Multi-time Scale Model Predictive Control of Wastewater Treatment Process

Abstract

A multi-time scale model predictive control method for wastewater treatment process is designed to control the dissolved oxygen concentration and nitrate nitrogen concentration in different time scales to ensure that the effluent quality meets the standard. In view of the difference of time scales in wastewater treatment process caused by different sampling periods of dissolved oxygen concentration and nitrate nitrogen concentration, prediction models with different time scales are firstly designed to unify the prediction outputs to the fast time scale. Then, the gradient descent algorithm is used to solve the optimal solution with fast time scale to control the wastewater treatment system. It not only conforms to the operation characteristics of wastewater treatment process, but also solves the problem of poor operation performance of multiobjective model predictive control caused by different time scales. The experimental results show that the multi-time scale model predictive control method can achieve accurate on-line control of dissolved oxygen concentration and nitrate nitrogen concentration with fast time scales.

Claims

1. A multi-time scale model predictive control method of wastewater treatment process, comprising the following steps: (1) the multi-time scale model predictive control system for wastewater treatment process control comprising a set of measuring devices arranged to obtain a dataset, measuring devices include dissolved oxygen detector, nitrate nitrogen detector, the dataset comprises a plurality of process variables related to a parameter of wastewater treatment process; a programmable logic controller arranged to perform digital/analog conversion and analog/digital conversion; a variable-frequency drive arranged to control the air-blower and electronic valve by changing the working power frequency of motor; an air-blower arranged to provide the required oxygen to the microorganisms in the wastewater treatment process; an electronic valve arranged to adjust internal return flow; a multi-time scale model predictive control module arranged to calculate the control law to track the dissolved oxygen concentration and nitrate nitrogen concentration in wastewater treatment process with different time scales; the multi-time scale model predictive control module comprising two fuzzy neural network to predict the system outputs, a time scale conversion mechanism to unify the prediction time scales to fast time scale, and an optimization control module to calculate the control law; (2) the time scales of dissolved oxygen concentration and nitrate nitrogen concentration in wastewater treatment process are different, specifically: T.sub.f is the sampling interval of dissolved oxygen concentration, T.sub.f∈[6, 10] is a positive integer in minutes, t.sub.f=fT.sub.f represents the sampling instant of dissolved oxygen concentration, f is the number of sampling steps of dissolved oxygen concentration, and f∈[1, 1000] is a positive integer; T.sub.s is the sampling interval of nitrate nitrogen concentration, T.sub.s∈[12, 20] is a positive integer in minutes, t.sub.s=sT.sub.s represents the sampling instant of nitrate nitrogen concentration, s is the number of sampling steps of nitrate nitrogen concentration, and s∈[1, 400] is a positive integer; ζ is the maximum common divisor of T.sub.f and T.sub.s, t.sub.η=ηζ is the prediction instant of slow sampling fuzzy neural network, η is the number of prediction steps of slow sampling fuzzy neural network, η∈[1, 2000] is a positive integer; (3) a fast sampling fuzzy neural network is designed to predict dissolved oxygen concentration with time scale T.sub.f, which is as follows: the input of the fast sampling fuzzy neural network is x.sub.f(t.sub.f)=[x.sub.f1(t.sub.f−1), x.sub.f2(t.sub.f−1), x.sub.f3(t.sub.f−1)].sup.T, T is the transposition of the matrix, and the output of the fast sampling fuzzy neural network is the predicted value of dissolved oxygen concentration ŷ.sub.f(t.sub.f) at time t.sub.f, the output is defined as follows $\begin{array}{cc}{\hat{y}}_f\left(t_f\right)=\frac{{.Math.}_{j=1}^6{w}_{\mathrm{fj}}\left(t_f\right)e^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{fi}}\left(t_f-1\right)-c_{\mathrm{fij}}\left(t_f\right)\right)}^2}{2{\sigma }_{\mathrm{fij}}^2\left(t_f\right)}}}{{.Math.