Chap 18 Marlin 2002

7/29/2019 Chap 18 Marlin 2002

1/37

CHAPTER 18: LEVEL CONTROL

When I complete this chapter, I want to be

able to do the following.

Determine the proper location and volume

of liquid inventories in a process

Determine the dynamics of typical level

processes

Tune level controllers for two typical

control objectives

7/29/2019 Chap 18 Marlin 2002

2/37

Outline of the lesson.

Levels, where are they?

Levels - good and bad aspects

Level dynamics

Level tuning Determining inventory size


7/29/2019 Chap 18 Marlin 2002

3/37

1

2

3

15

16

17

LC-1

LC-3

LC-2

dP-1

dP-2

T5

T6

TC-7

AC-1

PC-1

P3

F3

F4

F7

F8

F9

T10

L4


Where are liquid inventories?

Why do we design equipment with inventories?

7/29/2019 Chap 18 Marlin 2002

4/37


Where are liquid inventories?

1

2

3

15

16

17

LC-1

LC-3

LC-2

dP-1

dP-2

T5

T6

TC-7

AC-1

PC-1

P3

F3F4

F7

F8

F9

T10

L4

7/29/2019 Chap 18 Marlin 2002

5/37


Where are liquid inventories? Why?

1

2

3

15

16

17

LC-1

LC-3

LC-2

dP-1

dP-2

T5

T6

TC-7

AC-1

PC-1

P3

F3

F4

F7

F8

F9

T10

L4

Liquid on trays, allows

liquid-vapor equilibrium

Liquid mixing

reduces effects of

composition

disturbances

Flow to tower can be

constant in spite of

fluctuation in feed

flow

Allows uninterrupted

reflux and product

flows in spite of

variable condensation

Uninterrupted

fluid flow to

pump

Liquid covers the heat

exchanger transfer

area

7/29/2019 Chap 18 Marlin 2002

6/37


How do inventories affect performance of the

process containing the liquid?

Strongly Weakly Insignificant

Volume of

chemical reactors,

volume has strong

effect on

conversion

Fast material

degradation (reduce

residence time)

Equilibrium stages,

both phases must

be present, but

amount beyond

minimum does not

affect process

Heat exchangers,

must have contact

with area

Drums and tanks,no change to

material properties

But these inventories

have strong effects

on the other processes

influenced by the flows

from these inventories

7/29/2019 Chap 18 Marlin 2002

7/37


What are ++ and -- for having liquid inventories?

NEGATIVE ASPECTSPOSITIVE ASPECTS

Conclusion: ??

