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GATE SOLVED PAPER Chemical Engineering Instrumentation Instrumen tation and Process Control Copyright © By NODIA & COMPANY
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GATE SOLVED PAPER - CH INSTRUMENTATION AND PROCESS CONTROL
YEAR 2011 Q. 1
ONE MARK
Match the process parameters in Group I with the measuring instruments in Group II. Group I P. Flame tteemperature
I.
Q. Composition of LPG
II. Radiation pyrometer
R. Liquid aaiir tteempe perrature (A) P-III, Q-I, R-II (C) P-II, Q-III, R-I Q. 2
Group II Thermocouple
Y N A P
III III. Gas cch hromatograph (B) P-I, Q-III, R-II (D) P-II, Q-I, R-III
The range of standard current signal in process instruments is 4 to 20 mA . Which one of the following is the reason for choosing the minimum signal as 4 mA instead of zero? (A) To minimise resistive heating in instruments (B) To distinguish between signal failure and minimum signal condition (C) To ensure a smaller difference between maximum and minimum signals
C O M O & A I D O N ©
(D) To ensure compatibility with other instruments YEAR 2011 Q. 3
TWO MARKS
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 V 1 and V 2 = Control valves Which one of the following statements is true? (A) Changing the level controller set point affects the opening of V 2 only (B) Changing the temperature temp erature controller set point affects the opening of V 2 only (C) Changing the temperature controller set point affects the opening of both V 1 and V 2
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
(D) Changing the level controller controller set point affects the opening op ening of both V 1 and V 2
Stat Stateme emen nt For Li Link nked ed Answ Answer er Q. 4 an and d5:
^h
A PID controller output p t , in time domain is given by t
= 30 + 5 e t
de t
# ^ h ^ h ^ h ^ h ^ h is the error at time t . The transfer function of the process to be controlled is G ^s h ^ s h . p t
where, e
e t dt + 15
+ 1.25
dt
0
t
=
p
10
200 + 1
Y ^ h (B) N s A s s ^ h (D) P
The measurement of the controlled variable is instantaneous and accurate. Q. 4
The transfer function of the controller is (A)
h h
2
2
5 12s + 3s + 1
3s 2
3
5 12s + 4s + 1
5 12
M O & & C A I D O N © (C)
Q. 5
^ ^
5 12s + 4s + 1
4s
2
+3 +1
4s
the characteristic equation of the closed-loop is (B) 700s2 + 102s + 25 = 0 (A) 6s2 + 102s + 1 = 0 (C)
100s 2
−
196s
−
25
=
0
(D)
240s 3 + 812s 2 + 204s + 1 = 0
YEAR 2010
Q. 6
ONE MARK
Match the location of the poles/zeroes in the s -plane listed in Group I with the system response characteristics in Group II. Group I
Group II
P. Pole in the right half plane
1. Stable respon ponse
Q. Pole at origin
2. Integrating response
R. Zero iin n tth he rriight h haalf p pllane
3. Inverse rreespo pon nse 4. Inverse erse resp respon onse se
Codes (A) (B) (C) (D)
P 1 3 2 1
Q 2 4 2 4
R 3 1 4 3
Q. 7
Flow measuring instruments with different specifications (zero and span) are available ava ilable for an application that requires flow rate measurements in the range of 300 L/h to 400 L/h . The appropriate instrument for this application is the one whose specifications are (A) zero = 175 L/h , span = 150 L/h (B) zero = 375 L/h , span = 100 L/h (C) zero = 275 L/h , span = 150 L/h (D) zero = 475 L/h , span = 100 L/h
Q. 8
The transfer function G
^ h whose asymptotic Bode diagram is shown below, is s
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(A) (C)
INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
10s + 1
(B) (D)
s + 10
s - 10 10s - 1
YEAR 2010
Q. 9
Y N A P ^h O O M C & A I D O N © A block diagram for a control system is shown below.
