NODIA AND COMPANY. GATE SOLVED PAPER Chemical Engineering Instrumentation and Process Control. Copyright By NODIA & COMPANY

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1 No part of thi publication may be reproduced or ditributed in any form or any mean, electronic, mechanical, photocopying, or otherwie without the prior permiion of the author. GATE SOLVED PAPER Chemical Engineering Copyright By NODIA & COMPANY Information contained in thi book ha been obtained by author, from ource believe to be reliable. However, neither Nodia nor it author guarantee the accuracy or completene of any information herein, and Nodia nor it author hall be reponible for any error, omiion, or damage ariing out of ue of thi information. Thi book i publihed with the undertanding that Nodia and it author are upplying information but are not attempting to render engineering or other profeional ervice. NODIA AND COMPANY B-8, Dhanhree Tower It, Central Spine, Vidyadhar Nagar, Jaipur Ph : enquiry@nodia.co.in

2 Year 0 One Mark Q. Match the proce parameter in Group I with the meauring intrument in Group II. Group I Group II P. Flame temperature I. Thermocouple Q. Compoition of LPG II. Radiation pyrometer R. Liquid air temperature III. Ga chromatograph P-III, Q-I, R-II (B) P-I, Q-III, R-II (C) P-II, Q-III, R-I (D) P-II, Q-I, R-III Q. The range of tandard current ignal in proce intrument i 4 to 0 ma. Which one of the following i the reaon for chooing the minimum ignal a 4 ma intead of zero? To minimie reitive heating in intrument (B) To ditinguih between ignal failure and minimum ignal condition (C) To enure a maller difference between maximum and minimum ignal (D) To enure compatibility with other intrument Year 0 Two Mark Q. 3 The following diagram how a CSTR with two control loop. A liquid phae, endothermic reaction i taking place in the CSTR and the ytem i initially at teady tate. Aume that the change in phyical propertie of the ytem are negligible. TC = Temperature controller, LC = Level controller TT = Temperature tranmitter, LT = Level tranmitter V and V = Control valve Which one of the following tatement i true? Changing the level controller et point affect the opening of V only (B) Changing the temperature controller et point affect the opening of V only (C) Changing the temperature controller et point affect the opening of both V and V

3 (D) Changing the level controller et point affect the opening of both V and V Statement or Linned Aner Q 4 and 5 : A PID controller output p^th, in time domain i given by de^t h pt ^ h = et ^ h+. 5 # et ^ h + 5 where, e^th i the error at time t. The tranfer function of the proce to be controlled i Gp ^h = 0 ^00 + h. The meaurement of the controlled variable i intantaneou and accurate. Q. 4 The tranfer function of the controller i 5 ^ 4 h 3 (B) 5 ^ 4 (C) h 4 (D) 0 t 5 ^ h 3 5 ^ h 4 Q. 5 the characteritic equation of the cloed-loop i (B) = 0 (C) = 0 3 (D) = 0 Year 00 One Mark Q. 6 Match the location of the pole/zeroe in the -plane lited in Group I with the ytem repone characteritic in Group II. Group I Group II P. Pole in the right half plane. Stable repone Q. Pole at origin. Integrating repone R. Zero in the right half plane 3. Invere repone 4. Invere repone Code P Q R 3 (B) 3 4 (C) 4 (D) 4 3 Q. 7 Flow meauring intrument with different pecification (zero and pan) are available for an application that require flow rate meaurement in the range of 300 Lh / to 400 Lh /. The appropriate intrument for thi application i the one whoe pecification are zero = 75 Lh /, pan = 50 Lh / (B) zero = 375 Lh /, pan = 00 Lh / (C) zero = 75 Lh /, pan = 50 Lh / (D) zero = 475 Lh /, pan = 00 Lh / Q. 8 The tranfer function G^h whoe aymptotic Bode diagram i hown below, i