7/29/2019 Chap 18 Marlin 2002

8/37

7/29/2019 Chap 18 Marlin 2002

9/37


To design control, we

need to understand the

process dynamics

control objectives

algorithm & tuning

level sizing

Lets determine the

dynamics for each of the

designs

7/29/2019 Chap 18 Marlin 2002

10/37


Self-regulatory Non-self-regulatory

0 5 10 15 20 25 30 35 40 45-2

-1.5

-1

-0.5

0

Time

Level

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Time

Flow

out

0 5 10 15 20 25 30 35 40 45-2

-1.5

-1

-0.5

0

Time

Level

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Time

Flow

out

outin FFdt

dLA =

Fout does not depend on the level

outin FFdt

dLA =

Fout increases as level increases

Quick reminder of key property of dynamic process behavior

New steady stateNo new steady state

7/29/2019 Chap 18 Marlin 2002

11/37


0dt

dL

)( LKF

FFdtdLA

in

outin

=

=

21 PPKF

FFdt

dLA

in

outin

=

=

P1= pump head + gL

21 PPKF

FFdt

dLA

in

outin

=

=

P1

= P3

+ gL 0

0 5 10 1 5 20 2 5 3 0 35 4 0 4 5-2

-1.5

-1

-0.5

0

Time

Level

0 5 10 1 5 20 2 5 3 0 35 4 0 4 50

0.5

1

1.5

2

Time

Flow

out

Non-Self-regulatory

0 5 10 15 20 25 30 35 40 45-2

-1.5

-1

-0.5

0

Time

Level

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5

2

Time

Flow

out

Self-regulatoryConstant

0 5 10 1 5 2 0 25 30 3 5 40 4 5-2

-1.5

-1

-0.5

0

Time

Level

0 5 10 1 5 2 0 25 30 3 5 40 4 50

0.5

1

1.5

2

Time

Flow

out

Non-Self-regulatory 0

Determine if each level is self-regulatory or not

7/29/2019 Chap 18 Marlin 2002

12/37



process dynamics

control objectives

algorithm & tuning

level sizing

Lets determine the

control objectivesfor level control


LC

Fin

Fout

What is important?

The level

The manipulated flow

7/29/2019 Chap 18 Marlin 2002

13/37

7/29/2019 Chap 18 Marlin 2002

14/37

To design control, weneed to understand the

process dynamics

control objectives

algorithm & tuning

Lets determine the




process dynamics

control objectives

algorithm & tuning

level sizing

Lets determine the

algorithm & tuningfor level control


LC

Fin

Fout

1. Is the control in the figure

a. feedback

b. feedforward

c. neither

d. both

2. What makes control difficult?

7/29/2019 Chap 18 Marlin 2002

15/37


LC

Fin

Fout

1. Is the control in the figure

a. feedback

b. feedforward

c. neither

d. both

2. What makes control difficult?

Dead time makes feedback

difficult, but we see that

this process has negligibledead time!

Feedback: The flow out

has a causal effect on the

level.

Since this is feedback,

lets use the old

standard, PI control(D isnt needed).

7/29/2019 Chap 18 Marlin 2002

16/37

LC

D = Fin

MV = Fout

CV = L


Controller Tuning

Can we use the standard PI

tuning approach shown in

the schematic?

S-LOOP plots deviation variables (IAE = 608.1005)

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

Time

Ma

nipulatedVariable 0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1DYNAMIC SIMULATION

Time

ControlledVariable

Determine a model

using the process

reaction curve

experiment.

Kc TI

Determine the initialtuning constants from

a correlation.

0 20 40 60 80 100 1200

0.5

1

1.5


Time

ControlledVariable

0 20 40 60 80 100 1200

0.5

1

1.5

Time

ManipulatedVariable

Apply and fine tune

as needed.

IdttLL

T

tLLKtFt

SP

I

SPCout+

+=

0

'))'((1

))(()(

7/29/2019 Chap 18 Marlin 2002

17/37

LC

D = Fin

MV = Fout

CV = L



0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

Time

Ma

nipulatedVariable 0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1DYNAMIC SIMULATION

Time

ControlledVariable Cannot determine a

model using the

process reaction

curve experiment.

Kc TI

Cannot determine

the initial tuningconstants from

Ciancone (or Ziegler-

Nichols step)

correlation.

0 5 10 15 20 25 30 35 40 45Time

Level

0 5 10 15 20 25 30 35 40 45Time

Flow

out

Standard tuningcharts are not

applicable to a non-

self-regulating level.

The level process isunstable. Without

control, it never

reaches a new steady

state

7/29/2019 Chap 18 Marlin 2002

18/37

Gd(s)

GP(s)Gv(s)GC(s)

GS(s)

D(s)

CV(s)

CVm(s)

SP(s) E(s) MV(s)+

+

+

-LC

D = Fin

MV = Fout

CV = L


Lets build a model of the process with the controller, i.e, the closed-

loop system. We will ignore the fast sensor and valve dynamics.

Using block diagram algebra, we obtain

A = cross

sectional

area

)()(1

)(

)(

)(

sGsG

sG

sF

sL

PC

D

in+

=

With Gc(s) being eitherP-only of PI

For a non-self regulating level

AssGsG

DP1)()( ==

7/29/2019 Chap 18 Marlin 2002

19/37

LC

D = Fin

MV = Fout

CV = L


We substitute the appropriate models

for each process and controller to

obtain the following transfer function

models, which we can solve

analytically for a step disturbance!

