Fuzzy Control of the Activated Sludge Wastewater Treatment Process

Tong, R.M., Beck, M.B. and Latten, A.

IIASA Professional PaperNovember 1979

Tong, R.M., Beck, M.B. and Latten, A. (1979) Fuzzy Control of the Activated Sludge Wastewater Treatment

Process. IIASA Professional Paper. Copyright © November 1979 by the author(s). http://pure.iiasa.ac.at/1202/ All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or

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FUZZY CONTROL OF TEE ACTIVATEDSLUDGE WASTEWATER TREATMENTPROCESS

R.M. Tong11. B. BeckA. Latten

November 1979PP-79-7

Professional Papers do not report on work of theInternational Institute for Applied SystemsAnalysis,but are produced and distributed by the Institute asan aid to staff members in furthering their profes-sional activities. Views or opinions expressedarethose of the author(s) and should not be interpretedas representingthe view of either the Institute orits National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSISA-2361 Laxenburg, Austria

M.B. BECK is a researchscientistat the International Institutefor Applied ｾ ｹ ｳ ｴ ･ ｭ ｳ Analysis, Schloss Laxenburg, 2361 Laxenburg,Austria.

A. LATTEN is the managerof ｾ ｨ ｩ ｴ ｬ ｩ ｮ ｧ ｨ ｡ ｲ ｮ TreatnentWorks, AnqlianWater Authority, Trowse, Norwich, United Kingdom.

R.M. TONG is with the Electronics ResearchLaboratory, Universityof California, Berkeley, California 94720, USA.

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PREFACE

Two previous papers (IIASA ProfessionalPapersPP-78-10and PP-79-3) have reported some of the results ｦ ｲ ｯ ｾ a smallcollaborativeproject investigating the modeling and controlof the activated sludge processof wastewatertreatment.This brief paper provides a more detailed evaluationof afuzzy controller for the activatedsludge process. Such anapproachto processcontrol utilizes the empirical operatingexperienceof the plant manager. ｾ ｾ ｯ ｳ ｴ conventional controlsystemdesign procedures,in contrast, are basedupon analysisof a model of processdynamic behavior. Given the currentlimitations in understandingand instrumentationof the acti-vated sludge process, fuzzy control appearsto be a particularlyappropriateapproachto adopt for processcontrol.

iii

ACKNOWLEDGEMENTS

The authors are grateful to the Anglican water Authorityfor their financial support in this project. One of theauthors (RMT) would also like to acknowledgethe financialsupport provided by a SRC/NATO PostdoctoralFellowship.

v

SUMMARY

The activatedsludge processis a commonly used methodfor treating sewage and waste waters. It is characterizedby a lack of relevant instrumentation,control goals thatare not always clearly stated, the use of qualitative infor-mation in decision making and poorly understoodbasic behaviormechanisms. In this brief paper we examine the behavior ofan experimentalfuzzy control algorithm constructedto reflectactual operationalpracticp.. We conclude that this algorithmdoes rather well and that a fuzzy controller would be auseful and practical way of regulating the activated sludgeprocess.

vii

1. !ntroduction.

Fuzzy controllers have been successfullyused in a

variety of applications (seeTong, 1977 for a review). In all

of these applications,however, the control goals were clearly

specified, accurateand reliable measurementsof the relevant

processvariableswere available and, perhapsmore importantly,

none of the controlled processeshad more than two inputs or

two outputs. It would be hard to argue, therefore, that these

were "difficult" control problems. Nonetheless,the success

has encouragedthe belief, at least amongst its advocates,

that the fuzzy approachcan be used on a wide variety of pro-

cesses.

In this ｾ ｡ ｰ ･ ｲ we report on some results ｦ ｲ ｯ ｾ a con-

tinuing study of the role of fuzzy set theory in the control

of the activatedsludge wastewatertreatmentprocess (ASP).

