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UNIVERSITY COLLEGE LONDON

EXAMINATION FOR INTERNAL STUDENTS

MODULE CODE : CENG3OOIASSESSMENT : CENG3001APATTERNMODULE NAME : Process Dynamics and GontrolDATE : 24-Apr-08TIME :14:30TIME ALLOWED : 3 Hours 0 Minutes

2007 | o8-cENG300 1 A-00 1 -EXAM-4 1@2007 University College London TURN OVER

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Answer FOUR questions,TWOfrom Part A and TWOfrom Part B.Onlj, the first TWO answers from each part will be marked. -'ALL questions carry a total of 25 MARKS each, distributed as shown llPART A.l. a) Define what is meant by the stability of a system. I2l

b) What are poles in relation to process control and how can they assist in thequalitative analysis of the stability of system responses? What is the criterionfor a stable response? I4lc) A first order system with the following transfer function:

G-= 5" 0.ls+lis to be controlled using a proportional-integral controller. The final controlelement has a transfer function Gr : 7 and the transfer function of themeasuring device is:

G^= t^s*7i)If K^ and r^ are both equal to 1, use the Routh-Hurwitz stability criterion toshow that the general condition which must be satisfied by the controller gain,Kr, and integral time, q, for the system to remain stable is:

0.trilt*sr")> o.sK.t8lii) Setting Kr= | Nrd q: 0.1, examine the effect of changing r^ andK. on thestability of the closed loop response.

iii) Based on the result of (ii), comment on the effect that the measurementdynamics have on the stability of the closed loop response and the reason forthis in relation to the type of controller used. 121iv) Comment on and sketch the expected closed loop responses for this systemfor the following two cases: I4lI ) K, increaSes, z7 remains constant2) q decreases, K, remains constant

Question I continued overCONTINUED

K^

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The Routh-Hurwitz Arrav:Row:

I23

45

n+l wr w, w,

ao a2al a3Ar A2Br 82Cr C2

a4 a6a5 a'l

A3B3

c3

where:

^ dldz - dod3Al =-t atA,a, -a,AtI>r =

-.

'Ar

^ dtd4 - 303Stl1 =

-,

alArar -atA,E1=--Al

^ 3td6 - aodTA3 =- al

BrAz -ArBzvl - ----------:-- t v2 -'Bletc....

BlA3 - Al83Br

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., A surge tank system is to be installed as part of a pilot plantinitial proposed design has a configuration as shown in Figure 1.5 metres in height and 3 metres in diameter. The designq;= 13.5 m'min-'.q, (m3 min-r;

facility. TheEach tank isflowrate is

Figure 1.

Assuming that the valves on the exit lines act as linear resistances (i.e.qt: hrlRl and q2 : hzlRz) and that they are adjusted so that each tank is halffull at the nominal design condition of qi:13.5 m'min-':a) Find the value of the resistances Rr and Rz t5lb) Show that the transfer function relating the level in tank 2 to the inletflowrate q; (in terms of deviation variables) is second order, that the process iscritically damped and that the value of the time constant is 1.31 min and thegain is 0.185.An improved design is suggested, namely replacing the two-tank system witha single tank that is 4 metres in diameter, buj has the same total volume (i.e.V:V1+V). The tank is half full at qi: 13.5 m' min''.c) Which surge system (two-tank or single tank) can handle the largest stepchange in qi,? Il2l

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3. a) Explain, briefly, what is offset and why there is always offset associatedwith proportional-only control. ' I4lb) Show, graphically, the difference between the offset in set-point trackingand disturbance rejection when proportional-only control is used on a firstorder lag process with a unit step change to the input function.c) For which situations would you introduce integral control?

l2lI2l

The tank shown in Figure 2(a) is represented by a first-order lag transferfunction, Gp(s), with static gain of 2. The height of the tank is 5 meters and thediameter is 3 meters. At steady state the level of liquid in the tank is 3.5meters. The valve on the exit line acts as a linear resistance, i.e. Fo : h/R,where R is the resistance to flow.d) Stating all your assumptions, find the value of the process time constant, zr.I4le) Show that, if there is a unit step change (increase) in 4 the tank willoverflow. t3lF, (-'s-t)

r"(-"-t)Figure 2(a)r' (*3 r-t)

Fo(."-t)Figure 2(b)A feedback control system is now added to the tank, as shown in Figure 2(b).Assuming that the transfer functions of valve and measuring device are bothequal to I and KGf -:!- , Kd: Ko and Kr:lT^S + I

Question 3 continued overCONTINUED

onuollerh CN

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f) Show that, by adding a proportional-only controller, the tank now does notoverflow when there is a unit step change (increase) in Ft and find the value ofthe offset. Islg) Show, by adding a proportional-Integral controller, that the order of theclosed loop response is increased and that the offset is eliminated. t5I

