CN114879487A - Sewage treatment process robust model prediction control method based on interval two-type fuzzy neural network - Google Patents
Sewage treatment process robust model prediction control method based on interval two-type fuzzy neural network Download PDFInfo
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Abstract
The invention provides a robust model prediction control method for a sewage treatment process based on a two-type fuzzy neural network, which aims at the problems of easy external interference, uncertainty and accurate tracking of influence variables in the sewage treatment process and realizes stable and accurate control of the concentration of dissolved oxygen and the concentration of nitrate nitrogen in the sewage treatment process. The control method adopts an interval type two fuzzy neural network estimation prediction model, so that a robust prediction controller without terminal constraint is obtained to weaken the influence of interference on the control performance and stability. Experimental results show that the method can realize stable and accurate on-line control of the concentration of dissolved oxygen and the concentration of nitrate nitrogen, and promote efficient and stable operation of a sewage treatment plant.
Description
Technical Field
The method effectively inhibits the influence of disturbance in the sewage treatment process by using the zone two type fuzzy neural network-based sewage treatment process robust model prediction control method, and realizes the stable and high-precision control of process variables, namely the dissolved oxygen concentration and the nitrate nitrogen concentration, which are key control parameters in the sewage treatment process and have important influence on the effluent quality and energy consumption; the stable control of the concentration of dissolved oxygen and the concentration of nitrate nitrogen in the sewage treatment process is an important branch of the advanced manufacturing technology field as an important link of sewage treatment, and belongs to both the process control field and the water treatment field.
Background
At present, the social economy of China is continuously developed, the urban scale is continuously enlarged, the problems of water resource shortage and water pollution are increasingly highlighted, and the problems of water resource pollution and shortage become one of the most concerned focuses in the world. The urban sewage treatment process can realize sustainable utilization and virtuous cycle of water resources, can effectively relieve water resource crisis, and is an important measure for urban development.
As key process variables in the sewage treatment process, the concentration of dissolved oxygen and the concentration of nitrate nitrogen play a direct control role in the biochemical reaction process in the sewage treatment process; the dissolved oxygen concentration of the aerobic zone of the sewage treatment unit directly influences the nitration reaction process, the concentration of the effluent ammonia nitrogen and the total nitrogen in the system can be inhibited by the excessively high dissolved oxygen concentration, but when the dissolved oxygen concentration reaches a certain value, the variation range of the ammonia nitrogen in the effluent can be weakened. Meanwhile, the nitrate nitrogen concentration in the anoxic zone of the sewage treatment unit is an important index for measuring the denitrification effect, the excessively low nitrate nitrogen concentration reduces the denitrification effect of the denitrification reaction, and the nitrate nitrogen concentration is controlled within a proper range, so that the potential of the denitrification reaction can be improved. Therefore, it is very important to control the concentration of dissolved oxygen and the concentration of nitrate nitrogen in the sewage treatment unit.
However, the biochemical reaction process of urban sewage treatment is complex and changeable, the mechanism is abnormal and complex, the inflow rate and the inflow component change are large, the pollutant types and the organic matter concentration are passively accepted and are seriously interfered by weather change, operation conditions and the like, and the sewage treatment process is a typical multi-interference nonlinear complex dynamic system and always runs in a non-stable state. Therefore, stable control of the sewage treatment process is a rather complicated problem.
In recent years, although a large number of robust control methods emerging in the control industry can suppress the influence of interference to a certain extent, the control effect still has the problems of poor stability, low tracking accuracy and the like, and the control performance cannot be maintained at an expected level in real time. Therefore, an efficient robust control method is sought, stable operation of the sewage treatment process under the condition of strong interference is ensured, and accurate control of process variables is achieved, so that the method has important research value.
The invention designs a robust model prediction control method for a sewage treatment process based on a two-section fuzzy neural network, which mainly establishes a data model through the two-section fuzzy neural network, thereby designing a robust model prediction controller without terminal constraint and realizing the stable and accurate tracking of dissolved oxygen and nitrate nitrogen in the sewage treatment process.