the steady state gain of the closed-loop system, between output point R s , is (A) 5/9 (B) 4/9 (C) 1/3 (D) 2/9
Q. 10
TWO MARKS
^ h and set
Y s
Consider the cascade control configuration shown in the figure below:
K
The 3/4 system is stable when (A) (C) 5/4
Q. 11
, 2 c
is
(B) 1 (D) 3/2
Consider the process as shown below:
A constant head pump transfers a liquid flow, 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 L/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
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
the flow rate. If the flow is reduced to 500 L/min , then the pressure drop across the control valve is (A) 30 psi (B) 50 psi (C) 80 psi (D) 150 psi YEAR 2009 Q. 12
Q. 13
ONE MARK
Which one of the following sensors is used for the measurement of temperature in a combustion process T > 1800 cC (A) Type J thermocouple (B) Thermistor (C) Resistance temperature detector (D) Pyrometer
^
h
Y N A P M O & & C A I D O N ©
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
YEAR 2009
Q. 14
The inverse Laplace transform of
(A) (C)
Q. 15
Q. 16
-t/2
e
-t
e
-t
- e
(B) 2e /2 - e (D) e - e / 2 -t
-t
-t
-t
The characteristic equation of a closed-loop system using a proportional controller with gain K c c is 3 2 12s + 19s + 8s + 1 + Kc = 0 At the onset of instability, the value of K c c is (A) 35/3 (B) 10 (C) 25/3 (D) 20/3
The block diagram for a control system is shown below.
For a unit step change in the set point, Y s is (A) 0.2 (C) 0.4
^h
Q. 17
is
2
2s + 3s + 1
t / 2
- 2e
1
TWO MARKS
^ h, the steady state offset in the output
R s
(B) 0.3 (D) 0.5
2 and inlet flow rate (Q i i in cm3 /s ), For a tank of cross-sectional area 100 cm the outlet flow rate (Q 0 in cm3 /s ) is related to the liquid height ( H in cm ) as Q 0 = 3 H (see figure below).
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
^h ^ h
H s (overbar indicates deviation variables) of the Q i s process around the steady state point, Q is = 18 cm3 /s and H s = 36 cm , is
Then the transfer function
(A) (C)
1
(B)
3 300s + 1
(D)
100s + 1
2 200s + 1
4 400s + 1
Y N A P O O M ^ h C ^ h ^ h & A I D O N © YEAR 2008
Q. 18
The unit impulse response of a first order process is given by time constant of the process are, respectively (A) 4 and 2 (B) 2 and 2
(C) 2 and 0.5
Q. 19
0.5 t
2e
TWO MARKS
. The gain and
(D) 1 and 0.5
A unit step input is given to a process that is i s represented by the transfer function s + 2 . The initial value t = 0 + of the response of the process to the step input s + 5
is (A) 0 (C) 1
Q. 20
(B) 2/5 (D) 3
3 3 and height 1 m has water flowing in at 0.05 m A tank of volume 0.25 m / min . The outlet flow rate is governed b by y the relation F = 0.1 h where, h is the height of the water in the tank in metre and F is the outlet flow rate in m3 /min . o out ut
o out ut
3
The inlet flow rate changes suddenly from its nominal value of 0.05 m / min to 3 0.15 m / min and remains there. The time (in min ) at which the tank will begin to overflow is given by (A) 0.28 (B) 1.01 (C) 1.73 (D) 3
Q. 21
Which one of the following transfer functions corresponds to an inverse response process with a positive gain? (A) (C)
Q. 22
1 2 − 2s + 1 3s + 1
^
h
3 0.5s − 1
^ s h^s h 2 +1
+1
(B)
2 5 − s + 1 s + 10
(D)
5 3 − s + 1 2s + 1
Match the List I with List II and select the correct answer using the codes given below the lists. List I
List II
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
P. Temperature
1.
Hot wire anemometry
Q. Pressure
2.
Strain gauge
R. Flow
3.
Chromatographic analyzer
4.
Pyrometer
Codes (A) (B) (C) (D)
Q. 23
1P 4 1 4
2Q 1 2 2
3R 3 4 1
Y N A P M O & & C A I D O N ©
Match the List I with List II and select the correct answer using the codes given below the lists. List I
List II
P. Ziegler-Nichols
1.
Process reaction curve
Q. Underdamped response
2.
Decay ratio
R. Feed-forward control
3.
Frequency response
4.
