Identification of a Potabilization Process in the Florence City Water Treatment Planto

Copyright © IFAC 3. System Approach for Development Rabat. Morocco. 1980

IDENTIFICATION OF A POTABILIZATION PROCESS IN THE FLORENCE CITY WATER TREATMENT PLANTO C. Manfredi and E. Mosca SA IS, Istituto di Elettronica, Facoltd di Ingegneria, Universitd di Firenze Via S. Marta 3, 50139 Firenze, Italy

Abstract. This paper presents preliminary results on the determination from operating records of stochastic dynamic models that can adequately describe the clarification process of the Arno River water taking place in the Florence City (FC) Water Treatment Plant. The work was underta ken in view of ascertain the possibility of replacing the present plant manual management, based on rigid and static rules, by computerized adaptive control techniques. Besides the specific characteristics of the Arno River and the plant here considered, it is to be expected that the feasibility study here began will be of some interest wherever raw river water is potabilized for domestic use. Keywords.

Adaptive control; Chemical variables control; Identification; Stochastic systems.

1. I NTRODUCTI ON This paper deals with the problem of determl ning suitable dynamical stochastic models of a water potabilization process from input-ou! put records. The process takes place in the Florence city water treatment plant and co~ sists of a water clarification process whose goal is to reduce the raw water turbidity to levels acceptable for domestic use. The i~ put to the treatment plant consists of the A~ no river water. The clarification process is accomplished by adding flocculants (suitable chemicals) to raw water and sending the mixt~ re to sedimentation tanks where the physicochemical mechanism of flocculation occurs, yielding clarified water at the output of the treatment plant. The flocculant addition sho uld be provided so as to guarantee a conv! nient chemical concentration in the sedimenta tion tanks. This concentration should vary according to input turbidity and other physl co-chemical characteristics of the input raw water. Unfortunately, the Arno river chara~ teristics are quickly varying and the turbidl ty ranges from five up to five hundred F.T.U. and no quantitative physico-chemical models of the process are available. Consequently, the chemical addition is carried out manually according to empirical rules yielding eccessi

ve chemical feed consumption and hi~h costs of operation. The basic goal of the study d! scribed in the paper, was to verify the possl bility of identifying in real-time stochastic dynamic models from input-output records that can adequately represent the time-varying b! havior of process and consequently be used in adaptive control schemes, whose implement~ tion could provide better water quality and reduced costs of operation. 2. PLANT DESCRIPTION AND DATA COLLECTION As shown in Fig.l, the potabilization process considered hereafter consists essentially of several physico-chemical treatments, specifi cally: chlorine addiction, flocculant addi ~ tion, sand filters and ozonization. Of the overall potabilization process, the study was focused on determining the dynamic behavior of the clarification process consisting of three external variables: v ' the raw water t turbidity of the Arno river feeding the pot~ bilization plant; Ut' the flocculant (alumi num polichloride) feed-rate and Yt' the turbi dity of the clarified water. The reason for concentrating the study mainly on the clarifi cation process was motivated by the fact that the flocculant addition represents one of the most costly operations in the Plant. There fore, the automatization of the present man~ al and rigid addiction of flocculants could

°This work was partially supported by the Florence City Administration within a SAIS-FC Water Department joint research program. CSAD _ P

353

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354

Manfredi and E. Mosca

provide high economic benefit consisting of several thousand dollars of annual savings for chemical feed only. The variables v and t Yt were automatically recorded in continuous tlme, whereas Ut' the manipolable variable of the process, in all the experiments was kept at a constant value over time intervals of 30 minutes of duration. All water turbi dities were expressed in F.T.U. (Formazine Turbidity Units). 3. STOCHASTIC DYNAMIC MODELS FOR THE CLARIFICATION PROCESS The main goal was the determination of discre te-time linear stochastic dynamic models c~ pable of describing the behavior of the cl~ rification process. The models taken into consideration were Autoregressive Models with Exogenous Variables (ARX) (Box and Jenkins, 1970; Goodwin and Payne, 1977): A(q

-1

)Yt+k

were: t is the Yt is the me t; v is the t Ut is the et is the

W(q

-1

)v t + B(q

-1

JUt + e t +k (1)

data sampling time, t = 1,2, ... ; clarified water turbidity at ti raw water turbidity; flocculant feed rate; residual;