4 0 + (B) - 0 (C) + 0 (D) 0 - Year 00 Q. 9 A block diagram for a control ytem i hown below. Two Mark the teady tate gain of the cloed-loop ytem, between output Y^h and et point R^h, i 5/9 (B) 4/9 (C) /3 (D) /9 Q. 0 Conider the cacade control configuration hown in the figure below: The ytem i table when K c, i 3/4 (B) (C) 5/4 (D) 3/ Q. Conider the proce a hown below: A contant head pump tranfer a liquid flow, a tank maintained at 0 pi to a reactor operating at 00 pi, through a heat exchanger and a control valve. At the deign condition, the liquid flow rate i 000 L/min, while the preure drop acro the heat exchanger i 40 pi, and that acro the control valve i 0 pi. Aume that the preure drop acro the heat exchanger varie a the quare of

5 the flow rate. If the flow i reduced to the control valve i 30 pi (C) 80 pi 500 L/min, then the preure drop acro (B) 50 pi (D) 50 pi Year 009 One Mark Q. Which one of the following enor i ued for the meaurement of temperature in a combution proce ^T > 800cCh Type J thermocouple (B) Thermitor (C) Reitance temperature detector (D) Pyrometer Q. 3 The root of the characteritic equation of an underdamped econd order ytem are real, negative and equal (B) real, negative and unequal (C) real, poitive and unequal (D) complex conjugate Year 009 Q. 4 The invere Laplace tranform of i -t/ t e - - e t/ (B) e - e -t -t/ (C) e - e - (D) e - - e - -t Two Mark Q. 5 The characteritic equation of a cloed-loop ytem uing a proportional controller with gain K c i Kc = 0 At the onet of intability, the value of K c i 35/3 (B) 0 (C) 5/3 (D) 0/3 Q. 6 The block diagram for a control ytem i hown below. For a unit tep change in the et point, R^h, the teady tate offet in the output Y ^ h i 0. (B) 0.3 (C) 0.4 (D) 0.5 Q. 7 For a tank of cro-ectional area 00 cm 3 and inlet flow rate (Q i in cm / ), 3 the outlet flow rate (Q 0 in cm / ) i related to the liquid height (H in cm) a Q0 = 3 H (ee figure below).

6 H^h Then the tranfer function (overbar indicate deviation variable) of the Q i ^ h 3 proce around the teady tate point, Qi = 8 cm / and H = 36 cm, i (B) (C) 3 (D) Year Q. 8 The unit impule repone of a firt order proce i given by e time contant of the proce are, repectively 4 and (B) and (C) and 0.5 (D) and t Two Mark. The gain and Q. 9 A unit tep input i given to a proce that i repreented by the tranfer function ^ + h. The initial value t = 0 + ^ h of the repone of the proce to the tep input ^ + 5h i 0 (B) /5 (C) (D) 3 Q. 0 A tank of volume 05. m 3 and height m ha water flowing in at 005. m 3 /min. The outlet flow rate i governed by the relation F out = 0. h where, h i the height of the water in the tank in metre and F out i the outlet flow rate in m 3 /min. 3 The inlet flow rate change uddenly from it nominal value of 005. m /min to m /min and remain there. The time (in min) at which the tank will begin to overflow i given by 0.8 (B).0 (C).73 (D) 3 Q. Which one of the following tranfer function correpond to an invere repone proce with a poitive gain? (B) ^. h (C) ^+ h^+ h (D) Q. Match the Lit I with Lit II and elect the correct anwer uing the code given below the lit. Lit I Lit II