Di Dist stur urba banc ncee m mea easu sure reme men nt
Codes (A) (B) (C) (D)
P 3 1 3 1
Q 2 2 4 4
R 4 3 2 2
Stat Stateme emen nt For Li Link nked ed Answ Answer er Q. 24 an and d 2255 :
The cross-over frequency associated with a feedback loop employing a proportional controller to control the process represented by the transfer function
^h ^
G p s =
−s
2e
τs +
h , (unit of time is minute)
1
2
is found to be 0.6 rad/ min . Assume that the measurement and valve transfer functions are unity. Q. 24 The time constant (A) 1.14 (C) 3.23 Q. 25
τ
(in min) is (B) 1.92 (D) 5.39
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 YEAR 2007
Q. 26
An operator was told to control the temperature of a reactor at
ONE MARK
60cC .
The
operator set-p set-point of the temperature 60. The scale actually indicatedsets 0 tothe 100% of oint a temperature range of 0controller to 200cCat . This caused a runaway reaction by over pressurizing the vessel, which resulted in injury to the operator. op erator.
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The actual set-point temperature was (A) 200cC (C) 120cC
(B) (D)
60cC 100cC
YEAR 2007 Q. 27
TWO MARKS
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 q 2 and feed temperature of T s with a cold water feed stream entering the tank at a flow rate q 1 and feed temperature of T 0 . A water stream is drawn from the tank bottom at a flow rate of q 4 by a pump and the level in the tank is proposed to be controlled by drawing another water stream at a flow rate q 3 . Neglect evaporation and other heat losses from the tank.
Y N A P O O M C ^ h & ^ h A I ^ h ^ h ^ h D O N © The dynamic model for the tank is given as (A) dV dt
(B) dV dt
(C) dV dt
=
dT q1 + q 2 − q 3 , V dt
=
q1
=
q1 + q 2 − q 4 ,
−
d VT dt
q 4 ,
=
=
q1 T0 + q 2 Ts − q 3 T
q1 Ts
d VT dt
=
−
q1 T0 + q 2 Ts − q 4 T
q + q 2 − q 3 − q 4 d VT , (D) dV = 1 dt
dt
Q. 28
q4 T
=
q1 T0 − T
+ q2
Ts − T
Match the transfer functions with the responses to a unit step input shown in the figure.
1. 3.
^
h
− 2.5 − 4s + 1 2
4s + 4s + 1 −5 − 20s + 1
2. 4.
− 10s
− 2e 10s + 1 - 0.1
s
GATE SOLVED PAPER - CH
5.
Q. 29
INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
4s + 3 2s + 1
Codes 1 (A) E (B) A
2 C B
3 A C
4 D D
5 B E
(C) (D)
A A
C C
E B
D D
B E
Consider the following instrumentation diagram for a chemical reactor. represents a concentration set-point.
Y N A P M O & & C A I D O N ©
C SSP P
Match the List I with List II and select the correct answer using the codes given below the lists. List I
List II
P. Control strategy
1.
Feed forward control
Q. Primary control variable
2.
Cascade control
R. Slowest controller
3.
Concentration in the reactor
S.
4.
Reactor temperature
5.
Jac Jacket temp tempeeratu rature re
6.
Co Conc ncen entr trat atio ion n co con ntrol trolle lerr
7.
Re Reac acto torr tempe tempera ratu ture re cont contro roll ller er
8.
Jac Jacke kett tempe tempera ratu ture re con control trolle lerr
9.
Flow low controller
Fastest controller
10. 10. Se Sele lect ctiv ivee ccon ontr trol ol Codes (A) (B) (C) (D) Q. 30
P 2 1 10 1
Q 3 4 7 8
R 6 8 9 5
S 9 7 6 9
The first two rows of Routh’s tabulation of a third order equation are 2 2 s 3 2 s 4 4 Select the correct answer from the following choices. (A) The equation has one root in the right half s -plance
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
(B) The equation has two roots on the j -axis at d = 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 - 2 j . The third root is in the left half plane (D) The equation has two roots on the j -axis at s = 2j and - 2 j . The third root is in the right half plane
Common Com mon Dat Dataa For Que Questi stions ons.. 31 31,, 332 2 and and 33 : 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 3 3 81 nm /h . The normal flow rate through the valve is 32.4 nm /h corresponding to the value of set point for pressure = 1 bar (g) and to give the flow, the valve must be 40% opened. The control valve has linear characteristics and is fall-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 per cent controller output (CO% TO).
