tut - control and mathematical modelling solutions

8/13/2019 Tut - Control and Mathematical Modelling Solutions

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Tutorial

Control and Mathematical Modelling

1. Define the following terms:a) Load or disturbanceb) Manipulated variablec) Controlled variabled) Set pointe) Feedback controlf) Feedforward controlg) Cascade controlh) Ratio control

2. Consider the distillation column reboiler shown.Design a cascade control system to control thecolumn temperature using the reboiler steam flow

rate. The system must compensate for steam supply

pressure changes before it affects the temperature.

3. Sketch a control concept diagram for a chemicalreactor that is cooled by generating steam

Steam drum pressure iscontrolled by the valve in

the steam exit line Condensate flow is

ratioed to steam dlow

Steam drum liquid level iscontrolled by adjusting

the condensate to steam

ratio

Feed is flow controlled Reactor liquid level is

controlled by productwithdrawal

Reactor temperature is controlled by resetting the setpoint of the steampressure controller

4. One of the distillation column control strategies is termed the LBconfiguration.

This control scheme incorporates the following control loops


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a) level control of reflux drum by distillate flowrateb) level control of column base by energy input to reboiler (vapour flow - boilup)c) top product composition by reflux flowrated) bottom product composition by bottoms flowratee) pressure by flooded condenser methodDraw the control system based on the above.

5. Develop a separate model in each case for aCSTR in which the following elementary

reactions occur

a) b)

Assumptions:- The following variables have constant values in this problem: F, V, and

reactor temperature (heat transfer, work, and heat of reaction are all

negligible).

- The reactor is well mixed.

- The density is constant.

- Only reactant A (no product) exists in the feed to the reactor.

6. Consider the continuous stirred tank reactor shown below. An endothermicreaction,

A+BC

, takes place in the reactor (in the liquid phase). Thereaction is first order with respect to A and second order with respect to

B. The heat required for the reaction comes from steam that flows through

a jacket around the reactor. Constant densities may be assumed. Model the

system in order to find the state equations that define the dynamics of the

system assuming that only components A and B enter with the feed.

steam

TS

TS


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(A) The factor that is changed to keep a measured variable at set point.

(B) An undesired change in a factor that can affect the process variable.

(C) A value or range of values for a process variable that must be maintained to keep

the process running properly.

(D) A control operation that directly involves human action.

(E) A mathematical expression of a control function


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FF

FF

dt

dV

FFdt

Vd

i

i

ii

0

volumeanddensityconstantat

:balanceMass

Similarly

FF

FFdt

dV

FFdt

Vd

i

i

ii

0


:balanceMass

Similarly

FF

FFdt

dV

FFdt

Vd

i

i

ii

0


:balanceMass

AAAiA

AAAiA

AAiAiA

AAi

AAiAiAiA

rccV

Fdt

dc

VrFcFcdt

dcV

VrFcFcdt

dcV

dy

dVc

dt

Vcd

VrFcFcdtVcd

dtdn

:balanceAComponent

AAAiA

AAAi

A

AAiAiA

AAi

AAiAiAiA

ckccV

Fdt

dc

VckFcFcdt

dc

V

VckFcFcdt

dcV

dy

dVc

dt

Vcd

VrFcFcdt

Vcd

dt

dn

1

1

1

:balanceAComponent

BCC

BABB

ckcV

Fdt

dc

ckckcV

Fdt

dc

2

21

:balanceCComponent

:balanceBComponent

BAAAiA

BAAAiA

BAAiAiA

AAi

AAiAiAiA

ckckccV

Fdt

dc

VckVckFcFcdt

dcV

VckVckFcFcdt

dcV

dy

dVc

dt

Vcd

VrFcFcdt

Vcd

dt

dn

21

21

21

:balanceAComponent

BABB ckckc

VF

dt

dc21

:balanceBComponent


5/5

QTHcTHcTHcFTTcTHcTHcFdt

dH

QTHcTHcTHcFTTcThFdt

dH

QTFhThFdt

dH

dt

dH

dt

dU

dt

dE

UPKUE

nnnTHH

CCBBAAipiBBiiAAi

CCBBAAipi

iii

CBA

,,,

:balanceEnergy

VrFcTHVrFcFcTHVrFcFcTHdt

dTVc

dt

dH

THn

HTH

n

HTH

n

HVc

T

H

dtdn

nH

dtdn

nH

dtdn

nH

dtdT

TH

dtdH

CCCBBiBiBAAiAiAp

C

C

B

B

A

A

p

C

C

B

B

A

A

;;;

QTTcFTHTHTHrVdt

dTVc

QTTcFVrTHVrTHVrTHdt

dTVc

VrFcTHVrFcFcTHVrFcFcTHdt

dT

Vc

QTHcTHcTHcFTTcTHcTHcF

ipCBAp

ipCCBBAAp

CCCBBBiBAAAiAp

CCBBAAipiBBiiAAi

rrrccVekr CBART

E

oA B

2

p

iRp

ipRp

c

QTTFH

c

rV

dt

dTV

QTTcFHrVdt

dTVc

BBBiB rcc

VF

dt

dc

:BforSimilarly

CCC rc

VF

dt

dc

:CforSimilarly

tut - control and mathematical modelling solutions

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