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

1

2007 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2007

Consider the following instrumentation diagram for a chemical reactor. C_sp represents a concentration setpoint.
Match the items in group 1 with the corresponding items given in column B.

Column A	Column B
P) control strategy	1) feed forward control
Q) primary control variable	2) cascade control
R) slowest controller	3) concentration in the reactor
S) fastest controller	4) reactor temperature
	5) jacket temperature
	6) concentration controller
	7) reactor temperature controller
	8) jacket temperature controller
	9) flow controller
	10) selective control

A

P-2, Q-3, R-6, S-9

B

P-1, Q-4, R-8, S-7

C

P-10, Q-7, R-9, S-6

D

P-1, Q-8, R-5, S-9

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2

2007 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2007

The first two rows of Routh's tabulation of a third order equation are

\(s^3\)	2	2
\(s^2\)	4	4

Select the correct answer from the following choices:

A

The equation has one root in the right half s-plane.

B

The equation has two roots on the j axis at s = j and -j. The third root is in the left half plane.

C

The equation has two roots on the j axis at s = 2j and s = -2j. The third root is in the left half plane.

D

The equation has two roots on the j axis at s = 2j and s = -2j. The third root is in the right half plane.

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3

2007 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2007

A cascade control system for pressure control is shown in the figure given below. The pressure transmitter has a range of 0 to 6 bar(g) and the flow transmitter range is 0 to 81 nm³/hr. The normal flow rate through the valve is 32.4 nm³/hr corresponding to the value of set point for pressure = 1bar(g) and to give the flow, the valve must be 40% opened. The control valve has linear characteristics and is fail-open (air to close). Error, set point and control variable are expressed in percentage transmitter output(%TO). Proportional gain is expressed in the units of % controller output (CO/%TO).

The types of action for the two controllers are

A

direct acting for the pressure control and direct acting for the flow control

B

indirect acting for the pressure control and indirect acting for the flow control

C

direct acting for the pressure control and indirect acting for the flow control

D

indirect acting for the pressure control and direct acting for the flow control

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4

2007 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2007

Given that the actual tank pressure is 4 bar(g) and a proportional controller is employed for pressure control, the proportional band setting of the pressure controller required to obtain a set point to the flow controller equal to 54 nm³/hr is

A

50%

B

100%

C

150%

D

187%

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5

2008 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2008

If the control loop is to operate at a gain margin of 2.0, the gain of the proportional controller must equal

A

0.85

B

2.87

C

3.39

D

11.50

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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

2016 · Chemical Engineering · Instrumentation and Process Control · Feedback Control and Stability

Chemical Engineering (CH) 2016

A PI controller with integral time constant of 0.1 min is to be designed to control a process with transfer function
\[G_p(s) = \frac{10}{s^2 + 2s + 100}\]
Assume the transfer functions of the measuring element and the final control element are both unity (G_m = 1, G_f = 1). The gain (rounded off to the first decimal place) of the controller that will constitute the critical condition for stability of the PI feedback control system is ______

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17

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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18

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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19

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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20

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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