Hierarchical Model Predictive Control Method of Wastewater Treatment Process based on Fuzzy Neural Network

Abstract

A hierarchical model predictive control (HMPC) method based on fuzzy neural network for wastewater treatment process (WWTP) is designed to realize hierarchical control of dissolved oxygen (DO) concentration and nitrate nitrogen concentration. In view of the difference of time scales in WWTP, it is difficult to accurately control the concentration of DO and nitrate nitrogen. The disclosure establishes a HMPC structure according to different time scales. Then, the concentration of DO and nitrate nitrogen is controlled with different frequencies. It not only conforms to the operation characteristics of WWTP, but also solves the problem of poor operation performance of multivariable model predictive control. The experimental results show that the HMPC method can achieve accurate on-line control of DO concentration and nitrate nitrogen concentration with different time scales.

Claims

1. A hierarchical model predictive control (HMPC) method of wastewater treatment process (WWTP) based on fuzzy neural network (FNN), comprising the following steps: (1) according to different time scales, a hierarchical control structure of HMPC module is designed to control dissolved oxygen (DO) concentration and nitrate nitrogen concentration in WWTP: a high-level controller comprises high-level FNN and high-level model predictive controller, sampling period of nitrate nitrogen concentration 2T being taken as time scale to track set values of nitrate nitrogen concentration and DO concentration, and calculates a high-level control law, t.sub.1=2mT is a sampling time of nitrate nitrogen concentration, and m is sampling steps of nitrate nitrogen concentration; a low-level controller comprises low-level FNN and low-level model predictive controller, sampling period of DO concentration T being taken as time scale to track set values of DO concentration and the high-level control law calculated by the high-level controller, and calculates a low-level control law, t.sub.2=kT is sampling time of DO concentration, and k is sampling steps of DO concentration; (3) the high-level FNN is designed to predict a concentration of nitrate nitrogen at each sampling time t.sub.1, which is as follows: 1) set q=1; 2) an input of the high-level FNN is x.sub.1(t.sub.1)=[y.sub.1(t.sub.1), u.sub.21(t.sub.1), u.sub.22(t.sub.1)].sup.T, y.sub.1(t.sub.1)=[y.sub.1(t.sub.1−1), y.sub.1(t.sub.1−2)], t.sub.21(t.sub.1)=[u.sub.21(t.sub.2−5), u.sub.21(t.sub.2−6)], u.sub.22(t.sub.1)=[u.sub.22(t.sub.2−5), u.sub.22(t.sub.2−6)], y.sub.1(t.sub.1−1) is an actual value of nitrate nitrogen concentration at t.sub.1−1, y.sub.1(t.sub.1−2) is an actual value of nitrate nitrogen concentration at t.sub.1−2, u.sub.21(t.sub.2−5) is an aeration rate at t.sub.2−5, u.sub.21(t.sub.2−6) is an aeration rate at t.sub.2−6, u.sub.22(t.sub.2−5) is an internal reflux in WWTP at t.sub.2−5, u.sub.22(t.sub.2−6) is an internal reflux in WWTP at t.sub.2−6, T is a transpose of matrix, an output of the high-level FNN is a predicted value of nitrate nitrogen concentration ŷ.sub.1(t.sub.1) at t.sub.1, an output expression is as follows: $\begin{array}{cc}{\hat{y}}_1\left(t_1\right)=\frac{{.Math.}_{j=1}^8{w}_{\mathrm{hj}}\left(t_1\right)e^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{1i}\left(t_1\right)-c_{\mathrm{hij}}\left(t_1\right)\right)}^2}{2{\sigma }_{\mathrm{hij}}^2\left(t_1\right)}}}{{.Math.}_{j=1}^8{e}^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{1i}\left(t_1\right)-c_{\mathrm{hij}}\left(t_1\right)\right)}^2}{2{\sigma }_{\mathrm{hij}}^2\left(t_1\right)}}},& \left(25\right)\end{array}$ where x.sub.1i(t.sub.1) is ith input of the high-level FNN at t.sub.1, w.sub.hj(t.sub.1) is connection weight between jth neuron in a rule layer and an output neuron at t.sub.1, j∈[1, 8], c.sub.hij(t.sub.1) is a center value of jth radial basal neuron corresponding to ith input neuron at t.sub.1, i∈[1, 6], σ.sub.hij(t.sub.1) is a center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.1, e=2.72, parameter update rules are as follows:
w.sub.hj(t.sub.1+1)=w.sub.hj(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂w.sub.hj(t.sub.1),
c.sub.hij(t.sub.1+1)=c.sub.hij(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂c.sub.hij(t.sub.1),
σ.sub.hij(t.sub.i+1)=σ.sub.hij(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂σ.sub.hij(t.sub.1),  (26) where w.sub.hj(t.sub.1+1) is a connection weight between the jth neuron in the rule layer and the output neuron at t.sub.1+1, c.sub.hij(t.sub.1+1) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.1+1, σ.sub.hij(t.sub.1+1) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.1+1, E.sub.1(t.sub.1)=½[y.sub.1(t.sub.1)−ŷ.sub.1(t.sub.1)].sup.2 is an error between an actual and a predicted nitrate nitrogen concentration at t.sub.1; 3) set q=q+1, if q≤20 is true, go to step 2), otherwise, exit the cycle; (4) the low-level FNN is designed to predict DO concentration at each sampling time t.sub.2, which is as follows: I set r=1; II an input of the low-level FNN is x.sub.2(t.sub.2)=[y.sub.2(t.sub.2), u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T, y.sub.2(t.sub.2)=[y.sub.2(t.sub.2−1), y.sub.2(t.sub.2−2)], u.sub.21(t.sub.2)=[u.sub.21(t.sub.2−5), u.sub.21(t.sub.2−6)], u.sub.22(t.sub.2)=[u.sub.22(t.sub.2−5), u.sub.22(t.sub.2−6)], y.sub.2(t.sub.2−1) is an actual value of DO concentration at t.sub.2−1, y.sub.2(t.sub.2−2) is an actual value of DO concentration at t.sub.2−2, an output of the low-level FNN if the predicted value of DO concentration ŷ.sub.2(t.sub.2) at t.sub.2, an output expression is as follows: $\begin{array}{cc}{\hat{y}}_2\left(t_2\right)=\frac{{.Math.}_{j=1}^8{w}_{\mathrm{lj}}\left(t_2\right)e^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{2i}\left(t_2\right)-c_{\mathrm{lij}}\left(t_2\right)\right)}^2}{2{\sigma }_{\mathrm{lij}}^2\left(t_2\right)}}}{{.Math.}_{j=1}^8{e}^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{2i}\left(t_2\right)-c_{\mathrm{lij}}\left(t_2\right)\right)}^2}{2{\sigma }_{\mathrm{lij}}^2\left(t_2\right)}}},& \left(27\right)\end{array}$ where x.sub.2i(t.sub.2) is ith input of the low-level FNN at t.sub.2, w.sub.lj(t.sub.2) is a connection weight between the jth neuron in the rule layer and the output neuron at t.sub.2, j∈[1, 8], c.sub.lij(t.sub.2) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.2, i∈[1, 6], σ.sub.lij(t.sub.2) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.2, parameter update rules are as follows:
w.sub.lj(t.sub.2+1)=w.sub.li(t.sub.2)−0.2∂E.sub.2(t.sub.2)/∂w.sub.lj(t.sub.2),
c.sub.lij(t.sub.2+1)=c.sub.lij(t.sub.2)−0.2∂E.sub.2(t.sub.2)/∂c.sub.lij(t.sub.2),
σ.sub.hj(t.sub.2+1)=σ.sub.hj(t.sub.2)−0.2∂E.sub.2(t.sub.2)/σ.sub.hj(t.sub.2),  (28) where w.sub.lj(t.sub.2+1) is the connection weight between the jth neuron in the rule layer and the output neuron at t.sub.2+1, c.sub.lij(t.sub.2+1) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.2+1, σ.sub.lij(t.sub.2+1) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.2+1, E.sub.2(t.sub.2)=¼[y.sub.2(t.sub.2)−ŷ.sub.2(t.sub.2)].sup.2, is the error between the actual and predicted DO concentration at t.sub.2; III set r=r+1, if r≤20 is true, go to step II, otherwise, exit the cycle; (5) an optimization control module of HMPC module is designed as follows: {circle around (1)} set k=0, m=0; {circle around (2)} according to Eq.(1) and Eq.