PART B4. A process controlled by a feedback loop is known to exhibit first order

dynamics and contains a time delay. The process gain is Kp, the time constantis r, and the dead time e. The dynamics for the valve and measurement can beneglected. The controller is a proportional controller with gain K". Adisturbance d(s) with transfer function Ga(s) is present.a) Set up the block diagram for the closed loop system. I2lb) Find the transfer function relating set point and load changes with theoutput variable. I2lc) Find expressions for the amplitude ratio and the phase shift for the openloop process consisting of the process and the proportional controller. 141Assuming no disturbance and keeping the controller gain at K" : 1, anexperiment is performed to determine the time constant r, and the time delay14 of the process. It is found that the overall process gain is 2 and the crossoverfrequency for the process is @ro= 20 rad min-'.d) At the crossover frequency, the amplitude ratio is equal to 0.0198. What isthe process time constant ro? 16le) What is the process deadtime ra? 16l0 With the values for the time constant q and the time delay ra of the processfound above, sketch the open loop response for the process (without thecontroller) to a unit step in the input. Indicate on your sketch the process gainKo, the time constant r, and the dead time e. Isl

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5. a) Vapour feed to an adiabatic tubular reactor is heated to about 370oC in afumace, as illustrated in Figure 3. The reaction in the reactor is endothermic.The exit temperature of gas leaving the reactor is to be controlled at 31OoC.Draw an instrumentation and control diagram that accomplishes the followingobjectives:l) Feed is flow controlled.2) Fuel gas is flow controlled and ratioed to the feed rate.3) The fuel to feed ratio is cascaded with a furnace exit temperature controller.4) The set point of the furnace exit temperature controller is adjusted by areactor exit temperature controller.5) Furnace exit temperature is not to exceed 400oC.6) High furnace stack-gas temperature should override the fuel gas controlvalve. [10]

Fuel gas

Figure 3. Furnace heating feed to adiabatic tubular reactor.b) The heated tank shown in Figure 4 (over) is known to be subject todisturbances in the feed temperature. What would be the appropriate measuredand manipulated variables that would be chosen for:i) A feed-back controller?ii) Feed-forward controller?What are the main advantases and disadvantases of feed-forward controllers?

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Question 5 continued overCONTINUED

tq

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-_-+ Fo, To

Figure 4. Heated tankc) Consider the cascade system illustrated in Figure 5. The transfer functionsare given by:

F,, T,

c-= 4-P (2s+1)(4s+1)'IGdt = rr;' G dz = 7' G-t

G.,= 5' s+l= 0.05, G rz =0.2

i) Find the transfer function for the inner, or secondary, loop of the cascadesystem. What is the main purpose of the secondary loop?ii) Assume a proportional controller is used in the inner loop, l.e. Gc2 : Kcz.Find the characteristic equation for the whole cascade system.iii) What is the typical controller tuning procedure for a cascade controlsystem? I10l

Figure 5. Cascade block diagram.

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6. a) Consider the continuous stirred tank reactor (CSTR) shown in Figure 6. Theinlet flow rate Fl is used to control the product concentration Ct floop l) andthe coolant flow rate Fcw to control the tank temperature I (loop 2). The inputstream is coming from an upstream unit and might vary both in concentrationCti and temperature I,.i) Explain how the two control loops may interact for this system.ii) Explain why interactions in multivariable processes are undesirable from acontrol point of view.

I7lTiti,,,

Loop4.I (CC)\-/Arr iFcw

Figure 6. Control loops for CSTR.b) It is proposed to implement heat integration on the exothermic reactorprocess given in Figure 7.i) Propose a heat integration scheme for this process.ii) What is the main potential benefit from the heat integration scheme?iii) What are the potential control problems associated with the heatintegration scheme?

I6lHotoil

Coldfeed HotfeedI

Cold oilFigure 7. Exothermic reactor with feed pre-heater.

Hotproduct

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c) Control valves and Safety Interlock System (SIS):i) Pneumatic control valves are to be specified for the applications listedbelow. State whether a Fail-Open or a Fail-Closed valve should be specifiedfor the following manipulated variables and give reason(s).l. Steam pressure in a reactor heating coil2. Flow of effluent from a wastewater holding tank into a river3. Flow of cooling water to a distillation condenserii) What is the purpose of a Safety Interlock System (SISXiii) Why must the Safety Interlock System (SIS) be independent of theregulatory control system?

t6ld) A2x2 process is given by: t1l, =

-|ft1t'-lll1s+1 0.ls+1-0.2 0.8V" =

-tli,---lli"0.5s+l's+l '

The Relative Gain Array (RGA) of the process is:

*oo = [o't o']10.2 0 81The manipulated variable z7 is used to control y7 in control loop I and mz tocontrol y2 inloop 2.i) Do dynamic considerations suggest the same pairing?ii) Assume loop I is open. Based on the values of the RGA, sketch the openloop time response in y 1 to a unit step in m 1 for the following situations:1. The second loop is open and m2 is constant2. Both loops are closed Mdyt is constant

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