Q. 31
Q. 32
Y N A P O O M C & A I D O N ©
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 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
The bias values for the two controllers, controllers, so that no offset occurs o ccurs in either controller are (A) pressure controller : 40%, flow controller : 60% (B) pressure controller : 33%, flow controller : 67% (C) pressure controller : 67%, flow controller : 33% (D) pressure controller : 60%, flow controller : 40%
Q. 33
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 3 controller required to obtain a set point to the flow controller equal to 54 nm /h is (A) 50% (B) 100% (C) 150% (D) 187%
YEAR 2006 Q. 34
ONE MARK
The control valve characteristics for three types of control valves ( P , Q , and R
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
) are given in the figure below. Match the control valve with its characteristics.
Y N A P M O ^ h & & C A I D O ^ h ^ h N © (A) P -Quick opening, Q -Linear, R -Equal percentage (B) P -Linear, Q -Square root, R -Equal percentage
(C) P -Equal percentage, Q -Linear, R -Quick opening (D) P -Square root, Q -Quick opening, R -Linear YEAR 2006
Q. 35
The Laplace transform of the input function
X t
TWO MARKS
, given in the figure below, is
given by
(A)
(C)
Q. 36
1
2
2s 1
2
s
^
-2s
1 - e
h
+2s
1 + e
(B)
(D)
1
2
2s 1
2
s
^
−2s
1 + e
h
-2s
1 - e
A liquid level control system is configured as shown in the figure below. If the Level Transmitter Transmitter (LT) is direct acting and the pneumatic control valve is air to open, what kind of control action should the controller (LC) have and why?
(A) Direct acting since the control valve is direct acting (B) Reverse acting since the control valve is reverse acting (C) Direct acting since the control valv valvee is reverse acting (D) Reverse acting since the control valve is direct acting Q. 37
A 2-output process can be described in the Laplace transform domain as 2-input, given below.
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
^h h ^h ^h h ^h ^h ^h
^ ^
^h ^h ^h ^h
τ 1 s + 1 Y1 s = K1 U1 s + K 2 U 2 s + K 4 Y1 s τ 2 s + 1 Y2 s = K 3 U 2 s where U 1 and U 2 are the inputs and Y 1 and Y 2 are the outputs. The gains of the transfer functions Y1 s /U2 s and Y2 s /U 2 s , respectively are (A) K 2 and K 3 (B) K 1 and K3 + K2 K 4 (D) K 2 and K3 + K2 K 4 (C) K 2 and K3 + K1 K 4 Q. 38
A process is perturbed p erturbed by a sinusoidal input u output is
^h t
= A sin
ωt
. The resulting process
^ h ^ h^ h . If y ^0h 0 , the differential equation representing the process is dy ^ t h dy ^ t h (A) y ^ t h Ku ^ t h (B) y^t h KAu^t h dt dt dy ^ t h dy ^ t h (C) y ^ t h Ku ^ t h (D) c y ^ t h m K Au ^ t h dt dt Y s
KAω
=
τs
2
+ 1 s + ω
2
=
+τ
=
+
τ
=
Y N A P O O M C & A I D O N © +
τ
=
+
τ
=
Comm Co mmon on Da Data ta For Qu Quest estio ions ns.. 39 aand nd 4400 :
The block diagram of a closed-loop control system is shown in the figure below. Y is the controlled variable, D is disturbance, Y SP is the set point, G 1 , G 2 , and G 3 are transfer functions, and K c c is the proportional controller.
Q. 39
(A) (C)
Q. 40
^ h/ ^ h is given by (B) ^ h (D) ^ h ^ h 1/^ 1h. A step change of magnitude M is
The closed-loop transfer function Y
h
G 3
G 3
h
D s
G 1 1 + G1 G 3 + G 2 Kc
G 3 G 1 1 + G1 G 3 + G 2 Kc
^ ^ ^h
s
1 + G1 + G 2 G 3 Kc
1 + G1 G 3 + G 2 Kc
^h
s + Let G1 s = 1 and G2 s = G 3 s = made in the set point. The steady state offset of the closed-loop response resp onse Y is
(A) (C)
M 1 + 2K c
^
(B)
h
M K c − 1 1 + 2K c
M
1 + K c
(D) 0
Stat Statem emen entt For Li Link nked ed An Answ swer er Q. 41 an and d 4422 : For the ssystem ystem shown below, 1 G1 s =
^h
s + 1
τ1.
