TYPE-2 FUZZY NEURAL NETWORK-BASED COOPERATIVE CONTROL METHOD FOR WASTEWATER TREATMENT PROCESS

Abstract

A cooperative fuzzy-neural control method is designed in this present invention. Due to the difficulty for cooperatively controlling the concentrations of the dissolved oxygen and nitrate nitrogen in wastewater treatment process, a cooperative fuzzy-neural control method is investigated. In this proposed method, firstly, a interval type-2 fuzzy neural network is employed to construct the cooperative fuzzy-neural controller. Secondly, a parameter cooperative strategy is proposed to cooperatively optimize the global and local parameters of the cooperative fuzzy-neural controller to meet the control requirements. This proposed cooperative fuzzy-neural control method can cooperatively control the concentrations of the dissolved oxygen and nitrate nitrogen in wastewater treatment process. The results illustrate that the proposed cooperative fuzzy-neural control method can achieve the high control accuracy and guarantee the normal operations of wastewater treatment process under the different operation conditions.

Claims

1. A type-2 fuzzy neural network-based cooperative control method for controlling dissolved oxygen (DO) and nitrate nitrogen (NO.sub.3N) concentrations of wastewater treatment process (WWTP), wherein aeration value and internal backflow value are used as control variables, the DO and NO.sub.3N concentrations are used as controlled variables, the method comprising the following steps: (1) design a type-2 fuzzy neural network (T2FNN) for controlling the DO and NO.sub.3N concentrations, the T2FNN contains five-layers: an input layer, a membership layer, a rule layer, a consequent layer and an output layer, wherein: the input layer contains 4 input neurons and an input vector is:
X(t)=[x.sub.1(t),x.sub.2(t),x.sub.3(t),x.sub.4(t)].sup.T(1) where X(t) is the input vector of T2FNN at time t, x.sub.1(t) is an error between a set-point and a measured value of DO concentration at time t, x.sub.2(t) is an error variation between the set-point and the measured value of DO concentration at time t, x.sub.3(t) is an error between a set-point and a measured value of NO.sub.3N concentration at time t, x.sub.4(t) is an error variation between the set-point and the measured value of NO.sub.3N concentration at time t, T represents a revolution of the matrix and vector; the membership layer contains P membership neurons and a neuron represents an interval type-2 membership function: $\begin{array}{cc}{\underset{\_}{m}}_{\mathrm{ij}}\left(x_i\left(t\right)\right)=\{\begin{array}{c}{e}^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right)\left({\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)+{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\right).Math.\text{/}.Math.2\\ e^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right)>\left({\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)+{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\right).Math.\text{/}.Math.2\end{array}& \left(2\right)\\ {\stackrel{\_}{m}}_{\mathrm{ij}}\left(x_i\left(t\right)\right)=\{\begin{array}{c}{e}^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right){\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)\\ 1,{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)<x_i\left(t\right)<{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\\ e^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right){\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\end{array}& \left(3\right)\end{array}$ where P is the total number of membership neurons, P=4M, M is the total number of rule neurons, 1<M15, m.sub.ij(t) is a lower membership value of ith input to jth rule neuron at