CN109782594B - Design method of safe water supply controller of water service system - Google Patents
Design method of safe water supply controller of water service system Download PDFInfo
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Abstract
The invention discloses a design method of a safe water supply controller of a water service system for supplying water safely. The invention establishes a design method of a safe water supply controller of a water service system by means of data acquisition, model establishment, optimization and the like, can effectively solve the problems of valve saturation caused by overlarge flow of a water delivery pipe and a water delivery pipe of the system, valve failure caused by full-load operation and influence of external uncertain environmental factors on the flow of inflow valves, and ensures that the system has good control effect on the premise of stability.
Description
The technical field is as follows:
the invention belongs to the technical field of automation, and relates to design methods such as non-fragile control and switching control in an automation technology.
Background art:
with the development of the world economy, the population is growing, the cities are increasing and expanding, and the water consumption of each place is increasing. According to the estimate of the united nations, the water consumption in the world is only 4000 billionths of a cubic meter per year, and the water demand is increased to 80000 billionths of a cubic meter per year by the forecast of 2100 years. The water consumption in Asia is the most, and reaches 32000 billion cubic meters per year. By 2100 years, the national water demand in China was expected to be 8814 billionths of cubic meters. Along with the development of production, the contradiction between supply and demand of water resources in many areas and countries is increasingly prominent.
The city water supply system is one part of city utility. Urban water supply system planning is an integral part of urban overall planning. A municipal water supply system is generally composed of a water source, a water delivery conduit, a water plant and a water distribution network. After water is taken from a water source, the water is sent to a water plant through a water delivery pipe duct for water quality treatment, and the treated water is pressurized and then sent to users through a water distribution pipe network. On water supply in cities, water supply systems are built in more than 300 cities in China at present, the daily water supply capacity of tap water is 4000 ten thousand tons, and the annual water supply amount is 100 billion cubic meters; the daily water supply capacity of the self-provided water sources of urban industrial and mining enterprises and public institutions is 6000 to ten thousand tons in total, and the annual water supply amount is 170 billion cubic meters; 7400 Water supply facilities are built in 28% of a plurality of built towns, the daily water supply capacity is about 800 ten thousand tons, and the annual water supply amount is 29 billion cubic meters. The shortage of water in cities is a worldwide problem. Therefore, the reasonable distribution of water resources and the protection of water resources are very important for the development of cities, and become inseparable components of the development of cities gradually.
In many cities in China, the problem of water resource shortage affects people's normal lives. For Beijing with water shortage, about 190 million m3 tap water is consumed each day, and the amount of tap water consumed each day is rapidly increased to 300 million m3 by the peak of water consumption. The water supply system needs to run at full load all day long, so that the water flow of a water delivery pipe channel is too saturated, the failure of a pump station valve is caused, the accuracy of the water quantity controlled by the valve is insufficient, and the problem is the typical failure problem of an actuator. During the operation of the water service system, external disturbance caused by various environmental factors can influence the stable operation of the system. Therefore, it is necessary to study the stability of the positive switching system with external disturbance input. If a reasonable water supply scheme is not adopted, water shortage and water cut-off phenomena can occur frequently. The water quantity at the water service pipe network node is used as a research object, some scholars establish a water supply and drainage system model described by a state space, and the state variable of the system is always non-negative. A system is called a positive system if its state is non-negative at any time. Considering the switching of network management nodes, it is necessary to use a positive switching system to depict the switching process in the water business process.
The invention content is as follows:
the invention aims to provide a design method of a safe water supply controller of a water service system by means of data acquisition, model establishment, optimization and the like, aiming at the problems of valve saturation caused by overlarge water flow of a water delivery pipe and a water delivery pipe of the water service system, pump station valve failure caused by full-load operation and influence of external uncertain environmental factors on a valve.
The method comprises the following steps:
step 1, establishing a state space model of a water affair system, wherein the specific method comprises the following steps:
1.1, acquiring input and output data of a valve of a water service system and describing an actual water supply network:
we consider a municipal water service system water supply network. A water supply network typically comprises a set of water supply pipes, water tanks of different volumes, and a plurality of pumping stations and valves for managing the water flow to supply water to users. Fig. 1 (see fig. 1 of the specification) illustrates the relationship between these elements. The water tank of fig. 1 provides water storage capacity for the entire water supply network to ensure the water demand of the user. In the case of shortage of water resource, the water pressure is reduced at the peak of water utilization, and the requirement of supplying water to a plurality of users at the same time cannot be met, so that the water supply is carried out in different sections and time periods. For example, when water use is scarce, turning on the pump 1 for a period of time turns off the pump 2 and the pump 3 only supplies water to the user 1; the next time period, the pump 2 or the pump 3 is turned on to supply water only to the user 2 or the user 3, which well solves the problem of insufficient water supply.
