Fuzzy control of the activated sludge wastewater treatment process

Aulomatica, Vol. 16, pp. 659 701

0005-1098/80/I 101-0695 $02.00/0

Pergamon Press Ltd. 1980, Printed in Great Britain t International Federation of Automatic Control

Brief Paper Fuzzy Control of the Activated Sludge Wastewater Treatment Process* R. M. T O N G t , M. B. BECK++ and A. LATTEN§ Key W o r d s ~ o m p u t e r

control; fuzzy control; water pollution; water resources; control system synthesis; controllers; process control.

Abstract The activated sludge process is a commonly used method for treating sewage and waste waters. It is characterised by a lack of relevant instrumentation, control goals that are not always clearly stated, the use of qualitative information in decision making and poorly understood basic biological behaviour mechanisms. In this brief paper we examine the behaviour of an experimental fuzzy control algorithm constructed to reflect actual operational practice. We conclude that this algorithm does rather well and that a fuzzy controller would be a useful and practical way of regulating the activated sludge process.

2. The activated sludge wastewater treatment process

The ASP is one of a number of unit processes used for the treatment of sewage and wastewaters. The basic feature of the process is the decomposition of complex dissolved and suspended organic substrates into simple end-products such as carbon dioxide and water. Decomposition is achieved by a heterogeneous culture of micro-organisms (the activated sludget, which in part utilize the waste organic substrates in the systhesis of their own biological cell material. Our studies have been concerned primarily with a particular ASP plant at the Whitlingham Treatment Works, Norwich, England. This installation is shown diagrammatically in Fig. 1. If we consider only that part of the diagram within the dotted lines, we see that there are two stages in the overall process: an aeration tank followed by a clarifier/settler. Correct operation of the process requires, a m o n g other things, the following three items. First, the influent sewage entering the process has to be mixed intimately with the recycled sludge; in principle there exist ranges of desirable proportions 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 necessary aerobic environment for growth of the sludge organisms, and can be a key factor in operational control (Olsson and Andrews, 1978). Third, the settler must effect good separation between the biological floc (sludge) and the clarified effluent; excess biological solids in the ASP may be manipulated by the removal of waste sludge. Recent work on the application of automation and control to the ASP is surveyed by Olsson (1977). Local (i.e. single-loop) control action is taken at the Norwich ASP to help achieve these aims. Thus, as shown in Fig. 1, recycle sludge ratio (defined as the ratio of influent flow rate, Q~, to recycled sludge flow rate, QR) is regulated by feedforward control of QR using measurements of Qv The objectives of this control action are to maintain a desirable ratio of substrate/organism concentrations and to manipulate (to a limited extent) the distribution of sludge between the aeration tank and the clarifier. Dissolved oxygen (DO) level in the aeration tank is regulated by feedback control of the air-blowers using a measurement of DO. Maintenance of a higher set-point for DO may be necessary when, as is often the case, it is desirable to oxidize nitrogen-bearing waste materials (i.e. nitrification). Waste sludge flow, Ow, is set by the plant manager. This third control action is intended to regulate both the total amount and average retention time of the sludge retained in the unit (aeration tank and clarifier); higher retention times (sludge ages) are generally necessary in order to achieve nitrification. An ASP that is performing as required will be producing an effluent that meets some standard, In Britain, this is simply a recommendation that the total (5-day) biochemical oxygen demand exerted by the effluent should be less than 20 g 3 and that the amount of suspended solid material in the effluent should be less than 30g 3. Whilst these are hard constraints on the process, a plant manager can choose to operate as close to them as he feels is practical. In a real sense, therefore, there is some fuzziness associated with these values. There are