Disclosure of Invention
The invention obtains a robust model prediction control method for a sewage treatment process based on a two-section fuzzy neural network, which mainly adopts the two-section fuzzy neural network to estimate a prediction model, thereby obtaining a robust prediction controller without terminal constraint to weaken the influence of interference on the control performance and stability, realizing the stable and accurate on-line control of the concentration of dissolved oxygen and the concentration of nitrate nitrogen, and promoting the efficient and stable operation of a sewage treatment plant;
the invention adopts the following technical scheme and implementation steps:
1. a sewage treatment process robust model prediction control method based on a two-type fuzzy neural network is characterized by comprising the following steps:
(1) determining a control object; controlling dissolved oxygen and nitrate nitrogen in a sequencing batch type intermittent activated sludge system, wherein the aeration amount of a blower and the internal circulation reflux amount are controlled amounts, and the concentrations of the dissolved oxygen and the nitrate nitrogen are controlled amounts;
(2) according to the strong interference characteristic of the sewage treatment process, designing an objective function of a robust model prediction control method for stably controlling the concentration of dissolved oxygen DO and nitrate nitrogen in the sewage treatment process:
wherein J 1 (t) is an objective function for dissolved oxygen at time t, J 2 (t) is an objective function for nitrate nitrogen at time t, r 1 (t)＝[r 1 (t+1),r 1 (t+2),...,r 1 (t+H p -1)] T Is the desired output vector, r, of the dissolved oxygen DO concentration at time t 2 (t)＝[r 2 (t+1),r 2 (t+2),…,r 2 (t+H p -1)] T Is the expected output vector of nitrate nitrogen concentration at time t,
is a predicted output vector of the dissolved oxygen DO concentration at time t,
is the predicted output vector of nitrate nitrogen concentration at time t, H p Is a prediction time domain, [ Δ u (t) ] [ Δ u [ ] 1 (t),Δu 2 (t),Δu 1 (t+1),Δu 2 (t+1),...,Δu 1 (t+H u -1),Δu 2 (t+H u -1)] T Is the aeration and internal reflux adjustment vector, Deltau, of the blower at time t 1 Is the amount of change in aeration of the blower, Deltau 2 Is the amount of internal reflux variation, H u Is the time domain of variation (H) of the control variable p ≥H u ) T is the transpose of the formula, α 1 ∈[0.5,1.5]，α 2 ∈[0.5,1.5]，β 1 ∈[0.5,1.5]，β 2 ∈[0.5,1.5]Is a control parameter, λ 1 >1,λ 2 >1，P 1 ∈[0.5,1.5]，P 2 ∈[0.5,1.5]The limiting conditions are as follows:
wherein, Δ u 1,max Is the maximum aeration adjustment amount allowed by the control system u 1,min Is the minimum aeration rate allowed by the control system equipment, u 1,max Is the maximum aeration rate, delta u, allowed by the control system equipment 2,max Is the maximum internal recycle back adjustment allowed by the control system equipment, u 2,max Is the maximum internal circulation reflux amount, u, allowed by the control system equipment 2,max Is the maximum internal circulation reflux amount allowed by the control system equipment; Δ u 1,max 、u 1,min 、u 1,max 、Δu 2,max 、u 2,min 、u 2,max Controlling according to the control system equipment;
(3) designing an interval two-type fuzzy neural network topological structure for a prediction control method of the concentrations of dissolved oxygen and nitrate nitrogen in the sewage treatment process; the network structure has five layers: the input layer, the membership function layer, the activation layer, the back part layer and the output layer, and the input of the interval two-type fuzzy neural network is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Y (t-1) is the actual value of the dissolved oxygen DO concentration in the sewage treatment process at time t-1, K L a (t-5) is the aeration rate in the sewage treatment process at the time of t-5, Q a (t-5) is the internal reflux amount in the sewage treatment process at the time of t-5, and the output is the predicted value of the concentration of dissolved oxygen DO and nitrate nitrogen in the sewage treatment system
And
the output expression of the interval type two fuzzy neural network is as follows:
wherein q (t) is a proportional value of the output lower bound of the two-type fuzzy neural network in the time interval t, and q (t) is epsilon (0, 1);y(t)＝[y 1 (t),y 2 (t)] T is the lower bound of the output of the fuzzy neural network of the type II at the time interval t,
the upper bound of the output of the two-type fuzzy neural network in the t time interval is as follows:
m represents the number of active neurons in the activation layer, h j (t) activation layer jth neuron and back-part layer neuron at time tCoefficient of etching, f j (t) is the lower bound of the j-th neuron of the activation layer,
