Adaptive MPC for ozone dosing process of drinking water treatment based on RBF modeling

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Adaptive MPC for ozone dosing process of drinking water treatment based on RBF modeling

Transactions of the Institute of Measurement and Control 2014, Vol. 36(1) 58–67 Ó The Author(s) 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0142331213485614 tim.sagepub.com

Dongsheng Wang1,2,3, Shihua Li2,3, Jun Yang2,3, Zhilei You4 and Xingpeng Zhou2,3

Abstract The practical ozone dosing process of drinking water treatment is essentially a complicated nonlinear process with time delay. It is difficult to establish an exact mathematical model and implement a satisfying real-time control for the frequent changes of water quality, water flow rate and process operational conditions. In this paper, the control strategy of keeping a constant ozone exposure is attempted instead of conventional keeping a constant ozone dosage or dissolved ozone residual. To this end, an adaptive model predictive control (MPC) scheme based on the radial basis function (RBF) neural network model is proposed to maintain a constant ozone exposure by adjusting ozone dosage. With the proposed control scheme, a RBF neural network model is established as the prediction model of practical ozone dosing process. Then an adaptive model predictive controller is designed. Owing to the online updating of RBF neural-network weights, the proposed MPC scheme can cope with the frequent changes of water quality, water flow rate and process operational conditions. Both simulation and experimental results demonstrate the effectiveness and practicality of this real-time control method.

Keywords Ozone dosing process, drinking water treatment, RBF neural network, model predictive control, adaptive control

Introduction Ozone has been commonly used to be an attractive alternative to chlorine for drinking water disinfection and oxidation of various organic and inorganic contaminants (Hoigne´, 1998; von Gunten, 2003). In addition, ozone can also increase the biodegradability of natural organic materials in water, which can be removed by subsequent biological activated carbon (BAC) filtration (van der Kooij et al., 1989; Camel and Bermond, 1998). During the ozonation process, ozone exposure (namely, Ct10 , which is defined as dissolved ozone residual C (mg/l) multiplied by effective detention time t10 (min)) is a leading parameter to determine the disinfection and bromate formation (Bonnelye and Richard, 1997; Elovitz and von Gunten, 1999; Gujer and von Gunten, 2003; Rietveld et al., 2010; Garcia-Ac et al., 2010). For adequate disinfection and oxidation with water matrix compounds, a large enough Ct10 is required. However, too large a Ct10 will result in the excessive formation of undesired by-product bromate, which is considered to be a potential human carcinogen (von Gunten, 2003; Sohn et al., 2004). A low drinking water standard of 10 mg/l has been set for bromate in both the European Union and the US. Thus, compared with conventional control strategies of keeping a constant ozone dosage or keeping a constant dissolved ozone residual (Elovitz et al., 2000; Courtois, 2005; van der Helm et al., 2009), keeping a suitable constant Ct10 , which fulfils both validity of ozonation and restriction of

bromate formation, is more preferable (Cho et al., 2003; Kang et al., 2008). As a result of its high reactivity, ozone is an unstable oxidant in water and reacts with water matrix components easily. Many attempts have been made through the laboratoryscale experiments to describe the ozone reaction process in water (Staehelin and Hoigne´, 1982; Bu¨hler et al., 1984; Staehelin et al., 1984; Elovitz et al., 2000; Park et al., 2001). However, due to the complexity of practical ozonation process, the characteristics of ozone reacting with water matrix components in the practical drinking water producing process is often dissimilar from the experimental results of laboratory scale. Moreover, all of these models are only used for the offline decision support to technologists and cannot be directly used for real-time control purposes of a practical ozone dosing process. 1

School of Instrument Science and Engineering, Southeast University, Nanjing, P.R. China 2 Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, P.R. China 3 School of Automation, Southeast University, Nanjing, P.R. China 4 Suzhou Water Company, Suzhou, P.R. China Corresponding author: Shihua Li, School of Automation, Southeast University, Nanjing 210096, P.R. China. Email: [email protected]