I. Introduction

F u z z y controllers have been used successfully in a variety of applications (see Tong, 1977, for a review). We contend, however, that although poorly understood process behaviour was the rationale for attempting the fuzzy approach, this uncertainty was of limited extent and that, as a result, these were not very difficult control problems. Thus in most cases, it was reasonably clear what the controlled response should be and which inputs should be used as control variables. Furthermore, because all the processes were of a mechanistic type, the underlying laws of behaviour were well understood. Taken together, these factors enabled controllers to be constructed with relative ease. In this paper we report on some results from an initial study of the role of fuzzy set theory in the control of the activated sludge wastewater treatment process (ASP). The ASP is characterised by a lack of relevant instrumentation, control goals that are not always clearly stated, the use of qualitative information in decision making and poorly understood basic biological behaviour mechanisms. As such, it appears to be an ideal candidate for fuzzy control and is certainly a more severe test of the methodology than previous applications. Our aims in this paper are twofold. Firstly, we are interested in examining the feasibility of the fuzzy approach in tackling a really difficult control task. Then secondly, we hope to say something useful about the behaviour and control of this important process. Section 2 of the paper outlines the behaviour of the ASP and highlights the principal control problems. Section 3 starts with a brief review of the fuzzy controller paradigm. Then follows a discussion of one particular controller with which we have experimented, together with an analysis of some of the resulting closed loop responses. We conclude by making some general observations on fuzzy controller design,

*Received October 22 1979; revised May 27 1980. The original version of this paper was not presented at any IFAC Meeting. This paper was recommended for publication in revised form by associate editor H. Kwakernaak. ?Department of Electrical Engineering and Computer Science and the Electronics Research Laboratory, University of California, Berkeley, California 94720, U.S.A. +International Institute for Applied Systems Analysis, Schloss Laxenburg, 2361 Laxenburg, Austria. §Manager, Whitlingham Treatment Works, Anglian Water Authority, Trowse, Norwich, U.K. 695

696

Brief Paper

Air

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secondary goals, 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 a m m o n i a in tbe effluent is kept at acceptably low levels. The major disturbances to the process are in the form of fluctuations in the composition and flow of the influent. There are short-term diurnal variations as well as longer-term trends which together can easily produce changes of up to 50 per cent in the average quality of the influent. The longer-term variations in the input disturbances can, in combination with a specific set of operating conditions, induce subtle but important changes in the state of the activated sludge. Even though these complex changes occur slowly they may' eventually lead to relatively rapid loss of desirable performance in the process. Two notable examples of this kind of process "'failure" are conditions referred to as "'bulking sludge" and "'rising sludge". A bulking sludge is caused by the presence of filamentous bacteria that prevent settling of the sludge in the clarifier; the growth of the filamentous bacteria is partly governed by the rate of aeration and hence by the operating set-point for DO in the aerator. A rising sludge is caused by denitrification whereby nitrogen gas is formed and then rises to the surface of the clarifier bringing sludge with it. Among other factors, a rising sludge is related to the amount of nitrification achieved in the aeration tank and hence, as with a bulking sludge, to the operating set-point for DO. Both conditions eventually lead to a significant increase of suspended solids m the effluent from the clarifier. Our control problem is thus simply stated, ttow can we manipulate recycle ratio set-point (RRSP), dissolved oxygen set-point IDOSP) and waste sludge flow (SWR) st) that we maintain effluent quality despite tbe large variations in the influent and so that we can prevenL or quickly recover from, the kind of process failures described above. Note, therefore, lhat the problem as stated is actually the upper level of a two-level hierarchical control problem in which coordination of tim lower-level individual set points, RRSP, DOSP and SWR, are acbieved subject to tire physical constraints on the equipment (pumps, blowers) used to apply the control inputs. Note also that in this context the fuzzy controller developed below is designed to exploit the plant manager's empirical operating experience of overall coordination of plant control. An approach with several similarities to the present approach has been reported for the control of a lnedium-sized wastewater treatment plant at GS.vle in Sweden (Gillblad and ()lsson, 1977). Our objectives are twofold. First. tim fuzzy