time t, m.sub.ij(t) is an upper membership value of the ith input to the jth rule neuron at time t, 0<m.sub.ij(t)<m.sub.ij(t)1, e is a natural constant and e=2.7183, c.sub.ij(t) is a lower center of the ith input with the jth rule neuron at time t, c.sub.ij(t) is an upper center of the ith input with the jth rule neuron at time t, 1<c.sub.ij(t)<c.sub.ij(t)<5, .sub.ij(t) is standard deviation of the ith input with the jth rule neuron at time t, i is the number of inputs in the T2FNN and i=1, 2, 3, 4, j is the number of rule neurons and j=1, 2, . . . , M; the rule layer contains M rule neurons, an output of each neuron is: $\begin{array}{cc}{F}_j\left(t\right)=\left[{\underset{\_}{f}}_j\left(t\right),{\stackrel{\_}{f}}_j\left(t\right)\right]& \left(4\right)\\ {\underset{\_}{f}}_j\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.{\underset{\_}{m}}_{\mathrm{ij}}\left(t\right),{\stackrel{\_}{f}}_j\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.{\stackrel{\_}{m}}_{\mathrm{ij}}\left(t\right)& \left(5\right)\end{array}$ where F.sub.j(t) is firing strength of jth rule neuron at time t, f.sub.j(t) is lower firing strength of the jth rule neuron at time t, f.sub.j(t) is upper firing strength of the jth rule neuron at time t, 0f.sub.j(t)<f.sub.j(t)1; the consequent layer contains 4 consequent neurons, an output of each neuron is: $\begin{array}{cc}{\underset{\_}{y}}_k\left(t\right)=\frac{\underset{j=1}{\overset{M}{.Math.}}.Math.{\underset{\_}{f}}_j\left(t\right).Math.h_j^k\left(t\right)}{\underset{j=1}{\overset{M}{.Math.}}.Math.{\underset{\_}{f}}_j\left(t\right)},{\stackrel{\_}{y}}_k\left(t\right)=\frac{\underset{j=1}{\overset{M}{.Math.}}.Math.{\stackrel{\_}{f}}_j\left(t\right).Math.h_j^k\left(t\right)}{\underset{j=1}{\overset{M}{.Math.}}.Math.{\stackrel{\_}{f}}_j\left(t\right)}.Math..Math.h_j^k\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.w_{\mathrm{ij}}^k\left(t\right).Math.x_i\left(t\right)+b_j^k\left(t\right)& \left(6\right)\end{array}$ where y.sub.k(t) is a lower output of consequent neuron with respect to kth output neuron at time t, y.sub.k(t) is an upper output of consequent neuron with respect to the kth output neuron at time t, hk j(t) is jth consequent factor with respect to the kth output at time t, wk ij(t) is a consequent weight of ith input with respect to jth rule neuron and the kth output at time t, bk j (t) is the deviation of the jth rule neuron with respect to the kth output at time t, k=1, 2; the output layer contains 2 neurons, an output of each neuron is:
u.sub.k(t)=q.sup.k(t)y.sub.k(t)+(1q.sup.k(t))y.sub.k(t)(7) where u.sub.k(t) is an output of kth output neuron at time t, q.sup.k(t) is a scale factor of the kth output neuron, 0<q.sup.k(t)<1; (2) train T2FNN, which includes: 1) divide parameters of T2FNN into global and local parameters, and define a global parameter vector and a local parameter vector as:
.sub.g(t)=[c.sub.ij(t),c.sub.ij(t),.sub.ij(t)]
.sub.l(t)=[w.sub.ij.sup.k(t),b.sub.j.sup.k(t),q.sup.k(t)](8) where .sub.g(t) is the global parameter vector at time t, .sub.l(t) is the local parameter vector at time t, and an objective function is: $\begin{array}{cc}l\left(t\right)=\left(t\right).Math.l^1\left(t\right)+\left(1-\left(t\right)\right).Math.l^2\left(t\right).Math..Math.\left(t\right)=\frac{.Math.l^1\left(t\right).Math.}{.Math.l^1\left(t\right).Math.+.Math.l^2\left(t\right).Math.