for the upper bound of the j-th neuron of the activation layer, their expression is as follows:
where n denotes the number of input neurons in the input layer, i ═ 1,2, … n, x (t) ═ x 1 (t),x 2 (t),…,x n (t)]Is an input vector of the neural network, w ij (t)＝[w 1 ij (t),w 2 ij (t)] T Is that the ith input corresponds to the back-part weight for the jth activation layer neuron, b j (t) is the jth weight bias at time t,u ij (t) is the lower bound membership value for the jth membership layer neuron at time t at the ith input,
is the upper bound membership value of the jth membership function layer neuron at the ith input at time t,
the calculation formula is as follows:
wherein G (-) represents a Gaussian membership function, G (x) i (t)；m ij (t),σ ij (t))＝exp{-(x i (t)-m ij (t)) 2 /(2σ ij (t) 2 )}，m ij (t) is the lower bound of the ith neuron in the input layer with respect to the central value of the neurons in the jth membership function layer,
is the ith neuron of the input layer with respect to the jth membership function layerUpper bound of the value of the metacenter, σ ij (t) is the width value of the jth membership function layer neuron when the ith neuron of the layer is input at the moment t;
the error function is defined as:
wherein the content of the first and second substances,
for the actual output of the neural network at time t, y (t) ═ y 1 (t),y 2 (t)] T For the actual output of the system at time t, y 1 (t) is the actual output of the DO concentration of the system dissolved oxygen, y 2 (t) is the actual output of the nitrate nitrogen concentration of the system;
(4) the two types of fuzzy neural networks in training interval specifically are:
given a section two-type fuzzy neural network, the input is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Training neurons of a membership function layer and an activation layer which are 8, and setting the calculation step number l to be 1;
secondly, updating parameters of the interval two-type fuzzy neural network:
wherein m is ij (t +1) is the lower bound of the j-th membership function layer neuron central value at the ith input at the time of t +1,
the upper bound of the j-th membership function layer neuron central value is the ith input at the moment of t + 1; sigma ij (t +1) is the width value of the jth membership function layer neuron at the ith input time of t +1, q (t +1) is the proportion value of the lower bound of the two-type fuzzy neural network output at the interval of t +1, b j (t +1) is the weight bias at time t +1, w ij (t +1) is the weight coefficient at time t +1, η 1 ∈(0,1]、η 2 ∈(0,2]、η 3 ∈(0,1]、η 4 ∈(0,1]And η 5 ∈(0,1]A learning rate that is a parameter;
c, repeating the first step and the second step, stopping calculation when the L reaches a set step number L, wherein L belongs to (100, 500);
(5) the method is designed for a stable tracking control strategy of the set values of dissolved oxygen DO and nitrate nitrogen in the disturbed sewage treatment process, and specifically comprises the following steps:
calculating the output of interval two-type fuzzy neural network according to formula (3)
The concentration prediction value of dissolved oxygen DO and nitrate nitrogen of the sewage treatment system at the time t is obtained;
solving the updated value of each parameter according to a formula (8);
designing a target function for predicting and controlling the robust model to track the DO concentration and the nitrate nitrogen concentration of the dissolved oxygen:
J(t)＝ρ 1 J 1 (t)+ρ 2 J 2 (t) (9)
where ρ is 1 ∈(0,1]，ρ 2 ∈(0,1]Is a weight parameter, satisfies rho 1 +ρ 2 ＝1；
And fourthly, calculating the robust model prediction control law through a minimization formula (9):
wherein eta is u Control learning rate, α, is represented by 10 1 ＝1，α 2 ＝0,8，β 1 ＝1，β 2 1.5 is a control parameter, u (t +1) ═ u 1 (t+1),u 2 (t+1)] T Control vector, u, at time t +1 1 (t +1) is the aeration amount of the blower at time t +1, u 2 (t +1) is the internal reflux quantity at the time t +1, and the first value delta u (t) taken by the delta u (t) is used as an adjusting vector of the controller, namely the aeration quantity and the internal reflux quantity of the sewage treatment process at the time t are adjusted:
u(t+1)＝u(t)+Δu(t)； (11)
(6) and controlling dissolved oxygen DO and nitrate nitrogen by using solved u (t), wherein u (t) is input of a frequency converter and a sensor at the time t, the frequency converter achieves the purpose of controlling the air blower by adjusting the rotating speed of the motor, the sensor achieves the purpose of controlling a valve by adjusting the opening of an instrument, finally controlling the aeration amount and the internal reflux, and the output of the whole control system is the actual values of the concentration of the dissolved oxygen and the concentration of the nitrate nitrogen.
