CHE3162.Lecture11 Cascade

8/11/2019 CHE3162.Lecture11 Cascade

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Learning Objectives

Understand when, why & how to apply

cascade control

Understand benefits of cascade control

loops

Draw a cascade block diagram and

analyse response

Be able to simplify cascade control loops


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What about the extra disturbance

to the heat exchanger?

Steam supply

pressure may

vary

Steam flow

will change

without valve

movement

This is a

disturbance

to a

manipulated

variable

Cold fluid

T change

Hot fluid

Steam

TC

101

TT

101

SP

Steam supply pressure Ps


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Cascade Control: Controllingfor Manipulated Variable

DisturbancesCold fluidT change

Hot fluid

SteamTT

101

TC

101

TSP

FC

101

FSP

Steam pressure disturbance

T control is the OUTER loop

F control is the INNER loop


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Heat exchanger control: Feedback

control


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Cascade control heat exchanger:

Option 1 Option 2Smith & Corropio


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Cascade control example

Smith & Corropio


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Cascade Control to jacketed reactor

Cooling water

Variablesupply P

Outer

Temp

Controller

InnerFlow

controller

TC101

SP

FC101


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Simplified Block Diagram

Simplify inner loopreplace with single

transfer function

GpYFs

1Tm

GD

++

SP E

+-

Kc(1+1/Tis) GVU

Kc2+

-

D2

+

Outer loopInner loop

KC2Gv1+KC2Gv

D11

1+KC2Gv


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Analysis of a Cascade Loop:

1 - Inside the Inner Loop

0.5s1

0.5

c2K1

0.5s1

0.5

c2K

F

sF

SP

FSP

IF Kc2= 10

0.083s1

0.83

F

sF

SP

0.5

1 +0.5s

UKc2

+ -

4e-2s

1 + 15s

TFs

1Tm

1e-s

1+5s

TD

++

Ts E

+-

Kc(1+1/Tis)

Ps

+


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1 - Equivalent Block for Inner Loop

FSP

0.083s1

0.83

F

sF

SP

4e-2s

1 + 15s

TFs

1Tm

1e-s

1+5s

TD

++

Ts E

+-

Kc(1+1/Tis)0.83

1 + 0.083s


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2Impact of second disturbance

1

sP

sF

If Kc2= 10

Fset0.5

1 +0.5s

UKc2

+ -

4e-2s

1 + 15s

TFs

1Tm

1e-s

1+5s

TD

++

Ts E

+-

Kc(1+1/Tis)

Ps

+

No cascade:

Unit change

in Ps gives unit

change in Fs

With cascade:

Unit change

in Ps gives 1/6change in Fs

(final value theorem)

Open loop TF:

0.5s1

0.5

c2K1

1

sP

sF

Closed loop TF:


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Reactor with preheater:

feedback controlMaintain constant temperature

in the reactor (controlled variable)

By manipulating fuel to the

preheater furnace

Feed temperature

Is a disturbance

Smith & Corropio


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Reactor with preheater:

Cascade control

Smith & Corropio


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FEEDBACK

CONTROL

Smith & Corropio


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CASCADE

CONTROLInner loop

= Preheater loop

Smith & Corropio


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Tuning Cascade loops

Inner loop is a normal feedback loop Tune by ZN ultimate frequency, ZN quarter decay, or

CohenCoon method

Then start tuning the outer loop : Set inner loop to automatic mode

Tune by ZN ultimate frequency

A one-step method (Austin and Lopez) also

existssee Smith Ch 9 and table 9.31 Find gain, timeconstant and deadtime of both loops Set parameters via table


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2005 EXAM: Question 2Solution slides by Prof Brisk

You have recently been assigned the task of examining acascade control system on a furnace. The previous engineer incharge of this system has told you that the transfer functionrelating gas flow to the burner, F, to the signal from the slavecontroller is first order with a gain of 0.2 and a time constant of

10 s. The transfer function relating the change in furnacetemperature , T, to the gas flow, F, is first order + dead timewith a gain of 10, a time constant of 100 s, and a dead time of1 s. In the absence of control it was found that when the gaspressure, P, increased by one unit, the gas flowrate reached

63% of its final value in 10 s, and the temperature increasedby 100oC at steady state. The master controller is PI and theslave controller is P.

The topic areas for this question are Block Diagrams,Cascade Control and Controller Tuning


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Solution to Q2a

Draw a block diagram of the system

10e-s

1 + 100s

TTs E

+-

Kc(1+1/Tis)

1ry loop

2ry loop

Kc2FU 0.2

1 +10s+-

Fs +

10

1+10sP

Product ofthese = 100

PI control: Kc(1+1/[Tis]) Note block diagrammust have signs shownfor feedback, setpoint

and disturbance


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Solution to Q2b / Learning item:

Closed Loop Transfer Eqns & Fns.Determine the closed-loop transfer functions F/FSand F/P asfunctions of the secondary controller gain Kc2, where FSis theinner controller set point

YKcGc U

Km

Gm

Ym

KdGdD

++

Ys E+

-

KvGv KpGp

D

mG

mKp

Gp

Kv

Gv

Kc

Gc

K1d

Gd

K

sY

mG

mK

pG

pKv

Gv

Kc

Gc

K1

pG

pKv

Gv

Kc

Gc

KY

Forward1+Forward*Feedback


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Solution to Q2b - continued

Kc2

FU 0.2

1 +10s+-

Fs

)s101/(K2.01

)s101/(K2.0

F

F

2c

2c

s

2c

2c

K2.0s101K2.0

s)]K2.01/(10[1

)K2.01/(K2.0

2c

2c2c

Do NOT leave in this form

Ts1

K

This standard form allowsclear physical interpretation


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Solution to Q2b - continued

Kc2

FU 0.2

1 +10s+-

Fs

)s101/(K2.01

)s101/(10

P

F

2c

2cK2.0s10110

s)]K2.01/(10[1

)K2.01/(10

2c

2c

+

10

1+10sP

Kv= 0.2 here

Ts1

K

We see immediately that theeffect of the disturbance is

reduced by (1 +KvKc2)


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Solution to Q2c

Draw a simplified block diagram of the cascade control system

+-

UKc2

0.2

1 +10s

10

1+10s

P

F+

FsTs E

+-

Kc(1+1/Tis)10e-s

1 + 100s

T


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Solution to Q2c

Draw a simplified block diagram of the cascade control system

Fs F+

Ts E

+-

Kc(1+1/Tis)10e-s

1 + 100s

T

s)]K2.01/(10[1

)K2.01/(K2.0

2c

2c2c

s)]K2.01/(10[1

)K2.01/(10

2c

2c

P

Equivalent TF for inner loop

EquivalentTF for inner loop

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CHE3162.Lecture11 Cascade