The water supply network takes into account two control actuators: valves and pumps. Assuming that the valve is open, indicating a negative valve opening value, the valve is fully closed, indicating a valve opening value of 0. The valve has a limit on the amount of water flowing through it and is in a saturated state when the amount of water reaches the limit.
Nodes represent network points where water flow converges or diverges in the network and must adhere to mass conservation relationships.
Considering the elements described above, a control-oriented model can be obtained by adding these elements and the corresponding dynamic descriptions. In a general form, a water volume dynamic expression that considers all of these elements can be written as
Wherein
The status of the system is indicated,
record as system input (i.e. opening values for valves and pump stations), g: Rn×Rm→RnIs an arbitrary system state function, k is equal to N+。
1.2 Using the above data to build a state space model of the water service system valves, in the water supply network contemplated by the present invention, a continuous time state space model can be written in the form:
y(t)＝Cσ(t)x(t),
wherein x (t) ═ x1(t),x2(t),...,xn(t),]TThe water flow rate of the water conveying pipe flowing into the valve is shown, and n represents the number of the valves. y (t) is the valve control output,
for controlling the opening degree of the valve after the valve failure,
is an immeasurable external disturbance factor influencing the opening of the control valve, the function sat (is) is a vector value saturation function, and the control valve opening saturation function after the valve failure meets sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T. The function σ (t) is a mapping of the switching signal representation from [0, ∞ ] to a finite set S ═ 1, …, N },
Aσ(t)for a Metzler matrix, there is B for each σ (t) ∈ Sσ(t)≥0，Cσ(t)≥0，Dσ(t)≥0。
Step 2, in practice, in a peak period of water use, the pump station valve is over saturated due to overlarge water flow of the water delivery pipe channel, and in order to deal with the situation, the following saturation function is given:
wherein 0 is less than or equal to etas≤1，
Step 3, in order to maintain the water flow of the water service system input pipe canal within a certain range all the time, the following cone domains are given:
wherein, c is more than 0,
. We give the matrix
And is
Meanwhile, the design performance index function meets the following requirements:
Fisis represented by FiA row matrix composed of the ith row elements.
Step 4, when the system valve fails due to unknown factors, the control valve opening can be described as follows:
wherein L isdi≤Li≤Lui≤ρLdi，Ldi≥0,Lui≥0,ρ≥1。
Step 5, designing a water service system state feedback controller, which comprises the following specific steps:
5.1 design switching Signal σ (t) with 0 ≦ t0T is less than or equal to t, and the following conditions are met:
wherein N isσ(t0T) is that the switching system is in (t)0Number of handovers in t), τ00 is the average residence time (ADT), N of the switching signal0≥0。
5.2 designing a non-fragile controller with water service system valve failure as follows:
wherein the content of the first and second substances,
is a general gain matrix and
ΔKi＝EiHiis a matrix of the perturbation of the gain,
is a known non-fragile matrix, satisfies the conditions
(0＜δ1＜δ2＜1)。
5.3 design
The Metzler matrix simultaneously meets the conditions of the step 2 and the step 3. Considering the influence of external uncertain disturbance factors on the valve opening degree, a function xi (t) | | | y (t) | non |1-γ||ω(t)||1. At t ∈ [ t ]k,tk+1) The following design is linear to the positive lyapunov function:
Vi(x(t))＝x(t)Tυi,
the following conditions are satisfied:
5.4 design constant rho is more than or equal to 1, mu is more than 0, lambda is more than 1, gamma,
sum vector
So that it satisfies the following conditions:
wherein the content of the first and second substances,
is a constant that is known to be,
Θis2＝ρBiGsLdi，
Θis4＝ρBiGsLdiEi，
is a known constant vector. Under the condition of average residence time
5.5 design water affair system
T ∈ [0, ∞) is globally consistent exponentially stable under a switching signal σ (t), and is specific to an arbitrary initial state x (t)0) The constants ε and η are designed such that the system state response satisfies the following condition:
wherein, epsilon is 1, eta is mu0。
5.6 from step 5.5 the above formula can be converted to:
according to step 5.1, the product is obtained
Combining the formula in step 5.6 to obtain:
the upper type is divided on both sides
Obtaining:
further obtaining:
from step 5.4:
the above inequality is derived:
combining the steps of 5.4 to obtain:
5.7 according to the conditions designed in step 4, the following results can be obtained:
further, the method can be obtained as follows:
5.8 combining the 7 th condition in step 5.4 with steps 5.6 and 5.7 can obtain the water flow rate state feedback of the water service system in case of valve failure as follows:
the invention provides a design method of a safe water supply controller of a water service system. The method establishes a state space model of the system aiming at the problems of valve saturation caused by overlarge water flow of a water delivery pipe and a water delivery pipe of a water service system, pump station valve failure caused by full-load operation and influence of external uncertain environmental factors on the valve. The state feedback controller is designed by designing the Lyapunov function of the system, so that the switching system is ensured to be stable.