The ASP is characterizedhy a lack of relevant instrumentation,

control goals that are not always clearly stated, the use of

qualitative information in decision making and poorly under-

stood basic behavior mechanisms. As such, it appearsto be

an ideal candidatefor fuzzy control and is certainly a more

severe test of the methodology than previous applications.

Section two of the paper outlines the behavior of the ｾ ｓ ｐ

and highlights the principal control problems. Section three

discussesone particular controller with which we have experi-

mented and analyzes some of the resulting closed loop re-

sponses. We then make some general comments on the design of

fuzzy controllers.

-1-

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2. The Activated Sludge wastewaterTreatmentProcess.

The ASP is one of a number of unit processesused for the

treatnentof sewageand waste waters. The basic feature of the

processis the decompositionof complex dissolvedand suspended

organic substratesinto simple end-productssuch as carbon

dioxide and water. Decompositionis achievedby a hetero-

geneousculture of micro-organisms(the activatedsludge), which

in part utilize the waste organic substratesin the synthesis

of their own biological cell material.

Our studieshave been concernedprimarily with a particu-

lar ASP plant at the ｾ ｦ ｵ ｩ ｴ ｬ ｩ ｮ ｧ ｨ ｡ ｭ TreatmentWorks, Norwich,

England. This installation is shown diagramatically in Figure ｬ ｾ

If we consider only that part of the diagram within the dotted

lines, we see that there are two stagesin the overall process:

an aeration tank followed by a clarifier/settler. Correct

operationof the processrequires, among other things, the

following three items. First, the influent sewageentering

the processhas to be mixed intimately with the recycled sludge;

in principle there exist rangesof desirableproportions in

which substrate(sewage) and organism (sludge) should be mixed

(cashion, Keinath, and Schuk, 1977). Second, air is blown

into the Mixed liquor through diffusers placed along the base

of the tank; this gives the required agitation of the mixed

liquor, provides the necessaryaerobic environment for growth

of the sludge organisms, and can be a key factor in operational

control (Olsson and Andrews, 197C). Third, the settler must

effect good separationbetween the biological floc (sludge)

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and the clarified effluent; excessbiological solids in the

ASP ｾ｡ｹ be manipulatedby the removal of waste sludge. Recent

work on the application of automation and control to the ASP

is surveyedby Olsson (1977).

Local control action is taken at the Norwich ASP to help

achieve these aims. Thus, as shown in Figure 1, recycle sludge

ratio (defined as the ratio of influent flow rate, QI' to

recycled sludge flow rate, QR) is regulatedby feedforward

control of QR using measurementsof QI. Dissolved oxygen

(DO) in the aeration tank is regulatedby feedback control of

the airblowers using a measurementof DO. v]aste sludge flow,

Qw' is set by the plant manager.

An ASP that is performing as required will be producing

an effluent that meets some standard. In Britain, this is

simply a ｲ･｣ｯｾｾ･ｮ､｡ｴｩｯｮ that the total (S-day) biochemical

oxygen demand exertedby the effluent should be less than

20 gm-3 and that the amount of suspendedsolid material in the

-3effluent should be less than 30 gm . Whilst these are

hard constraintson the process,a plant managercan choose

to operateas close to them as he feels is practical. In

a real sense, therefore, there is Borne fuzziness associated

with thesevalues. There are secondarygoals, but these

will differ from installation to installation and will depend

primarily on the quality and type of sewage that the process

receives. However, one of the most important of these is

that ammonia in the effluent is kept at acceptablelevels.

The major disturbancesto the processare in the form of

fluctuations in the composition and flow of the influent.

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There are short term diurnal variations as well as long term

trends which together can easily produce changesof up to

50% in the averagequality of the influent.

Our control problem is thus simply stated. How can we

manipulate recycle ratio set point (RRSP), dissolved oxygen

set point (DOSP) and waste sludge flow (SWR) so that we main-

tain effluent quality despite these large variations in the

influent?