-1 q is the one-step delay, e.g. , q-1 Yt = Yt-l -1 -n A(q-l) 1 + alq + ... + anq W( q-1)

wlq

-1 +

+ wrq

B( q-1 )

blq

-1 +

+ b q-s s

-r

The time shift k is introduced in (1) to take into account the delay by which the output (clarified water) turbidity is influenced by a variation of input (raw water) turbidity and/or flocculant feed-rate. Notice that in (1) the polinomials A(q-l), W(q-l), B(q-l) have different degrees, respectively n, r, s. The need of introducing in (1) polynomials with different degrees was found necessary in order to provide a better description of the experimental data. For this reason, here after the model (1) will be denoted as ARX ( n , r , s ) . Since it is to be expected that the clarifi cation process behaves in a higly nonlinear way, the variables Yt' vt and Ut of (1) are

"centered" variables, viz., if y~, v; and u; are the effective recorded variables and

vt

Yt ,

and Ut their corresponding average evol~

tions, which will be defined in Sect.4, thus ~

~

~

Yt = Yt - Yt ' vt = vt - vt ' Ut = Ut - Ut· In such a way (1) is regarded as modelling the variations of the process external varia bles from their average evolutions. In the model (1), the variables Yt+k' vt ' Ut can be assumed to be known in that they are recorded by sampling the external variables of the process. On the contrary, the delay k and the model orders n, r, s, as well as the n+r+s+l parameters a., w., b. and 1

0

1

1

He~J,

2

must be determined by finding that particular model that fits the available data in the most accurate way. The identification procedure here adopted b~ sically consists of three different steps. Step 1 - Determination of the delay k. This is accomplished by performing the foll~ wing experiment. A negative step function is superimposed at a given sampling time to the usual level of the flocculant feed-rate Ut and the corresponding evolution of the output turbidity is recorded. The delay k+l is then set to be equal to the time delay, expressed in terms of numbers of sampling ti mes, after which a substantial increase of turbidity is produced at the process output. The evolutions of the process variables u~ der the experiment described above are shown in Fig.2. From this figure one obtains k

=4

(2 hours). This number is in good agreement with what can be estimated on the grounds of physical dimensions and flow rates. Step 2 - Parameter estimation for a given ARX(n,r,s). Here it is temporarily assumed that the model orders of ARX(n,r,s) be given. Thus, the following row-vector

(2)

made up of past samples of output turbidity and exogenous variables, can be constructed. In addition, let the free parameters of ARX(n,r,s) be represented by a column-vector

Identification of a Potabilization Process

355

ven by (3)

2

(N/2)ln[cr (N)J + (n + r + s + 1) where the prime denotes matrix transposition. Thus, (1) can be rewritten as follows: (4)

Since, as usual in ARX models, the stochastic process {et} is assumed to be Gaussian, zeromean and wnite, the Maximum Likelihood estima te and the Least Squares (LS) estimate of s coincide. Therefore, the only estimate e of s considered hereafter is the vector of appr~ priate dimensions minimizing T 2 L

(y. - y.s)

i=l 1 1 On the other hand, since the process under con sideration is time-varying and the determin~ tion of its time variations was one of the ob jectives of the study, for each experiment a sequence of LS estimates St(N) of s was found by minimizing t 1:

i =t-N+ 1

(y. - y . s) 1

2

t=N,N+l, ... ,T

1

where T is the number of samples of each varia ble recorded during a given experiment, and N is the lenght of a moving wjndow comprising all the past data on which St(N) is based. The number N should be chosen so as to satisfy conflicting requirements of good estimate ac curacy (large N) and small time variations of the model parameters (small N). By defining the following column-vector

and the following matrix ,

Yt-N+l

J'

(6)

the desidered estimate is given by

It is also convenient to define the ding residuals

correspo~

(8)

Step 3 - Determination of model orders. The choice of model orders is made essential ly according to the AIC (Akaike Information Criterion) (Akaike, 1974). As seen at Step 2, to any ARX(n,r,s) model corresponds a se quence of estimates 8 (N), t=N, ... ,T and at related sequence of residuals et(N). Thus, the AI-number associated to ARX(n,r,s) is gl

where 2

cr (N) = (T - N + 1)

