CN111287256B - Saturation control method for water supply of urban water service system - Google Patents

Saturation control method for water supply of urban water service system Download PDF

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CN111287256B
CN111287256B CN202010104361.6A CN202010104361A CN111287256B CN 111287256 B CN111287256 B CN 111287256B CN 202010104361 A CN202010104361 A CN 202010104361A CN 111287256 B CN111287256 B CN 111287256B
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water
water supply
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CN111287256A (en
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张俊锋
邵宇
丁丹
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Shanghai Juzhong Water Technology Group Co ltd
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Hangzhou Dianzi University
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    • E—FIXED CONSTRUCTIONS
    • E03—WATER SUPPLY; SEWERAGE
    • E03B—INSTALLATIONS OR METHODS FOR OBTAINING, COLLECTING, OR DISTRIBUTING WATER
    • E03B7/00—Water main or service pipe systems
    • E03B7/07—Arrangement of devices, e.g. filters, flow controls, measuring devices, siphons or valves, in the pipe systems
    • E—FIXED CONSTRUCTIONS
    • E03—WATER SUPPLY; SEWERAGE
    • E03B—INSTALLATIONS OR METHODS FOR OBTAINING, COLLECTING, OR DISTRIBUTING WATER
    • E03B7/00—Water main or service pipe systems
    • E03B7/07—Arrangement of devices, e.g. filters, flow controls, measuring devices, siphons or valves, in the pipe systems
    • E03B7/072—Arrangement of flowmeters

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  • Life Sciences & Earth Sciences (AREA)
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Abstract

The invention discloses a control method for water supply of an urban water service system. The invention has the following steps: step 1, carrying out data acquisition on a water service system model, and establishing a network state space positive system model related to urban water service water supply; step 2, constructing an event trigger condition when the water supply peak period water pressure of the water service system is insufficient; and 3, designing an event trigger controller aiming at the positive system, controlling the water supply quantity in real time when the water supply of the system is insufficient, avoiding the occurrence of flow break and achieving the stable operation of the system. The method can effectively solve the problem of unstable urban water supply caused by the valve threshold limit in the urban water service network system.

Description

Saturation control method for water supply of urban water service system
Technical Field
The invention belongs to the technical field of automation, and relates to a modeling method for a water service system and a state saturation positive system of a valve threshold opening problem of the water service system, which realizes stable control of a water service pipe network and the valve threshold opening problem by modeling the water service system and can be applied to an urban water service water supply and drainage system.
Background
With the acceleration of the urbanization process, people have higher and higher pursuits for the quality of life. Water resources are an indispensable part of urban life and production and are life resources on which human beings rely for survival. In the 21 st century, the phenomena of excessive consumption, pollution and the like of water resources occur, and the situations of water resource shortage and water supply difficulty occur in the construction process of cities. Therefore, the environmental protection and reasonable distribution of water resources are important for the development of cities. The water supply and drainage system and the water service pipe network of the city form a key component part for stable operation and development of the city. In cities, the demands for water consumption in various time periods and different areas are different, and reasonable allocation of water resources is required under limited water resources. In the process, the opening problem of the valve threshold value, the water storage capacity of the pipe network and the like all have certain influence on stable water supply. Therefore, the stable and effective water supply scheme is adopted, and the key to solve the problems of the valve threshold opening degree and the water storage capacity of the water service pipe network in the urban water service water supply system is solved.
In real life, there is a class of variables that always remain non-negative, such as the number of biological populations, the concentration of substances in a chemical reaction, the number of waiting people in a queue, etc. Such systems consisting of non-negative quantities can be described precisely by positive system modeling. Positive systems require that their input and output states remain non-negative. Because the volumes of water in the pumping station and the pipe network of the urban water service system are non-negative, the positive system modeling method is adopted in the research of the application. Meanwhile, the water storage capacity of a pipe network of the water service system is limited, and the opening degree of a pump station and a valve is also limited, which are the saturation problems of the system. Therefore, the water service system is more reasonable by utilizing the state saturation positive system to model, and the controller based on the event trigger mechanism is adopted to appropriately limit the flow in the period of insufficient water quantity of a pipe network or peak water consumption of residents, so that the stable operation of the urban water supply system can be ensured.