3. The Fuzzy Controller

At the core of the controller is a fuzzy algorithm for

determining the appropriatecontrol actions given the current

state of the process. Becausethe algorithm expects fuzzy

sets as inputs, the non-fuzzy processmeasurementshave to be

converted in some way. \1e have adopted the conventional

technique of representationby fuzzy singletons. Similarly,

since the processrespondsonly to non-fuzzy control actions,

the fuzzy control sets generatedby the algorithm have to be

de-fuzzified. We do this by selecting that control value

which divides the area under the membershipfunction in half.

The closed loop configuration is thus as shown in Figure 2.

The basic design problem is to construct the fuzzy algo-

rithm. In doing this we have relied on the considerableprac-

tical experienceof one of us (AL) in the day-to-daymanagement

of the ASP. The first task is to determine the fuzzy input

(measurement)variables for the algorithm, the fuzzy output

(control) variables and the primary fuzzy sets associatedwith

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each of these. The set definitions have not been included here

becauseof space limitations; however, the input and output

variables are listed in Table 1.

We have experimentedwith several algorithms but will re-

strict our discussionto one that has several interesting

features. It ·is shown in Table 2 and consistsof 20 rules.

Symbols such as S, ｾ ｌ and SP are mnemonics for fuzzy sets

which in this case are "small," "not large" and "small positive."

Each rule in the algorithm is interpretedas a fuzzy statement

of the form

WHEN:t.. DO ｾ

where ｾ is a fuzzy proposition about processconditions in terms

of the measurementsand whpre Q is a fuzzy proposition about

appropriatecontrol actions. The propositionsare interpreted

as multi-dimensional fuzzy sets and the rule itself is defined

as their cartesianproduct. Individual rules are cOIDbined

using the union Ｈ ａ ｡ ｸ ｩ ｾ ｵ ｍ Ｉ operation to forn the overall con-

troller relation.

The reasoningbehind the algorithm is briefly as follows

(for a more detailed descriptionof the role of similar rules

see Beck, Latten, and Tong, 1978). Rules 1-3 are resetting

rules in that, if the process is in a satisfactorystatebut

DOSP and/or SWR are at abnormal levels, then DOSP and/or SWR

are adjustedaccordinqly. Rules 4-7 deal with high effluent

suspendedsolids causedby a rising or bulking sludge (these

terms are briefly defined in Table 1). Rules 8-11 deal with

high NII 3-N levels in the effluent. Rules 12-13 cater for high

-6-

effluent solids causedby factors other than FIL or DNIT and

rules 14-18 describethe required control action if MLSS is

outside its normal range. Rules 19-20 deal with the problem

of a high effluent BOD.

Notice that most rules are concernedwith changesto SWR.

This reflects the fact that in practice waste sludge flow is

used most often to correct for effluent quality variations.

Notice too, that the rule set does not, by any means, exhaust

all the possibleprocessstates. It may be thought of as a

"sparsealgorithm." To test this algorithr'l we ran a simula-

tion of the ASP using a non-linear differential equation

model (with 14 state variables) and applying a disturbance

sequencederived from correspondingobservationsrecordedat

the Norwich plant. Conceptualaspectsof the model are described

in Beck, Latten, and Tong (1978); some accompanyingidentifi-

cation results are reported in Beck (1979).

Figure 3 shows thus the open loop responseof ESS and

ETBD on an hourly basis for 600 hours (i.e., 25 days). Clearly,

the processis not functioning properly. There are large

excursionsin both ESS and ETBD in the early and late parts

of the simulatjon (causedin fact by a bulking sludge condi-

tion). Also, NE 3-N levels in the effluent are high except for

the first 100 hours.