Wang et al. Artificial neural networks are an effective nonlinear modeling means due to their excellent ability to perform complex nonlinear mapping from input–output data. A radial basis function (RBF) neural network has been proved to posses a very excellent approximation property and has been widely used in various nonlinear modeling processes (Poggio and Girosi, 1990; Molina-Vilaplana et al., 2004; Dang and Tan, 2007; You et al., 2008; Li et al., 2012). In a RBF neural network, the parameters including centers and widths of RBFs and weights between the hidden and output layers have great influence on the performance of a network (Chen et al., 1992; Knopf and Sangole, 2004). Traditional training algorithm based on gradient descent (GD) method has the disadvantages of slow convergence speed and easy trapping into local minimum. Owing to these limitations, global optimization methods such as genetic algorithm (GA) and particle swarm optimization (PSO) algorithms have been developed and widely used for training RBF neural networks (Sergeev et al., 1998; Liu et al., 2004). PSO is a swarm intelligence algorithm inspired by the social behavior of bird flocking and fish schooling. It carries on the intelligent search for the solution space through ‘‘cooperative’’ strategy unlike GA, which utilizes a ‘‘competitive’’ strategy. Suboptimal solutions in the PSO algorithm can therefore survive and contribute to the search process at later stage of iteration. PSO has been proved to perform better error precision as well as faster convergence rate than GA in terms of training neural network (Grimaldi et al., 2004; Wang et al., 2010). For an operating drinking water treatment plant, the effective detention time t10 is determined by the design structure of ozone contactor and varies with water flow rate. Thus, in order to keep a constant Ct10 , the desired value of dissolved ozone residual varies with the water flow rate too. To date, the practical ozone dosing process is still controlled by manual adjustment or PID control (Elovitz et al., 2000; Courtois, 2005; van der Helm et al., 2009), of which the control action is determined based on the deviation between a set point and actual value of process output. It is difficult to achieve a good control performance as the complicated nonlinearity and time delay of practical ozone dosing process. In comparison, the control action of model predictive control (MPC) is determined based on the deviation between a set point and predictive value of the process output. The predictive output can predict the future behavior by using the prediction model of controlled process. Hence, it can drive future process outputs ‘‘closer’’ to the set-point. MPC has become one of the most popular advanced control methods used on industrial process

Figure 1. Flow diagram of drinking water treatment process.

59 control for its excellent ability to handle the problems of finite control horizon, constraints, complicated nonlinear and time delay (Niemi et al., 1997; Ramasamy et al., 2005; Chen et al., 2007; Yang et al., 2011; Liu and Li, 2012). The objective of this paper is to develop a more effective real-time control method for the practical ozone dosing process of drinking water treatment. First, a RBF neural network model trained by a PSO algorithm is established as the prediction model of a practical ozone dosing process. Then, a model predictive controller based on the established RBF neural network model is designed to insure the control strategy of keeping a constant Ct10 . In order to further improve the adaptivity of proposed real-time control scheme, the RBF neural network weights are on-line updated with the recursive leastsquares (RLS) algorithm to cope with the frequent changes of water flow rate, water quality and process operational conditions. To date, the work of this manuscript have been simulated and experimented successfully in the practical ozone dosing process control system of Xiangcheng water treatment plant (XWTP) in Suzhou, China. The rest of the paper is organized as follows. The process features of drinking water treatment and ozonation process are illustrated in Section 2. RBF neural network modeling is described in detail in Section 3. After a brief description of the adaptive MPC, simulation and experiments are conducted in Section 4. Finally, conclusions are given in Section 5.