, G2
^h
s =
1 and τ 2 .s + 1
t2
= 2t 1 .
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
^h
When the system is excited by the sinusoidal input response Y is given by Y = A sin ωt + φ .
^
Q. 41
h
= sin
If the response of Y lags behind the input X by 45c and frequency ω is (A) 1 (B) π/4 (C) 0
Q. 42
X t
(D)
, the intermediate
ωt
τ1
=
1, then the input
-1
Y N A P M O hh ^ h ^ & & C A I D O N © For the same input, the amplitude of the output Z will be (A) 1.00 (B) 0.62 (C) 0.42 (D) 0.32 YEAR 2005
Q. 43
The unit step response of a first order system with time constant state gain K p is given by -
-t /τ
-
(A) K 1 e 2t / (C) K p 1 - e
Q. 44
τ
and steady
-t /τ
(B) K 1 t / e (D) K p e /τ
p
-
ONE MARK
p
-
τ
τ
An example of an open-loop econd order under-damped system is (A) liquid level in a tank (B) U-tube manometer (C) thermocouple in a thermo-well (D) two non-interacting non-interacting first order ssystems ystems in series
Q. 45
Q. 46
The control valve characteristics characteristics is selected such that the product of process pro cess gain and the valve gain (A) is a linearly increasing function of the manipulated variable (B) is a linearly decreasing function of the manipulated variable (C) remains constant as the value of the manipulated variable changes (D) is an exponentially exp onentially increasing function of the manipulated variable Cascade control comes under the control configuration which uses (A) one measurement and one manipulated variable (B) more than one measurements and one manipulated variable (C) one measurement and more than one manipulated variables (D) more than one measurements and more than one manipulated vgariables YEAR 2005
Q. 47
TWO MARKS
Match the process variables in Group I given below with the measuring devices in Group II. Group I P. High temperature
Group II 1.
Orifice meter
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
Q. Flow
2.
Chromatograph
R. Composition
3.
Radiation pyrometer
4.
Bi Bi-m -met etal alli licc Th Ther ermo mome mete terr (B) P-1, Q-3, R-2 (D) P-4, Q-2, R-1
(A) P-1, Q-2, R-3 (C) P-3, Q-1, R-2 Q. 48
Given the characteristic equation below, select the number of roots which will be located to the right of the imaginary axis s 4 + 5s 3 − s2 − 17s + 12 = 0 . (A) One (B) Two (C) Three (D) Zero
Q. 49
Given the process transfer function G p = 4/ τs + 1 2 and the disturbance transfer function Gd = 2 τs + 1 , select the correct transfer function for the Feed F Forward orward Controller for perfect disturbance rejection. (A) − 2 τs + 1 (B) - 1 (C) − 0.5 τs + 1 (D) − τs + 1 2
^
^
Q. 50
^
h
^
h
h
h Y N 20/ ^s 2h and controller transfer A ^
h
P O O M C & A I D O N ©
Given the process transfer function G p function Gc = K c and assuming the transfer functions of all other elements in the control loop are unity, select the range of K c c for which the closed-loop response will be stable. (B) K c < 1 (A) K c < 1 =
−
100
10
(C)
Q. 51
1 1 < K c < 100 10
(D)
K c >
1 10
The value of ultimate period of oscillation P u is 3 min , and that of the ultimate controller gain K is 2. Select the correct set of tuning parameters (controller gain K c c , the derivative time constant τ D in minute, and the integral time constant τ I in minute) for a PID controller using Ziegler-Nichols controller settings. (A) K c = (B) K c = 1.1; τ I = 2.1, τ D = 1.31 1.5 ; τ I = 1.8 , τ D = 0.51 c cu u
(C)
K c = 1.5 ;
τ I
= 1.8 ,
τ D
= 0.51
(D)
K c = 1.2 ;
τ I
= 1.5 ,
τ D
YEAR 2004
Q. 52
^h
For the ti time me domain function f t by (A) (C)
1 3
2s 1 3
s
ONE MARK t
=
t , the Laplace transform of
# f^t hdt is given 0
(B)
2
s 3
(D) 22
s
YEAR 2004 Q. 53
= 0.38
TWO MARKS
Match first order system given in Group I with the appropriate time constant in Group II. Group I P. Thermometer
Group II 1.