The controlled responsesto the saMe disturbancesequence

are shown in Figures 4-6. The controller sampling period is

set at 4 hours in this run (i.e., six possiblechangesin con-

trol action in each 24 hours). Figure ｌ ｾ shows the hourly ESS

and ETBD values; Figure 5 shows the hourly NH 3-N and MLSS

-7-

values and Figure 6 shows the correspondingvalues of RRSP,

DOSP and SWR. Notice, straight away, that the early and late

bulking sludge conditions have been suppressed. Notice too

that the ETBD and ESS levels are well within the 20:30 limits,

except for three occasionsbetween 400 hours and 475 hours.

These three occasions,which representa significant loss of

solids over the clarifier weir, are precipitatedby problems

of a rising and a bulking sludge, with both problems being

partly a complex function of over-aeration(see DOSP in Figure

6). There is generally good nitrification throughout the

period with ｎ ｈ ｾ Ｍ ｎ rarely being above 15 gm-3J

Our preliminary conclusion must be that the controller

works rather wAll. However, it does have some defects and in

exploring these we shall make use 0f an analytical tool which

we call a "rule activity chart." Figure 7 shows the rule

activity for 6DOSP (top two traces) and for 6RRSP (lower four

traces). Figure B shows the rule activity for 6SWR. The

horizontal axis is time and the vertical axis is the degree

to which the input propositionL is satisfied. Thus these

charts tell us which rules are contributing to the non-fuzzy

control actions applied to the process.

Since in this paper we are primarily concernedwith the

operationalaspectsof the fuzzy algorithm, rather than a

detailed analysis of the ASP's responses,we shall limit

ourselvesto a discussionof just two featuresof the closed

loop behavior. Despite our assertionthat in practice SWR

is the most often used control variable, we see from Figure 6

-8-

that RRSP is frequently changed. The activity charts of

Figure 7 indicate ｴ ｨ ｾ ｴ this is primarily due to rules 12 and

17. But notice that these rules are often activatedat very

low levels. This suggeststhat \>ore ｭｩｾｨｴ introduce some kind

of threshold for rule activation.

A way of doing this that is consistentwith the fuzzy

set theory is to employ the concept of "truth qualification"

(see Zadeh.. 1978). Thus we can modify the rules in our

algorithm so ｴ ｨ ｾ ｴ they have thp. form

where T is a fuzzy truth set which modifies the proposition

t . +:t. 0 glve 1.. • +Following Zadeh, Y is defined by a membership-function such that

ｾ +(y)Y-

= ｾｔＨｾ (y))Y-

A suitable choice for T will achieve the desiredeffect (e.g.,

ｾ (t) = t if t > threshold, ｾ (t) = 0 if t < threshold).T - T

We believe that this techniquecould have been applied to

all the fuzzy controllers that have been reported. Because

it allows us to weight the importanceof individual rules,

it is a very flexible and useful design tool.

The secondpoint we should like to highlight is the

behavior of the control variable SWR. A comparisonof the two

responsesshows that SWR is highly correlatedwith MLSS but

lags it by approximately 20 hours (see Figures 5 and 6). There

are two main reasonsfor this. Firstly, becauseof the

-9-

incremental form of the rules for SNR it takes tiMe for SWR to

achieve the necessarylevels demandedby the processconditions.

Then secondly, becausethe rules do not take into account

rate-of-change of MLSS they cannot ､ ｩ ｾ ｴ ｩ ｮ ｧ ｵ ｩ ｳ ｨ between a

condition in which action is required (e.g., MLSS low and

decreasing)and one in which it is probably not (e.g., MLSS

low but increasing). Thus SWR is being changedlong after

such changesare required. Consequently,it is felt that in

general an incremental fuzzy algorithm should take account

of both the level and rate-of-changeof the appropriate

measuredvariables. We note that many of the pUblished algo-

rithms do exactly this.

Obviously, there are many other featuresof these responses

which are of interest. However, they require a detailed under-

standing of the ASP and are outside the scope of this paper.

4. Conclusions.

Our aim in this brief paper has not been to presenta

final solution to the ASP control problem. Rather it has been

to show that a fuzzy algorithm basedon practical experience

can be made to work on this difficult process. In doing so,

we have made some general comments about the form and struc-

ture that fuzzy algorithms should take.