Disclosure of Invention
The invention aims to solve the problems of instability of water storage capacity in a pump station, pipe network threshold values and water flow distribution process in an urban water supply system, and provides a control method of a state saturation positive system based on an event trigger mechanism. By constructing event trigger conditions and designing an event trigger controller, the problem of unreasonable distribution of a water supply system of water services is solved, real-time supply of water is realized, the problems of water supply shortage, difficulty and the like are avoided, and the life quality of urban residents is improved. The specific technical scheme is as follows:
the method comprises the following specific steps:
step 1, establishing a state space model of the urban water service water supply system by acquiring water flow data of a pipe network of the urban water supply system:
x(t+1)＝sat(Ax(t))+Bu(t)，
wherein
Figure BDA0002387990570000021
Showing the water flow in the water storage tanks of the urban water service system at the time t, n showing the number of the water storage tanks,
Figure BDA0002387990570000022
the opening degree of the water pipe network or the water pipe valve at t sampling moments is shown, m represents the number of the water valves,
Figure BDA0002387990570000023
a real column vector expressed in m dimensions;
Figure BDA0002387990570000024
and
Figure BDA0002387990570000025
a matrix representing the appropriate dimensions, A, B is a matrix of weighting constants designed by the modeling system based on the acquired data; considering the fact that the water system requires water flow to be non-negative, i.e., ensuring that x (t) and u (t) are always non-negative, the present invention models the water system according to a positive system model, satisfying A ≧ 0, B ≧ 0, for each element in matrices A and B, i.e., requiring all elements in matrix A, B to be non-negative.
sat:
Figure BDA0002387990570000026
Is a compound defined as sat (u) ═ sat (u)1),...,sat(um))TSaturation vector function of, wherein sat (u)l)＝sgn(ul)min{|ul|,1},l∈{1,...,m}。
Step 2, establishing an event trigger control mechanism of the water supply system
Figure BDA0002387990570000027
Where theta is a constant and has theta > 0,
Figure BDA00023879905700000212
is the sampling error. II-1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all elements within the vector.
Step 3, designing an event trigger controller of the water supply system, comprising the following steps:
step 3.1 design event trigger controller
Figure BDA00023879905700000210
Wherein the content of the first and second substances,
Figure BDA00023879905700000211
f is a controller gain matrix of the designed water affair system;
step 3.2 following step 1, step 2 and step 3.1:
Figure BDA00023879905700000213
Figure BDA00023879905700000214
step 3.3 following step 1, step 3.1 and step 3.2:
Figure BDA0002387990570000039
wherein
Figure BDA0002387990570000031
Step 3.4, a linear residual positive Lyapunov function is constructed for the water service network management system:
V(t)＝xT(t)v，
wherein the value of the vector satisfies that v is more than 0, namely each element in the vector is a positive number, and
Figure BDA0002387990570000038
is a real column vector of dimension n. In order to ensure the stable operation of the water affair system, the difference equation for calculating the Lyapunov function is as follows:
ΔV＝V(t+1)-V(t)＝xT(t+1)v-xT(t)v，
where the symbol T represents the transpose of a matrix or vector.
Step 3.5 design constants λ > 0, θ > 0, ρ > 0, and β > 0, ξ if there is an n-dimensional variable vector v > 0s＞0,ξ＞0,zl< 0, z < 0 such that the following inequality
Figure BDA0002387990570000032
Figure BDA0002387990570000033
Figure BDA0002387990570000034
zl＜z,ξs＜ξ，
Figure BDA0002387990570000035
Figure BDA0002387990570000036
βv-ξs≥0，
1.. 2. for each lnN is true, i 1, …, m, and s 1,
wherein
Figure BDA0002387990570000037
Step 3.6, designing a water supply pipe network system x (t +1) ═ sat (ax (t)) + Bu (t)) for water service, and triggering a controller at event
Figure BDA0002387990570000041
Next, the modeling system is positive and stable; first, according to step 3.3, the positivity of the system is ensured by the lower bound of the modeling system function, i.e.