Drawings
FIG. 1 is a schematic diagram of a prior art water supply network of the present invention.
Detailed Description
The water flow of the water delivery pipe canal of the water service system is used as an actual object, the opening of a control valve is used as control input, and the water flow of the valve control output is used as output, so that a dynamic model of the water flow of the water delivery pipe canal is established.
Step 1, establishing a state space model of a water affair system, wherein the specific method comprises the following steps:
we consider a municipal water service system water supply network. A water supply network typically comprises a set of water supply pipes, water tanks of different volumes, and a plurality of pumping stations and valves for managing the water flow to supply water to users. Fig. 1 (see fig. 1 of the specification) illustrates the relationship between these elements. The water tank of fig. 1 provides water storage capacity for the entire water supply network to ensure the water demand of the user. In the case of shortage of water resource, the water pressure is reduced at the peak of water utilization, and the requirement of supplying water to a plurality of users at the same time cannot be met, so that the water supply is carried out in different sections and time periods. For example, when water use is scarce, turning on the pump 1 for a period of time turns off the pump 2 and the pump 3 only supplies water to the user 1; the next time period, the pump 2 or the pump 3 is turned on to supply water only to the user 2 or the user 3, which well solves the problem of insufficient water supply.
Firstly, acquiring input and output data of a valve of a water service system, and establishing a state space model of the valve of the water service system by using the data, wherein the form is as follows:
y(t)＝Cσ(t)x(t),
wherein x (t) is the water flow rate of the water pipe flowing into the valve, y (t) is the valve control output,
for controlling the opening degree of the valve after the valve failure,
is an immeasurable external disturbance factor influencing the opening of the control valve, the function sat (is) is a vector value saturation function, and the control valve opening saturation function after the valve failure meets sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T. The function σ (t) is a mapping of the switching signal representation from [0, ∞ ] to a finite set S ═ 1, …, N },
Aσ(t)for a Metzler matrix, there is B for each σ (t) ∈ Sσ(t)≥0，Cσ(t)≥0，Dσ(t)≥0。
Step 2, in practice, in a peak period of water use, the pump station valve is over saturated due to overlarge water flow of the water delivery pipe channel, and in order to deal with the situation, the following saturation function is given:
wherein 0 is less than or equal to etas≤1，
Step 3, in order to maintain the water flow of the water service system input pipe canal within a certain range all the time, the following cone domains are given:
wherein, c is more than 0,
. We give the matrix
And is
Meanwhile, the design performance index function meets the following requirements:
Fisis represented by FiA row matrix composed of the ith row elements.
Step 4, when the system valve fails due to unknown factors, the control valve opening can be described as follows:
wherein L isdi≤Li≤Lui≤ρLdi，Ldi≥0,Lui≥0,ρ≥1。
Step 5, designing a water service system state feedback controller, which comprises the following specific steps:
5.1 design switching Signal σ (t) with 0 ≦ t0T is less than or equal to t, and the following conditions are met:
wherein N isσ(t0T) is that the switching system is in (t)0Number of handovers in t), τ00 is the average residence time (ADT), N of the switching signal0≥0。
5.2 designing a non-fragile controller with valve failure as follows:
wherein the content of the first and second substances,
is a general gain matrix and
ΔKi＝EiHiis a matrix of the perturbation of the gain,
is a known non-fragile matrix, satisfies the conditions
(0＜δ1＜δ2＜1)。
5.3 design
The Metzler matrix simultaneously meets the conditions of the step 2 and the step 3. Considering the influence of external uncertain disturbance factors on the valve opening degree, a function xi (t) | | | y (t) | non |1-γ||ω(t)||1. At t ∈ [ t ]k,tk+1) The following design is linear to the positive lyapunov function:
Vi(x(t))＝x(t)Tυi,
the following conditions are satisfied:
5.4 design constant rho is more than or equal to 1, mu is more than 0, lambda is more than 1, gamma,
sum vector
So that it satisfies the following conditions:
wherein the content of the first and second substances,
is a constant that is known to be,
Θis2＝ρBiGsLdi，
Θis4＝ρBiGsLdiEi，
is a known constant vector. Under the condition of average residence time
5.5 design water affair system
T ∈ [0, ∞) is globally consistent exponentially stable under a switching signal σ (t), and is specific to an arbitrary initial state x (t)0) The constants ε and η are designed such that the system state response satisfies the following condition:
wherein, epsilon is 1, eta is mu0。
5.6 from step 5.5 the above formula can be converted to:
according to step 5.1, the product is obtained
Combining the formula in step 5.6 to obtain:
the upper type is divided on both sides
Obtaining:
further obtaining:
from step 5.4:
the above inequality is derived:
combining the steps of 5.4 to obtain:
5.7 according to the conditions designed in step 4, the following results can be obtained:
further, the method can be obtained as follows:
5.8 combining the 7 th condition in step 5.4 with steps 5.6 and 5.7 can obtain the water flow rate state feedback of the water service system in case of valve failure as follows:
Claims (1)
1. a design method of a safe water supply controller of a water service system is characterized by comprising the following steps:
step 1, establishing a state space model of a water affair system, wherein the specific method comprises the following steps:
firstly, acquiring input and output data of a valve of a water service system, and establishing a state space model of the valve of the water service system by using the data, wherein the form is as follows:
y(t)＝Cσ(t)x(t),
wherein x (t) is the water flow rate of the water pipe flowing into the valve, y (t) is the valve control output,
for controlling the opening degree of the valve after the valve failure,
is an immeasurable external disturbance factor influencing the opening of the control valve, the function sat (is) is a vector value saturation function, and the control valve opening saturation function after the valve failure meets sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T(ii) a The function σ (t) is a mapping of the switching signal representation from [0, ∞ ] to a finite set S ═ 1, …, N },
Aσ(t)for a Metzler matrix, there is for each σ (t) ∈ S
Step 2, in practice, in a peak period of water use, the water flow of the water delivery pipe canal is too large, so that a pump station valve is too saturated, and in order to deal with the situation, the following saturation function is given:
wherein 0 is less than or equal to etas≤1，
Step 3, in order to maintain the water flow of the water service system input pipe canal in a certain preset range all the time, the following cone domains are given:
wherein, c is more than 0,
given matrix
And is
Meanwhile, the design performance index function meets the following requirements:
Fisis represented by FiA row matrix composed of the ith row elements of (1);
step 4, when the system valve fails due to unknown factors, at this time, the ith subsystem is in an operating state, and the control valve opening is described as follows:
wherein the content of the first and second substances,
step 5, designing a water service system state feedback controller, which comprises the following specific steps:
5.1 design switching Signal σ (t) with 0 ≦ t0T is less than or equal to t, and the following conditions are met:
wherein N isσ(t0T) is that the switching system is in (t)0Number of handovers in t), τ00 is the average residence time (ADT), N of the switching signal0≥0；
5.2 designing a non-fragile controller with valve failure as follows:
wherein the content of the first and second substances,
is a general gain matrix and
ΔKi＝EiHiis a matrix of the perturbation of the gain,
is a known non-fragile matrix, satisfies the conditions
5.3 design
The Metzler matrix simultaneously meets the conditions of the step 2 and the step 3; considering the influence of external uncertain disturbance factors on the valve opening degree, a function xi (t) | | | y (t) | non |1-γ||ω(t)||1(ii) a At t ∈ [ t ]k,tk+1) The following design is linear to the positive lyapunov function:
Vi(x(t))＝x(t)Tυi,
the following conditions are satisfied:
5.4 design constant rho is more than or equal to 1, mu is more than 0, lambda is more than 1, gamma, zetaiSum vector
So that it satisfies the following conditions:
wherein the content of the first and second substances,
is a constant that is known to be,
Θis4＝ρBiGsLdiEi，
is a known constant vector; under the condition of average residence time
(0≤μ0≤μ)；
5.5 design water affair system
T ∈ [0, ∞) is globally consistent exponentially stable under a switching signal σ (t), and is specific to an arbitrary initial state x (t)0) The constants ε and η are designed such that the system state response satisfies the following condition:
wherein, epsilon is 1, eta is mu0；
5.6 from step 5.5 the above formula can be converted to:
according to step 5.1, the product is obtained
Combining the formula in step 5.6 to obtain:
the upper type is divided on both sides
Obtaining:
further obtaining:
from step 5.4:
the above inequality is derived:
combining the steps of 5.4 to obtain:
5.7 according to the conditions designed in step 4, the following results can be obtained:
further, the method can be obtained as follows:
5.8 combining the 7 th condition in step 5.4 with steps 5.6 and 5.7 can obtain the water flow rate state feedback of the water service system in case of valve failure as follows:
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