Our results must clearly be qualified by the fact that

evaluationof the controller has been undertakenwith a

processsimulation. The present level of accuracy for such

models for biological waste treatmentprocessesis but little

advancedbeyond the primitive stage. Nevertheless,we do not

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hesitate in assertingthat a fuzzy algorithm would be a

useful and practical way of regulating the activatedsludge

process. Indeed, a recent ｳ ｵ ｾ Ｌ ･ ｹ of factors limiting waste-

water treatmentplant performanceby Hegg, Raknessand

Schultz (1978) lends substantialsupport to our argument.

They observed, in particular, that:

"The highest ranking factor contributing toroor plant performancewas operatorapplica-tion of conceptsand testing to processcon-trol."

" •.• presentplant personnelare an untappedsource for achieving improved performance."

TABLE 1.

Input Variable

ETBD

ESS

MLSS

RASS

DNIT

DOSP

SWR

Output variable

DOSP

RRSP

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Description

the rotal BOD exertedby the effluent

the suspendedsolids in the effluent

the suspendedsolids in the sludge

leaving the aeration tanks (the mixed

liquor)

the suspendedsolids in the recycled

sludge

the ammonia-N in the effluent

a measureof a condition in the clari-

fier called "bulking sludge"; this is

causedby the presenceof filamentous

bacteriawhich prevent settling.

a measureof a condition in the clari-

fier called "rising sludge"; this is

causedby denitrification whereby

nitrogen gas is fermed and then rises

to the surface of the clarifier ｢ ｲ ｩ ｮ ｾ ｩ ｮ ｧ

sludge with it.

the DO set point in the aeration tank

the waste sludge flow rate

Description

change in DOSP; i.e., DOSP(t)=DOSP(t-l)

+llDOSP(t)

change in recycle ratio set point; i.e.,

RRSP(t)=k+llRRSP(t) where k is a constant

SWR

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change in SWR: i.e., ｓ ｗ ｒ Ｈ ｴ Ｉ ｾ ｓ ｗ ｒ Ｈ ｴ Ｍ ｬ Ｉ

Ｋ ｌ ｜ ｳ ｾ ｭ (t)

TABLE 2.

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0Z 0-, P-t P4'-

P4 U) U) p::(lJ Cl U) U) I E-i p:: 0 p:: ｾr-l o::l U) U) U) M H H U) ..-::l E-i U) H ｾ

::r: H Z 0 :?: Cl p:: U)

p:: ｾ ｾ ｾ Z ｾ Cl Cl U) <J <J <J

1 S S M M S L LN

2 S S M H S S SP

3 S S M M S L SN

4 M 1 SP

5 L 1 LP

6 M 1 SN

7 L 'I LN

8 S M SP

9 S M SN

10 S L LP

11 S L LN

12 .L M SP

13 L L LP

14 L LP

15 S SN

16 VS LN

17 VS S SP

18 L L SN

19 M S S SN

20 L S S LN

REFERENCES

Beck, M.B. (1979) On-line Estimation of Nitrification Dynamics.(Submitted to Proc. Am. Soc. Civil Engrs., J. Env.Engng. Div. for possibJepublication).

Beck, ｾ Ｑ Ｎ ｂ Ｎ Ｌ A. Latten and R.M. Tong (1978) Modelling andOperationalControl of the Activated Sludge ProcessinWastewaterTreatment. PP-78-10. Laxenburg, Austria:International Institute for Applied SystemsAnalysis.

Cashion, B.S., T.M. Keinath, and W.W. Schuk (1977) Evaluationof instantaneousF/M control strategiesfor the activatedsludge process. Progr. Nat. Technol., 9, Nos. 5/6.