}_{j=1}^6{e}^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{fi}}\left(t_f-1\right)-c_{\mathrm{fij}}\left(t_f\right)\right)}^2}{2{\sigma }_{\mathrm{fij}}^2\left(t_f\right)}}}& \left(1\right)\end{array}$ where x.sub.fi(t.sub.f−1) is the ith input of the fast sampling fuzzy neural network at time t.sub.f, i=1, 2, 3, w.sub.fj(t.sub.f) is the weight between the jth regular layer neuron and the output layer neuron of the fast sampling fuzzy neural network at time t.sub.f, w.sub.fj(t.sub.0) is randomly assigned within [0, 1], j=1, 2, 3, 4, 5, 6, t.sub.0 is the initial instant, c.sub.fij(t.sub.f) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f, c.sub.fij(t.sub.0) is randomly assigned within [0,1], σ.sub.fij(t.sub.f) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f, and σ.sub.fij(t.sub.0) is randomly assigned within [0,1]; (4) a slow sampling fuzzy neural network is designed to predict nitrate nitrogen concentration with time scale ζ, which is as follows: The input of the slow sampling fuzzy neural network is x.sub.s(t.sub.η)=[x.sub.s1(t.sub.η−1), x.sub.s2(t.sub.η−1), x.sub.s3(t.sub.η−1)].sup.T, and the output of the slow sampling fuzzy neural network is the predicted value of nitrate nitrogen concentration ŷ.sub.s(t.sub.η) at time t.sub.η, the output is defined as follows $\begin{array}{cc}{\hat{y}}_f\left(t_{\eta }\right)=\frac{{.Math.}_{j=1}^6{\omega }_{\mathrm{sj}}\left(t_{\eta }\right)e^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{si}}\left(t_{\eta }-1\right)-c_{\mathrm{sij}}\left(t_{\eta }\right)\right)}^2}{2{\sigma }_{\mathrm{sij}}^2\left(t_{\eta }\right)}}}{{.Math.}_{j=1}^6{e}^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{si}}\left(t_{\eta }-1\right)-c_{\mathrm{sij}}\left(t_{\eta }\right)\right)}^2}{2{\sigma }_{\mathrm{sij}}^2\left(t_{\eta }\right)}}}& \left(2\right)\end{array}$ where x.sub.si(t.sub.η−1) is the ith input of the slow sampling fuzzy neural network at time t.sub.η, w.sub.sj(t.sub.η) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.η, w.sub.sj(t.sub.0) is randomly assigned within [0, 1], c.sub.sij(t.sub.η) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η, c.sub.sij(t.sub.0) is randomly assigned within [0,1], σ.sub.sij(t.sub.η) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η, and σ.sub.sij(t.sub.0) is randomly assigned within [0,1]; a dataset Ω whose time scale is ζ is constructed as follows, when t.sub.s≤t.sub.η<t.sub.s+1:
u.sub.s1.sup.η(t.sub.η)=u.sub.s1(t.sub.s)  (3)
u.sub.s2.sup.η(t.sub.η)=u.sub.s2(t.sub.s)  (4)
y.sub.s.sup.η(t.sub.η)=y.sub.s(t.sub.s)+T.sub.s(y.sub.s(t.sub.s+1)−y.sub.s(t.sub.s))/t.sub.η  (5) where u.sub.s1.sup.η(t.sub.η) is the virtual value of aeration rate at time t.sub.η, u.sub.s1(t.sub.s) is the actual value of aeration rate at time t.sub.s, u.sub.s2.sup.η(t.sub.η) is the virtual value of internal reflux at time t.sub.η, u.sub.s2(t.sub.s) is the actual value of internal reflux at time t.sub.s, y.sub.s.sup.η(t.sub.η) is the virtual estimated value of nitrate nitrogen concentration at time t.sub.η, y.sub.s(t.sub.s) is the actual value of the nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.s, y.sub.s(t.sub.s+1) is the actual value of the nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.s+1; the dataset Ω is composed of u.sub.s1.sup.η(t.sub.η), u.sub.s2.sup.η(t.sub.η), and y.sub.s.sup.η(t.sub.η); The dataset Ω is used to pre-train the slow sampling fuzzy neural network offline, and the training input is x.sub.s.sup.η(t.sub.η)=[y.sub.s.sup.η(t.sub.η−1), u.sub.s1.sup.η(t.sub.η−1), u.sub.s2.sup.η(t.sub.η−1)].sup.T, y.sub.s.sup.η(t.sub.η−1) is the nitrate nitrogen concentration at time t.sub.η−1 in Ω, u.sub.s1.sup.η(t.sub.η−1) is the aeration rate at time t.sub.η−1 in Ω, u.sub.s2.sup.η(t.sub.η−1) is the internal reflux at time t.sub.η−1 in Ω, the training output is the prediction value of nitrate nitrogen concentration ŷ.sub.s.sup.η(t.sub.η) at time t.sub.η; using the error between nitrate nitrogen concentration value in dataset Ω and predicted value E.sub.s.sup.η(t.sub.η)=½[y.sub.s.sup.η(t.sub.η)−ŷ.sub.s.sup.η(t.sub.η)].sup.2 at time t.sub.η, correct parameters of slow sampling fuzzy neural network:
w.sub.sj(t.sub.η+1)=w.sub.sj(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂w.sub.sj(t.sub.η)  (6)
c.sub.sij(t.sub.η+1)=c.sub.sij(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂c.sub.sij(t.sub.η)  (7)