^mC h/^hAh p
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
Q. Mixing
2.
q/V
3. V/q
^hAh/^mC h
4.
p
(A) P-4, Q-2
(B) P-4, Q-3
(C) P-1, Q-2 Q. 54
(D) P-1, Q-3
^h
The experimental response of the controlled variable y t for a step change of magnitude P , in the manipulated variable x t is shown below.
^h
Y N A P M O ^ h ^ h & & C ^ h A ^ h I ^ h ^ h D O N ^ h ^ h^ h^ h © The appropriate transfer function of the process is Q/P e ^ Q/Rhs Q/R e s (A) (B) τ d s + 1 6 Q/P s + 1@ Q/P e s Q/R e ^ P/Q hs (C) (D) τ d s + 1 6 Q/R s + 1@ −
− τd
− τd
Q. 55
−
Consider a system with open-loop transfer function
G s
=
1
s+1
2s + 1 5s + 1
Match the range of ω (frequency) in Group I with the slope of the asymptote of the log AR (amplitude ratio) versus log ω plot in Group II. Group I P. Q.
Group II
0
1
1. 2.
-5
3.
-2
4.
-1
5.
0
-3
(A) P-5, Q-2 (C) P-5, Q-3 Q. 56
(B) P-4, Q-2 (D) P-4, Q-1
The process and disturbance transfer functions for a system sys tem are given by
^ h ^^ hh ^ s h^ s h and ^ h dy ^s s h s s The feed forward controller transfer function that will keep the process output ^ h ^ is h^ h constant for changes in disturbance
G p s = Gd s
=
y s
=
m s
=
2
2 +1 5 +1 1
2 +1 5 +1
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(A)
INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
^ s h ^ s h (B) (D) ^ s h^ s h 2 +1
2
^ s h ^ s h 2 +1
2
5 +1
5 +1
2
2
2
(C) 1/2 Q. 57
2
2 +1 5 +1
For the block diagram shown b below, elow,
the characteristic equation is (A) τl s τ p s + 1 + Kc K p τ l + 1 e s = 0 (B) τ m s + 1 τ p s + 1 + Km K p e s = 0 (C) τl s τ m s + 1 τ p s + 1 + Kc Km K p τ l s + s = 0 1 e (D) τ m s + 1 τ p s + 1 + Kc Km K p e s = 0
^ h ^ ^ h^ h ^ h^ h ^ h^ h
h
− τd
Y N A P O O M C & A I D O N © − τ d
^
h
− τd
− τ d
YEAR 2003
Q. 58
Match the measured process variables with the list of measuring devices given below. List I (Measured process variable)
Q. 59
List II (Measuring device)
P. Temperature
1. Bourdon tube element
Q. Pressure
2. Orifice plates
R. Flow
3. Infrared analyzer
S. Liquid level
4. Displacer devices
T. Composition Codes P Q R (A) 5 1 2
S 4
T 3
(B) (C) (D)
2 2 4
5 5 5
3 1 3
1 3 1
4 4 2
5. Pyrometer
Suppose that the gain, time constant, and dead time of a process with the following transfer function Gc s = 10 exp − 0.1s / 0.5s + 1 are known with a possible error of ! 20% of their values. The largest permissible gain K c c of a proportional controller needs to be calculated by taking the values of process gain, time constant and dead time as (A) 8, 0.6, 0.08 (B) 12, 0.6, 0.12 (C) 8, 0.6, 0.12 (D) 12, 0.4, 0.08
^h
Q. 60
ONE MARK
^
h^
h
Water is flowing through a series of four tanks and getting heated as shown in figure. It is desired to design a cascade control scheme for controlling the temperature of a water leaving the Tank 4 as there is a disturbance in the
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temperature of a second s econd stream entering the Ta Tank nk 2. Select the best place to take the secondary measurement for the secondary loop.