7 P. Temperature. Hot wire anemometry Q. Preure. Strain gauge R. Flow 3. Chromatographic analyzer Code P Q R 3 (B) 4 3 (C) 4 (D) 4 4. Pyrometer Q. 3 Match the Lit I with Lit II and elect the correct anwer uing the code given below the lit. Lit I Lit II P. Ziegler-Nichol. Proce reaction curve Q. Underdamped repone. Decay ratio R. Feed-forward control 3. Frequency repone 4. Diturbance meaurement Code P Q R 3 4 (B) 3 (C) 3 4 (D) 4 Statement or Linned Aner Q 4 and 5 : The cro-over frequency aociated with a feedback loop employing a proportional controller to control the proce repreented by the tranfer function Gp ^ e h =, (unit of time i minute) ^τ + h i found to be 06. rad/min. Aume that the meaurement and valve tranfer function are unity. Q. 4 The time contant τ (in min) i.4 (B).9 (C) 3.3 (D) 5.39 Q. 5 If the control loop i to operate at a gain margin of.0, the gain of the proportional controller mut equal 0.85 (B).87 (C) 3.39 (D).50 Year 007 One Mark Q. 6 An operator wa told to control the temperature of a reactor at 60c C. The operator et the et-point of the temperature controller at 60. The cale actually indicated 0 to 00% of a temperature range of 0 to 00c C. Thi caued a runaway reaction by over preurizing the veel, which reulted in injury to the operator.

8 The actual et-point temperature wa 00c C (B) 60cC (C) 0c C (D) 00cC Year 007 Two Mark Q. 7 The dynamic model for a mixing tank open to atmophere at it top a hown below i to be written. The objective of mixing i to cool the hot water tream entering the tank at a flow rate q and feed temperature of T with a cold water feed tream entering the tank at a flow rate q and feed temperature of T 0. A water tream i drawn from the tank bottom at a flow rate of q 4 by a pump and the level in the tank i propoed to be controlled by drawing another water tream at a flow rate q 3. Neglect evaporation and other heat loe from the tank. The dynamic model for the tank i given a dv = q q q + 3, V dt = qt qt qt 0+ 3 (B) dv dvt ^ h = q q 4, = qt qt 4 (C) dv dvt ^ h = q q q + 4, = qt 0+ qt qt 4 (D) dv q q q3 q4 = + dvt ^ h, = q T T q T T 0 + ^ h ^ h Q. 8 Match the tranfer function with the repone to a unit tep input hown in the figure ^ 4 + h e

9 Code E C A D B (B) A B C D E (C) B A C E D (D) E A C B D Q. 9 Conider the following intrumentation diagram for a chemical reactor. C SP repreent a concentration et-point. Match the Lit I with Lit II and elect the correct anwer uing the code given below the lit. Lit I Lit II P. Control trategy. Feed forward control Q. Primary control variable. Cacade control R. Slowet controller 3. Concentration in the reactor S. Fatet controller 4. Reactor temperature 5. Jacket temperature 6. Concentration controller 7. Reactor temperature controller 8. Jacket temperature controller 9. Flow controller 0. Selective control Code P Q R S (B) (C) (D) Q. 30 The firt two row of Routh tabulation of a third order equation are Select the correct anwer from the following choice. The equation ha one root in the right half -plance

10 (B) The equation ha two root on the j -axi at d = j and - j. The third root i in the left half plane (C) The equation ha two root on the j -axi at = j and - j. The third root i in the left half plane (D) The equation ha two root on the j -axi at = j and - j. The third root i in the right half plane Common Data or Quetion 3, 3 and 33 : A cacade control ytem for preure control i hown in the figure given below. The preure tranmitter ha a range of 0 to 6 bar (g) and the flow tranmitter range i 0 to nm / h. The normal flow rate through the valve i 3. 4 nm / h correponding to the value of et point for preure = bar (g) and to give the flow, the valve mut be 40% opened. The control valve ha linear characteritic and i fall-open (air to cloe). Error, et point and control variable are expreed in percentage tranmitter output (% TO). Proportional gain i expreed in the unit of per cent controller output (CO% TO). Q. 3 The type of action for the two controller are direct acting for the preure control and direct acting for the flow control (B) indirect acting for the preure control and indirect acting for the flow control (C) direct acting for the preure control and indirect acting for the flow control (D) indirect acting for the preure control and direct acting for the flow control Q. 3 The bia value for the two controller, o that no offet occur in either controller are preure controller : 40%, flow controller : 60% (B) preure controller : 33%, flow controller : 67% (C) preure controller : 67%, flow controller : 33% (D) preure controller : 60%, flow controller : 40% Q. 33 Given that the actual tank preure i 4 bar (g) and a proportional controller i employed for preure control, the proportional band etting of the preure 3 controller required to obtain a et point to the flow controller equal to 54 nm / h i 50% (B) 00% (C) 50% (D) 87% Year 006 One Mark Q. 34 The control valve characteritic for three type of control valve (P, Q, and R