A = cross

sectional

area

A

KTand

K

AT

ss

K

T

sF

sL

CI

C

I

C

I

in

)(

2

1

12)(

)(22

=

=

++

=

Proportional-only control

Proportional-integral control

1

1

)(

)(

+

=

sK

A

K

sF

sL

C

C

in

+=

+

+=

sTKsG

IdttLLT

tLLKtF

I

CC

t

SP

I

SPCout

11)(

'))'((1

))(()(0

[ ]CC

SPCout

KsG

ItLLKtF

=+=

)(

)()(

7/29/2019 Chap 18 Marlin 2002

20/37


Stable, first order

Never underdamped

Non-zero s-s offset

Stable, second order

Underdamped when < 1(We want overdamped!)

Zero s-s offset

P-only PI

=

c

KAt

Cin eKFtL

/

11)('

=

c

KAt

in etA

FtL

2/

)('

Disturbance step response Disturbance step response

[ ] ItLLKtF SPCout += )()( IdttLLT

tLLKtFt

SP

I

SPCout+

+= 0 '))'((

1))(()(

7/29/2019 Chap 18 Marlin 2002

21/37


P-only Tuning

Determine the expected maximum step disturbance size (Fmax) and

calculate the Kc to give the maximum allowed change in the level(Lmax) .

LC

Fout

Fmax

Lmax

Note, level does

not return to its

set point.

When is this O.K?

Kc = - (Fmax)/ (Lmax)

Fout = ??

[ ] ItLLKtF SPCout += )()(

7/29/2019 Chap 18 Marlin 2002

22/37


PI Tuning

Determine the expected maximum step disturbance size (Fmax) andcalculate the Kc and TI to give the maximum allowed change in the level

(Lmax). Set tuning so that damping coefficient, = 1.

LCFout

Fmax

Lmax

Note, level returns

to its set point.

Fout = ??

Kc = - 0. 736 (Fmax)/ (Lmax) TI = 4 (2) A/(-Kc)

Fout

IdttLL

T

tLLKtFt

SP

I

SPCout +

+=

0

'))'((1

))(()(

7/29/2019 Chap 18 Marlin 2002

23/37


Lets use these results for averaging and tight level control.

LC

Fin

Fout

P-only control: Kc = - (Fmax)/ (Lmax)PI Control: K

c= - 0. 736 (F

max

)/ (Lmax

) TI

= 4 (2) A/(-Kc

)

Averaging level control, Lmax 40% of maximum rangeTight level control, Lmax 5% of maximum range

7/29/2019 Chap 18 Marlin 2002

24/37



process dynamics

control objectives algorithm & tuning

Lets determine the




process dynamics

control objectives

algorithm & tuning

level sizing

Lets look again at the

process


How do we determine the proper vessel volume?

LC

Fin

FoutV = ?

That is a good question.

Averaging level control will notprovide improvement unless the

vessel is large enough!

7/29/2019 Chap 18 Marlin 2002

25/37


One key design goal: maintain the rate of change of themanipulated flow below a maximum when using averaging

tuning. This protects the downstream units from fast

disturbances.

LCFout

Fmax

max

dt

dFout

V = ?

max

2max )(84.1

=

dt

dF

FV

out

The equation is based on a PI controller

with the averaging tuning recommended

in this chapter.See Chapter 18 for derivation

IdttLLT

tLLKtF

t

SP

I

SPCout +

+= 0 '))'((

1))(()(

Lmax

7/29/2019 Chap 18 Marlin 2002

26/37



process dynamics

control objectives

algorithm & tuning

level sizing


LC

Fin

Fout

Now, we understand control of a single level!

How small can we make the levels?

Do we have a guideline?

7/29/2019 Chap 18 Marlin 2002

27/37


Process plants have many units in series. Inventory control behavessimilar to a series of tanks. How should they be controlled?

F0

LC LC LC

F1 F2 F3

Feed push with levels adjusting flows out

F0

LC LC LC

F1 F2 F3

Product pull with levels adjusting flows in

7/29/2019 Chap 18 Marlin 2002

28/37


For a series of levels, what is the importance of damping?