The innovation of the invention is realized
(1) The invention aims at that the sewage treatment process is a typical multi-interference nonlinear complex dynamic system and always runs in a non-steady state, and meanwhile, an accurate mathematical model of the sewage treatment process is difficult to express;
(2) based on the established prediction model, the invention designs a robust model prediction controller without terminal constraint to control the dissolved oxygen concentration and the nitrate nitrogen concentration in the sewage treatment process, weakens the influence of interference on the control performance and stability, and solves the problem that the variables in the sewage treatment process are difficult to control stably and accurately;
particular attention is paid to: the invention is only for the convenience of description, the concentration of dissolved oxygen and nitrate nitrogen is controlled, and the invention can also be applied to the control of ammonia nitrogen in the sewage treatment process, and the like, and the invention is within the scope of the invention as long as the control is carried out by adopting the principle of the invention.
Drawings
FIG. 1 shows the inlet flow Q of the present invention 0 And feed water ammonia concentration NH 0 Perturbation map of
FIG. 2 is a graph showing the results of controlling the concentration of dissolved oxygen in accordance with the present invention
FIG. 3 is an error chart of the result of controlling the concentration of dissolved oxygen according to the present invention
FIG. 4 is a graph showing the control result of nitrate nitrogen concentration according to the present invention
FIG. 5 is an error chart of the control result of nitrate nitrogen concentration according to the present invention
Detailed Description
1. A sewage treatment process robust model prediction control method based on a two-type fuzzy neural network is characterized by comprising the following steps:
(1) determining a control object; controlling dissolved oxygen and nitrate nitrogen in a sequencing batch type intermittent activated sludge system, wherein the aeration amount of a blower and the internal circulation reflux amount are controlled amounts, and the concentrations of the dissolved oxygen and the nitrate nitrogen are controlled amounts;
(2) according to the strong interference characteristic of the sewage treatment process, designing an objective function of a robust model prediction control method for stably controlling the concentration of dissolved oxygen DO and nitrate nitrogen in the sewage treatment process:
wherein J 1 (t) is an objective function for dissolved oxygen at time t, J 2 (t) is an objective function for nitrate nitrogen at time t, r 1 (t)＝[r 1 (t+1),r 1 (t+2),…,r 1 (t+H p -1)] T Is the desired output vector, r, of the dissolved oxygen DO concentration at time t 2 (t)＝[r 2 (t+1),r 2 (t+2),…,r 2 (t+H p -1)] T Is the expected output vector of nitrate nitrogen concentration at time t,
is a predicted output vector of the dissolved oxygen DO concentration at time t,
is the predicted output vector of nitrate nitrogen concentration at time t, H p Is a prediction, H p ＝3，Δu(t)＝[Δu 1 (t),Δu 2 (t),Δu 1 (t+1),Δu 2 (t+1),…,Δu 1 (t+H u -1),Δu 2 (t+H u -1)] T Aeration and internal reflux of the blower at time tAdjustment vector, Δ u 1 Is the amount of change in aeration of the blower, Deltau 2 Is the amount of internal reflux variation, H u Is the time domain of variation (H) of the control variable p ≥H u )，H u T is the transpose of the formula, α 1 ＝1，α 2 ＝0,8，β 1 ＝1，β 2 1.5 is a control parameter, λ 1 ＝5，λ 2 ＝3，P 1 ＝1，P 2 1.2, the limitation:
wherein, Δ u 1,max Is the maximum aeration adjustment amount allowed by the control system u 1,min Is the minimum aeration quantity, u, allowed by the control system equipment 1,max Is the maximum aeration rate, delta u, allowed by the control system equipment 2,max Is the maximum internal recycle back adjustment allowed by the control system equipment, u 2,max Is the maximum internal circulation reflux amount, u, allowed by the control system equipment 2,max Is the maximum internal circulation reflux amount allowed by the control system equipment; Δ u 1,max 、u 1,min 、u 1,max 、Δu 2,max 、u 2,min 、u 2,max Controlling according to the control system equipment;
(3) designing an interval two-type fuzzy neural network topological structure for a prediction control method of the concentrations of dissolved oxygen and nitrate nitrogen in the sewage treatment process; the network structure has five layers: the input layer, the membership function layer, the activation layer, the back part layer and the output layer, and the input of the interval two-type fuzzy neural network is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Y (t-1) is the actual value of the dissolved oxygen DO concentration in the sewage treatment process at time t-1, K L a (t-5) is the aeration rate in the sewage treatment process at the time of t-5, Q a (t-5) is the internal reflux amount in the sewage treatment process at the time of t-5, and the output is the predicted value of the concentration of dissolved oxygen DO and nitrate nitrogen in the sewage treatment system
And
the output expression of the interval type two fuzzy neural network is as follows:
wherein q (t) is a proportional value of the output lower bound of the two-type fuzzy neural network in the time interval t, and the initial q (t) is 0.67;y(t)＝[y 1 (t),y 2 (t)] T is the lower bound of the output of the two-type fuzzy neural network in the t time interval,
the upper bound of the output of the two-type fuzzy neural network in the t time interval is as follows:
m ═ 8 denotes the number of activated neurons in the activation layer, h j (t) is the coefficient of the j-th neuron of the activation layer and the neuron of the back-part layer at the time t,f j (t) is the lower bound of the j-th neuron of the activation layer,
for the upper bound of the j-th neuron of the activation layer, their expression is as follows:
n ═ 3 denotes the number of input neurons in the input layer, i ═ 1,2, … N, x (t) ═ x 1 (t),x 2 (t),…,x n (t)]Is an input vector of the neural network, w ij (t)＝[w 1 ij (t),w 2 ij (t)] T Is that the ith input corresponds to the back-part weight for the jth activation layer neuron, b j (t) is the jth weight bias at time t,u ij (t) Is the lower bound membership value of the jth membership function layer neuron at the ith input at time t,
is the upper bound membership value of the jth membership function layer neuron at the ith input at time t,
the calculation formula is as follows:
wherein G (-) represents a Gaussian membership function, G (x) i (t)；m ij (t),σ ij (t))＝exp{-(x i (t)-m ij (t)) 2 /(2σ ij (t) 2 )}，m ij (t) is the lower bound of the ith neuron in the input layer with respect to the central value of the neurons in the jth membership function layer,
is the upper bound, σ, of the i-th neuron of the input layer with respect to the central value of the neurons of the j-th membership function layer ij (t) is the width value of the jth membership function layer neuron when the ith layer neuron is input at the time t;
the error function is defined as:
wherein the content of the first and second substances,
for the actual output of the neural network at time t, y (t) ═ y 1 (t),y 2 (t)] T For the actual output of the system at time t, y 1 (t) is the actual output of the DO concentration of the dissolved oxygen in the system, y 2 (t) is the actual output of the nitrate nitrogen concentration of the system;
(4) the two types of fuzzy neural networks in training interval specifically are:
given a section two-type fuzzy neural network, the input is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Training neurons of a membership function layer and an activation layer which are 8, and setting the calculation step number l to be 1;
secondly, updating parameters of the interval two-type fuzzy neural network:
wherein m is ij (t +1) is the lower bound of the j-th membership function layer neuron central value at the ith input at the time of t +1,
the upper bound of the j-th membership function layer neuron central value is the ith input at the moment of t + 1; sigma ij (t +1) is the width value of the jth membership function layer neuron at the ith input time of t +1, q (t +1) is the proportion value of the lower bound of the two-type fuzzy neural network output at the interval of t +1, b j (t +1) is the weight bias at time t + 1, w ij (t +1) is the weight coefficient at time t + 1, η 1 ＝0.08、η 2 ＝1.1、η 3 ＝0.1、η 4 0.5 and η 5 Learning rate with 0.5 as parameter;
c, repeating the first step and the second step, stopping calculating when the L reaches a set step number L, and setting the L to be 500;
(5) the method is designed for a stable tracking control strategy of the set values of dissolved oxygen DO and nitrate nitrogen in the disturbed sewage treatment process, and specifically comprises the following steps:
calculating the output of interval two-type fuzzy neural network according to formula (3)
The concentration prediction value of dissolved oxygen DO and nitrate nitrogen of the sewage treatment system at the time t is obtained;
solving the updated value of each parameter according to a formula (8);
designing a target function for predicting and controlling the robust model to track the DO concentration and the nitrate nitrogen concentration of the dissolved oxygen:
J(t)＝ρ 1 J 1 (t)+ρ 2 J 2 (t) (9)
where ρ is 1 ＝0.7，ρ 2 0.3 is a weight parameter, and satisfies ρ 1 +ρ 2 ＝1；
And fourthly, calculating the robust model prediction control law through a minimization formula (9):
wherein eta is u Control learning rate, α, is represented by 10 1 ＝1，α 2 ＝0,8，β 1 ＝1，β 2 1.5 is a control parameter, u (t +1) ═ u 1 (t+1),u 2 (t+1)] T Control vector, u, at time t +1 1 (t +1) is the aeration amount of the blower at time t + 1, u 2 (t +1) is the internal reflux quantity at the time t + 1, and the first value delta u (t) taken by the delta u (t) is used as an adjusting vector of the controller, namely the aeration quantity and the internal reflux quantity of the sewage treatment process at the time t are adjusted:
u(t+1)＝u(t)+Δu(t)； (11)
(6) and controlling dissolved oxygen DO and nitrate nitrogen by using solved u (t), wherein u (t) is input of a frequency converter and a sensor at the time t, the frequency converter achieves the purpose of controlling the air blower by adjusting the rotating speed of the motor, the sensor achieves the purpose of controlling a valve by adjusting the opening of an instrument, finally controlling the aeration amount and the internal reflux, and the output of the whole control system is the actual values of the concentration of the dissolved oxygen and the concentration of the nitrate nitrogen. Fig. 2 shows the dissolved oxygen concentration value of the system, X-axis: time, in days, Y-axis: dissolved oxygen concentration value, unit is mg/l, solid line is dissolved oxygen concentration set value, dotted line is actual dissolved oxygen concentration value; the error between the actual dissolved oxygen concentration and the set dissolved oxygen concentration is shown in FIG. 3, X-axis: time, in days, Y-axis: dissolved oxygen concentration error in units of milligrams per liter; fig. 4 shows the nitrate nitrogen concentration values of the system, X-axis: time, in days, Y-axis: the nitrate nitrogen concentration value is in milligram/liter, the solid line is the nitrate nitrogen concentration set value, and the dotted line is the actual nitrate nitrogen concentration value; the error between the actual nitrate nitrogen concentration value and the set nitrate nitrogen concentration value is shown in figure 5, and the X axis: time, in days, Y-axis: the nitrate nitrogen concentration error value is expressed in milligram/liter, and the result proves the effectiveness of the method.