Figure BDA0002387990570000042
Step 3.7, calculating a difference equation of the Lyapunov function of the modeling system to satisfy the following conditions:
ΔV＜0.
step 3.8 obtained according to step 3.3 and step 3.4:
Figure BDA0002387990570000043
step 3.9 according to the conditions set forth in step 3.5, one can obtain
Figure BDA0002387990570000044
Figure BDA0002387990570000045
Further, it can be deduced
Figure BDA0002387990570000046
Figure BDA0002387990570000047
Step 3.10 from step 3.8 and step 3.9 can be obtained
Figure BDA0002387990570000048
Thus combining the positive of the system in step 3.6: x (k) ≧ 0, we can get
ΔV＜0；
Step 3.11 in summary, combining step 3.1 to step 3.10, the gain matrix of the event-triggered controller can be obtained as follows:
Figure BDA0002387990570000049
and the controller auxiliary gain matrix is:
Figure BDA00023879905700000410
the invention provides a control method for improving stable operation of an urban water supply system, which provides a state saturation control technology based on event triggering according to the problems of water supply shortage or shortage and the like in the operation process of the current water supply system.
Detailed Description
The present invention is further explained below.
The saturation control method for the water supply of the urban water service system comprises the following steps:
step 1, firstly, collecting data of water storage capacity change in a pump station and a water service pipe network in an urban water service water supply system, and establishing a following space state model by using the data:
x(t+1)＝sat(Ax(t)+Bu(t))，
wherein
Figure BDA0002387990570000051
Representing the water flow in the water storage tanks of the urban water service system at time t, n representing the number of water service pipe networks,
Figure BDA0002387990570000052
representing the opening of the valves on the pump station or water service pipe network at the moment t, and m representing the number of the valves, wherein
Figure BDA0002387990570000053
And
Figure BDA0002387990570000054
representing the real column vectors in the n and m dimensions, respectively.
Figure BDA0002387990570000055
And
Figure BDA0002387990570000056
moments representing appropriate dimensionsA, B is a weighted constant matrix designed by the modeling system based on the collected data; considering the actual situation that the water affair system requires that the water flow is all non-negative, namely, ensuring that x (t) and u (t) are always non-negative, the invention models the water affair system according to a positive system model, and satisfies that A is more than or equal to 0, B is more than or equal to 0, and more than or equal to each element in the matrix AB, namely all elements in the matrix AB are required to be non-negative.
sat:
Figure BDA0002387990570000057
Is a compound defined as sat (u) ═ sat (u)1),...,sat(um))TSaturation vector function of, wherein sat (u)l)＝sgn(ul)min{|uι|,1},ι∈{1,...,m}。
Step 2, establishing an event trigger mechanism of the urban water supply system
Figure BDA0002387990570000058
Wherein the constant theta is greater than 0 and,
Figure BDA0002387990570000059
indicating the sampling error, i.e. the difference between the value of the sampling instant and the current instant,
Figure BDA00023879905700000510
‖·‖1represents the 1 norm of the vector, i.e., the sum of the absolute values of all elements within the vector.
Step 3, designing an event trigger controller of the water supply system, which is characterized by comprising the following steps:
step 3.1 design event trigger controller
Figure BDA0002387990570000061
Wherein the content of the first and second substances,
Figure BDA0002387990570000062
f is a controller gain matrix of the designed water affair system;
combining with the step 2 to obtain
Figure BDA0002387990570000063
Further, it can be deduced
Figure BDA0002387990570000064
Wherein
Figure BDA0002387990570000065
And is
Figure BDA00023879905700000614
Is a set of n x n dimensional diagonal matrices with diagonal elements of 0 or 1.