Ozonation process description Drinking water treatment process The XWTP (capacity of 300,000 m3/day) was originally put into service in 2007, and the raw water is captured from Tai Lake. The overall drinking water treatment process of XWTP comprises pre-ozonation, coagulation, flocculation, sedimentation, sand filtration, main ozonation, BAC filtration and chlorination as shown schematically in Figure 1. Pre-ozonation is mainly utilized to be a flocculation aid, as well as removing algae, taste, odors, color and viruses. Coagulation is a primary process used to hasten the agglomeration of fine particles in turbidity. This process is followed by flocculation. The combination of coagulation and flocculation constitute a solid–liquid separation process for destabilizing dissolved and colloidal impurities and producing large floc aggregates that can be removed from the water in the subsequent sedimentation/filtration processes (Gao et al., 2002). Sedimentation allows large floc-particle masses to

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Transactions of the Institute of Measurement and Control 36(1) a slower ozone decay step (Cho et al., 2003; Kang et al., 2008). The amount of ozone consumed during the rapid consumption stage can be represented by the parameter ID (instantaneous ozone demand), which corresponds to the difference between the administered dissolved ozone and the amount of dissolved ozone measured after a few seconds. The slower decay step is kinetically first order Hoigne´ and Bader, 1994), which can be expressed as d½O3  =  kc ½O3  dt

Figure 2. Main ozonation process.

x1 1

x2

2

y

n

xn Figure 3. Structure of the RBF neural network.

settle prior to filtration (Jakubowski and Craun, 2002). Physical removal of turbidity and microorganisms from water is ultimately accomplished by sand filtration (Cornwell et al., 2003). The combination of main ozonation and BAC is mainly used for disinfection, oxidation of organic contamination, oxidation of specific contaminant and removal of pathogens, etc. (Audenaert et al., 2010). The final chlorination process is adopted for sufficient mix of chlorine and water in the clearwell and keeping dissolved chlorine residual at a certain level in water before entering into the drinking water distribution system.

Ozonation process As shown in Figure 1, there are two ozonation steps during drinking water treatment process in the XWTP: pre-ozonation step and main ozonation step. Main ozonation step is the key step of disinfection and oxidation, which directly affects the treated water quality. Thus, the process modeling and realtime control focus on the main ozonation step in this paper. The schematic diagram of main ozonation process is shown in Figure 2. A fine bubble aeration device is utilized for ozone gas injecting into the water. Considering ozonation efficiency and minimal bromate formation, three-level serial dosing manner with ratio 3:1:1 is adopted in the XWTP. Owing to the milder fluctuation, dissolved ozone residual of the third level is taken nearly as the effluent dissolved ozone residual. As shown in Figure 2, an off-gas ozone destruction device is equipped to convert non-dissolved ozone residual to oxygen for guaranteeing the ozone concentration of treated off-gas lower than 0.1 ppm (Cromphout et al., 2005). The typical description of an ozonation process in natural water consists of a rapid ozone consumption step followed by

ð1Þ

where ½O3  the ozone concentration in water (mg/l) and kc the first-order rate constant for ozone decay (l/min). Many studies based on laboratory-scale experiments have been conducted to illustrate that the ID and kc depend on water quality, temperature, alkalinity, etc. (Elovitz et al., 2000; Park et al., 2001; van der Helm et al., 2007). Since the changes of water flow rate, water quality and process operational conditions are simultaneous and full of uncertainty, the practical ozonation process is much more complex than the laboratory-scale experiment.

Ozone dosing process modeling The practical ozone dosing process exhibits complicated nonlinearity characteristic with time delay, which brings barriers to accurate mathematical model. In this paper, RBF neural network model is established to predict the process output (dissolved ozone residual), and PSO algorithm is adopted to train the RBF neural network parameters.

RBF neural network structure A RBF neural network is an effective feed-forward neural network of one hidden layer. It has been shown that a RBF neural network has a great nonlinear mapping ability (Park and Sandberg, 1991). As shown in Figure 3, the structure of the basic RBF neural network contains one input layer, one hidden layer and one output layer. The output of a singleoutput RBF neural network can be described as y=

q X

vk fk (X)

ð2Þ

k =1

where X the input vector, q the number of hidden nodes, vk the neural network weight that connects the k th hidden node and output, and fk the output of the k th hidden node, which is often defined by a Gaussian function shown as follows: fk (X) = e

jjXmk jj2  2 dk

,

k = (1, 2, . . . , q)

ð3Þ

where mk is the center of the k th hidden node and dk the variance of the k th hidden node. The number of hidden nodes q is the key factor that affects the prediction performance of the neural network. If it is over large, the generalization capability of the neural network might be debased and it may even result in the problem of

Wang et al.