Y N A P M O & & C A I D O N © (A) Tank 1 (C) Tank 3
(B) Tank 2 (D) Tank 4
YEAR 2003
Q. 61
Water is entering a storage tank at a temperature T 0 and flow rate Q 0 and leaving at a flow rate Q and temperature T . There are negligible heat losses in the tank. The area of cross-section of the tank is Ac . The model that describes the dynamic variation of water temperature in the tank with time is given as
^
(A) Q 0 T0
^
(C) Q T0 Q. 62
−
−
T
T
h
h
=
=
dT Ac h dt
(B) Q 0 T0
^
dT Ac h dt
(D) Q T0
−
−
QT T
=
dT Ac h dt
h A h d ^dt Th h =
c
Find the ultimate gain and frequency for a proportional controller in the case of a process having the following transfer function.
^ h ^ s h^ s h^s h 1
G p s =
Q. 63
TWO MARKS
(A)
ω
(C)
ω
=
1 14
=
1;
;
K c =
K c = 13
4 +1 2 +1
45 7
14
+1
(B)
ω
=
7 6
;
K c =
46 3
(D)
ω
=
7 8
;
K c =
45 4
Match the type of controller given in Group II that is most suitable for each application given in Group I.
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INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
List I
List II
P. Dist Distilla illatio tion n col column umn bo botto ttoms ms lev level el to be con contro trolled lled 1. P control with bottom flow Q. Dist Distilla illatio tion n colu column mn pre pressu ssure re to be con contro trolled lled b by y 2. manipulating vapour flow from the top plate R. Flo Flow w co cont ntrol rol a in liqu liquid id line ffrom rom a pu pump mp b by y 3. positioning the of valve the
Pl control
PID
control
S. Con Contro troll of ttempe emperat rature ure ooff a CS CSTR TR wi with th ccoola oolant nt flow in the jacket (A) P-1, Q-1, R-2, S-3 (B) P-2, Q-2, R-3, S-3 (C) P-2, Q-2, R-1, S-1 (D) P-2, Q-3, R-2, S-3 Q. 64
In 1. 2. 3.
the case of a feed forward control scheme, which of the following is not true? It is insensitive to modeling errors. It cannot cope with unmeasured disturbances. It w waits aits un until til the effect of the disturbance has been felt b by y the system before control action is taken.
Y N A P O O M C & A I D O N © 4.
It requires good kno knowledge wledge of the process model.
5.
It requires iden identification tification of all possible disturbances and their direct measurement. (A) 1 and 3 (B) 1 and 4 (C) 2 and 5 (D) 3 and 4
Q. 65
Temperature control of an exothermic chemical reaction taking place in a CSTR is done with the help of cooling water flowing in a jacket around the reactor. The types of valve and controller action to be b e recommended are (A) air to open valve with the controller direct acting
(B) air to close valve with the controller indirect acting (C) air to open valve with the controller indirect acting (D) air to close valve with the controller direct acting
YEAR 2002
Q. 66
ONE MARK
The closed-loop poles of a stable second order system could be (A) both real and positive (B) complex conjugate with positive real parts (C) both real and negative (D) one real positive and the other real negative
Q. 67
A first order system with unity gain and time constant τ is subjected to a sinusoidal input of frequency ω = 1 . The amplitude ratio for this system is τ
(A) 1 (C)
1 2
(B)
0.5
(D)
0.25
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YEAR 2002 Q. 68
TWO MARKS
The frequency response of a first order system has a phase shift with lower and upper bounds given by (A)
9-
(C)
9- 2 , 0C
3,
2 C
π
(B)
9- 2 , 2 C p
p
π (D) 90, 2 C
π
YEAR 2001 Q. 69
ONE MARK
The calibration data of a thermocouple with its cold junction at below.