σ.sub.sij(t.sub.η+1)=σ.sub.sij(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂σ.sub.sij(t.sub.η)  (8) where w.sub.sj(t.sub.η+1) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.η+1, c.sub.sij(t.sub.η+1) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η+1, σ.sub.sij(t.sub.η+1) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η+1; (5) The multi-time scale model predictive control method is designed to control the dissolved oxygen concentration and nitrate nitrogen concentration in time scale T.sub.f, specifically: {circle around (1)} set s=1, f=1, η=1; {circle around (2)} according to the sampling information converted by programmable logic controller, predict nitrate nitrogen concentration at time t.sub.η using slow sampling fuzzy neural network; the inputs of the slow sampling fuzzy neural network are as follows: x.sub.s1(t.sub.η−1) is the actual value of nitrate nitrogen concentration y.sub.s(t.sub.η−1) at time t.sub.η−1, x.sub.s2(t.sub.η−1) is the aeration rate u.sub.1(t.sub.η−1) at time t.sub.η−1, x.sub.s3(t.sub.η−1) is the internal reflux u.sub.2(t.sub.η−1) at time t.sub.η−1; the output of the slow sampling fuzzy neural network is the prediction value of nitrate nitrogen concentration ŷ.sub.s(t.sub.η) at time t.sub.η; {circumflex over (3)} if t.sub.η=t.sub.f, set ŷ.sub.s(t.sub.f)=ŷ.sub.s(t.sub.η), where ŷ.sub.s(t.sub.f) is the prediction value of nitrate nitrogen concentration at time t.sub.f, go to step {circle around (6)} after performing step {circle around (4)}; if t.sub.η≠t.sub.f, go to step {circle around (6)} after performing step {circle around (5)}; {circle around (4)} if t.sub.η=t.sub.s, increase the value of s by 1, update the parameters of the slow sampling fuzzy neural network by the error between the predicted value and the actual value of nitrate nitrogen concentration E.sub.s(t.sub.η)=½[y.sub.s(t.sub.s)−ŷ.sub.s(t.sub.η)].sup.2:
w.sub.sj(t.sub.η+1)=w.sub.sj(t.sub.η))−0.2∂E.sub.s(t.sub.η)/∂w.sub.sj(t.sub.η)  (9)
c.sub.sij(t.sub.η+1)=c.sub.sij(t.sub.η)−0.2∂E.sub.s(t.sub.η)/∂c.sub.sij(t.sub.η)  (10)
σ.sub.sij(t.sub.η+1)=σ.sub.sij(t.sub.η)−0.2∂E.sub.s(t.sub.η)/∂σ.sub.sij(t.sub.η)  (11) if t.sub.η≠t.sub.s, the parameters of slow sampling fuzzy neural network are not updated; {circumflex over (5)} set y.sub.s(t.sub.η)=ŷ.sub.s(t.sub.η), u.sub.1(t.sub.η)=u.sub.1(t.sub.f), u.sub.2(t.sub.η)=u.sub.2(t.sub.f), increase the value of η by 1, go to step {circle around (2)}, where y.sub.s(t.sub.η) is the actual nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.η, u.sub.1(t.sub.η) is the aeration rate at time t.sub.η, u.sub.2(t.sub.η) is the internal reflux at time t.sub.η, u.sub.1(t.sub.f) is the aeration rate at time t.sub.f, u.sub.2(t.sub.f) is the internal reflux at time t.sub.f; {circumflex over (6)} predict dissolved oxygen concentration at time t.sub.f by the fast sampling fuzzy neural network; the inputs of the fast sampling fuzzy neural network are as follows: x.sub.f1(t.sub.f−1) is the actual value of dissolved oxygen concentration y.sub.f(t.sub.f−1) converted by the programmable logic controller at time t.sub.f−1, x.sub.f2(t.sub.f−1) is the aeration rate u.sub.1(t.sub.f−1) at time t.sub.f−1, x.sub.f3(t.sub.f−1) is the internal reflux u.sub.2(t.sub.f−1) at time t.sub.f−1; the output of the fast sampling fuzzy neural network is the prediction value of dissolved oxygen concentration ŷ.sub.f(t.sub.f) at time t.sub.f; update the parameters of the fast sampling fuzzy neural network by the error between the predicted value and the actual value of dissolved oxygen concentration E.sub.f(t.sub.f)=½[y.sub.f(t.sub.f)−ŷ.sub.f(t.sub.f)].sup.2:
w.sub.fj(t.sub.f+1)=w.sub.fj(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂w.sub.fj(t.sub.f)  (12)
c.sub.fij(t.sub.f+1)=c.sub.fij(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂c.sub.fij(t.sub.f)  (13)
σ.sub.fij(t.sub.f+1)=σ.sub.fij(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂σ.sub.fij(t.sub.f)  (14) where w.sub.fj(t.sub.f+1) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.f+1, c.sub.fij(t.sub.f+1) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f+1, σ.sub.fij(t.sub.f+1) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f+1; {circle around (7)} design an objective function of multi-time scale model predictive control to track the set-points of nitrate nitrogen concentration and dissolved oxygen concentration, and calculate the control law at time t.sub.f:
J(t.sub.f)=0.25[[r.sub.f(t.sub.f)−ŷ.sub.f(t.sub.f)].sup.T[r.sub.f(t.sub.f)−ŷ.sub.f(t.sub.f)]+Δu(t.sub.f).sup.TΔu(t.sub.f)]+0.45[r.sub.s(t.sub.f)−ŷ.sub.s(t.sub.f)].sup.T[r.sub.s(t.sub.f)−ŷ.sub.s(t.sub.f)]Δu(t.sub.f).sup.TΔu(t.sub.f)  (15) where r.sub.f(t.sub.f)=[r.sub.f(t.sub.f+1), r.sub.f(t.sub.f+2), r.sub.f(t.sub.f+3)].sup.T is the set-point of dissolved oxygen concentration, r.sub.f(t.sub.f+1)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+1, r.sub.f(t.sub.f+2)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+2, r.sub.f(t.sub.f+3)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+3; ŷ.sub.f(t.sub.f)=[ŷ.sub.f(t.sub.f+1), ŷ.sub.f(t.sub.f+2), ŷ.sub.f(t.sub.f+3)].sup.T is the prediction output of the fast sampling fuzzy neural network, ŷ.sub.f(t.sub.f+1) is the prediction value of dissolved oxygen concentration at time t.sub.f+1, ŷ.sub.f(t.sub.f+2) is the prediction value of dissolved oxygen concentration at time t.sub.f+2, ŷ.sub.f(t.sub.f+3) is the prediction value of dissolved oxygen concentration at time t.sub.f+3; r.sub.s(t.sub.f)=[r.sub.s(t.sub.f+1), r.sub.s(t.sub.f+2), r.sub.s(t.sub.f+3)].sup.T is the set-point of nitrate nitrogen concentration; r.sub.s(t.sub.f+1)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+1, r.sub.s(t.sub.f+2)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+2, r.sub.s(t.sub.f+3)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+3; ŷ.sub.s(t.sub.s)=[ŷ.sub.s(t.sub.s+1), ŷ.sub.s(t.sub.s+2), ŷ.sub.s(t.sub.s+3)].sup.T is the prediction output of slow sampling fuzzy neural network, ŷ.sub.s(t.sub.f−1) is the prediction value of nitrate nitrogen concentration at time t.sub.f+1, ŷ.sub.s(t.sub.f+2) is the prediction value of nitrate nitrogen concentration at time t.sub.f+2, ŷ.sub.s(t.sub.f+3) is the prediction value of nitrate nitrogen concentration at time t.sub.f+3; Δu(t.sub.f)=[Δu.sub.1(t.sub.f), Δu.sub.2(t.sub.f)].sup.T is the incremental control moves at time t.sub.f, Δu.sub.1(t.sub.f) is the aeration rate adjustment amount at time t.sub.f, Δu.sub.2(t.sub.f) is the internal reflux adjustment amount at time t.sub.f, where
Δu(t.sub.f)=u(t.sub.f+1)−u(t.sub.f)  (16)
|Δu(t.sub.f)|≤Δu.sub.max  (17) u(t.sub.f)=[u.sub.1(t.sub.f), u.sub.2(t.sub.f)].sup.T is control vector converting into analog signal through programmable logic controller and transmitting to variable frequency driver at time t.sub.f, u(t.sub.f+1)=[u.sub.1(t.sub.f+1), u.sub.2(t.sub.f+1)].sup.T is control vector converting into analog signal through programmable logic controller and transmitting to variable frequency driver at time t.sub.f+1, u.sub.1(t.sub.f+1) is the aeration rate at time t.sub.f+1, u.sub.2(t.sub.f+1) is the internal reflux at time t.sub.f+1; Δu.sub.max=[ΔK.sub.La.sub.max, ΔQ.sub.amax].sup.T is the maximum adjustment vector allowed by the controller, ΔK.sub.La.sub.max=100 L/min is the maximum aeration adjustment amount, ΔQ.sub.amax=50000 L/min is the maximum internal reflux adjustment amount, Δu.sub.max is set through the blower and internal reflux valve in the control system equipment; an aeration rate and internal reflux adjustment vector are calculated by minimizing Eq.(15): $\begin{array}{cc}\Delta u\left(t_f\right)=\left(0.4{\left(\frac{\partial {\hat{y}}_f\left(t_f\right)}{\partial u\left(t_f\right)}\right)}^T\left[r_f\left(t_f\right)-{\hat{y}}_f\left(t_f\right)\right]+0.08{\left(\frac{\partial {\hat{y}}_s\left(t_f\right)}{\partial u\left(t_f\right)}\right)}^T\left[r_s\left(t_f\right)-{\hat{y}}_s\left(t_f\right)\right]\right)& \left(18\right)\end{array}$ adjust the aeration rate and internal reflux at time t.sub.f:
u(t.sub.f+1)=u(t.sub.f)+Δu(t.sub.f)  (19) {circle around (8)} if f≤1000, increase the value of f by 1, increase the value of η by 1, go to step {circle around (2)}; if f>1000, end the cycle; (6) the concentration of nitrate nitrogen and dissolved oxygen is controlled by u(t.sub.f), and u(t.sub.f)=[u.sub.1(t.sub.f), u.sub.2(t.sub.f)].sup.T is transferred to programmable logic controller for digital/analog conversion to obtain U(t.sub.f)=[U.sub.1(t.sub.f), U.sub.2(t.sub.f)].sup.T, which is the input of variable-frequency drive, the variable-frequency drive changes the working power frequency of motor to control the aeration pump and electronic valve, then, the aeration rate and internal reflux are controlled, the output of the system is the actual value of nitrate nitrogen concentration and dissolved oxygen concentration.