}.Math..Math.l^1\left(t\right)=y_d^1\left(t\right)-y^1\left(t\right).Math..Math.l^2\left(t\right)=y_d^2\left(t\right)-y^2\left(t\right)& \left(9\right)\end{array}$ where l(t) is a composite error at time t, (t) is an error coefficient at time t, l.sup.2(t) is the error between the set-point and measured value of DO concentration at time t, l.sup.2(t) the error between the set-point and measured value of NO.sub.3N concentration at time t, y1 d(t) is the set-point of DO concentration at time t, y2 d(t) is the set-point of NO.sub.3N concentration at time t, y.sup.1(t) is a real value of DO concentration at time t, y.sup.2(t) is a real value of NO.sub.3N concentration at time t; 2) utilize parameter cooperative strategy to optimize the global and local parameters of T2FNN cooperatively, an updating rule of parameters is: $\begin{array}{cc}.Math.\left(t+1\right)=\left(t\right)+{\left(H\left(t\right)+\left(t\right).Math.I\right)}^{-1}.Math.G_l\left(t\right).Math..Math..Math.H\left(t\right)=J^T\left(t\right).Math.J\left(t\right).Math..Math..Math.G_l\left(t\right)=J^T\left(t\right).Math.l\left(t\right).Math..Math..Math.\left(t\right)=.Math.\frac{l\left(t\right)}{l\left(t\right)+l\left(t-1\right)}.Math..Math.\left(t-1\right).Math..Math.J(.Math.t)=[.Math.\frac{l\left(t\right)}{{}_g\left(t\right)},.Math.\frac{l\left(t\right)}{{}_l\left(t\right)}]=.Math..Math.[.Math.\frac{l\left(t\right)}{{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{w_{\mathrm{ij}}^k\left(t\right)},.Math.\frac{l\left(t\right)}{b_{\mathrm{ij}}^k\left(t\right)}.Math.,.Math.\frac{l\left(t\right)}{q^k\left(t\right)}]& \left(10\right)\end{array}$ where (t+1) is a parameter vector at time t+1, (t) is a parameter vector at time t, I is a unit matrix, H(t) is a quasi Hessian matrix at time t, G.sub.l(t) is an error gradient vector at time t, (t) is an adaptive learning rate at time t and (t)(0, 1], J(t) is a Jacobian vector at time t, l(t)/.sub.g(t) is a partial derivative of the composite error with respect to the global parameter vector at time t, l(t)/.sub.l(t) is a partial derivative of the composite error with respect to the local parameter vector at time t, l(t)/c.sub.ij(t) is partial derivatives of the composite error with respect to lower uncertain center at time t, l(t)/c.sub.ij(t) is partial derivatives of the composite error with respect to the upper uncertain center at time t, l(t)/.sub.ij(t) is partial derivatives of the composite error with respect to the standard deviation at time t, l(t)/wk ij(t) is partial derivative of the composite error with respect to the consequent weight at time t, l(t)/bk j(t) is partial derivative of the composite error with respect to the deviation at time t, l(t)/q.sup.k(t) is partial derivative of the composite error with respect to the scale factor at time t; (3) design the type-2 fuzzy neural network-based cooperative control method for controlling the DO and NO.sub.3N concentrations of WWTP, which includes: 1) calculate outputs of T2FNN according to Eq. (7); 2) compare a value of composite error with a pre-set threshold, if l(t)>, go to step 3), and if l(t), go to step 4), where is the pre-set threshold and =0.01; 3) calculate updated values of parameters according to Eq. (10); 4) calculate control outputs at current time:
u.sub.k(t)=u.sub.k(t1)+u.sub.k(t)(11) where u.sub.k(t) is kth control output at time t, u.sub.1(t) is the control output with respect to an aeration value at time t, u.sub.2(t) is the control output with respect to an internal backflow value at time t, u.sub.k(t1) is kth control output at time t1, 5) enter u.sub.k(t) into WWTP to control the DO and N.sub.3N concentrations, return to step 1); (4) use u.sub.1(t) and u.sub.2(t) to control the concentration of DO and NO.sub.3N in WWTP, u.sub.1(t) is the control input of the aeration value at time t, u.sub.2(t) is the control input of the internal backflow value at time t, the control results are the concentrations of DO and NO.sub.3N in WWTP.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] FIG. 1 shows the control scheme of this present invention.