(3), the outputs of the high-level FNN ŷ.sub.1(t.sub.1) and the low-level FNN ŷ.sub.2(t.sub.2) are calculated respectively, ŷ.sub.1(t.sub.1)=[ŷ.sub.1(t.sub.1+1), ŷ.sub.1(t.sub.1+2), . . . , ŷ.sub.1(t.sub.1+5)].sup.T, ŷ.sub.2(t.sub.2)=ŷ.sub.2(t.sub.2+1), ŷ.sub.2(t.sub.2+2), . . . , ŷ.sub.2(t.sub.2+5)].sup.T, ŷ.sub.1(t.sub.1+1) is the predicted value of nitrate nitrogen concentration at t.sub.1+1, ŷ.sub.1(t.sub.1+2) is the predicted value of nitrate nitrogen concentration at t.sub.1+2, ŷ.sub.1(t.sub.1+5) is the predicted value of nitrate nitrogen concentration at t.sub.1+5, ŷ.sub.2(t.sub.2+1) is the predicted value of DO concentration at t.sub.2+1, ŷ.sub.2(t.sub.2+2) is the predicted value of DO concentration at t.sub.2+2, ŷ.sub.2(t.sub.2+5) is the predicted value of DO concentration at t.sub.2+5; {circle around (3)} an objective function of high-level MPC is designed to track the set value of nitrate nitrogen concentration and DO concentration, and the high-level law at t.sub.1 is calculated:
J.sub.1(t.sub.1)=λ.sub.1[α.sub.1e.sub.p1(t.sub.1).sub.Te.sub.p1(t.sub.1)+ρ.sub.1Δu.sub.1(t.sub.1).sup.TΔu.sub.1(t.sub.1)]+λ.sub.2[α.sub.2e.sub.p2(t.sub.2).sup.Te.sub.p2(t.sub.2)+ρ.sub.2Δu.sub.1(t.sub.1).sup.TΔu.sub.1(t.sub.1)],   (29) where e.sub.p1(t.sub.1)=r.sub.1(t.sub.1)−ŷ.sub.1(t.sub.1) is an error vector between the set value of nitrate nitrogen concentration at t.sub.1 and the predicted value of nitrate nitrogen concentration, e.sub.p1(t.sub.1)=[e.sub.p1(t.sub.1+1), e.sub.p1(t.sub.1+2), . . . , e.sub.p1(t.sub.1+5)].sup.T, r.sub.1(t.sub.1)=[r.sub.1(t.sub.1+1), r.sub.1(t.sub.1+2), . . . , r.sub.1(t.sub.1+5)].sup.T, e.sub.p1(t.sub.1+1) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+1, e.sub.p1(t.sub.1+2) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+2, e.sub.p1(t.sub.1+5) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+5, r.sub.1(t.sub.1+1) is the set value of nitrate nitrogen concentration at t.sub.1+1, r.sub.1(t.sub.1+2) is the set value of nitrate nitrogen concentration at t.sub.1+2, r.sub.1(t.sub.1+5) is the set value of nitrate nitrogen concentration at t.sub.1+5, e.sub.p2(t.sub.2)=r.sub.2(t.sub.2)−ŷ.sub.2(t.sub.2) is the error vector between the set value of DO concentration at t.sub.2 and the predicted value of DO concentration, e.sub.p2(t.sub.2)=[e.sub.p2(t.sub.2+1), e.sub.p2(t.sub.2+2), . . . , e.sub.p2(t.sub.2+5)].sup.T, r.sub.2(t.sub.2)=[r.sub.2(t.sub.2+1), r.sub.2(t.sub.2+2), . . . , r.sub.2(t.sub.2+5)].sup.T, e.sub.p2(t.sub.2+1) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+1, e.sub.p2(t.sub.2+2) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+2, e.sub.p2(t.sub.2+5) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+5, r.sub.2(t.sub.2+1) is the set value of DO concentration at t.sub.2+1, r.sub.2(t.sub.2+2) is the set value of DO concentration at t.sub.2+2, r.sub.2(t.sub.2+5) is the set value of DO concentration at t.sub.2+5, Δu.sub.1(t.sub.1)=[Δu.sub.11(t.sub.1), Δu.sub.11(t.sub.1)].sup.T is the control vector adjustment amount at t.sub.1, Δu.sub.11(t.sub.1) is the adjustment amount of blower aeration at t.sub.1, Δu.sub.12(t.sub.1) is the adjustment amount of internal reflux at t.sub.1, λ.sub.1=0.5, λ.sub.2=0.5 are weight parameters, α.sub.1=30, ρ.sub.1=10, α.sub.2=0.5, ρ.sub.2=0.5 are control parameters, where
Δu.sub.1(t.sub.1)=u.sub.1(t.sub.1+1)−u.sub.1(t.sub.1),