Description

DESCRIPTION OF DRAWINGS

[0037] FIG. 1 is diagram of the multi-time scale model predictive control system of wastewater treatment process.

[0038] FIG. 2 is a control structure diagram of the invention.

[0039] FIG. 3 is an algorithm diagram of the invention.

[0040] FIG. 4 is the time diagram of the invention.

[0041] FIG. 5 is the result diagram of the dissolved oxygen concentration control in this invention.

[0042] FIG. 6 is the error diagram of the dissolved oxygen concentration control result in this invention.

[0043] FIG. 7 is the result diagram of nitrate nitrogen concentration control in this invention.

[0044] FIG. 8 is the error diagram of the nitrate nitrogen concentration control result in this invention.

DETAILED DESCRIPTION OF THE INVENTION

[0045] 1. A multi-time scale model predictive control method of wastewater treatment process, comprising the following steps:

[0046] (1) the multi-time scale model predictive control system for wastewater treatment process control comprising a set of measuring devices arranged to obtain a dataset, measuring devices include dissolved oxygen detector, nitrate nitrogen detector, the dataset comprises a plurality of process variables related to a parameter of wastewater treatment process; a programmable logic controller arranged to perform digital/analog conversion and analog/digital conversion; a variable-frequency drive arranged to control the air-blower and electronic valve by changing the working power frequency of motor; an air-blower arranged to provide the required oxygen to the microorganisms in the wastewater treatment process; an electronic valve arranged to adjust internal return flow; a multi-time scale model predictive control module arranged to calculate the control law to track the dissolved oxygen concentration and nitrate nitrogen concentration in wastewater treatment process with different time scales; the multi-time scale model predictive control module comprising two fuzzy neural network to predict the system outputs, a time scale conversion mechanism to unify the prediction time scales to fast time scale, and an optimization control module to calculate the control law;

[0047] (2) the time scales of dissolved oxygen concentration and nitrate nitrogen concentration in wastewater treatment process are different, specifically:

[0048] T.sub.f is the sampling interval of dissolved oxygen concentration, T.sub.f∈[6, 10] is a positive integer in minutes, t.sub.f=fT.sub.f represents the sampling instant of dissolved oxygen concentration, f is the number of sampling steps of dissolved oxygen concentration, and f∈[1, 1000] is a positive integer;

[0049] T.sub.s is the sampling interval of nitrate nitrogen concentration, T.sub.s∈[12, 20] is a positive integer in minutes, t.sub.s=sT.sub.s represents the sampling instant of nitrate nitrogen concentration, s is the number of sampling steps of nitrate nitrogen concentration, and s∈[1, 400] is a positive integer;

[0050] ζ is the maximum common divisor of T.sub.f and T.sub.s, t.sub.η=ηζ is the prediction instant of slow sampling fuzzy neural network, η is the number of prediction steps of slow sampling fuzzy neural network, η∈[1, 2000] is a positive integer;

[0051] (3) a fast sampling fuzzy neural network is designed to predict dissolved oxygen concentration with time scale T.sub.f, which is as follows:

[0052] the input of the fast sampling fuzzy neural network is x.sub.f(t.sub.f)=[x.sub.f1(t.sub.f−1), x.sub.f2(t.sub.f−1), x.sub.f3(t.sub.f−1)].sup.T, T is the transposition of the matrix, and the output of the fast sampling fuzzy neural network is the predicted value of dissolved oxygen concentration ŷ.sub.f(t.sub.f) at time t.sub.f, the output is defined as follows

[00004]$\begin{array}{cc}{\hat{y}}_f\left(t_f\right)=\frac{{.Math.}_{j=1}^6{w}_{\mathrm{fj}}\left(t_f\right)e^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{fi}}\left(t_f-1\right)-c_{\mathrm{fij}}\left(t_f\right)\right)}^2}{2{\sigma }_{\mathrm{fij}}^2\left(t_f\right)}}}{{.Math.}_{j=1}^6{e}^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{fi}}\left(t_f-1\right)-c_{\mathrm{fij}}\left(t_f\right)\right)}^2}{2{\sigma }_{\mathrm{fij}}^2\left(t_f\right)}}}& \left(20\right)\end{array}$

where x.sub.fi(t.sub.f−1) is the ith input of the fast sampling fuzzy neural network at time t.sub.f, i=1, 2, 3, w.sub.fj(t.sub.f) is the weight between the jth regular layer neuron and the output layer neuron of the fast sampling fuzzy neural network at time t.sub.f, w.sub.fj(t.sub.0) is randomly assigned within [0, 1], j=1, 2, 3, 4, 5, 6, t.sub.0 is the initial instant, c.sub.fij(t.sub.f) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f, c.sub.fij(t.sub.0) is randomly assigned within [0,1], σ.sub.fij(t.sub.f) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f, and σ.sub.fij(t.sub.0) is randomly assigned within [0,1];

[0053] (4) a slow sampling fuzzy neural network is designed to predict nitrate nitrogen concentration with time scale ζ, which is as follows:

[0054] The input of the slow sampling fuzzy neural network is x.sub.s(t.sub.η)=[x.sub.s1(t.sub.η−1), x.sub.s2(t.sub.η−1), x.sub.s3(t.sub.η−1)].sup.T, and the output of the slow sampling fuzzy neural network is the predicted value of nitrate nitrogen concentration ŷ.sub.s(t.sub.η) at time t.sub.η, the output is defined as follows

[00005]$\begin{array}{cc}{\hat{y}}_f\left(t_{\eta }\right)=\frac{{.Math.}_{j=1}^6{\omega }_{\mathrm{sj}}\left(t_{\eta }\right)e^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{si}}\left(t_{\eta }-1\right)-c_{\mathrm{sij}}\left(t_{\eta }\right)\right)}^2}{2{\sigma }_{\mathrm{sij}}^2\left(t_{\eta }\right)}}}{{.Math.}_{j=1}^6{e}^{-\underset{i=1}{\overset{3}{.Math.}}\frac{{\left(x_{\mathrm{si}}\left(t_{\eta }-1\right)-c_{\mathrm{sij}}\left(t_{\eta }\right)\right)}^2}{2{\sigma }_{\mathrm{sij}}^2\left(t_{\eta }\right)}}}& \left(21\right)\end{array}$

where x.sub.si(t.sub.η−1) is the ith input of the slow sampling fuzzy neural network at time t.sub.η, w.sub.sj(t.sub.η) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.η, w.sub.sj(t.sub.0) is randomly assigned within [0, 1], c.sub.sij(t.sub.η) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η, c.sub.sij(t.sub.0) is randomly assigned within [0,1], σ.sub.sij(t.sub.η) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η, and σ.sub.sij(t.sub.0) is randomly assigned within [0,1];