controller should bc capable of successful operation m the face of the difficulties of ASP control as outlined ill the introduction to the paper. Second, the ultimate goal is to use the study in order to improve (where possible) the plant manager's operating strategy, although it must be admitted that tile following is merely indicative of preliminary resuhs. 3. The.luzzy c(mtroller Tbe fuzzy approach to control rests on two basic premises. t;irstly, that there is often qualitative information about the process which remains unutilized by conventional approaches but which could be very important in achieving good controlled performance. Then secondly, that ;t useful way of representing and manipulating this information is through a linguistic interpretation of the fuzzy set theory. The first publisbed attempt to put these ideas into practice was by Mamdani (1974) and most of the applications studies have adopted a similar basic approach to his. The mare features ol lifts are as follows. The central idea is that of a linguistic control rule. l-his can take several forms, but basically it should be viewed as a statement about what control actions to take given certain process conditions. The power of the approach derives from the linguistic flexibility with which these actions and conditions can be described. Tbus statements aboul control action might have the form "make a small reduction m Q , s . or "increase DOSP by a large amount". Whereas statements about process conditions might be similar to "'MLSS is xer~ high", or "ETBD is more or less correct". The key terms here tire "small", "large", "very high" and "more or tcs~, corrccf'. They correspond to imprecise, but useful, reformation about the process and in our approach tire represented by fuzz} subsets of a suitably defined universe of discoursc. In general, of course, many control rules will be needed to specify a ~atisfactory controller. We shall call this set of ruJcs a "'fu//v control algorithm". More formally, each rule of the algorithm is asstnned lo be a statement of the form W H E N "'Y" 1)O "'U'" where Y is a fuzzy proposition about process conditions in terms of the measurements and U is a fuzzy proposition about appropriate control actions. The propositions :ire interpreted as multi-dimensional fuzzy sets and the rule ilself is defined as their cartesian product. Thus s~. t r., i:: rain I :,,.It 1./,, t,)]

Brief Paper

697

Disturbance Non-fuzzycontrots

Non-fuzzy measurements

I

>

ASP 1

Fuzzification 1

Defuzzification

l

Fuzzy

Atgorithm

FIG. 2. Closed loop configuration.

T A B L E 1. I N P U T

Input variable

Description

ADOSP ARRSP

change in DOSP; i.e. D O S P ( t ) = DOSP(t-- 1 )+ ADOSP(t) change in RRSP; i.e. RRSP(t )=/, + ARRSP(t) where k is a constant reference value for RRSP change i n S W R : i . e . SWR(t)=SWR(t I)+ASWR(t)

ASWR

symbol for membership function and y, u the appropriate multi-dimensional space. The ri, are combined using the union operator to controller relation, R. That is, #R (Y, U) = max [#,,(y, u )]. i

To make the algorithm operational a rule of inference is needed and we define this using max-min composition. Thus, if the actual process measurements are described by a fuzzy set, Y*, then the corresponding control action, U*, is given by Pu.(u) = max min [Pv.(Y), #g (Y, u)] y

Since the instrumentation on the ASP produces non-fuzzy measurements, these have to be fuzzified in some way and we have adopted the conventional technique of representation by fuzzy singletons. Similarly, since the ASP cannot respond to fuzzy controls directly, the fuzzy control sets generated by the algorithm have to be de-fuzzified. We do this by selecting that control value which divides the area under the membership function in half. The closed loop configuration is thus as shown in Fig. 2. Notice that if We view this structure conventionally, the overall input-output behaviour of the controller (i.e. fuzzifier+algorithm+defuzzifier) is non-fuzzy, although its specification is done at the linguistic level. However, a more useful point of view is to consider the F

CONTROLLER

the total BOD exerted by the effluent the suspended solids in the effluent the suspended solids in the sludge leaving the aeration tanks (the mixed liquor) the suspended solids in the recycled sludge the ammonia-N in the effluent a measure of a condition in the clarifier called "bulking sludge" a measure of a condition in the clarifier called "rising sludge" the DO set point in the aeration tank the waste sludge flow rate

Output variable

AUTO

ASP

Description

ETBD ESS MLSS RASS NH3-N FIL DNIT DOSP SWR

where # is the denote points in individual rules, form the overall

A N D O U T P U T VARIABLES F O R

defuzzifier+ASP+fuzzifier as a fuzzy process, in which case the controller (i.e. the algorithm alone) is then truly fuzzy. An illuminating analogy would be with the conventional controller design practice of incorporating actuator and measurement device dynamics in the process model. Clearly then, the basic design problem is to construct the fuzzy algorithm. In doing this we have relied on the considerable practical experience of one of us (AL) in the dayto-day management 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 associated with each of these. The set definitions have not been included here because of space limitations; however, the input and output variables are listed in Table 1. The measurements used as inputs to the controller are therefore the total (5-day) biochemical oxygen demand and suspended solids concentrations of the effluent (ETBD and ESS respectively), the mixed liquor and recycled sludge suspended solids concentrations (MLSS and RASS respectively), and the ammonia-nitrogen content of the effluent (NH 3 N). These measurements are assumed to be available at the sampling frequency of the controller, that is, once every 4 hours in this case. Such an assumption is clearly not valid for ETBD, which in practice would have to be substituted by measurements of chemical oxygen demand, for example. ETBD is retained here because of the particular formulation of the process model: we shall, however, refer below to the significance of ETBD in the performance of the controller.