|Δu.sub.1(t.sub.1)|≤Δu.sub.max,  (30) u.sub.1(t.sub.1)=[u.sub.11(t.sub.1), u.sub.12(t.sub.1)].sup.T is the control vector at t.sub.1, u.sub.11(t.sub.1) is the aeration rate of the blower at t.sub.1, u.sub.12(t.sub.1) is the internal reflux at t.sub.1, u.sub.1(t.sub.1+1)=[u.sub.11(t.sub.1+1), u.sub.12(t.sub.1+1)].sup.T is the control vector at t.sub.1+1, u.sub.11(t.sub.1+1) is the aeration rate of the blower at t.sub.1+1, u.sub.12(t.sub.1+1) is the internal reflux flow at t.sub.1+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 is the maximum aeration adjustment amount, ΔQ.sub.amax 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 of the high-level MPC are calculated by minimizing Eq.(5): $\begin{array}{cc}\Delta u_1\left(t_1\right)={\eta }_1\left({{\xi }_1\left(\frac{\partial {\hat{y}}_1\left(t_1\right)}{\partial u_1\left(t_1\right)}\right)}^T{e}_{p1}\left(t_1\right)+{{\xi }_2\left(\frac{\partial {\hat{y}}_2\left(t_2\right)}{\partial u_1\left(t_1\right)}\right)}^T{e}_{p2}\left(t_2\right)\right),& \left(31\right)\end{array}$ where η.sub.1=0.8, ξ.sub.1=3, ξ.sub.2=1 are control parameters to adjust the aeration rate and internal reflux at t.sub.1:
u.sub.1(t.sub.1+1)=u.sub.1(t.sub.1)+Δu.sub.1(t.sub.1),  (32) {circle around (4)} an objective function of the low-level MPC is designed to track the concentration of DO and the control law calculated by the high-level controller, and the low-level control law is calculated at t.sub.2;
J.sub.2(t.sub.2)=γ.sub.1e.sub.p2(t.sub.2).sup.2+γ.sub.2[u.sub.22(t.sub.2)−u.sub.12(t.sub.1)].sup.2+γ.sub.3Δu.sub.2(t.sub.2).sup.TΔu.sub.2(t.sub.2),  (33) where u.sub.22(t.sub.2) is an internal reflux of the low-level MPC at t.sub.2, u.sub.12(t.sub.1) is an internal reflux calculated by the high-level controller at t.sub.1, Δu.sub.2(t.sub.2)=[Δu.sub.21(t.sub.2), Δu.sub.22(t.sub.2)].sup.T is a control vector adjustment amount at t.sub.2, Δu.sub.21(t.sub.2) is a blower aeration adjustment amount at t.sub.2, Δu.sub.22(t.sub.2) is an internal reflux adjustment amount at t.sub.2, γ.sub.1=30, γ.sub.2=10, γ.sub.3=1 are control parameters, where
Δu.sub.2(t.sub.2)=u.sub.2(t.sub.2+1)−u.sub.2(t.sub.2),
|Δu.sub.2(t.sub.2)|≤Δu.sub.max,  (34) where u.sub.2(t.sub.2)=[u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T is the control vector at t.sub.2, u.sub.21(t.sub.2) is the aeration rate of the blower at t.sub.2, u.sub.22(t.sub.2) is the internal reflux flow at t.sub.2, u.sub.2(t.sub.2+1)=[u.sub.21(t.sub.2+1), u.sub.22(t.sub.2+1)].sup.T is the control vector at t.sub.2+1, u.sub.21(t.sub.2+1) is the aeration rate of the blower at t.sub.2+1, u.sub.21(t.sub.2+1) is the internal reflux flow at t.sub.2+1; the aeration rate and internal reflux adjustment vector of the low-level MPC are calculated by minimizing Eq.(9): $\begin{array}{cc}\Delta u_2\left(t_2\right)={\eta }_2\left[{{\gamma }_1\left(\frac{\partial {\hat{y}}_2\left(t_2\right)}{\partial u_2\left(t_2\right)}\right)}^T{e}_{p2}\left(t_2\right)-{{\gamma }_2\left(\frac{\partial u_{22}\left(t_2\right)}{\partial u_2\left(t_2\right)}\right)}^T\left(u_{22}\left(t_2\right)-u_{12}\left(t_1\right)\right)\right],& \left(35\right)\end{array}$ where η.sub.2=8.4 is control parameter to adjust the aeration rate and internal reflux at t.sub.2:
u.sub.2(t.sub.2+1)=u.sub.2(t.sub.2)+Δu.sub.2(t.sub.2),  (36) {circle around (5)} set k=k+1, if k=2(m+1) is true, set m=m+1 and go to step {circle around (2)}, otherwise, go to step {circle around (6)}; {circle around (6)} if k≤200 is true, calculate the output of the low-level FNN ŷ.sub.2(t.sub.2)=ŷ.sub.2(t.sub.2+1), ŷ.sub.2(t.sub.2+2), . . . , ŷ.sub.2(t.sub.2+5)].sup.T by Eq.(3), and go to step {circle around (4)}, otherwise, end the cycle; (6) the concentration of nitrate nitrogen and DO is controlled by u.sub.2(t.sub.2) solved by the low-level controller, u.sub.2(t.sub.2)=[u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T is an input of a inverter and a sensor at t.sub.2, the inverter controls the blower by adjusting a speed of a motor, and the sensor controls a valve by adjusting opening of an instrument, then, the aeration rate and internal reflux are controlled, the output of the system is the actual value of nitrate nitrogen concentration and DO concentration.