[0029] FIG. 2 shows the structure of T2FNN in T2FNN-CC method FIG. 3 shows the control results of DO concentration in T2FNN-CC method.

[0030] FIG. 4 shows the control errors of DO concentration in T2FNN-CC method.

[0031] FIG. 5 shows the control results of NO.sub.3N concentration in T2FNN-CC method.

[0032] FIG. 6 shows the control errors of NO.sub.3N concentration in T2FNN-CC method.

DETAILED DESCRIPTION

[0033] In this present invention, a T2FNN-CC method is designed. This proposed T2FNN-CC method can solve the control values of the DO and NO.sub.3N concentrations, and utilize the aeration value and internal backflow value to achieve the cooperative control of the DO and NO.sub.3N concentrations. The proposed T2FNN-CC method can ensure that the discharge standards are met, and improve the stability of WWTP under the different operation conditions.

[0034] The present invention adopts the following technical scheme and implementation steps:

[0035] A type-2 fuzzy neural network-based cooperative control method for controlling the dissolved oxygen (DO) and nitrate nitrogen (NO.sub.3N) concentrations of wastewater treatment process (WWTP), wherein aeration value and internal backflow value are used as control variables, the DO and NO.sub.3N concentrations are used as controlled variables, the control scheme is shown in FIG. 1, the method comprising the following steps:

[0036] (1) design a type-2 fuzzy neural network (T2FNN) for controlling the DO and NO.sub.3N concentrations, the T2FNN contains five-layers: an input layer, a membership layer, a rule layer, a consequent layer and an output layer, the structure of T2FNN is shown in FIG. 2 and the details of the layers:

[0037] wherein:

[0038] the input layer contains 4 input neurons and an input vector is:

X(t)=[x.sub.1(t),x.sub.2(t),x.sub.3(t),x.sub.4(t)].sup.T(1)

where X(t) is the input vector of T2FNN at time t, x.sub.1(t) is an error between a set-point and a measured value of DO concentration at time t, x.sub.2(t) is an error variation between the set-point and the measured value of DO concentration at time t, x.sub.3(t) is an error between a set-point and a measured value of NO.sub.3N concentration at time t, x.sub.4(t) is an error variation between the set-point and the measured value of NO.sub.3N concentration at time t, T represents a revolution of the matrix and vector;

[0039] the membership layer contains P membership neurons and a neuron represents an interval type-2 membership function:

[00006]$\begin{array}{cc}{\underset{\_}{m}}_{\mathrm{ij}}\left(x_i\left(t\right)\right)=\{\begin{array}{c}{e}^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right)\left({\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)+{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\right).Math.\text{/}.Math.2\\ e^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right)>\left({\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)+{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\right).Math.\text{/}.Math.2\end{array}& \left(2\right)\\ {\stackrel{\_}{m}}_{\mathrm{ij}}\left(x_i\left(t\right)\right)=\{\begin{array}{c}{e}^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right){\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)\\ 1,{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)<x_i\left(t\right)<{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\\ e^{-\frac{1}{2}.Math.{\left(\frac{x_i\left(t\right)-{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)}\right)}^2},x_i\left(t\right){\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)\end{array}& \left(3\right)\end{array}$

where P is the total number of membership neurons, P=4M, M is the total number of rule neurons, 1<M15, m.sub.ij(t) is a lower membership value of ith input to jth rule neuron at time t, m.sub.ij(t) is an upper membership value of the ith input to the jth rule neuron at time t, 0<m.sub.ij(t)<m.sub.ij(t)1, e is a natural constant and e=2.7183, c.sub.ij(t) is a lower center of the ith input with the jth rule neuron at time t, c.sub.ij(t) is an upper center of the ith input with the jth rule neuron at time t, 1<c.sub.ij(t)<c.sub.ij(t)<5, .sub.ij(t) is standard deviation of the ith input with the jth rule neuron at time t, i is the number of inputs in the T2FNN and i=1, 2, 3, 4, j is the number of rule neurons and j=1, 2, . . . , M;

[0040] the rule layer contains M rule neurons, an output of each neuron is:

[00007]$\begin{array}{cc}{F}_j\left(t\right)=\left[{\underset{\_}{f}}_j\left(t\right),{\stackrel{\_}{f}}_j\left(t\right)\right]& \left(4\right)\\ {\underset{\_}{f}}_j\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.{\underset{\_}{m}}_{\mathrm{ij}}\left(t\right),{\stackrel{\_}{f}}_j\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.{\stackrel{\_}{m}}_{\mathrm{ij}}\left(t\right)& \left(5\right)\end{array}$

where F.sub.j(t) is firing strength of jth rule neuron at time t, f.sub.j(t) is lower firing strength of the jth rule neuron at time t, f.sub.j(t) is upper firing strength of the jth rule neuron at time t, 0<f.sub.j(t)<f.sub.j(t)1;