61 where i = 1, 2, . . . , n, n the number of particles, vi k the present velocity of the particle i, xi k the present position of the particle i, k the inertia number, c1 and c2 the acceleration constants, r1 and r2 the random numbers selected between ½0, 1, hk the inertia weight, which can be described as follows:

Start

Initialize kmax

h(k) = (h1  h2 )(kmax  k)=kmax + h2 Calculate

h(k)

and Fitness

Update Pi and Pg

ð6Þ

where kmax is the maximum inertia number, h1 and h2 the initial inertia weight and final inertia weight, respectively. The fitness function of a particle is shown in the following equation:

No

Fitness =

Update v(k+1) and x(k+1)

N 1X (yi  yt )2 N i=1

ð7Þ

where N the number of training samples, yi the ideal output and yt the actual output. The training process of a RBF neural network model parameters with PSO can be shown in Figure 4.

Meet the maximum iteration steps? Yes Map Pg to the RBF neural network parameters

Modeling results

End

Figure 4. Training process of RBF neural network model parameters with PSO.

over-learning. If it is over small, a desired prediction performance may be not achieved.

The training algorithm The RBF neural network model parameters such as centers and widths of the hidden RBF functions and weights connected the hidden nodes with the output nodes have an important influence on the performance of RBF neural network model. The PSO algorithm has proved to be competitive with GA in parameter training (Sousa et al., 2004; Liu et al., 2012). In this paper, a PSO algorithm is adopted to train the parameters of RBF neural network model. A PSO algorithm is a global optimization technology based on the group intelligence, which carries on the intelligent search for the solution space through mutual effect in order to discover the global optimal solution (Kannan et al., 2004). Particle swarms explore the search space through a population of particles. Each particle tries to try to find the global best solution by adjusting the trajectory towards its own best position pi and the best particle of the swarm pg at each iteration. The velocity and position are updated according to the following equations:

The structure of the RBF neural networks model as shown in Figure 5 is selected in this paper, and kd is the time delay. For determining the numbers of hidden nodes, RBF neural networks with different hidden nodes have been tried, and four hidden nodes are selected by considering the tradeoff between modeling accuracy and computational complexity. The 2000 groups of historical input and output data obtained in the XWTP are divided into two parts. The first 1000 groups are used for training and the remaining 1000 groups are used for validation. It is noted that the data has been filtered to improve the modeling effect of the RBF neural network. The convergence of the training process has been controlled by the root-mean-square error (RMSE) between the model output and actual output. The RMSE is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn yi  yi ) 2 i = 1 (^ RMSE = n

ð8Þ

where ^yi is the model output, yi is the actual output and n is the sample number. In addition to the PSO algorithm, GD and GA are also adopted to train the RBF neural network model for

u (k kd ) 1 2

yˆ (k 1)

3

y (k )

4

vi (k + 1) = h(k) vi (k) + c1 r1 (pi (k)  xi (k)) + c2 r2 (pg (k)  xi (k) ) ð4Þ xi (k + 1) = xi (k) + vi (k)

ð5Þ

Figure 5. Model structure of the RBF neural network for the ozone dosing process.

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Transactions of the Institute of Measurement and Control 36(1) 0.5

0.5

Measured value RBF trained by PSO RBF trained by GA RBF trained by GD

RBF

P SO

0.45

RBF

0.45

RBF

0.4

GA

0.4

Dissolved ozone residual (mg/L)

GD

0.35

RMSE

0.3 0.25 0.2 0.15

0.35 0.3 0.25 0.2 0.15

0.1

0.1

0.05

0.05

0

0

0

50

100

150

200 250 Training times

300

350

400

0

200

400 600 Sample number

800

1000

Figure 6. Training results of the RBF neural network.