698

Brief Paper T.XBLE 2.

Rule No.

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ESS

MLSS

RASS

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We have experimented with several control algorithms but will restrict our discussion to one that has several interesting features. It consists of 20 rules as shown in Table 2. The entries in the table are mnemonics for fuzzy sets. Thus, S, M, L SN, LN, SP, LP, VS, ~ k and 1 correspond to "'small", "medium", "large", "~small negative", "'large negative", "small positive", "large positive", "very small", "not large" and "'indicated" respectively. The last one of these is simply a way of saying that the bulking sludge and rising sludge conditions have occurred. These conditions are essentially non-fuzzy and once detected through the ESS measurement the plant manager can confirm by inspection which specific condition obtains. So, rule 4 of the table is of the form W H E N "ESS is medium & D N I T is indicated" DO "'make a small positive change in SWR" Simihtrly, rule 17 is W H E N "MLSS is very small & SWR is small" DO "make a small positive change in RRSP" The reasoning behind the algorithm is briefly as follows (for a more detailed description of the role of similar rules see Beck, Latten and Tong, 1978). Rules I 3 are resetting rules in that, if the process is in a satisfactory state but D O S P and/or SWR are at abnormal levels, then D O S P and/or SWR are adjusted accordingly. Rules 4 7 deal with high effluent suspended solids caused by a rising or bulking sludge. Rules 8 11 deal with high NH3 N levels in the effluent. Rules 12 13 cater for high effluent solids caused by factors other than FIE or DNIT and rules 14 18 describe the required control action if MLSS is outside its normal range. Rules 19 20 deal with the problem of a high effluent BOD. There are several points to note concerning the structure of the controller. Most of the rules are concerned with changes to SWR. This reflects the fact that in practice waste sludge flow is used most often to correct for effluent quality variations. The rule set does not, by any means, exhaust all the possible process states and it may be thought of as a "'sparse algorithm". In addition, the constraints of using a model to simulate process dynamics prevents, at this stage of the analysis, the inclusion of control rules related to the qualitative observations that the plant manager makes of sludge colour and odour. Nor does the controller of Table 2 utilize information on the status of the controlling inputs (rate of aeration, for example); this too can be important for

LP

SN LN S L

SP SN SN I.N

determining control action. Lastly, notice that the overall character of the controller is somewhat unconventional: in the event of undesirable performance, incremental changes to the levels of the control variables are made until desirable performance is achieved; if the levels of the control variables (DOSP, SWR) which thus result are outside normal ranges, then D O S P and SWR are returned incrementally, and subject to desirable performance continuing, to normal levels. To test the algorithm of Table 2 we ran a simulation of the ASP using a non-linear differential equation model (with 14 state variables). Conceptual aspects of the model and timeseries data recorded at the Norwich plant arc reported m Beck, Latten and Tong (1978). Part of the model has becra identified by reference to these data (Beck. 1979). The simulated input disturbance sequences used for evaluation of the algorithm are also based on the conditions typical of the Norwich plant. Observed diurnal variations have been combined with a random sequence of longer-term ~ariations drawn from the sample characteristics of the Norwich data. We have not, as yet, tested the sensitivity of the algorithm to changes in the plant parameters and fuzzy membership functions. Figure 3 thus shows the open loop response of ESS and ETBD on an hourly basis for 600 hours (i.e. 25 days). Clearly, the process is not functioning properly. There are large excursions in both ESS and ETBD in the early and late parts of the simulation (caused in fact by a bulking sludge condition). Also, NH3 N levels in the effluent are high except for the first 100 hours. The controlled responses to the same disturbance sequence are shown in Figs 4 6. The controller sampling period is set at 4 hours in this run (i.e. six possible changes in conlrol action in each 24 hours). Figure 4 shows the hourly ESS and ETBD values; Fig. 5 shows the hourly NH.~ N and MLSS values and Fig. 6 shows the corresponding values 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 occasions between 400 hours and 475 hours. These three occasions, which represent a significant loss of solids over the clarifier weir, are precipitated by problems of a rising and a bulking sludge, with both problems being partly a complex function of over-aeration (see D O S P in Fig. 6). There is generally good nitrification throughout the period with NH 3 N rarely being above 15g 3. Our preliminary conclusion must be that the controller works rather well. Notice though that this assessment is