Description

DESCRIPTION OF DRAWINGS

[0037] FIG. 1 is diagram of the HMPC system of WWTP.

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

[0039] FIG. 3 is the result diagram of the DO concentration control in this invention.

[0040] FIG. 4 is the error diagram of the DO concentration control result in this invention.

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

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

DETAILED DESCRIPTION OF THE INVENTION

[0043] 1. A hierarchical model predictive control (HMPC) system of wastewater treatment process (WWTP) based on fuzzy neural network (FNN) is proposed to solve the problem that control variables have different time scales. Then, the effect of wastewater treatment is improved by hierarchical control of dissolved oxygen (DO) concentration and nitrate nitrogen concentration, comprising the following steps:

[0044] (1) The HMPC system for WWTP control comprising a set of measuring means arranged to obtain a dataset, the dataset comprises a plurality of process variables related to a parameter of WWTP; a programmable logic controller (PLC) arranged to perform D/A conversion and A/D conversion; a variable-frequency drive (VFD) arranged to control the aeration pump and electronic valve by changing the working power frequency of motor; a HMPC module arranged to calculate the control law to track the DO concentration and nitrate nitrogen concentration in WWTP with different time scales; the HMPC module comprising a hierarchical structure, in which each layer contains a FNN to predict the system output and an optimization control module to calculate the control law;

[0045] (2) According to different time scales, the hierarchical control structure of HMPC module is designed to control the DO concentration and nitrate nitrogen concentration in WWTP:

[0046] The high-level controller consists of high-level FNN and high-level model predictive controller, it takes the sampling period of nitrate nitrogen concentration 2T as the time scale to track the set values of nitrate nitrogen concentration and DO concentration, and calculates the high-level control law, t.sub.1=2mT is the sampling time of nitrate nitrogen concentration, and m is the sampling steps of nitrate nitrogen concentration;

[0047] The low-level controller consists of low-level FNN and low-level model predictive controller, it takes the sampling period of DO concentration T as the time scale to track the set values of DO concentration and the control law calculated by high-level controller, and calculates the low-level control law, t.sub.2=kT is the sampling time of DO concentration, and k is the sampling steps of DO concentration;

[0048] (3) The high-level FNN is designed to predict the concentration of nitrate nitrogen at each sampling time t.sub.1, which is as follows:

[0049] 1) Set q=1;

[0050] 2) The input of the high-level FNN is x.sub.1(t.sub.1)=[y.sub.1(t.sub.1), u.sub.21(t.sub.1), u.sub.22(t.sub.1)].sup.T, y.sub.1(t.sub.1)=[y.sub.1(t.sub.1−1), y.sub.1(t.sub.1−2)], u.sub.21(t.sub.1)=[u.sub.21(t.sub.2−5), u.sub.21(t.sub.2−6)], u.sub.22(t.sub.1)=[u.sub.22(t.sub.2−5), u.sub.22(t.sub.2−6)], y.sub.1(t.sub.1−1) is the actual value of nitrate nitrogen concentration at t.sub.1−1, y.sub.1(t.sub.1−2) is the actual value of nitrate nitrogen concentration at t.sub.1−2, u.sub.21(t.sub.2−5) is the aeration rate at t.sub.2−5, u.sub.21(t.sub.2−6) is the aeration rate at t.sub.2−6, u.sub.22(t.sub.2−5) is the internal reflux in WWTP at t.sub.2−5, u.sub.22(t.sub.2−6) is the internal reflux in WWTP at t.sub.2−6, T is the transpose of matrix, the output of the high-level FNN is the predicted value of nitrate nitrogen concentration ŷ.sub.1(t.sub.1) at t.sub.1, the output expression is as follows:

[00005]$\begin{array}{cc}{\hat{y}}_1\left(t_1\right)=\frac{{.Math.}_{j=1}^8{w}_{\mathrm{hj}}\left(t_1\right)e^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{1i}\left(t_1\right)-c_{\mathrm{hij}}\left(t_1\right)\right)}^2}{2{\sigma }_{\mathrm{hij}}^2\left(t_1\right)}}}{{.Math.}_{j=1}^8{e}^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{1i}\left(t_1\right)-c_{\mathrm{hij}}\left(t_1\right)\right)}^2}{2{\sigma }_{\mathrm{hij}}^2\left(t_1\right)}}},& \left(13\right)\end{array}$

where x.sub.1i(t.sub.1) is the ith input of the high-level FNN at t.sub.1, w.sub.hj(t.sub.1) is the connection weight between the jth neuron in the rule layer and the output neuron at t.sub.1, j∈[1, 8], c.sub.hij(t.sub.1) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.1, i∈[1, 6], σ.sub.hij(t.sub.1) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.1, e=2.72, the parameter update rules are as follows:

w.sub.hj(t.sub.1+1)=w.sub.hj(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂w.sub.hj(t.sub.1),

c.sub.hij(t.sub.1+1)=c.sub.hij(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂c.sub.hij(t.sub.1),

σ.sub.hij(t.sub.1+1)=σ.sub.hij(t.sub.1)−0.2∂E.sub.1(t.sub.1)/∂σ.sub.hij(t.sub.1)  (14)

where w.sub.hj(t.sub.1+1) is the connection weight between the jth neuron in the rule layer and the output neuron at t.sub.1+1, c.sub.hij(t.sub.1+1) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.1+1, σ.sub.hij(t.sub.1+1) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.1+1, E.sub.1(t.sub.1)=½[y.sub.1(t.sub.1)−ŷ.sub.1(t.sub.1)].sup.2 is the error between the actual and predicted nitrate nitrogen concentration at t.sub.1;

[0051] 3) Set q=q+1, if q≤20 is true, go to step 2), otherwise, exit the cycle;

[0052] (4) The low-level FNN is designed to predict the DO concentration at each sampling time t.sub.2, which is as follows:

[0053] I Set r=1;