Figure 7. Modeling results of the ozone dosing process.

comparison. Figure 6 shows the training results of RBF neural network and Figure 7 shows the modeling results. The results shown on training and modeling are based on a seriesparallel structure of RBF. In the series-parallel structure of RBF the output of the actual process is fed back as an input of RBF. This is beneficial to adjust the parameters reducing the computational overhead substantially over the parallel structure of the RBF neural network. It can be seen from the training and modeling results that the RBF neural network model trained by the PSO algorithm has a better modeling accuracy and a better convergence property than that by GD and GA algorithms.

network model is used to predict the process output, and the future control action is computed by real-time optimizing the following cost function:

Adaptive MPC scheme for the ozone dosing process Owing to the variation of effective detention time t10 which varies with the water flow rate, the dissolved ozone residual set point should also be varying to keep a constant Ct10 . Thus, the problem of keeping a constant Ct10 changes to the tracking problem of dissolved ozone residual set point.

Set-point trajectory In order to obtain the set-point trajectory of dissolved ozone residual, the effective detention time t10 should be calculated ahead. In this study the effective detention time t10 is calculated as the hydraulic detention time T (T = volume of water in ozone contactor / water flow rate) multiplying by the baffling factor t10 =T (Phares et al., 2009). The baffling factor t10 =T varies very slightly when the water flow rate varies in an ordinary operational range (AWWA Research Foundation, 1999; Phares et al., 2009). Thus, we can consider it as a constant value with the range of water flow rate of main ozone contactor inlet from 3500 to 6000 m 3 = h in the XWTP.

MPC scheme based on RBF The MPC scheme in this paper is based on the RBF neural network model and nonlinear optimizer. The RBF neural

J=

Ny X

½^y(k + j)  yr (k + j)2 +

j=1 Nu X

lj ½Du(k + j)2 +

j=1

Nu X

l9j ½u(k + j)2

ð9Þ

j=1

subject to ymin < ^y(k + j) < ymax

for 1 \ j \ Ny

umin < u(k + j) < umax

for 1 \ j \ Nu

jDu(k + j)j < Dumax

for 1 \ j \ Nu

ð10Þ

where Ny is the prediction horizon, Nu is the control horizon, lj and lj9 are the input weights of relative importance, ^y(k), yr (k) and Du(k) are the predictive output, reference set point and change in manipulated variable at time k, respectively. At time step k, the nonlinear optimizer computes the present and future manipulated variable moves such that the predictive output follows the reference set points through minimizing the cost function. Only the first move of manipulated variable is applied to the process and this step is repeated for next time step.

Adaptive mechanism There are various adaptive mechanisms adding to the MPC for controlling nonlinear processes from both academic and industrial perspectives (Alexandridis and Sarimveis, 2005; Wang et al., 2006; Fukushima et al., 2007). Most of these adaptive mechanisms primarily focus on updating the process predictive model, which includes updating the model parameters and model structures. When RBF neural network is used to model the nonlinear dynamic process, the sample set of off-line model training is usually chosen from experimental

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yr

63

u

Nonlinear optimizer

RBF neural network model



e

Adaptive mechanism

Figure 8. Adaptive MPC scheme based on RBF.

data and considered covering the entire process operating region. Thus, only the weight values of the RBF neural network are updated on-line to adapt the nonlinear time-varying dynamics in most applications (Yu and Yu, 2003; Wang et al., 2006; Babu et al., 2010). In this paper, a RLS algorithm is used for on-line updating of the RBF neural network weights when the modeling error is larger than a suitable threshold (RMSE . 0.2). It helps to guarantee the predictive accuracy over a wide range of operating conditions and provide a reliable MPC control performance. The equations of adaptive mechanisms based on RLS algorithm can be described as follows: L(k) =

P(k  1)f(k) l + fT (k)P(k  1)f(k)

ð11Þ

1 P(k  1)f(k)fT (k)P(k  1) ½P(k  1)   l l + fT (k)P(k  1)f(k)

ð12Þ

v ^ (k) = v ^ (k  1) + L(k)½y(k)  fT (k)^ v(k  1)

ð13Þ

P(k) =

Gp (s) =

y

Ozone dosing process

where 0 \ l \ 1 is the forgetting factor, v ^ (k) are the network weights, f(k) are the hidden mode outputs, P(k) and L(k) are the middle terms.