[0055] a dataset Ω whose time scale is ζ is constructed as follows, when t.sub.s≤t.sub.η<t.sub.s+1.

u.sub.s1.sup.η(t.sub.η)=u.sub.s1(t.sub.s)  (22)

u.sub.s2.sup.η(t.sub.η)==u.sub.s2(t.sub.s)  (23)

y.sub.s.sup.η(t.sub.η)=y.sub.s(t.sub.s)+T.sub.s(y.sub.s(t.sub.s+1)−y.sub.s(t.sub.s))/t.sub.η  (24)

where u.sub.s1.sup.η(t.sub.η) is the virtual value of aeration rate at time t.sub.η, u.sub.s1(t.sub.s) is the actual value of aeration rate at time t.sub.s, u.sub.s2.sup.η(t.sub.η) is the virtual value of internal reflux at time t.sub.η, u.sub.s2(t.sub.s) is the actual value of internal reflux at time t.sub.s, y.sub.s.sup.η(t.sub.η) is the virtual estimated value of nitrate nitrogen concentration at time t.sub.η, y.sub.s(t.sub.s) is the actual value of the nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.s, y.sub.s(t.sub.s+1) is the actual value of the nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.s+1; the dataset Ω is composed of u.sub.s1.sup.η(t.sub.η), u.sub.s2.sup.η(t.sub.η), and y.sub.s.sup.η(t.sub.η);

[0056] The dataset Ω is used to pre-train the slow sampling fuzzy neural network offline, and the training input is x.sub.s.sup.η(t.sub.η)=[y.sub.s.sup.η(t.sub.η−1), u.sub.s1.sup.η(t.sub.η−1), u.sub.s2.sup.η(t.sub.η−1)].sup.T, y.sub.s.sup.η(t.sub.η−1) is the nitrate nitrogen concentration at time t.sub.η−1 in Ω, u.sub.s1.sup.η(t.sub.η−1) is the aeration rate at time t.sub.η−1 in Ω, u.sub.s2.sup.η(t.sub.η−1) is the internal reflux at time t.sub.η−1 in Ω, the training output is the prediction value of nitrate nitrogen concentration ŷ.sub.s.sup.η(t.sub.η) at time t.sub.η; using the error between nitrate nitrogen concentration value in dataset Ω and predicted value E.sub.s.sup.η(t.sub.η)=½[y.sub.s.sup.η(t.sub.η)−ŷ.sub.s.sup.η(t.sub.η)].sup.2 at time t.sub.η, correct parameters of slow sampling fuzzy neural network:

w.sub.sj(t.sub.η+1)=w.sub.sj(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂w.sub.sj(t.sub.η)  (25)

c.sub.sij(t.sub.η+1)=c.sub.sij(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂c.sub.sij(t.sub.η)  (26)

σ.sub.sij(t.sub.η+1)=σ.sub.sij(t.sub.η)−0.2∂E.sub.s.sup.η(t.sub.η)/∂σ.sub.sij(t.sub.η)  (27)

where w.sub.sj(t.sub.η+1) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.η+1, c.sub.sij(t.sub.η+1) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t.sub.η+1, σ.sub.sij(t.sub.η+1) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the slow sampling fuzzy neural network at time t+1;

[0057] (5) The multi-time scale model predictive control method is designed to control the dissolved oxygen concentration and nitrate nitrogen concentration in time scale T.sub.f, specifically:

[0058] {circle around (1)} set s=1, f=1, η=1;

[0059] {circle around (2)} according to the sampling information converted by programmable logic controller, predict nitrate nitrogen concentration at time t.sub.η using slow sampling fuzzy neural network; the inputs of the slow sampling fuzzy neural network are as follows: x.sub.s1(t.sub.η−1) is the actual value of nitrate nitrogen concentration y.sub.s(t.sub.η−1) at time t.sub.η−1, x.sub.s2(t.sub.η−1) is the aeration rate u.sub.1(t.sub.η−1) at time t.sub.η−1, x.sub.s3(t.sub.η−1) is the internal reflux u.sub.2(t.sub.η−1) at time t.sub.η−1; the output of the slow sampling fuzzy neural network is the prediction value of nitrate nitrogen concentration ŷ.sub.s(t.sub.η) at time t.sub.η;

[0060] {circle around (3)} if t.sub.η=t.sub.f, set ŷ.sub.s(t.sub.f)=ŷ.sub.s(t.sub.η), where ŷ.sub.s(t.sub.f) is the prediction value of nitrate nitrogen concentration at time t.sub.f, go to step {circle around (6)} after performing step {circle around (4)}; if t.sub.η≠t.sub.f, go to step {circle around (6)} after performing step {circle around (5)};