Claims (1)
1. A sewage treatment process robust model prediction control method based on an interval two-type fuzzy neural network is characterized by comprising the following steps:
(1) determining a control object; controlling dissolved oxygen and nitrate nitrogen in a sequencing batch type intermittent activated sludge system, wherein the aeration amount of a blower and the internal circulation reflux amount are controlled amounts, and the concentrations of the dissolved oxygen and the nitrate nitrogen are controlled amounts;
(2) according to the strong interference characteristic of the sewage treatment process, designing an objective function of a robust model prediction control method for stably controlling the concentration of dissolved oxygen DO and nitrate nitrogen in the sewage treatment process:
wherein J 1 (t) is an objective function for dissolved oxygen at time t, J 2 (t) is an objective function for nitrate nitrogen at time t, r 1 (t)＝[r 1 (t+1),r 1 (t+2),…,r 1 (t+H p -1)] T Is the desired output vector, r, of the dissolved oxygen DO concentration at time t 2 (t)＝[r 2 (t+1),r 2 (t+2),…,r 2 (t+H p -1)] T Is the expected output vector of nitrate nitrogen concentration at time t,
is a predicted output vector of the dissolved oxygen DO concentration at time t,
is the predicted output vector of nitrate nitrogen concentration at time t, H p Is toTime domain measurement, Δ u (t) ═ Δ u 1 (t),Δu 2 (t),Δu 1 (t+1),Δu 2 (t+1),…,Δu 1 (t+H u -1),Δu 2 (t+H u -1)] T Is the aeration and internal reflux adjustment vector, Deltau, of the blower at time t 1 Is the amount of change in aeration of the blower, Deltau 2 Is the amount of internal reflux variation, H u Is the time domain of variation of the control variable, H p ≥H u T is the transpose of the formula, α 1 ∈[0.5,1.5]，α 2 ∈[0.5,1.5]，β 1 ∈[0.5,1.5]，β 2 ∈[0.5,1.5]Is a control parameter, λ 1 >1,λ 2 >1，P 1 ∈[0.5,1.5]，P 2 ∈[0.5,1.5]The limiting conditions are as follows:
wherein, Δ u 1,max Is the maximum aeration adjustment amount allowed by the control system u 1,min Is the minimum aeration rate allowed by the control system equipment, u 1,max Is the maximum aeration rate, delta u, allowed by the control system equipment 2,max Is the maximum internal recycle back adjustment allowed by the control system equipment, u 2,max Is the maximum internal circulation reflux amount, u, allowed by the control system equipment 2,max Is the maximum internal circulation reflux amount allowed by the control system equipment; Δ u 1,max 、u 1,min 、u 1,max 、Δu 2,max 、u 2,min 、u 2,max Controlling according to the control system equipment;
(3) designing an interval two-type fuzzy neural network topological structure for a prediction control method of the concentrations of dissolved oxygen and nitrate nitrogen in the sewage treatment process; the network structure has five layers: the input layer, the membership function layer, the activation layer, the back part layer and the output layer, and the input of the interval two-type fuzzy neural network is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Y (t-1) is the actual value of the dissolved oxygen DO concentration in the sewage treatment process at time t-1, K L a (t-5) is the aeration quantity in the sewage treatment process at the time of t-5, Q a (t-5) is the internal reflux amount in the sewage treatment process at the time of t-5And the output is the concentration predicted value of dissolved oxygen DO and nitrate nitrogen of the sewage treatment system
And
the output expression of the interval type two fuzzy neural network is as follows:
wherein q (t) is a proportional value of the output lower bound of the two-type fuzzy neural network in the time interval t, and q (t) is epsilon (0, 1);y(t)＝[y 1 (t),y 2 (t)] T is the lower bound of the output of the two-type fuzzy neural network in the t time interval,
the upper bound of the output of the two-type fuzzy neural network in the t time interval is as follows:
m represents the number of active neurons in the activation layer, h j (t) is the coefficient of the j-th neuron of the activation layer and the neuron of the back-part layer at the time t,f j (t) is the lower bound of the j-th neuron of the activation layer,
for the upper bound of the j-th neuron of the activation layer, their expression is as follows:
wherein n represents an input neuron in the input layerThe number i ═ 1,2, … n, x (t) ═ x 1 (t),x 2 (t),…,x n (t)]Is an input vector of the neural network,