11 ) are given in the figure below. Match the control valve with it characteritic. 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 006 Two Mark Q. 35 The Laplace tranform of the input function X^th, given in the figure below, i given by e ^ - - h (B) e ^ + h (C) e ^ + + h (D) e ^ - - h Q. 36 A liquid level control ytem i configured a hown in the figure below. If the Level Tranmitter (LT) i direct acting and the pneumatic control valve i air to open, what kind of control action hould the controller (LC) have and why? Direct acting ince the control valve i direct acting (B) Revere acting ince the control valve i revere acting (C) Direct acting ince the control valve i revere acting (D) Revere acting ince the control valve i direct acting Q. 37 A -input, -output proce can be decribed in the Laplace tranform domain a given below.

12 ^τ + hy^ h = KU ^h+ KU^h ^τ + hy^ h = KU 3 ^h+ K4Y^h where U and U are the input and Y and Y are the output. The gain of the tranfer function Y^h/ U^h and Y^h/ U^h, repectively are K and K 3 (B) K and K3+ KK4 (C) K and K + K K (D) K and K + K K Q. 38 A proce i perturbed by a inuoidal input ut ^ h = Ain ω t. The reulting proce output i Y ^ h = KAω ^τ+ h^ + ω h. If y^0h = 0, the differential equation repreenting the proce i dy^t h dy^t h + τ yt = Ku t ^ h ^ h (B) τ + yt = KAu t ^ h ^ h dy^t h dy^t h (C) τ + yt = Ku t ^ h ^ h (D) τ c + yt ^ hm = KAu t ^ h Common Data or Quetion 39 and 40 : The block diagram of a cloed-loop control ytem i hown in the figure below. Y i the controlled variable, D i diturbance, Y SP i the et point, G, G, and G 3 are tranfer function, and K c i the proportional controller. Q. 39 The cloed-loop tranfer function Y ^ h/ D ^ h i given by GG 3 (B) G + ^GG 3+ GhKc + ^GG 3+ GhK (C) G3 (D) G3 + ^G+ GhGK 3 c + ^GG 3+ GhK c c Q. 40 Let G ^h = and G^h= G3^h= / ^ + h. A tep change of magnitude M i made in the et point. The teady tate offet of the cloed-loop repone Y i M (B) M + K c + Kc (C) MK ^ c h + K c (D) 0 Statement or Linned Aner Q 4 and 4 : For the ytem hown below, G ^ h =, G τ. + ^ h = and t= t. τ. +