And is provided with
Figure BDA0002387990570000068
Can represent
Figure BDA0002387990570000069
Step 3.2 following step 1, step 2 and step 3.1:
Figure BDA00023879905700000610
step 3.3 following step 1, step 3.1 and step 3.2:
Figure BDA00023879905700000611
wherein
Figure BDA00023879905700000612
Step 3.4, a linear residual positive Lyapunov function is constructed for the water service network management system:
V(t)＝xT(t)v，
wherein the value of the vector satisfies that v is more than 0, namely each element in the vector is a positive number, and
Figure BDA00023879905700000613
is a real column vector of dimension n. In order to ensure the stable operation of the water affair system, the difference equation for calculating the Lyapunov function is as follows:
ΔV＝V(t+1)-V(t)＝xT(t+1)v-xT(t)v，
where the symbol T represents the transpose of a matrix or vector.
Step 3.5 design constants λ > 0, κ > 0, θ > 0, ρ > 0 and β > 0, and ξ if there is an n-dimensional variable vector v > 0s＞0,ξ＞0,zl< 0, z < 0, such that the following inequality
Figure BDA0002387990570000071
Figure BDA0002387990570000072
Figure BDA0002387990570000073
Figure BDA0002387990570000074
zl＜z,ξs＜ξ，
Figure BDA0002387990570000075
Figure BDA0002387990570000076
βv-ξs≥0，
1.. 2. for each lnWhere l is 1, …, m, and s is 1, …, n are all true,
wherein
Figure BDA0002387990570000077
Step 3.6, designing a water supply pipe network system x (t +1) ═ sat (ax (t)) + Bu (t)) for water service, and triggering a controller at event
Figure BDA0002387990570000078
Next, the modeling system is positive and stable; first, according to step 3.3, the positivity of the system is ensured by the lower bound of the modeling system function, i.e.
Figure BDA0002387990570000079
Step 3.7, calculating a difference equation of the Lyapunov function of the modeling system to satisfy the following conditions:
ΔV＜0；
step 3.8 obtained according to step 3.3 and step 3.4:
Figure BDA00023879905700000710
step 3.9 according to the conditions set forth in step 3.5, one can obtain
Figure BDA00023879905700000711
Figure BDA0002387990570000081
Further, it can be obtained
Figure BDA0002387990570000082
Figure BDA0002387990570000083
Step 3.10 from step 3.8 and step 3.9 can be obtained
Figure BDA0002387990570000084
Positive working of the system according to step 3.6, i.e.: x (k) is not less than 0, and we can deduce
ΔV＜0；
Step 3.11 in summary, combining step 3.1 to step 3.10, the gain matrix of the event-triggered controller can be obtained as follows:
Figure BDA0002387990570000085
and the controller auxiliary gain matrix is:
Figure BDA0002387990570000086

Claims (2)

1. a saturation control method for water supply of a municipal water service system based on state saturation positive system modeling of an event trigger mechanism is characterized by comprising the following steps:
step 1: establishing a state space model of the water supply quantity of a pipe network in the urban water service system;
step 2: constructing an event trigger control condition for stable water supply of water service;
and step 3: designing an event trigger controller of a water supply change threshold in a water service pipe network;
the step 1 is as follows:
firstly, data of water supply amount in an urban water service pipe network is collected in real time, and a state space model of the water supply amount of the urban water service system pipe network is established by utilizing the collected data and combining upper and lower boundary factors of a valve threshold of the water service pipe network, wherein the form is as follows:
x(t+1)＝sat(Ax(t)+Bu(t))，
wherein
Figure FDA0002703704150000011
Which indicates the amount of water in the water storage tanks of the municipal water service system at the t-th sampling time, n indicates the number of water storage tanks,
Figure FDA0002703704150000012
the opening degree of a water pipe network or a water pipe valve at t sampling moments is represented, and m represents the number of the water valves;
Figure FDA0002703704150000013
and
Figure FDA0002703704150000014
a matrix representing a suitable dimension, a and B being weighted constant matrices derived from the acquired data; considering the actual situation that the water quantity required by the water service system is all non-negative, namely ensuring that x (t) and u (t) are always non-negative, modeling the urban water service water supply system according to a positive system model, and meeting the condition that A is more than or equal to 0, B is more than or equal to 0, and more than or equal to each element in the matrixes A and B, namely requiring all elements in the matrixes A and B to be non-negative;
sat:
Figure FDA0002703704150000015
is a compound defined as sat (u) ═ sat (u)1),...,sat(um))TSaturation vector function of, wherein sat (u)ι)＝sgn(uι)min{|uι|,1},ι∈{1,...,m}；
The step 2 is as follows: event trigger control condition for establishing water service pipe network system
Figure FDA0002703704150000018
Wherein F is a controller gain matrix of the designed water affair system, and theta is a given constant and satisfies that theta is more than 0;
Figure FDA0002703704150000016
is a sampling error and satisfies
Figure FDA0002703704150000017
‖x‖1Represents the 1 norm of the vector x, represents the sum of the absolute values of all the elements of the vector, i.e.
