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THE UNIVERSITY OF THE WEST INDIES

EXAMINATIONS OF APRIL/MAY 2000

Code and Name of Course: CH26B Process Dynamics and Con ro! I Paper:

Date and Time: Duration: 3 hrs

INSTRUCTIONS TO C!NDID!TES: T"is paper "as " pa#es and " $uestions

Ca!c#!a ors may $e #sed in %is e&amina ion' T%ey m#s $e si!en ( cord!ess and non)*ro+ramma$!e'Ca!c#!a ors ,i!! $e e&amined o ens#re %a %ey com*!y ,i % %ese re-#iremen s'

Ans,er -#es ions .( 2( ( and ,o o -#es ions 1( ( 3( "'

.' For the following transfer functions, find (as appropriate) the time constant , dampingcoefficient , and steady-state gain . p K

(a) 164

)(+

=

s sG

(b) 246)( 2 ++=

s s sG

(c) !24)( 2 ++

=

s s sG

"10 marks #

2' Figure $2 is a feedbac% control bloc% diagram which depicts the proportional control of afirst-order-plus-deadtime process.

Figure $2 - &roportional feedbac% control

(a) 'eri e the closed-loop transfer function )()( s R sY and state the characteristic

e*uation. T%e 4ni5ersi y o %e 6es Indies Co#rse Code C7238 .999/2000

DO NOT 6RITE ON T7E 8AC: OF T7IS S7EET; 4SE ONE SIDE ONLY

INSTR4CTIONS; +ach page of this draft must be signed by the /+0 3 + 5 +0. 7ompleted forms should be handed to the 5ssistant0egistrar (+8aminations). he + +0 59 + 5 +0 is re*uested to sign the draft paper and return it with comments, if any, to the 5ssistant0egistrar (+8aminations).

.........................................:::::.. .........................................:::::::..First +8aminer ni ersity +8aminer

........................................:::::: ::::::::::::::::::econd +8aminer +8ternal +8aminer (where applicable)

'ate; 2

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(b) 7alculate the offset which the control loop would e8hibit following a unit stepincrease in setpoint. =ow would you modify the structure of the feedbac%

controller in order to produce a control system which asymptotically trac%s stepsetpoint changes>

(c) 0eplace the delay term in the characteristic e*uation deri ed in 2(a) with the &ad?appro8imation

s

se

d

d d s

)2(1)2(1

+

+stimate the ma8imum proportional gain max K for which the closed loop systemremains stable. n doing so, you may wish to ma%e use of the 0outh array

Row1

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' Figure $ .1 illustrates a cascade control scheme for the le el of li*uid in a cylindricalsurge tan% of cross-sectional area A.

Figure $ .1 - 9e el-flow cascade control

(a) Ahy are surge essels often installed between operating units in the chemicalindustries> s tight regulation of surge tan% le els normally re*uired>

(b) he effluent flow control al e is air-to-open, i.e. fail-shut. hould the direction of the flow controller FC be re erse (increase decrease) or direct (increase increase)>

hould the le el controller LC be configured as re erse-acting or direct-acting>

(c) Ahat are the ad antages and disad antages of the cascade control scheme of Fig.$ .1 as compared to the strategy of Fig. $ .2, in which the le el controller directly manipulates the effluent flow control al e>

Figure $ .2 - 9e el control by manipulation of effluent control al e

T%e 4ni5ersi y o %e 6es Indies Co#rse Code C7238 .999/2000

DO NOT 6RITE ON T7E 8AC: OF T7IS S7EET; 4SE ONE SIDE ONLY

INSTR4CTIONS; +ach page of this draft must be signed by the /+0 3 + 5 +0. 7ompleted forms should be handed to the 5ssistant0egistrar (+8aminations). he + +0 59 + 5 +0 is re*uested to sign the draft paper and return it with comments, if any, to the 5ssistant0egistrar (+8aminations).

.........................................::::::::: .........................................:::::::..First +8aminer ni ersity +8aminer

.........................................:::::::::. :::::::::::::::::::econd +8aminer +8ternal +8aminer (where applicable)

'ate; 2

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(d) 'eri e the plant transfer function describing the response of the surge tan% le el tochanges in the outlet olumetric flowrate when the 97 in Fig. $ .1 is running in

manual. t may be assumed that the inlet flowrate remains constant at its initialsteady-state alue ))(( isi qt q = and that the dynamics of the flow control loopare negligible (that is, the outlet flowrate )( t q o perfectly trac%s operator changesin the FC setpoint).

(e) how that Bero offset would be obtained following a unit step increase in le elsetpoint using proportional-only le el control (i.e. when the LC in Fig. $ .1 is a

proportional controller operating in automatic mode)

"20 marks #

1' 5 water heater in a fibre washing plant is controlled with a proportional controller and thetemperature of the water lea ing the unit is recorded in the plant data historian. hethermocouple is calibrated for the scale @< F to 1@< F and the controller operates with a2< psi range of air pressure. he set point of the controller is fi8ed at the desiredtemperature of 1

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Figure $6 - i8 tan%s in series

"25 marks #

"' wo isothermal well-stirred reactors are connected by a pipe as shown in Fig. $!. singthe symbols indicated, deri e the transfer function relating the concentration of the inletfeed )( < AC to that of the outlet of the second tan% )( 2 AC and sol e for the response toa unit step disturbance in .< AC he reaction in each tan% is irre ersible and first order;

!k

A

=ence the mass rate of disappearance of component A is )(11 t C " k A in tan% 1 and)(22 t C " k A in the second tan%. he flows and olumes are constant and there are no

thermal effects. 3ou may assume that no reaction or mi8ing occurs in the transfer pipeconnecting the two essels.

T%e 4ni5ersi y o %e 6es Indies Co#rse Code C7238 .999/2000

DO NOT 6RITE ON T7E 8AC: OF T7IS S7EET; 4SE ONE SIDE ONLY

INSTR4CTIONS; +ach page of this draft must be signed by the /+0 3 + 5 +0. 7ompleted forms should be handed to the 5ssistant0egistrar (+8aminations). he + +0 59 + 5 +0 is re*uested to sign the draft paper and return it with comments, if any, to the 5ssistant0egistrar (+8aminations).

.........................................::::::::: .........................................:::::::..First +8aminer ni ersity +8aminer

.........................................:::::::::. :::::::::::::::::::econd +8aminer +8ternal +8aminer (where applicable)

'ate; 2

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Figure $! - sothermal 7 0s in series

"25 marks #

END OF