is that the ith input corresponds to the back-part weight for the jth activation layer neuron, b j (t) is the jth weight bias at time t,u ij (t) is the lower bound membership value for the jth membership layer neuron at time t at the ith input,
is the upper bound membership value of the jth membership function layer neuron at the ith input at time t,
the calculation formula is as follows:
wherein G (-) represents a Gaussian membership function, G (x) i (t)；m ij (t),σ ij (t))＝exp{-(x i (t)-m ij (t)) 2 /(2σ ij (t) 2 )}，m ij (t) is the lower bound of the ith neuron in the input layer with respect to the central value of the neurons in the jth membership function layer,
is the upper bound, σ, of the input layer ith neuron with respect to the j membership function layer neuron center value ij (t) is the width value of the jth membership function layer neuron when the ith neuron of the layer is input at the moment t;
the error function is defined as:
wherein the content of the first and second substances,
for the actual output of the neural network at time t, y (t) ═ y 1 (t),y 2 (t)] T For the actual output of the system at time t, y 1 (t) is the actual output of the DO concentration of the system dissolved oxygen, y 2 (t) is the actual output of the nitrate nitrogen concentration of the system;
(4) the two types of fuzzy neural networks in training interval specifically are:
given a section two-type fuzzy neural network, the input is x (t) ═ y (t-1), K L a(t-5),Q a (t-5)]Training neurons of a membership function layer and an activation layer which are 8, and setting the calculation step number l to be 1;
secondly, updating parameters of the interval two-type fuzzy neural network:
wherein the content of the first and second substances,m ij (t +1) is the lower bound of the j-th membership function layer neuron central value at the ith input at the time of t +1,
the upper bound of the j-th membership function layer neuron central value is the ith input at the moment of t + 1; sigma ij (t +1) is the width value of the jth membership function layer neuron at the ith input time of t +1, q (t +1) is the proportion value of the lower bound of the two-type fuzzy neural network output at the interval of t +1, b j (t +1) is the weight bias at time t +1, w ij (t +1) is the weight coefficient at time t +1, η 1 ∈(0,1]、η 2 ∈(0,2]、η 3 ∈(0,1]、η 4 ∈(0,1]And η 5 ∈(0,1]A learning rate that is a parameter;
c, repeating the first step and the second step, stopping calculation when the L reaches a set step number L, wherein L belongs to (100, 500);
(5) the method is designed for a stable tracking control strategy of the set values of dissolved oxygen DO and nitrate nitrogen in the disturbed sewage treatment process, and specifically comprises the following steps:
calculating the output of interval two-type fuzzy neural network according to formula (3)
The concentration prediction value of dissolved oxygen DO and nitrate nitrogen of the sewage treatment system at the time t is obtained;
solving the updated value of each parameter according to a formula (8);
designing a target function for predicting and controlling the robust model to track the DO concentration and the nitrate nitrogen concentration of the dissolved oxygen:
J(t)＝ρ 1 J 1 (t)+ρ 2 J 2 (t) (9)
where ρ is 1 ∈(0,1]，ρ 2 ∈(0,1]Is a weight parameter, satisfies rho 1 +ρ 2 ＝1；
And fourthly, calculating the robust model prediction control law through a minimization formula (9):
wherein eta is u Control learning rate, α, is represented by 10 1 ＝1，α 2 ＝0,8，β 1 ＝1，β 2 1.5 is a control parameter, u (t +1) ═ u 1 (t+1),u 2 (t+1)] T Control vector, u, at time t +1 1 (t +1) is the aeration amount of the blower at time t +1, u 2 (t +1) is the internal reflux quantity at the time t +1, and the first value delta u (t) taken by the delta u (t) is used as an adjusting vector of the controller, namely the aeration quantity and the internal reflux quantity of the sewage treatment process at the time t are adjusted:
u(t+1)＝u(t)+Δu(t)； (11)
(6) and controlling dissolved oxygen DO and nitrate nitrogen by using solved u (t), wherein u (t) is input of a frequency converter and a sensor at the time t, the frequency converter achieves the purpose of controlling the air blower by adjusting the rotating speed of the motor, the sensor achieves the purpose of controlling a valve by adjusting the opening of an instrument, finally controlling the aeration amount and the internal reflux, and the output of the whole control system is the actual values of the concentration of the dissolved oxygen and the concentration of the nitrate nitrogen.
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