F0

LC LC LC

F1 F2 F3

Step

change

We see that flow variation increases with

number of levels in series

P-only control is not oscillatory

PI (=1) experiences overshoot PI (=0.5) experiences large oscillations

P-only

PI (=1)

PI (=0.5)

Best

Not acceptable

7/29/2019 Chap 18 Marlin 2002

29/37

CHAPTER 18: LEVEL CONTROL WORKSHOP 1

We can have a liquid inventory that is not controlled, if thevessel is large enough. Lets look at an example.

What is the minimum volume for

the storage tank?

Plot the level vs. time.

L

Fin

FoutTime (days)

Flow

rate

The flow in involves batches of 24,000 m3

delivered over 12 hours, with a batch

delivered every five days.

The flow out is the feed to the plant. It must

be continuous and have a constant value.

1/25

7/29/2019 Chap 18 Marlin 2002

30/37


The principles we have learned for liquid level control

apply to solid and gas inventories as well.

1. Think of an example in a process plant in which we need to have

an inventory of

a. (granular) solids

b. gas

2. Describe the storage equipment for each.

3. Select a sensor to measure the inventory for each

4. Determine whether the inventory is self-regulating or non-self-

regulating.

5. Sketch the process with control.

7/29/2019 Chap 18 Marlin 2002

31/37


Discuss how you determine the proper liquid

inventories for the following unit operations.

1. Liquid on the shell side of ashell and tube heat exchanger.

2. Liquid on a distillation tray

cooling

medium

TC

10

FC1

Bypass and

adjustable 3-way

mixing valve

1

2

3

15

16

17

LC-1

LC-3

AC-1

PC-1

F4

F7

F8

AC-1

7/29/2019 Chap 18 Marlin 2002

32/37


3. Liquid in a flash drum

4. Liquid in a CSTR

Feed

Vaporproduct

Liquid

productProcessfluid

Steam

F1

F2 F3

T1 T2

T3

T5

T4

T6 P1

LC

A1

L. Key

Discuss how you determine the proper liquid

inventories for the following unit operations.

L

F

T

A

7/29/2019 Chap 18 Marlin 2002

33/37


Calculate the level tuning for the situation described below.

Determine the tuning for tight and for averaging control.

LC

Fin

Fout

V = 50 m3

A = 25 m2

F = 1.5 m3/min

Fmax = 1.0 m3/min

For each tuning, what would be the maximum rate of change of the

manipulated flow for a step disturbance ofFmax = 1.0 m3/min?

7/29/2019 Chap 18 Marlin 2002

34/37

Lots of improvement, but we need some more study!

Read the textbook

Review the notes, especially learning goals and workshop

Try out the self-study suggestions Naturally, well have an assignment!


When I complete this chapter, I want to be

able to do the following.

Determine the location and volume of liquid

inventories in a process

Determine the dynamics of various level processes

Tune level controllers for both typical control

objectives

7/29/2019 Chap 18 Marlin 2002

35/37

7/29/2019 Chap 18 Marlin 2002

36/37

CHAPTER 18: SUGGESTIONS FOR SELF-STUDY

1. Storing hazardous materials increases the risk in case of

an accident. Search the WEB for information on the

incident at Bhopal, India. Discuss the effect of the

storage volume of methyl isocyanate on the number of

deaths. A good place to start is

http://www.unu.edu/unupress/unupbooks/uu21le/uu21le00.htm#Contents

2. You are designing a reflux drum for a distillation tower

that operates at 10 atm. How does the cost of a carbon

steel, horizontal drum depend on the volume?3. Discuss how you would monitor the performance of

averaging level control. Based on plant data, define

rules for fine tuning the controller.

7/29/2019 Chap 18 Marlin 2002

37/37

CHAPTER 18: SUGGESTIONS FOR SELF-STUDY

4. Inventories are provided for all essential materials.

Discuss how you would determine the proper storage

inventory for some key materials, such as

a. Blood for transfusions

b. Food, e.g., grains and rice

c. Water for a city

5. Describe the physical principles for sensors to measure

the inventory of liquids, gases, and solids.

Documents

Chap 18 Marlin 2002