-1

T 2

1: et(N) t=N and n+r+s+l is the number of free parameters in ARX(n,r,s), consisting of the coefficients a., w. , b. plus the variance of the process 1

{et}'

1

1

The AIC selects, among all possible

models, the one corresponding to the minimum AI-number. However, in the presence of co~ petitive ARX n,odels associated to very close AI-numbers, the model exhibiting a minimum of time-variations in its characterizing p~ rameters was selected as the most adequate one to the experimental data. 4. MODEL IDENTIFICATION FROM OPERATING RECORDS The collection of the clarification process external variables was executed by varying the flocculant feed-rate according to the tl me-behavior of pseudo-random sequences, and recording simultaneously the turbidity levels of input and output water. The data sampling interval, corresponding to the unit time-step in (1), was fixed once for all at 30 minutes. This choice resulted from observing that the process variables exhibit small changes wit~ in such a time-interval. Moreover, 30 min~ tes seem to correspond to a reasonable time duration over which the flocculant control va riable should be kept at a constant feed-rate value. Fig.3 and Fig.4 show the typical behavior of the time-evolution of the process external v~ riables during two experiments each of about one-day duration. Since the process was not equipped by a progammable feed-rate control ler, each one-day experiment involved the pr~ sence of human operators dedicated to this specific task over successive 24 hours acting according to a preassigned program of flocc~ lant time-variations. This was the main rea son why all the performed experiments were carried out during the period July-August 1979 and thereafter interrupted in view of the introduction in the plant of more adequ~ te sensors and programmable controllers. However,the experiments that could be carried out, yielded enough indication on the compl~ xity of the matematical models adequately r~ presenting the clarification process and the ir time-dependence.

c.

356

Manfredi and E. Mosca

Preliminary data analysis showed that a good choice for the lenght N of the moving window is N ~ 35, corresponding to 17.5 hours. Ac cordingly, the average evolutions of the pr~ cess external variables were defined as fol lows:

Next, AI-numbers were determined for various ARX(n,r,s) models . With reference to the ex periment of Fig.3, in Fig . 5 the AI-number is plotted for several values of the model or ders n, r, s . From this figure, one can see that AIC selects ARX(2,2,1) as the most adequate model for the process under consideration. Actually, one could a~ gue that ARX(2,1,1) and ARX(2,2,2) can still provide satisfactorily adequate models in that their corresponding AI-numbers are clo se enough to the minimum AI-number taken on at ARX(2,2,1). However, by comparing the tl me-variations of the estimated free parame ter vector 8 (35) based on the available d~ t ta, it was verified that the optimum model orders (2,2,1) yield estimates exhibiting a more constant behavior with respect to time. The five components of the estimated free pa rameter vector 8 (35) are reported in Tablet 1 and Table 2, respectively for the experl ments of Fig.3 and Fig.4. It is interesting to notice that going from one experiment to the other one gets a noticeable change for the values of the estimates, whereas within a single experiment the estimates tend to e~ hibit much more reduced variations with re spect to time. In particular, a positive va lue for the b coefficient is estimated at l all steps in the experiment of Fig.3, showing that an increase of the flocculant feed-rate produces an increase of output turbidity. This behavior should not be considered as an exceptional one, in that, as is well known to the experts of the physico-chemical phen~ mena taking place in the clarification pr~ cess, there may be conditions of excessive concentration of chemicals, under which the flocculants act in an opposite direction with respect to the desired one. On the contrary, a negative value for the b coefficient is l estimated at all steps except the last one in the experiment of Fig.4, showing that an