[0061] {circle around (4)} if t.sub.η=t.sub.s, increase the value of s by 1, update the parameters of the slow sampling fuzzy neural network by the error between the predicted value and the actual value of nitrate nitrogen concentration E.sub.s(t.sub.η)=½[y.sub.s(t.sub.s)−ŷ.sub.s(t.sub.η)].sup.2:

w.sub.sj(t.sub.η+1)=w.sub.sj(t.sub.η)−0.2∂E.sub.s(t.sub.η)/∂w.sub.sj(t.sub.η)  (28)

c.sub.sij(t.sub.η+1)=c.sub.sij(t.sub.η)−0.2∂E.sub.s(t.sub.η)/∂c.sub.sij(t.sub.η)  (29)

σ.sub.sij(t.sub.η+1)=σ.sub.sij(t.sub.η)−0.2∂E.sub.s(t.sub.η)/∂σ.sub.sij(t.sub.η)  (30)

if t.sub.η≠t.sub.s, the parameters of slow sampling fuzzy neural network are not updated;

[0062] {circle around (5)} set y.sub.s(t.sub.η)=ŷ.sub.s(t.sub.η), u.sub.1(t.sub.η)=u.sub.1(t.sub.f), u.sub.2(t.sub.η)=u.sub.2(t.sub.f), increase the value of η by 1, go to step {circle around (2)}, where y.sub.s(t.sub.η) is the actual nitrate nitrogen concentration converted by the programmable logic controller at time t.sub.η, u.sub.1(t.sub.θ) is the aeration rate at time t.sub.η, u.sub.2(t.sub.θ) is the internal reflux at time t.sub.η, u.sub.1(t.sub.f) is the aeration rate at time t.sub.f, u.sub.2(t.sub.f) is the internal reflux at time t.sub.f;

[0063] {circle around (6)} predict dissolved oxygen concentration at time t.sub.f by the fast sampling fuzzy neural network; the inputs of the fast sampling fuzzy neural network are as follows: x.sub.f1(t.sub.f−1) is the actual value of dissolved oxygen concentration y.sub.f(t.sub.f−1) converted by the programmable logic controller at time t.sub.f−1, x.sub.f2(t.sub.f−1) is the aeration rate u.sub.1(t.sub.f−1) at time t.sub.f−1, x.sub.f3(t.sub.f−1) is the internal reflux u.sub.2(t.sub.f−1) at time t.sub.f−1; the output of the fast sampling fuzzy neural network is the prediction value of dissolved oxygen concentration ŷ.sub.f(t.sub.f) at time t.sub.f; update the parameters of the fast sampling fuzzy neural network by the error between the predicted value and the actual value of dissolved oxygen concentration E.sub.f(t.sub.f)=½[y.sub.f(t.sub.f)−ŷ.sub.f(t.sub.f)].sup.2:

w.sub.fj(t.sub.f+1)=w.sub.fj(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂w.sub.fj(t.sub.f)  (31)

c.sub.fij(t.sub.f+1)=c.sub.fij(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂c.sub.fij(t.sub.f)  (32)

σ.sub.fij(t.sub.f+1)=σ.sub.fij(t.sub.f)−0.2∂E.sub.f(t.sub.f)/∂σ.sub.fij(t.sub.f)  (33)

where w.sub.fj(t.sub.f+1) is the weight between the jth regular layer neuron and the output layer neuron of the slow sampling fuzzy neural network at time t.sub.f+1, c.sub.fij(t.sub.f−1) is the center of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f+1, σ.sub.fij(t.sub.f+1) is the width of the ith input neuron corresponding to the jth radial basis function neuron of the fast sampling fuzzy neural network at time t.sub.f+1;

[0064] {circle around (7)} design an objective function of multi-time scale model predictive control to track the set-points of nitrate nitrogen concentration and dissolved oxygen concentration, and calculate the control law at time t.sub.f:

J(t.sub.f)=0.25[[r.sub.f(t.sub.f)−ŷ.sub.f(t.sub.f)].sup.T[r(t.sub.f)−ŷ.sub.f(t.sub.f)]+Δu(t.sub.f).sup.TΔu(t.sub.f)]+0.45[r.sub.s(t.sub.f)−ŷ.sub.s(t.sub.f)].sup.T[r.sub.s(t.sub.f)−ŷ.sub.s(t.sub.f)]+Δu(t.sub.f).sup.TΔu(t.sub.f)   (34)