13 When the ytem i excited by the inuoidal input repone Y i given by Y = Ain ^ωt + φh. Xt ^ h = in ω t, the intermediate Q. 4 If the repone of Y lag behind the input X by 45c and τ =, then the input frequency ω i (B) π /4 (C) 0 (D) - Q. 4 For the ame input, the amplitude of the output Z will be.00 (B) 0.6 (C) 0.4 (D) 0.3 Year 005 One Mark Q. 43 The unit tep repone of a firt order ytem with time contant τ and teady tate gain K p i given by -t/ τ Kp ^ - e h -t/ τ (B) Kp ^ - e h -t/ τ (C) Kp ^ - e h -t (D) Ke p / τ / τ Q. 44 An example of an open-loop econd order under-damped ytem i liquid level in a tank (B) U-tube manometer (C) thermocouple in a thermo-well (D) two non-interacting firt order ytem in erie Q. 45 The control valve characteritic i elected uch that the product of proce gain and the valve gain i a linearly increaing function of the manipulated variable (B) i a linearly decreaing function of the manipulated variable (C) remain contant a the value of the manipulated variable change (D) i an exponentially increaing function of the manipulated variable Q. 46 Cacade control come under the control configuration which ue one meaurement and one manipulated variable (B) more than one meaurement and one manipulated variable (C) one meaurement and more than one manipulated variable (D) more than one meaurement and more than one manipulated vgariable Year 005 Two Mark Q. 47 Match the proce variable in Group I given below with the meauring device in Group II. Group I Group II P. High temperature. Orifice meter

14 Q. Flow. Chromatograph R. Compoition 3. Radiation pyrometer 4. Bi-metallic Thermometer P-, Q-, R-3 (B) P-, Q-3, R- (C) P-3, Q-, R- (D) P-4, Q-, R- Q. 48 Given the characteritic equation below, elect the number of root which will be 4 3 located to the right of the imaginary axi = 0. One (B) Two (C) Three (D) Zero Q. 49 Given the proce tranfer function Gp = 4/ ^τ + h and the diturbance tranfer function Gd = ^τ + h, elect the correct tranfer function for the Feed Forward Controller for perfect diturbance rejection. ^τ + h (B) - (C) 05. ^τ + h (D) ^τ + h Q. 50 Given the proce tranfer function Gp = 0/ ^ h and controller tranfer function Gc = Kc and auming the tranfer function of all other element in the control loop are unity, elect the range of K c for which the cloed-loop repone will be table. K < 0 c (B) K < 00 c (C) K 00 < < 0 c (D) K > 0 c Q. 5 The value of ultimate period of ocillation P u i 3 min, and that of the ultimate controller gain K cu i. Select the correct et of tuning parameter (controller gain K c, the derivative time contant τ D in minute, and the integral time contant τ I in minute) for a PID controller uing Ziegler-Nichol controller etting. Kc =. ; τ I =., τ D = 3. (B) Kc = 5. ; τ I = 8., τ D = 05. (C) Kc = 5. ; τ I = 8., τ D = 05. (D) Kc =. ; τ I = 5., τ D = 038. Year 004 One Mark Q. 5 For the time domain function f^th = t, the Laplace tranform of # ft ^ h i given by 0 3 (B) 3 (C) (D) 3 t Year 004 Two Mark Q. 53 Match firt order ytem given in Group I with the appropriate time contant in Group II. Group I Group II P. Thermometer. ^mcph/ ^hah

15 Q. Mixing. q/ V 3. Vq / 4. ^hah/ ^mc p h P-4, Q- (B) P-4, Q-3 (C) P-, Q- (D) P-, Q-3 Q. 54 The experimental repone of the controlled variable y^th for a tep change of magnitude P, in the manipulated variable x^th i hown below. The appropriate tranfer function of the proce i ^QR / h τ d ^QPe / h ^QRe / h (B) τ d + 6 ^QP / h τ d ^PQ / h ^QPe / h ^QRe / h (C) (D) 6 ^QR / h τ d + Q. 55 Conider a ytem with open-loop tranfer function G ^ h = ^ + h^ + h^ 5 + h Match the range of ω (frequency) in Group I with the lope of the aymptote of the logar (amplitude ratio) veru log ω plot in Group II. Group I Group II P. 0 < ω < Q. ω > P-5, Q- (B) P-4, Q- (C) P-5, Q-3 (D) P-4, Q- Q. 56 The proce and diturbance tranfer function for a ytem are given by y ^ h Gp ^h = = m ^ h ^+ h^5+ h y ^ h and Gd ^h = = d ^ h ^+ h^5+ h The feed forward controller tranfer function that will keep the proce output contant for change in diturbance i