Simulation results The simulation of the proposed adaptive MPC scheme based on a RBF neural network model is performed in MATLAB. As in the above analysis, the actual ozone dosing process presents time-varying first order plus time delay (FOPTD) characteristics. Thus, a FOPTD model of Equation (14) is assumed as the actual ozone dosing process for simulation. Note that the unit of time constants is minute in this paper.

0:5 8s e 3s + 1

ð14Þ

The control objective of the ozone dosing process is to track the dissolved ozone residual set-point trajectory by adjusting the ozone dosage and hence to keep Ct10 at a desired constant value. A MPC scheme based on fixed RBF neural network model trained off-line and PI scheme with time delay were also conducted for comparison. For the proposed adaptive MPC scheme based on a RBF neural network model and the MPC scheme based on a fixed RBF neural network model, we select the prediction horizon Ny = 3, the control horizon Nu = 1, the input weights lj = 0:002 and l9j = 0:002, the input constraints jDu(k)j < 0:5 mg/l, 0 mg=l < u(k) < 1:5 mg/l. The tracking performance of dissolved ozone residual in the nominal case and model mismatch case are simulated respectively. The overshoot, settling time and integral of absolute error (IAE) are chosen as the quantitative indices to evaluate the closed-loop control performance. The IAE criterion is defined as IAE(t) =

T 1X jr(t)  y(t)j T t=1

ð15Þ

where r(t) is the reference set point and y(t) is the actual process output. When the predictive model is matched with the actual ozone dosing process, the simulation results and performance indices are shown in Figure 9 and Table 1, respectively. It can been seen that the proposed adaptive MPC scheme based on a RBF neural network model and MPC scheme based on a fixed RBF neural network model produce the same control performance because the adaptive mechanism does not work in the nominal case. Both of them provide smaller overshoots, shorter settling times and faster set-point tracking performances, while the PI scheme exhibits a bigger overshoot, a longer settling time and a slower set-point tracking performance. To confirm the adaptability of the proposed adaptive MPC scheme, 30% decreases of parameters in Equation (14) for the model mismatch case are simulated. The simulation results and performance indices are shown in Figure 10 and Table 2, respectively. Owing to the on-line updating of the model weights, the proposed adaptive MPC scheme based on a RBF neural network can adapt the time-varying dynamics of the ozone dosing process well, and is therefore more suitable for the long-time automatic control of ozone dosing process.

Table 1. Performance indices of the output response of dissolved ozone residual for the simulation results of the nominal case. Method

Adaptive MPC based on RBF MPC based on fixed RBF PI

0–50 min

50–100 min

Overshoot (%)

Settling time (min)

IAE (mg/L)

Overshoot (%)

Settling time (min)

IAE (mg/L)

10.9 10.9 20.4

20 20 27

0.003 0.003 0.007

2.1 2.1 6.1

15 15 20

0.003 0.003 0.007

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Transactions of the Institute of Measurement and Control 36(1) 0.5 0.45 0.4

4

0.35 0.3 0.25 0.2 0.15

Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

0.1 0.05 0

(b)

4.5

Ozone exposure (mg/L.min)

Dissolved ozone residual (mg/L)

5

(a)

0

20

40

60

80

3.5 3 2.5 2 1.5

Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

1 0.5 0

100

0

20

40

t(min)

60

80

100

t(min)

Figure 9. Simulation results of nominal case: (a) dissolved ozone residual; (b) ozone exposure.