where r.sub.f(t.sub.f)=[r.sub.f(t.sub.f−1), r.sub.f(t.sub.f+2), r.sub.f(t.sub.f+3)].sup.T is the set-point of dissolved oxygen concentration, r.sub.f(t.sub.f+1)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+1, r.sub.f(t.sub.f+2)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+2, r.sub.f(t.sub.f+3)=2 mg/l represents the set-point of dissolved oxygen concentration at time t.sub.f+3; ŷ.sub.f(t.sub.f)=[ŷ.sub.f(t.sub.f+1), ŷ.sub.f(t.sub.f+2), ŷ.sub.f(t.sub.f+3)].sup.T is the prediction output of the fast sampling fuzzy neural network, ŷ.sub.f(t.sub.f−1) is the prediction value of dissolved oxygen concentration at time t.sub.f+1, ŷ.sub.f(t.sub.f+2) is the prediction value of dissolved oxygen concentration at time t.sub.f+2, ŷ.sub.f(t.sub.f+3) is the prediction value of dissolved oxygen concentration at time t.sub.f+3; r.sub.s(t.sub.f)=[r.sub.s(t.sub.f+1), r.sub.s(t.sub.f+2), r.sub.s(t.sub.f+3)].sup.T is the set-point of nitrate nitrogen concentration; r.sub.s(t.sub.f+1)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+1, r.sub.s(t.sub.f+2)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+2, r.sub.s(t.sub.f+3)=1 mg/l represents the set-point of nitrate nitrogen concentration at time t.sub.f+3; ŷ.sub.s(t.sub.s)=[ŷ.sub.s(t.sub.s+1), ŷ.sub.s(t.sub.s+2), ŷ.sub.s(t.sub.s+3)].sup.T is the prediction output of slow sampling fuzzy neural network, ŷ.sub.s(t.sub.f+1) is the prediction value of nitrate nitrogen concentration at time t.sub.f+1, ŷ.sub.s(t.sub.f+2) is the prediction value of nitrate nitrogen concentration at time t.sub.f+2, ŷ.sub.s(t.sub.f+3) is the prediction value of nitrate nitrogen concentration at time t.sub.f+3; Δu(t.sub.f)=[Δu.sub.1(t.sub.f), Δu.sub.2(t.sub.f)].sup.T is the incremental control moves at time t.sub.f, Δu.sub.1(t.sub.f) is the aeration rate adjustment amount at time t.sub.f, Δu.sub.2(t.sub.f) is the internal reflux adjustment amount at time t.sub.f, where

Δu(t.sub.f)=u(t.sub.f+1)−u(t.sub.f)  (35)

|Δu(t.sub.f)|≤Δu.sub.max  (36)

u(t.sub.f)=[u.sub.1(t.sub.f), u.sub.2(t.sub.f)].sup.T is control vector converting into analog signal through programmable logic controller and transmitting to variable frequency driver at time t.sub.f, u(t.sub.f+1)=[u.sub.1(t.sub.f+1), u.sub.2(t.sub.f−1)].sup.T is control vector converting into analog signal through programmable logic controller and transmitting to variable frequency driver at time t.sub.f+1, u.sub.1(t.sub.f+1) is the aeration rate at time t.sub.f+1, u.sub.2(t.sub.f+1) is the internal reflux at time t.sub.f+1; Δu.sub.max=[ΔK.sub.La.sub.max, ΔQ.sub.amax].sup.T is the maximum adjustment vector allowed by the controller, ΔK.sub.La.sub.max=100 L/min is the maximum aeration adjustment amount, ΔQ.sub.amax=50000 L/min is the maximum internal reflux adjustment amount, Δu.sub.max is set through the blower and internal reflux valve in the control system equipment;

[0065] an aeration rate and internal reflux adjustment vector are calculated by minimizing Eq.(15):

[00006]$\begin{array}{cc}\Delta u\left(t_f\right)=\left(0.4{\left(\frac{\partial {\hat{y}}_f\left(t_f\right)}{\partial u\left(t_f\right)}\right)}^T\left[r_f\left(t_f\right)-{\hat{y}}_f\left(t_f\right)\right]+0.08{\left(\frac{\partial {\hat{y}}_s\left(t_f\right)}{\partial u\left(t_f\right)}\right)}^T\left[r_s\left(t_f\right)-{\hat{y}}_s\left(t_f\right)\right]\right)& \left(37\right)\end{array}$

adjust the aeration rate and internal reflux at time t.sub.f:

u(t.sub.f+1)=u(t.sub.f)+Δu(t.sub.f)  (38)

[0066] {circle around (8)} if f≤1000, increase the value of f by 1, increase the value of η by 1, go to step {circle around (2)}; if f>1000, end the cycle;

[0067] (6) the concentration of nitrate nitrogen and dissolved oxygen is controlled by u(t.sub.f), and u(t.sub.f)=[u.sub.1(t.sub.f), u.sub.2(t.sub.f)].sup.T is transferred to programmable logic controller for digital/analog conversion to obtain U(t.sub.f)=[U.sub.1(t.sub.f), U.sub.2(t.sub.f)].sup.T, which is the input of variable-frequency drive, the variable-frequency drive changes the working power frequency of motor to control the aeration pump and electronic valve, then, the aeration rate and internal reflux are controlled, the output of the system is the actual value of nitrate nitrogen concentration and dissolved oxygen concentration. FIG. 4 shows the dissolved oxygen concentration of the system, X-axis: time, unit: day, Y-axis: dissolved oxygen concentration, unit: mg/L, the solid line is the expected dissolved oxygen concentration, the dotted line is the actual dissolved oxygen concentration; the error between the actual output dissolved oxygen concentration and the expected dissolved oxygen concentration is shown in FIG. 5, X-axis: time, unit: day, Y-axis: dissolved oxygen concentration error, unit: mg/L FIG. 6 shows the nitrate concentration value of the system, X-axis: time, unit: day, Y-axis: nitrate concentration value, unit: mg/L, solid line is expected nitrate concentration value, dotted line is actual nitrate concentration value; the error between actual output nitrate concentration and expected nitrate concentration is shown in FIG. 7, X-axis: time, unit: day, Y-axis: nitrate concentration error value, unit: mg/L. The results show that the method is effective.