Y ^ h N A P M O & & C A I b l D O N © Hot junction temperature
^ Ch c
0
20
40
0cC are
60
80
given 100
Thermo-emf mV 0.00 0.80 1.61 2.43 3.26 4.10 The hot junction of the thermocouple is placed in a bath at 80cC while its cold junction is at 20cC. What is the emf of the thermocouple? (A) 3.26 mV (B) 0.80 mV (C) 2.46 mV (D) 2.43 mV
Q. 70
A process is initially at steady state with its output y = 1 for an input u = 1. The input is suddenly changed to 2 at time t = 0 . The output response is y t = 1 + 2t . The transfer function of the process is (B) 1 + 2 (A) 2 s
(C)
Q. 71
s 2
2 1+
s
(D)
1
s
2 1+
s
The inherent characteristics of an equal percentage p ercentage valve valve relating flow rate q with valve stem movement x are described by the equation (A)
dq = k dx
(B)
dq = kq dx
(C)
dq k = dx q
(D)
dq 2 = kq dx
YEAR 2001 Q. 72
Q. 73
^h
TWO MARKS
^ h
An ideal PID controller has the transfer function 61 + 1/ 0.5s frequency at which the Magnitude Ratio of the controller is 1, is (A)
0.5 0.2
(B)
(C)
0.2 # 0.5
(D)
@. The
+ 0.2s
0.2 0.5 1 0.2 # 0.5
The block diagram of an integrating level process is given below. For unit step change in the set point ∆h set = 1 with ∆d = 0 , the offset exhibited by the system is
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(A)
INSTRUMENTA INSTRUMENT ATIONANDPROCESSCONTROL
K c 1 + K c
(C) 0 Q. 74
(B)
1 1 + K c
(D)
2K c 1 + K c
A second order system can be obtained by connecting two first order systems 1 1 in series. The damping ratio of the resultant second order and τ s s + 1 τ 1 s + 1 system for the case t 1 = Y t 2 will be (A) > 1 (B) = 1 (C) < 1 (D) = t 1 /t 1
^
h
^
h
Y N A P ^ h^ h O O M C & A I D O N © YEAR 2000
Q. 75
Q. 76
Q. 77
Q. 78
The unit step response of the transfer function steady state asymptotically after (A) a monotonic increase (B) a monotonic increase (C) initially increasing and then decreasing (D) initially decreasing and then increasing
2s − 1 3s + 1 4s + 1
ONE MARK
reaches its final
The unit step response of the transfer function 2 1 s + 2s + 3 (A) has a non-zero slope at the origin (B) has a damped oscillatory characteristic (C) is overdamped (D) is unstable
Select the correct statement from the following. (A) The frequency response of a pure capacity process is unbounded (B) The phase lag of a pure time dela delay y system decreases with increasing frequency (C) The amplitude ratio of a pure capacity process is inversely proportional to the frequency (D) The amplitude ratio of a pure time delay system increases with frequency For a feedback control system to b bee stable, the (A) roots of the characteristic equation should be real (B) poles of the closed-loop transfer function should lie in the left half of the complex plane (C) Bode plots of the corresp corresponding onding open-lo open-loop op transfer function should monotonically decrease (D) poles of the closed-loop transfer function should lie in the right half of the complex plane
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YEAR 2000
TWO MARKS
^
+
h
^s h ^ s h +1
Q. 79
The initial value t = 0 of the unit step response resp onse of the transfer function is (A) 0 (B) 1/2 (C) 1 (D) 2
Q. 80
The time constant of a unity gain, first order plus time delay process is 5 min . If the phase lag at a frequency of 0.2 rad/ min is 60c, then the dead time (in min ) is (A)
5π 12 π
(B)
π
6 π
Y N A P M O & & C A I D O N © (C)
12
(D)
3
**********
2 +1
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ANSWER KEY INSTRUMENTATION AND PROCESS CONTROL
1
2
3
4
5
6
7
8
9
10
(C)
(B)
(D)
(C)
(B)
(C)
(C)
(C)
(B)
(D)
11
12
13
14
15
16
17
18
19
20
(B) 21
(D) 22
(D) 23
(A) 24
(A) 25
(A) 26
(D) 27
(A) 28
(C) 29
(C) 30
(*)
(D)
(A)
(D)
(B)
(C)
(D)
(A)
(A)
(B)
31
32
33
34
35
36
37
38
39
40
(D)
(D)
(B)
(A)
(A)
(A)
(D)
(C)
(D)
(A)
41
42
43
44
45
46
47
48
49
50
(A)
(D)
(A)
(B)
(D)
(B)
(C)
(B)
(C)
(D)
51
52
53
54
55
56
57
58
59
60
(D)
(C)
(D)
(C)
(C)
(C)
(C)
(A)
(B)
(C)
61
62
63
64
65
66
67
68
69
70
(B)
(D)
(C)
(A)
(C)
(A)
(C)
(C)
(D)
(C)
71 (A)
72 (D)
73 (C)
74 (A)
75 (C)
76 (B)
77 (C)
78 (B)
79 (B)
80 (A)
Y N A P O O M C & A I D O N ©