16 ^+ h ^5+ h (B) ^+ h ^5+ h (C) / (D) ^+ h^5+ h Q. 57 For the block diagram hown below, the characteritic equation i τ d τl^τp+ h+ KK c p^τl + he = 0 τ d (B) ^τm+ h^τp+ h+ KmKpe = 0 τ d (C) τl^τm+ h^τp+ h+ KcKmKp^τl + he = 0 τ d (D) ^τm+ h^τp+ h+ KK c mke p = 0 Year 003 One Mark Q. 58 Match the meaured proce variable with the lit of meauring device given below. Lit I (Meaured proce variable) Lit II (Meauring device) P. Temperature. Bourdon tube element Q. Preure. Orifice plate R. Flow 3. Infrared analyzer S. Liquid level 4. Diplacer device T. Compoition 5. Pyrometer Code P Q R S T (B) (C) (D) Q. 59 Suppoe that the gain, time contant, and dead time of a proce with the following tranfer function Gc ^h = 0 exp^ 0. h/ ^05. + h are known with a poible error of! 0% of their value. The larget permiible gain K c of a proportional controller need to be calculated by taking the value of proce gain, time contant and dead time a 8, 0.6, 0.08 (B), 0.6, 0. (C) 8, 0.6, 0. (D), 0.4, 0.08 Q. 60 Water i flowing through a erie of four tank and getting heated a hown in figure. It i deired to deign a cacade control cheme for controlling the temperature of a water leaving the Tank 4 a there i a diturbance in the

17 temperature of a econd tream entering the Tank. Select the bet place to take the econdary meaurement for the econdary loop. Tank (B) Tank (C) Tank 3 (D) Tank 4 Year 003 Two Mark Q. 6 Water i entering a torage 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 loe in the tank. The area of cro-ection of the tank i A c. The model that decribe the dynamic variation of water temperature in the tank with time i given a Q T T A h dt 0^ 0 h = c (B) QT QT Ah dt 0 0 = c (C) QT T A h dt dth ^ h ^ 0 h = c (D) QT T A h ^ 0 h = c Q. 6 Find the ultimate gain and frequency for a proportional controller in the cae of a proce having the following tranfer function. Gp ^h = ^4+ h^+ h^ + h ω = ; K 45 c = (B) ω = 7 ; K 46 c = (C) ω = ; Kc = 3 (D) ω = 7 ; K 45 c = 8 4 Q. 63 Match the type of controller given in Group II that i mot uitable for each application given in Group I.

18 Lit I P. Ditillation column bottom level to be controlled with bottom flow Q. Ditillation column preure to be controlled by manipulating vapour flow from the top plate R. Flow control of a liquid from a pump by poitioning the valve in the line Lit II. P control. Pl control 3. PID control S. Control of temperature of a CSTR with coolant flow in the jacket P-, Q-, R-, S-3 (B) P-, Q-, R-3, S-3 (C) P-, Q-, R-, S- (D) P-, Q-3, R-, S-3 Q. 64 In the cae of a feed forward control cheme, which of the following i not true?. It i inenitive to modeling error.. It cannot cope with unmeaured diturbance. 3. It wait until the effect of the diturbance ha been felt by the ytem before control action i taken. 4. It require good knowledge of the proce model. 5. It require identification of all poible diturbance and their direct meaurement. and 3 (B) and 4 (C) and 5 (D) 3 and 4 Q. 65 Temperature control of an exothermic chemical reaction taking place in a CSTR i done with the help of cooling water flowing in a jacket around the reactor. The type of valve and controller action to be recommended are air to open valve with the controller direct acting (B) air to cloe valve with the controller indirect acting (C) air to open valve with the controller indirect acting (D) air to cloe valve with the controller direct acting Year 00 One Mark Q. 66 The cloed-loop pole of a table econd order ytem could be both real and poitive (B) complex conjugate with poitive real part (C) both real and negative (D) one real poitive and the other real negative Q. 67 A firt order ytem with unity gain and time contant τ i ubjected to a inuoidal input of frequency ω =. The amplitude ratio for thi ytem i τ (B) 05. (C) (D) 05.