[0054] II The input of the low-level FNN is x.sub.2(t.sub.2)=[y.sub.2(t.sub.2), u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T, y.sub.2(t.sub.2)=[y.sub.2(t.sub.2−1), y.sub.2(t.sub.2−2)], u.sub.21(t.sub.2)=[u.sub.21(t.sub.2−5), u.sub.21(t.sub.2−6)], u.sub.22(t.sub.2)=[u.sub.22(t.sub.2−5), u.sub.22(t.sub.2−6)], y.sub.2(t.sub.2−1) is the actual value of DO concentration at t.sub.2−1, y.sub.2(t.sub.2−2) is the actual value of DO concentration at t.sub.2−2, the output of the low-level FNN if the predicted value of DO concentration ŷ.sub.2(t.sub.2) at t.sub.2, the output expression is as follows:

[00006]$\begin{array}{cc}{\hat{y}}_2\left(t_2\right)=\frac{{.Math.}_{j=1}^8{w}_{\mathrm{lj}}\left(t_2\right)e^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{2i}\left(t_2\right)-c_{\mathrm{lij}}\left(t_2\right)\right)}^2}{2{\sigma }_{\mathrm{lij}}^2\left(t_2\right)}}}{{.Math.}_{j=1}^8{e}^{-\underset{i=1}{\overset{6}{\stackrel{}{.Math.}}}\frac{{\left(x_{2i}\left(t_2\right)-c_{\mathrm{lij}}\left(t_2\right)\right)}^2}{2{\sigma }_{\mathrm{lij}}^2\left(t_2\right)}}},& \left(15\right)\end{array}$

where x.sub.2i(t.sub.2) is the ith input of the low-level FNN at t.sub.2, w.sub.lj(t.sub.2) is the connection weight between the jth neuron in the rule layer and the output neuron at t.sub.2, j∈[1, 8], c.sub.lij(t.sub.2) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.2, i∈[1, 6], σ.sub.lij(t.sub.2) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.2, the parameter update rules are as follows:

w.sub.lj(t.sub.2+1)=w.sub.lj(t.sub.2)−0.2∂E.sub.2(t.sub.2)/∂w.sub.lj(t.sub.2),

c.sub.lij(t.sub.2+1)=c.sub.lij(t.sub.2)−0.2∂E.sub.2(t.sub.2)/∂c.sub.lij(t.sub.2),

σ.sub.lij(t.sub.2+1)=σ.sub.lij(t.sub.2)−0.2∂E.sub.2(t.sub.2)/∂σ.sub.lij(t.sub.2),  (16)

where w.sub.lj(t.sub.2+1) is the connection weight between the jth neuron in the rule layer and the output neuron at t.sub.2+1, c.sub.lij(t.sub.2+1) is the center value of the jth radial basal neuron corresponding to the ith input neuron at t.sub.2+1, σ.sub.lij(t.sub.2+1) is the center width of the ith input neuron corresponding to the jth radial basal neuron at t.sub.2+1, E.sub.2(t.sub.2)=½[y.sub.2(t.sub.2)−ŷ.sub.2(t.sub.2)].sup.2, is the error between the actual and predicted DO concentration at t.sub.2;

[0055] III Set r=r+1, if r≤20 is true, go to step II, otherwise, exit the cycle;

[0056] (5) The optimization control module of HMPC module is designed as follows:

[0057] {circle around (1)} Set k=0, m=0;

[0058] {circle around (2)} According to Eq.(1) and Eq.(3), the outputs of the high-level FNN ŷ.sub.1(t.sub.1) and the low-level FNN ŷ.sub.2(t.sub.2) are calculated respectively, ŷ.sub.1(t.sub.1)=[ŷ.sub.1(t.sub.1+1), ŷ.sub.1(t.sub.1+2), . . . , ŷ.sub.1(t.sub.1+5)].sup.T, ŷ.sub.2(t.sub.2)=[ŷ.sub.2(t.sub.2+1), ŷ.sub.2(t.sub.2+2), . . . , ŷ.sub.2(t.sub.2+5)].sup.T, ŷ.sub.1(t.sub.1+1) is the predicted value of nitrate nitrogen concentration at t.sub.1+1, ŷ.sub.1(t.sub.1+2) is the predicted value of nitrate nitrogen concentration at t.sub.1+2, ŷ.sub.1(t.sub.1+5) is the predicted value of nitrate nitrogen concentration at t.sub.1+5, ŷ.sub.2(t.sub.2+1) is the predicted value of DO concentration at t.sub.2+1, ŷ.sub.2(t.sub.2+2) is the predicted value of DO concentration at t.sub.2+2, ŷ.sub.2(t.sub.2+5) is the predicted value of DO concentration at t.sub.2+5;

[0059] {circle around (3)} The objective function of high-level MPC is designed to track the set value of nitrate nitrogen concentration and DO concentration, and the high-level law at t.sub.1 is calculated:

J.sub.1(t.sub.1)=λ.sub.1[α.sub.1e.sub.p1(t.sub.1).sup.Te.sub.p1(t.sub.1)+ρ.sub.1Δu.sub.1(t.sub.1).sup.TΔu.sub.1(t.sub.1)]+λ.sub.2[α.sub.2e.sub.p2(t.sub.2).sup.Te.sub.p2(t.sub.2)+ρ.sub.2Δu.sub.1(t.sub.1).sup.TΔu.sub.1(t.sub.1)],   (17)

where e.sub.p1(t.sub.1)=r.sub.1(t.sub.1)−ŷ.sub.1(t.sub.1) is the error vector between the set value of nitrate nitrogen concentration at t.sub.1 and the predicted value of nitrate nitrogen concentration, e.sub.p1(t.sub.1)=[e.sub.p1(t.sub.1+1), e.sub.p1(t.sub.1+2), . . . , e.sub.p1(t.sub.1+5)].sup.T, r.sub.1(t.sub.1)=[r.sub.1(t.sub.1+1), r.sub.1(t.sub.1+2), . . . , r.sub.1(t.sub.1+5)].sup.T, e.sub.p1(t.sub.1+1) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+1, e.sub.p1(t.sub.1+2) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+2, e.sub.p1(t.sub.1+5) is the error between the set value of nitrate nitrogen concentration and the predicted value of nitrate nitrogen concentration at t.sub.1+5, r.sub.1(t.sub.1+1) is the set value of nitrate nitrogen concentration at t.sub.1+1, r.sub.1(t.sub.1+2) is the set value of nitrate nitrogen concentration at t.sub.1+2, r.sub.1(t.sub.1+5) is the set value of nitrate nitrogen concentration at t.sub.1+5, e.sub.p2(t.sub.2)=r.sub.2(t.sub.2)−ŷ.sub.2(t.sub.2) is the error vector between the set value of DO concentration at t.sub.2 and the predicted value of DO concentration, e.sub.p2(t.sub.2)=[e.sub.p2(t.sub.2+1), e.sub.p2(t.sub.2+2), . . . , e.sub.p2(t.sub.2+5)].sup.T, r.sub.2(t.sub.2)=[r.sub.2(t.sub.2+1), r.sub.2(t.sub.2+2), . . . , r.sub.2(t.sub.2+5)].sup.T, e.sub.p2(t.sub.2+1) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+1, e.sub.p2(t.sub.2+2) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+2, e.sub.p2(t.sub.2+5) is the error between the set value of DO concentration and the predicted value of DO concentration at t.sub.2+5, r.sub.2(t.sub.2+1) is the set value of DO concentration at t.sub.2+1, r.sub.2(t.sub.2+2) is the set value of DO concentration at t.sub.2+2, r.sub.2(t.sub.2+5) is the set value of DO concentration at t.sub.2+5, Δu.sub.1(t.sub.1)=[Δu.sub.11(t.sub.1), Δu.sub.12(t.sub.1)].sup.T is the control vector adjustment amount at t.sub.1, Δu.sub.11(t.sub.1) is the adjustment amount of blower aeration at t.sub.1, Δu.sub.12(t.sub.1) is the adjustment amount of internal reflux at t.sub.1, λ.sub.1=0.5, λ.sub.2=0.5 are weight parameters, α.sub.1=30, ρ.sub.1=10, α.sub.2=0.5, ρ.sub.2=0.5 are control parameters, where

Δu.sub.1(t.sub.1)=u.sub.1(t.sub.1+1)−u.sub.1(t.sub.1),

|Δu.sub.1(t.sub.1)|≤Δu.sub.max,  (18)

u.sub.1(t.sub.1)=[u.sub.11(t.sub.1), u.sub.12(t.sub.1)].sup.T is the control vector at t.sub.1, u.sub.11(t.sub.1) is the aeration rate of the blower at t.sub.1, u.sub.12(t.sub.1) is the internal reflux at t.sub.1, u.sub.1(t.sub.1+1)=[u.sub.11(t.sub.1+1), u.sub.12(t.sub.1+1)].sup.T is the control vector at t.sub.1+1, u.sub.11(t.sub.1+1) is the aeration rate of the blower at t.sub.1+1, u.sub.12(t.sub.1+1) is the internal reflux flow at t.sub.1+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 is the maximum aeration adjustment amount, ΔQ.sub.amax is the maximum internal reflux adjustment amount, Δu.sub.max is set through the blower and internal reflux valve in the control system equipment;

[0060] The aeration rate and internal reflux adjustment vector of the high-level MPC are calculated by minimizing Eq.(5):