Brief Paper

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699

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FIG. 7. Rule activity chart: I.

d i = max min [#v *(Y),l~v,(Y)] Y

So, for example, rule 7 is only active during one control period and d7 = 1.0 at that time. Similarly, rule 12 is active in many control periods with d~2 taking a range of values. Since in this paper we are primarily concerned with the operational aspects of the fuzzy algorithm, rather than a detailed analysis of the ASP's responses, we shall limit ourselves to a discussion of just two features of the closed loop behaviour. Despite our assertion that in practice SWR is the most often used control variable, we see from Fig. 6 that RRSP is frequently changed. The activity chatl, ,,I ]~e 7

56o

Time(hrs)

Time(hrs)

subjective in that we are applying no precise criteria to the controller responses. Indeed, the value of such criteria in evaluating the performance of a fuzzy controller is questionable. Some explicit fuzzy performance indices could perhaps be formulated but since, as yet, no fuzzy control theory exists these would be of limited value. We prefer, then, to keep our fuzzy judgments implicit. The controller does have some defects however, and in exploring these we shall make use of an analytical tool which we call a "rule activity chart". The purpose of such charts is to show which rules are active at any given time and thus contributing to the control action being taken. Figure 7 shows the rule activity for A D O S P (top two traces) and for ARRSP (lower four traces). Figure 8 shows the rule activity for ASWR. In all of these the horizontal axis is time and the vertical axis is the degree to which the current fuzzified measurement, Y*, is consistent with the input condition of the rule. Thus for each rule we have a degree of consistency, d~, defined by

n

coo

indicate that this is primarily due to rules 12 and 17. But notice that these rules are often activated at very low levels• This suggests that we might introduce some kind of threshold for rule activation. There are several ways we might do this, but one which is consistent with existing interpretations of the fuzzy set theory is as follows. Clearly, what we wish to do is de-activate a rule if the match between the current fuzzy measurement and the input condition falls below the threshold value. Thus in terms of our degrees of consistency, d~, we want to define a threshold function, r~, such that

r:,(di)-d i di>-o( =0

d~<~.

Now z~(di)= r~{max min [/lv,(y),/~v,(y)] I 3'

which, because z~( • ) is monotone increasing on [(), t], can be rewritten as r~(dl) = max min [z~(l~v,(y)),r~(#v(Y)t]. v

However, we have assumed that Y* will be a fuzzy singleton which means that Y* is unaffected by %( • ). So, max min [#v,(Y), z, (#v,(Y))].

ra(di) =

v

The computation of U~ then becomes ~t ?'(u ) = max min [#v ,(Y ), z-~(/~, ,(.v)). Lq, (u)]. v

Brief Paper Now in the spirit of Zadeh's (1978) concept of "truth qualification", the term z,(pvi(y)) may be interpreted as "YI is z," with the linguistic meaning of this being something like "Y~ is at least weakly satisfied" or "'Y~ is strongly satisfied" depending upon the-value of ~t that x~c select. Therefore, we can modify those rules to which wc x~.t,,h to apply a threshold by rewriting them as WHEN "Y is z," DO "'U" We believe that this technique is a very flexible and useful design tool and we can think of it as a way of weighting the importance of rules. Setting ~t to zero means that a rule is always active and thus very important. Setting ct close to unity, however, means that a rule is relatively unimportant and should only contribute to control action if its input conditions are strongly satisfied. The second point we should like to highlight is the behaviour of the control variable SWR. A comparison of the two responses shows that SWR is highly correlated with MLSS but lags it by approximately 20 hours (see Figs 5 and 6). There are two main reasons for this. Firstly, because of the incremental form of the rules for SWR it takes time for SWR to achieve the necessary levels demanded by the process conditions. Then secondly, because the rules do not take into account rate-of-change of MLSS they cannot distinguish 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 changed long after such changes are actually required. We recommend, therefore, that incremental algorithms should generally take account of both the level and rate-of-change of the appropriate measured variables. In conventional terms, this is equivalent to saying that proportional control on its own is not sufficient and that an integral term considerably improves the closed loop performance. We note that many of the published algorithms do exactly this. Obviously there are many other features of these responses that are of interest but they require a detailed understanding of the ASP and are outside the scope of this paper. We shall, however, make one further comment with considerable practical significance; it is concerned with the use of effluent BOD (ETBD) measurements, which, as noted earlier, are not available in practice. First, for this particular set of results, it can be observed that (in Fig. 3, for instance) ETBD variations are highly correlated with ESS variations. This is partly a function of the simulation, but it does indicate that the performance of the controller would be little different in the absence of ETBD measurements. In fact only two rules (19, 20) of the controller "cater for a situation in which the levels of ETBD and ESS would be markedly different from each other. Such a situation is unlikely to occur frequently in practice. When it does occur, in the event of a spillage of toxic substance into the sewer network for example, other more readily available mbasurements--the rate of aeration (a controlling input)--can be substituted in order to determine the operating condition of the plant.