[0041] the consequent layer contains 4 consequent neurons, an output of each neuron is:

[00008]$\begin{array}{cc}{\underset{\_}{y}}_k\left(t\right)=\frac{\underset{j=1}{\overset{M}{.Math.}}.Math.{\underset{\_}{f}}_j\left(t\right).Math.h_j^k\left(t\right)}{\underset{j=1}{\overset{M}{.Math.}}.Math.{\underset{\_}{f}}_j\left(t\right)},{\stackrel{\_}{y}}_k\left(t\right)=\frac{\underset{j=1}{\overset{M}{.Math.}}.Math.{\stackrel{\_}{f}}_j\left(t\right).Math.h_j^k\left(t\right)}{\underset{j=1}{\overset{M}{.Math.}}.Math.{\stackrel{\_}{f}}_j\left(t\right)}.Math..Math.h_j^k\left(t\right)=\underset{i=1}{\overset{4}{.Math.}}.Math.w_{\mathrm{ij}}^k\left(t\right).Math.x_i\left(t\right)+b_j^k\left(t\right)& \left(6\right)\end{array}$

where y.sub.k(t) is a lower output of consequent neuron with respect to kth output neuron at time t, y.sub.k(t) is an upper output of consequent neuron with respect to the kth output neuron at time t, hk j(t) is jth consequent factor with respect to the kth output at time t, wk ij(t) is a consequent weight of ith input with respect to jth rule neuron and the kth output at time t, bk j (t) is the deviation of the jth rule neuron with respect to the kth output at time t, k=1, 2;

[0042] the output layer contains 2 neurons, an output of each neuron is:

u.sub.k(t)=q.sup.k(t)y.sub.k(t)+(1q.sup.k(t))y.sub.k(t)(7)

where u.sub.k(t) is an output of kth output neuron at time t, q.sup.k(t) is a scale factor of the kth output neuron, 0<q.sup.k(t)<1;

[0043] (2) train T2FNN, which includes:

[0044] 1) divide parameters of T2FNN into global and local parameters, and define a global parameter vector and a local parameter vector as:

.sub.g(t)=[c.sub.ij(t),c.sub.ij(t),.sub.ij(t)]

.sub.l(t)=[w.sub.ij.sup.k(t),b.sub.j.sup.k(t),q.sup.k(t)](8)

where .sub.g(t) is the global parameter vector at time t, .sub.l(t) is the local parameter vector at time t, and an objective function is:

[00009]$\begin{array}{cc}l\left(t\right)=\left(t\right).Math.l^1\left(t\right)+\left(1-\left(t\right)\right).Math.l^2\left(t\right).Math..Math.\left(t\right)=\frac{.Math.l^1\left(t\right).Math.}{.Math.l^1\left(t\right).Math.+.Math.l^2\left(t\right).Math.}.Math..Math.l^1\left(t\right)=y_d^1\left(t\right)-y^1\left(t\right).Math..Math.l^2\left(t\right)=y_d^2\left(t\right)-y^2\left(t\right)& \left(9\right)\end{array}$

where l(t) is a composite error at time t, (t) is an error coefficient at time t, l.sup.1(t) is the error between the set-point and measured value of DO concentration at time t, l.sup.2(t) the error between the set-point and measured value of NO.sub.3N concentration at time t, y1 d(t) is the set-point of DO concentration at time t, y2 d(t) is the set-point of NO.sub.3N concentration at time t, y.sup.1(t) is a real value of DO concentration at time t, y.sup.2(t) is a real value of NO.sub.3N concentration at time t;

[0045] 2) utilize parameter cooperative strategy to optimize the global and local parameters of T2FNN cooperatively, an updating rule of parameters is:

[00010]$\begin{array}{cc}.Math.\left(t+1\right)=\left(t\right)+{\left(H\left(t\right)+\left(t\right).Math.I\right)}^{-1}.Math.G_l\left(t\right).Math..Math..Math.H\left(t\right)=J^T\left(t\right).Math.J\left(t\right).Math..Math..Math.G_l\left(t\right)=J^T\left(t\right).Math.l\left(t\right).Math..Math..Math..Math..Math.\left(t\right)=.Math.\frac{l\left(t\right)}{l\left(t\right)+l\left(t-1\right)}.Math..Math.\left(t-1\right).Math..Math.J(.Math.t)=[.Math.\frac{l\left(t\right)}{{}_g\left(t\right)},.Math.\frac{l\left(t\right)}{{}_l\left(t\right)}]=.Math..Math.[.Math.\frac{l\left(t\right)}{{\underset{\_}{c}}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{{\stackrel{\_}{c}}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{{}_{\mathrm{ij}}\left(t\right)},.Math.\frac{l\left(t\right)}{w_{\mathrm{ij}}^k\left(t\right)},.Math.\frac{l\left(t\right)}{b_{\mathrm{ij}}^k\left(t\right)}.Math.,.Math.\frac{l\left(t\right)}{q^k\left(t\right)}]& \left(10\right)\end{array}$

where (t+1) is a parameter vector at time t+1, (t) is a parameter vector at time t, I is a unit matrix, H(t) is a quasi Hessian matrix at time t, G.sub.l(t) is an error gradient vector at time t, (t) is an adaptive learning rate at time t and (t)(0, 1], J(t) is a Jacobian vector at time t, l(t)/.sub.g(t) is a partial derivative of the composite error with respect to the global parameter vector at time t, l(t)/.sub.l(t) is a partial derivative of the composite error with respect to the local parameter vector at time t, l(t)/c.sub.ij(t) is partial derivatives of the composite error with respect to lower uncertain center at time t, l(t)/c.sub.ij(t) is partial derivatives of the composite error with respect to the upper uncertain center at time t, l(t)/.sub.ij(t) is partial derivatives of the composite error with respect to the standard deviation at time t, l(t)/wk ij(t) is partial derivative of the composite error with respect to the consequent weight at time t, l(t)/bk j(t) is partial derivative of the composite error with respect to the deviation at time t, l(t)/q.sup.k(t) is partial derivative of the composite error with respect to the scale factor at time t;

[0046] (3) design the type-2 fuzzy neural network-based cooperative control method for controlling the DO and NO.sub.3N concentrations of WWTP, which includes:

[0047] 1) calculate outputs of T2FNN according to Eq. (7);

[0048] 2) compare a value of composite error with a pre-set threshold, if l(t)>, go to step 3), and if l(t), go to step 4), where is the pre-set threshold and =0.01;

[0049] 3) calculate updated values of parameters according to Eq. (10);

[0050] 4) calculate control outputs at current time:

u.sub.k(t)=u.sub.k(t1)+u.sub.k(t)(11)

where u.sub.k(t) is kth control output at time t, u.sub.1(t) is the control output with respect to an aeration value at time t, u.sub.2(t) is the control output with respect to an internal backflow value at time t, u.sub.k(t1) is kth control output at time t1,

[0051] 5) enter uk(t) into WWTP to control the DO and NO3-N concentrations, return to step 1);

[0052] (4) use u1(t) and u2(t) to control the concentration of DO and NO3-N in WWTP, u1(t) is the control input of the aeration value at time t, u2(t) is the control input of the internal backflow value at time t, the control results are the concentrations of DO and NO3-N in WWTP. FIG. 3 gives the control results of DO concentration, X axis shows the time, and the unit is day, Y axis is the DO concentration, and the unit is mg/L, the black solid line is the set-points of DO concentration, and the black dotted line is the real value of DO concentration. FIG. 4 gives the control errors of DO concentration, X axis shows the time, and the unit is day, Y axis is the errors of DO concentration, and the unit is mg/L. FIG. 5 gives the control results of NO.sub.3N concentration, X axis shows the time, and the unit is day, Y axis is the NO.sub.3N concentration, and the unit is mg/L, the black solid line is the set-points of N.sub.3N concentration, and the black dotted line is the real value of NO.sub.3N concentration. FIG. 6 gives the control errors of NO.sub.3N concentration, X axis shows the time, and the unit is day, Y axis is the errors of NO.sub.3N concentration, and the unit is mg/L.