Feedback Control and Stability - Instrumentation and Process Control - Chemical Engineering Previous Year Questions

1

2009 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2009

The characteristic equation of a closed loop system using a proportional controller with gain \(K_c\) is \(12{s^3} + 19{s^2} + 8s + 1 + {K_c} = 0\) At the onset of instability, the value of \(K_c\) is

A

35/3

B

10

C

25/3

D

20/3

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2

2009 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2009

The block diagram for a control system is shown below:
For a unit step change in the set point, \(R(s)\), the steady state offset in the output \(Y(s)\) is

A

0.2

B

0.3

C

0.4

D

0.5

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3

2010 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2010

Consider the cascade control configuration shown in the figure below:
The system is stable when K_c2 is

A

3/4

B

1

C

5/4

D

3/2

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4

2011 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2011

The following diagram shows a CSTR with two control loops. A liquid phase, endothermic reaction is taking place in the CSTR, and the system is initially at steady state. Assume that the changes in physical properties of the system are negligible.
TC: Temperature controller, LC: Level controller, TT: Temperature transmitter, LT: Level transmitter, V₁ and V₂: Control valves
Which ONE of the following statements is TRUE?

A

Changing the level controller set point affects the opening of V₂ ONLY

B

Changing the temperature controller set point affects the opening of V₂ ONLY

C

Changing the temperature controller set point affects the opening of BOTH V₁ and V₂

D

Changing the level controller set point affects the opening of BOTH V₁ and V₂

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5

2011 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2011

The characteristic equation of the closed loop is

A

\(6s^2+102s+1=0\)

B

\(700s^2+102s+25=0\)

C

\(100s^2-196s-25=0\)

D

\(240s^3+812s^2+204s+1=0\)

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6

2012 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2012

The Bode stability criterion is applicable when

A

Gain and phase curves decrease continuously with frequency

B

Gain curve increases and phase curve decreases with frequency

C

Gain curve and phase curve both increase with frequency

D

Gain curve decreases and phase curve increases with frequency

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7

2012 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2012

The characteristic equation for a system is \(s^3 + 9s^2 + 26s + 12(2 + K_c) = 0\). Using the Routh test, the value of \(K_c\) that will keep the system on the verge of instability is

A

20.9

B

18.4

C

17.5

D

15.3

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8

2012 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2012

The block diagram of a system with a proportional controller is shown below. A unit step input is introduced in the set point. The value of \(K_c\) to provide a critically damped response for \(U = 0\), \(\tau_p = 8\) and \(\tau_m = 1\) is

A

3.34

B

2.58

C

1.53

D

1.12

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9

2014 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2014

A process with transfer function \( G_p = \frac{2}{s-1} \) is to be controlled by a feedback proportional controller with a gain \( K_c \). If the transfer functions of all other elements in the control loop are unity, then which ONE of the following conditions produces a stable closed loop response?

A

\(K_c = 0.25 \)

B

\(0 < K_c < 0.25 \)

C

\(0.25 < K_c < 0.5 \)

D

\(K_c > 0.5 \)

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10

2014 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2014

Consider the following block diagram for a closed-loop feedback control system
A proportional controller is being used with \( K_c = -4 \). If a step change in disturbance of magnitude 2 affects the system, then the value of the offset is ______

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11

2017 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2017

The open loop transfer function of a process with a proportional controller (gain K_C) is
\[ G_{OL} = K_C \frac{e^{-2s}}{s} \]
Based on the Bode criterion for closed-loop stability, the ultimate gain of the controller, rounded to 2 decimal places, is ______.

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12

2017 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2017

The characteristic equation of a closed-loop system is
\[ 6s^3 + 11s^2 + 6s + (1 + K) = 0, \quad \text{where } K > 0 \]
The value of K beyond which the system just becomes unstable, rounded to the nearest integer, is ______.

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13

2018 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2018

A first-order process having a transfer function, G_p = \frac{2}{7s+1} is controlled by a proportional controller with gain of 3.2. The process time constant is in minutes. Addition of the integral control action with an integral time constant of 5 minutes leads to increase in

A

offset

B

speed of response

C

order of the closed loop system

D

proportional band

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14

2018 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2018

For a closed-loop system, consider the following transfer functions: process \( G_p(s) \), controller \( G_c(s) \), measuring device \( G_m(s) \), and final control element \( G_f(s) \) \( G_p(s) = \frac{2}{7s + 1} \) ; \( G_c(s) = 2 \) ; \( G_m(s) = 1 \) ; \( G_f(s) = 1 \) The offset in the closed loop response due to a unit step change introduced in the set point of the output variable is __________.

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15

2020 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2020

Consider the following closed loop system with \(G_c\) and \(G_p\) as the transfer functions of the process and the controller, respectively. For a unit step change in the set point (\(y_{sp}\)), the change in the value of the response (\(y\)) at steady state is __________ (round off to 1 decimal place).

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16

2020 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2020

Consider the following closed loop system.

\(G_c\), \(G_f\), and \(G_p\) are the transfer functions of the controller, the final control element and the process, respectively. \(Y\) and \(Y_{sp}\) are the response and its set point, respectively. For a gain margin of 1.6, the design value of \(K_c\) is __________ (correct up to one decimal place).

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17

2021 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2021

A feedforward controller can be used only if

A

the disturbance variable can be measured

B

the disturbance variable can be manipulated

C

the disturbance variable can be ignored

D

regulatory control is not required

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18

2021 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2021

It is required to control the volume of the contents in the jacketed reactor shown in the figure.

Which one of the following schemes can be used for feedback control?

A

Measure L101 and manipulate valve V-2

B

Measure T101 and manipulate valve V-1

C

Measure L101 and manipulate valve V-3

D

Measure F101 and manipulate valve V-1

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19

2021 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2021

Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?

A

Dead-time term(s) must be absent in the open-loop transfer function

B

Roots of the characteristic equation must have negative real part

C

All the elements in the left (first) column of the Routh array must have the same sign

D

Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency

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20

2022 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2022

A control system on the jacket side of a reactor is shown in the figure. Pressurized water flows through the jacket to cool the reactor. The heated water flashes in the boiler. The exothermic reaction heat thus generates steam. Fresh boiler feed water (BFW) is added to make-up for the loss of water as steam. Assume that all control valves are air-to-open. The controller action, 'direct' or 'reverse', is defined with respect to the controller. Select the option that correctly specifies the action of the controllers.

A

PC: Reverse, LC: Direct, TC: Reverse

B

PC: Direct, LC: Reverse, TC: Direct

C

PC: Direct, LC: Reverse, TC: Reverse

D

PC: Reverse, LC: Direct, TC: Direct

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