4. Conclusions Our aim in this brief paper has not been to present a final solution to the ASP control problem. Rather it has been to show that a fuzzy algorithm based on practical experience can be made to work on this difficult process. In doing so, we have made some general comments about the form and structure that fuzzy algorithms should take. Our results must clearly be qualified by the fact that evaluation of the controller has been u n d e r t a k e n w i t h a process simulation. The present level of accuracy for such modcl~ of biological waste treatment processes is not much

701

advanced beyond the primitive stage. System identification and model parameter estimation are particularly difficult and subtle problems for this type of system. Applications of related techniques to wastewater treatment plant operating data have been limited and have yielded little insight into the dominant mechanisms governing process dynamics (Beck, 1980). Nevertheless, we do not hesitate in asserting that a fuzzy algorithm would be a useful and practical way of regulating the activated sludge process. In particular, there does not at present appear to be any better way of solving the problem of coordinating the local control loops than by exploiting the plant manager's empirical operating experience. Indeed, a recent survey of factors limiting wastewater treatment plant performance by Hegg, Rakness and Schultz (1978) lends substantial support to our argument. They observed, in particular, that: "The highest ranking factor contributing to poor plant performance was operator application of concepts and testing to process control." "...present plant personnel are an untapped source for achieving improved performance."

Acknowledgments--The authors are grateful to the Anglian Water Authority for their financial support in this project. One of the authors (R. M. Tong) would also like to acknowledge the financial support provided by an SRC/NATO Postdoctoral Fellowship. This work was also supported, in part, by National Science Foundation grant ENG78-23143. References Beck, M. B. (1979). On-line Estimation of Nitrification Dynamics, PP-79-3. International Institute for Applied Systems Analysis, Laxenburg, Austria. Beck, M. B. (1980). Applications of system identification and parameter estimation in water quality modelling. In Hydrological Forecasting, Proc. Oxford Symposium, IAHSAISH Publication No. 129, 123-131. Beck, M. B., A. Latten and R. M. Tong (1978). Modelling and Operational Control of the Activated Sludge Process in Wastewater Treatment, PP-78-10. International Institute for Applied Systems Analysis, Laxenburg, Austria. Cashion, B. S., T. M. Keinath and W. W. Schuk (1977). Evaluation of instantaneous F/M control strategies for the activated sludge process. Progr. War. Technol. 9, Nos. 5/6. Gillblad, T. and G. Olsson (1977). Computer control of a medium-sized activated sludge plant. Progr. War. Technol. 9, Nos. 5/6. Hegg, R. A., K. L. Rakness and J. R. Schultz (1978). Evaluation of operation and maintenance factors limiting municipal wastewater treatment plant performance. J. Water Poll. Control Fedn. 50~ 419. Mamdani, E. H. (1974). Applications of fuzzy algorithms for control of a simple dynamic plant. Proc. IEE 121, 1585 1588. Olsson, G. (1977). State of the art in sewage treatment plant control. Am. Inst. Chemical Engrs Symposium Series, No. 159, 72, 52-76. Olsson, G. and J. F. Andrews 0978). The dissolved oxygen profile--A valuable tool for the control of the activated sludge process. Wat. Res. 12, 985. Tong, R. M. (1977). A control engineering review of fuzzy systems. Automatica 13, 559. Zadeh, L. A. (1978). P R U F - - a meaning representation language for natural languages. Int. J. Man-Machine Studies 10, 395.