19 Year 00 Two Mark Q. 68 The frequency repone of a firt order ytem ha a phae hift with lower and upper bound given by 9-3, π C p (B), p 9- C π (C) 9-, 0 C (D) 0, π 9 C Year 00 One Mark Q. 69 The calibration data of a thermocouple with it cold junction at 0c C are given below. Hot junction temperature ^cch Thermo-emf ^mvh The hot junction of the thermocouple i placed in a bath at 80c C while it cold junction i at 0c C. What i the emf of the thermocouple? 36. mv (B) 080. mv (C) 46. mv (D) 43. mv Q. 70 A proce i initially at teady tate with it output y = for an input u =. The input i uddenly changed to at time t = 0. The output repone i y^th= + t. The tranfer function of the proce i (B) + (C) + (D) b + l Q. 7 The inherent characteritic of an equal percentage valve relating flow rate q with valve tem movement x are decribed by the equation dq dq = k (B) = kq dx dx dq (C) = dx q k dq (D) = kq dx Year 00 Two Mark Q. 7 An ideal PID controller ha the tranfer function 6+ / ^05. h+ The frequency at which the Magnitude Ratio of the controller i, i 05. (B) (C) 0. # 05. (D) 0. # 05. Q. 73 The block diagram of an integrating level proce i given below. For unit tep change in the et point het = with d = 0, the offet exhibited by the ytem i

20 (C) 0 Kc + K c (B) (D) + Kc Kc + K c Q. 74 A econd order ytem can be obtained by connecting two firt order ytem ^τ + h and in erie. The damping ratio of the reultant econd order ^τ + h ytem for the cae t =Y t will be > (B) = (C) < (D) = t / t Year 000 Q. 75 The unit tep repone of the tranfer function teady tate aymptotically after a monotonic increae (B) a monotonic increae (C) initially increaing and then decreaing (D) initially decreaing and then increaing Q. 76 The unit tep repone of the tranfer function ha a non-zero lope at the origin (B) ha a damped ocillatory characteritic (C) i overdamped (D) i untable One Mark reache it final ^3+ h^4+ h Q. 77 Select the correct tatement from the following. The frequency repone of a pure capacity proce i unbounded (B) The phae lag of a pure time delay ytem decreae with increaing frequency (C) The amplitude ratio of a pure capacity proce i inverely proportional to the frequency (D) The amplitude ratio of a pure time delay ytem increae with frequency Q. 78 For a feedback control ytem to be table, the root of the characteritic equation hould be real (B) pole of the cloed-loop tranfer function hould lie in the left half of the complex plane (C) Bode plot of the correponding open-loop tranfer function hould monotonically decreae (D) pole of the cloed-loop tranfer function hould lie in the right half of the complex plane

21 Year 000 Two Mark Q. 79 ^ + h The initial value ^t = 0 h of the unit tep repone of the tranfer function ^ + h i 0 (B) / (C) (D) Q. 80 The time contant of a unity gain, firt order plu time delay proce i 5 min. If the phae lag at a frequency of 0. rad/min i 60c, then the dead time (in min) i 5π (B) π 6 (C) π (D) π 3 **********

22 ANSWER KEY (C) (B) (D) (C) (B) (C) (C) (C) (B) (D) (B) (D) (D) (D) (C) (C) (*) (D) (D) (B) (C) (D) (B) (D) (D) (B) (D) (C) (D) (D) (B) (D) (B) (C) (B) (C) (D) (D) (C) (D) (C) (C) (C) (C) (B) (C) (B) (D) (C) (C) (C) (C) (D) (C) (D) (C) (C) (B) (C) (B) (B)