increase of flocculant feed-rate yields, as desired, a decrease of output turbidity. Be cause of the time-varying behavior exhibited by the process during the several experiments carried out, it is to be expected that an online estimation of the sign of the b parame ter, during the normal operating con~itions­ of the potabilization process, could provide a very relevant piece of information on which to base an effective adaptive control of the plant. 5. CONCLUSIONS AND OPEN QUESTIONS Black-box identification techniques have been used in order to determine stochastic dynaml cal models for the water clarification process taking place in the Florence City Water Trea! ment Plant. The results obtained indicate that, according to AIC (Akaike Information Criterion), ARX(2,2,1) is the most adequate autoregressive model. Input-output data col lected from the plant during July-August 1979, reveal a time-varying behavior of the process dynamics as a result, presumably, of correspo~ ding time-variations of the physico-chemical characteristics of the raw input water and ch~ mical concentrations in the plant. It is be lieved that these time-variations of the pro cess should be tracked by suitable on-line identification algorithms, so as to be able to implement an effective chemical feed-rate automatic control, necessarily of an adaptive nature. Further efforts should be made in order to g~ ther larger sets of data from the existing plant, so as to test the adequacy of ARX mo dels over different periods of the year. It would also be interesting to use suitable se~ sors in order to acquire other physico-cheml cal variables, e.g., temperature, pH, dissol ved chlorine, alkalinity, hardness, etc., so as to correlate the process model time-vari~ tions with the changing characteristics of the incoming raw water of the Arno river. REFERENCES Akaike, H. (1974). A new look at the stati stical model identification. IEEE Trans. Autom. Control,~, 716-723. Box, G.E.P., and G.M. Jenkins (1970). Time Series Analysis. Forecasting and Control. Holden Day, San Francisco. Goodwin, G.C . , and R.L. Payne (1977). Dynamic System Identification : Experiment Design and Data Analysis. Academic Press, New York.

Identification of a Potabilization Process

to distribution

final chlorine addiction

357

sand filters

o o

turbidimeter flocculation and sedimentation tanks

k-----~~~~~--~ozone

L-..j--IO

o o

fl occu 1ants

pumps

chlorine addiction Arno River Ol----~

Ol-----of------r----< ...

O~---

pumps turbidimeter

Fig. 1.

Potabilization process.

[F.T.U.J

4[1 /h J

5

w.10

-1 300

4

y

3 200 2 120 100

u

80 60

o

2

Fig. 2.

3

4

5

6

7 [hour sJ

Evolutions of the process variables under the experiment for the determination of the time-delay k.

c.

358

Manfredi and E. Mosca .

[F.T.U.]

13

[l /h] w

12 11

10 9

8

100

7

u

80

6 60

5

40

4

3

Y

2

20 0

o

5

Fig . 3.

10

15

20

25

[hours]

Time-evolution of the process external variables during an experiment carried out in July 1979.

[F.T.U.]

[l /h ]

10 9 ' - - - -__ W

8

100

7

80

6

60 5 u

4 3

y

2

40 20

o

o

5

Fig. 4.

25 15 20 10 Time-evolution of the process external variables during an experiment carried out in August 1979 .

[hours]

Identification o f a Potabilization Process

359

AI-number

-70 ( 1,0,0)

(1,0,1 ) (2,0,2) (2,0,1 ) (2,0,0)

-75 (3,1,2 ) ( 1 , 1 , 1)

(2,1,2) (2,1,1 )

-80

(2,2,0)

(2,2,2) (2,2,1 )

-85

o

2

Fig . 5.

4

3

5

6

degrees of freedom

Behavior of the AI-number as a function of (n,r,s) for the experimental data of Fig. 3.

TABLE 1 Estimates of the free parameters of ARX(2,2,l) based on the experimental data of Fig. 3. a

l -.905 -.899 -.902 -.888 -.835 -.649 -.620 -.642 -.725 -.801

a

2 .341 .341 .339 .329 .304 .121 .153 .133 .138 .156

wl

w2

.077 .080 .081 . 084 .104 .092 .097 .098 .114 . 117

-.161 -.164 -.167 -.171 -.198 -.182 -.203 - . 198 -.198 -.193

b .10 3 1 0. 92 0.88 0.91 0.95 1. 25 1. 52 1. 76 1.46 1. 02 0.86

TABLE 2 Estimates of the free parameters of ARX(2,2,l) based on the experimental data of Fig. 4. a

l -1. 25 -1.29 -1.33 -1.34 -1.36 -1.40 -1.40 -1.43

a

2 .339 .368 .353 .362 . 376 .428 .459 .522

wl -.081 -.089 -.073 -.065 -.064 -.059 -.074 -.066

w2 .045 .065 .067 .065 .066 .066 .079 .080

b .10 3 1 -.85 -.94 -1.24 -1.03 -.92 -.65 -.32 .10