Hegg, R.A., K.L. Rakness,.andｾ Ｎ ｒ Ｎ Schultz (1978) Evaluatiopof operation and maintenancefactors limiting municipalwastewatertreatmentplant performance. J. Wat. PolluteContr. Fedn., 50, 419.

Olsson, G. (1977) State of the art in sewage treatmentplantcontrol. Am. Inst. Chemical Engrs. SymposiumSeries,No. 159, 72, pp 52-76.

Olsson G. and J.F. Andrews (1978) The dissolvedoxygen profile- A valuable tool for the control of the activatedsludgeprocess. Wat. Res., 12, 985.

Tong, ｒ Ｎ ｬ ｾ Ｎ (1977) A control engineeringreview of fuzzy systems.Automatica, 13, 559.

Zadeh, L.A. (1978) PRUF - a meaning representationlanguagefornatural languages. Int. J. Man-Machine Studies, 10, 395.

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Air

10- DOSPDO

ControllerrIIIL_ - __- __, ,

- ..,III

,..----------

RR

Influent? : ｾＫ,

IIIII

Aeration TankMixed

liquorClarifier

Effluent

ControllerI

! I Recycled sludge I ｾ __JL _Waste sludge

•

RRSP

OwController

SWR

Figure 1. Schematicof the Norwich ASP.

Disturbance

Non-fuzzy controls.--- ---1.1'-

7 Non - fu zzy measurements....

ASP

FuzzificationAlgorithm r'J"r-----1

III fuzzificat ion "-......r----...,III II IIL ｾ

r----- --- -- ---- -------- - -------- -- 1-----...,I I1 ｾ 7 II IIDe- ｖｴｾ｟ＭＭＭＴ Fuzzy ｾ Ｂ Ｂ Ｍ Ｍ Ｍ Ｍ Ｂ Ｇ Ｂ Ｇ Ｂ Ｂ Ｂ Ｂ Ｇ ｬ :

IIII

Figure 2. Closed loop configuration.

150·0

100.0

50.0

50.0

1.0.0

30.0

20·0

10.0

30·0

20·0

10·0

100·0 200.0 300·0 1.00·0 500·0

Time (hrs)

Figure 3. Open loop responses.

150·0

100·0

50·0

50·0

40·0

30·0

20·0

10·0

100·0 200·0 300·0 400·0 500·0

Time (hrs)

Figure 4. Closed loop responses: I.

r----r-----,----- --I ---,--------,,------;

15.0

10·0

5·0

3500·0

3000·0

2500·0

2000·0

'--__L-__LI__-1. I -L.__......J

100·0 200·0 300·0 400·0 500·0

Time (hrsl

Figure 5. Closed loop responses: II.

30·0

20.0

10·0

RRSP

'·0

o·gI

0·8

1.0

o·g

0·8

0·7

0·6

l

100·0 200·0 300·0 400·0 500·0

Time (hrs)

Figure 6. Closed loop control actions.

I:: 1Rule7

,::("le8

100·0IJ

200·0iii

300·0 400·0 500·0

Time (hrs)

Rule 121.0

·5

r500·0

11r

400·0I

300·0

Time thrsl

,200·0

': 1Rule 13

'.: ｬｊｦＱＫＭＭＭＭＭＮＭＭｄＧＭＭＭＭＭＮＬＮＮＮＮＭＭＭＭＭＭＭＭＭｲＭＭＭｾｊＮＮＮ｟｟Ｌ _Oil

':1Rule'B

I

100·0

Figure 7. Rule activity chart: I.

Rule 2

1::l C c\ ｾ lilli

101Rule 3

·5

ｾ ｏｾI

101Rule 5

U·5

i

10lRule14

)0·5

Cl o nni

1:(IJCD ｄｾ J[I

1:lJf1p ｾ OILi

'.: (1019Lrb no ｾ , oWn Do

1·01Rule 20

·5n IJ

i I , J i

1000 200·0 300·0 400·0 500·0

Time (hrs)

Figure 8. Rule activity chart: II.