Table 2. Performance indices of the output response of dissolved ozone residual for the simulation results of the model mismatch case. Method

0–50 min

Adaptive MPC based on RBF MPC based on fixed RBF PI

0.5

Overshoot (%)

Settling time (min)

IAE (mg/L)

Overshoot (%)

Settling time (min)

IAE (mg/L)

0 3.2 18.8

22 22 28

0.004 0.041 0.009

0 0 1.9

17 17 21

0.004 0.041 0.009

5

(a)

0.45 0.4

4

0.35 0.3 0.25 0.2 0.15 Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

0.1 0.05 0

(b)

4.5

Ozone exposure (mg/L.min)

Dissolved ozone residual (mg/L)

50–100 min

0

20

40

60

80

3.5 3 2.5 2 1.5

Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

1 0.5 100

0

0

20

40

t(min)

60

80

100

t(min)

Figure 10. Simulation results of the model mismatch case: (a) dissolved ozone residual; (b) ozone exposure.

Experimental results In order to test the practical application effects of the proposed adaptive MPC scheme based on a RBF neural network model. Experiments of the proposed adaptive MPC scheme based on a RBF neural network model together with the MPC scheme based on a fixed RBF neural network model

and the PI scheme are performed in the XWTP. The control algorithms are coded on the commercial SCADA software of Siemens Wincc. All of the on-line signals from or to the ozone dosing process control system are interconnected through DCS as shown in Figure 11. Process data are saved in a database on a PC server, and the control schemes are programmed on the PC and executed through a programmable logic

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Configuration Monitor Data analysis Graphs, etc

Monitor Supervision Data base, etc

CPU 315-2DP

I/O modules

Water flow Water temperature rate COD Turbidity Dissolved ozone residual, etc

PC

PC Server

PLC Siemens S7-300

Ozone gas flow rate Ozone gas concentration

Figure 11. Distributed control system for the ozone dosing process.

0.5

5

(a)

0.45

4 Ozone exposure(mg/L.min)

Dissolved ozone residual(mg/L)

0.4 0.35 0.3 0.25 0.2 0.15

Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

0.1 0.05 0

(b)

4.5

0

20

40

60

80

3.5 3 2.5 2 1.5

Adaptive MPC based on RBF MPC based on fixed RBF PI Set−point

1 0.5 100

0

0

20

t(min)

40

60

80

100

t(min)

Figure 12. Experimental results: (a) dissolved ozone residual; (b) ozone exposure.

Table 3. Performance indices of the output response of dissolved ozone residual for the experimental results. Method

Overshoot (%)

Settling time (min)

IAE (mg/L)

Adaptive MPC based on RBF MPC based on fixed RBF PI

1.5

18

0.011

2.7

22

0.014

9.2

26

0.015

controller (PLC). The ozone dosage can be adjusted on-line by changing the gas flow rate and/or the concentration of ozone in the gas flow of the ozone generators. It can be seen from the experimental results in Figure 12 and Table 3 that the control performance of the proposed adaptive MPC scheme based on a RBF neural network model is better than the MPC scheme based on a fixed RBF neural network model and the PI scheme for the nonlinear dynamics of practical ozone dosing process. This is

consistent with the previous theoretical analysis and simulation results.

Conclusion The control strategy of keeping a constant Ct10 has been attempted for the ozone dosing process of drinking water treatment in this paper. An adaptive MPC scheme based on a RBF neural network model has been proposed. The RBF neural network trained by a PSO algorithm has been used to model the practical ozone dosing process. The weights of RBF neural network have been updated on-line to adapt the nonlinear timevarying dynamics. Simulation and experimental results have demonstrated significant performance improvements compared with the MPC scheme based on a fixed RBF neural network model and the PI scheme. For realizing more reliable real-time automatic control of the ozone dosing process, the proposed adaptive MPC scheme based on a RBF neural network model should be investigated in a longer experiment and further stability evaluations should be conducted.

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Transactions of the Institute of Measurement and Control 36(1)

Funding

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The work was supported in part by National Natural Science Foundation of China (grant number 61203011) and Natural Science Foundation of Jiangsu Province (grant number BK2012327).

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