1)^2} \) where, the natural period of oscillation is in min. The amplitude ratio at a frequency of 0.5 rad/min is __________ (rounded off to second decimal place).

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16

2019 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2019

Consider 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 \(q_{ss} = 16\) cm³/s. The transfer function relating the deviation variables \(\tilde{h}_2\) (cm) to flow rate \(\tilde{q}\) (cm³/s) is,

A

\(\frac{2}{(56s+1)^2}\)

B

\(\frac{2}{(62s+1)^2}\)

C

\(\frac{2}{(36s+1)^2}\)

D

\(\frac{2}{(49s+1)^2}\)

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17

2019 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2019

Choose the option that correctly matches the step response curves on the left with the appropriate transfer functions on the right. The step input change occurs at time t=0.

A

P – III, Q – IV, R – II, S – I

B

P – III, Q – I, R – IV, S – II

C

P – IV, Q – III, R – II, S – I

D

P – III, Q – II, R – IV, S – I

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18

2021 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2021

A system has a transfer function G(s) = 3e^{-4s} / (12s + 1). When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is _______.

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19

2021 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2021

A process has a transfer function G(s) = Y(s)/X(s) = 20 / (90000s² + 240s + 1).
Initially the process is at steady state with x(t = 0) = 0.4 and y(t = 0) = 100. If a step change in x is given from 0.4 to 0.5, the maximum value of y that will be observed before it reaches the new steady state is _______ (round off to 1 decimal place).

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20

2022 · Chemical Engineering · Instrumentation and Process Control · Process Modelling and Dynamic Response

Chemical Engineering (CH) 2022

A process described by the transfer function
\( G_p(s) = \frac{(10s + 1)}{(5s + 1)} \)
is forced by a unit step input at time t = 0. The output value immediately after the step input (at t = 0⁺) is __________ (rounded off to the nearest integer).

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