[00007]$\begin{array}{cc}\Delta u_1\left(t_1\right)={\eta }_1\left({{\xi }_1\left(\frac{\partial {\hat{y}}_1\left(t_1\right)}{\partial u_1\left(t_1\right)}\right)}^T{e}_{p1}\left(t_1\right)+{{\xi }_2\left(\frac{\partial {\hat{y}}_2\left(t_2\right)}{\partial u_1\left(t_1\right)}\right)}^T{e}_{p2}\left(t_2\right)\right),& \left(19\right)\end{array}$

where η.sub.1=0.8, ξ.sub.1=3, ξ.sub.2=1 are control parameters to adjust the aeration rate and internal reflux at t.sub.1:

u.sub.1(t.sub.1+1)=u.sub.1(t.sub.1)+Δu.sub.1(t.sub.1),  (20)

[0061] {circle around (4)} The objective function of the low-level MPC is designed to track the concentration of DO and the control law calculated by high-level controller, and the low-level control law is calculated at t.sub.2;

J.sub.2(t.sub.2)=γ.sub.1e.sub.p2(t.sub.2).sup.2+γ.sub.2[u.sub.22(t.sub.2)−u.sub.12(t.sub.1)].sup.2+γ.sub.3Δu.sub.2(t.sub.2).sup.TΔu.sub.2(t.sub.2),  (21)

where u.sub.22(t.sub.2) is the internal reflux of the low-level MPC at t.sub.2, u.sub.12(t.sub.1) is the internal reflux calculated by the high-level controller at t.sub.1, Δu.sub.2(t.sub.2)=[Δu.sub.21(t.sub.2), Δu.sub.22(t.sub.2)].sup.T is the control vector adjustment amount at t.sub.2, Δu.sub.21(t.sub.2) is the blower aeration adjustment amount at t.sub.2, Δu.sub.22(t.sub.2) is the internal reflux adjustment amount at t.sub.2, γ.sub.1=30, γ.sub.2=10, γ.sub.3=1 are control parameters, where

Δu.sub.2(t.sub.2)=u.sub.2(t.sub.2+1)−u.sub.2(t.sub.2),

|Δu.sub.2(t.sub.2)|≤Δu.sub.max,  (22)

where u.sub.2(t.sub.2)=[u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T is the control vector at t.sub.2, u.sub.21(t.sub.2) is the aeration rate of the blower at t.sub.2, u.sub.22(t.sub.2) is the internal reflux flow at t.sub.2, u.sub.2(t.sub.2+1)=[u.sub.21(t.sub.2+1), u.sub.22(t.sub.2+1)].sup.T is the control vector at t.sub.2+1, u.sub.21(t.sub.2+1) is the aeration rate of the blower at t.sub.2+1, u.sub.21(t.sub.2+1) is the internal reflux flow at t.sub.2+1;

[0062] The aeration rate and internal reflux adjustment vector of the low-level MPC are calculated by minimizing Eq.(9):

[00008]$\begin{array}{cc}\Delta u_2\left(t_2\right)={\eta }_2\left[{{\gamma }_1\left(\frac{\partial {\hat{y}}_2\left(t_2\right)}{\partial u_2\left(t_2\right)}\right)}^T{e}_{p2}\left(t_2\right)-{{\gamma }_2\left(\frac{\partial u_{22}\left(t_2\right)}{\partial u_2\left(t_2\right)}\right)}^T\left(u_{22}\left(t_2\right)-u_{12}\left(t_1\right)\right)\right],& \left(23\right)\end{array}$

where η.sub.2=8.4 is control parameter to adjust the aeration rate and internal reflux at t.sub.2:

u.sub.2(t.sub.2+1)=u.sub.2(t.sub.2)+Δu.sub.2(t.sub.2),  (24)

[0063] {circle around (5)} Set k=k+1, if k=2(m+1) is true, set m=m+1 and go to step {circle around (2)}, otherwise, go to step {circle around (6)};

[0064] {circle around (6)} If k≤200 is true, calculate the output of the low-level FNN ŷ.sub.2(t.sub.2)=[ŷ.sub.2(t.sub.2+1), ŷ.sub.2(t.sub.2+2), . . . , ŷ.sub.2(t.sub.2+5)].sup.T by Eq.(3), and go to step {circle around (4)}, otherwise, end the cycle;

[0065] (6) The concentration of nitrate nitrogen and DO is controlled by u.sub.2(t.sub.2) solved by the low-level controller, u.sub.2(t.sub.2)=[u.sub.21(t.sub.2), u.sub.22(t.sub.2)].sup.T is the input of inverter and sensor at t.sub.2, the inverter controls the blower by adjusting the speed of motor, and the sensor controls the valve by adjusting the opening of instrument, then, the aeration rate and internal reflux are controlled, the output of the system is the actual value of nitrate nitrogen concentration and DO concentration. FIG. 3 shows the DO concentration of the system, X-axis: time, unit: day, Y-axis: DO concentration, unit: mg/L, the solid line is the expected DO concentration, the dotted line is the actual DO concentration; the error between the actual output DO concentration and the expected DO concentration is shown in FIG. 4, X-axis: time, unit: day, Y-axis: DO concentration error, unit: mg/L FIG. 5 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. 6, X-axis: time, unit: day, Y-axis: nitrate concentration error value, unit: mg/L. The results show that the method is effective.