Figure FDA0002703704150000021
Wherein xiRepresenting the ith element of the vector x.
2. The method for saturation control of water supply of a municipal water service system based on state saturation positive system modeling of event triggered mechanisms according to claim 1, wherein: the step 3 is as follows:
step 3.1 the event trigger controller is designed as follows:
Figure FDA0002703704150000022
wherein the content of the first and second substances,
Figure FDA0002703704150000023
f is a controller gain matrix of the designed water affair system;
step 3.2 following step 1, step 2 and step 3.1:
Figure FDA0002703704150000024
step 3.3 following step 1, step 3.1 and step 3.2:
Figure FDA0002703704150000025
wherein
Figure FDA0002703704150000026
Step 3.4, a linear residual positive Lyapunov function is constructed for the water service network management system:
V(t)＝xT(t)v,
wherein the value of the vector satisfies
Figure FDA0002703704150000028
I.e. each element in the vector is a positive number, and
Figure FDA0002703704150000027
is a real column vector of dimension n; in order to ensure the stable operation of the water affair system, the difference equation for calculating the Lyapunov function is as follows:
ΔV＝V(t+1)-V(t)＝xT(t+1)v-xT(t)v,
where the symbol T represents the transpose of a matrix or vector;
step 3.5 design constants λ > 0, θ > 0, ρ > 0 and β > 0, and ξ if there is an n-dimensional variable vector v > 0s＞0,ξ＞0,zι< 0, z < 0, such that the following inequality
Figure FDA0002703704150000031
Figure FDA0002703704150000032
Figure FDA0002703704150000033
zι＜z,ξs＜ξ,
Figure FDA0002703704150000034
Figure FDA0002703704150000035
βv-ξs≥0,
1.. 2. for each lnI 1, 1.. m, and s 1.. n are all true, where
Figure FDA0002703704150000036
Step 3.6, designing a water supply pipe network system x (t +1) ═ sat (ax (t) + Bu (t))) for water service, and triggering a controller at event
Figure FDA0002703704150000037
Next, the modeling system is positive and stable; first, according to step 3.3, the positivity of the system is guaranteed by means of the positivity of the lower bound system, i.e. the system is guaranteed
Figure FDA0002703704150000038
Step 3.7, calculating a difference equation of the Lyapunov function of the modeling system to satisfy the following conditions: delta V is less than 0;
step 3.8 obtained according to step 3.3 and step 3.4:
Figure FDA0002703704150000039
step 3.9 according to the conditions set forth in step 3.5, one can obtain
Figure FDA0002703704150000041
Figure FDA0002703704150000042
Further, it can be deduced
Figure FDA0002703704150000043
Figure FDA0002703704150000044
Step 3.10 from step 3.8 and step 3.9 can be obtained
Figure FDA0002703704150000047
Thus the positivity of the system according to step 3.6:
Figure FDA0002703704150000048
we can get Δ V < 0;
step 3.11 in summary, combining step 3.1 to step 3.10, the gain matrix of the event-triggered controller can be obtained as follows:
Figure FDA0002703704150000045
the controller auxiliary gain matrix is:
Figure FDA0002703704150000046
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