CN113374449B - Control method and system for lifting underground mixture of gas of coal seam - Google Patents

Control method and system for lifting underground mixture of gas of coal seam Download PDF

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CN113374449B
CN113374449B CN202110622578.0A CN202110622578A CN113374449B CN 113374449 B CN113374449 B CN 113374449B CN 202110622578 A CN202110622578 A CN 202110622578A CN 113374449 B CN113374449 B CN 113374449B
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lifting
coal
sliding mode
gas
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CN113374449A (en
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李自成
朱钰辉
桑树勋
周效志
曹丽文
刘世奇
王海文
刘会虎
贾金龙
王后能
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Wuhan Institute of Technology
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    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21BEARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/006Production of coal-bed methane
    • EFIXED CONSTRUCTIONS
    • E21EARTH OR ROCK DRILLING; MINING
    • E21BEARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/12Methods or apparatus for controlling the flow of the obtained fluid to or in wells
    • E21B43/121Lifting well fluids

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Abstract

The invention discloses a control method and a system for lifting a downhole mixture of a gas of a coal seam. The method comprises the following steps: deducing a mathematical model under the control of a pump valve control system, and establishing a state space expression of the pump valve control system; the system is subjected to linearization and decoupling control through state feedback precise linearization; removing system instability caused by time lag by using an improved Smith predictor; the problems of uncertain parameters and system robustness in the process of lifting gas, water and coal are solved by adopting sliding mode control on the basis; the buffeting of the sliding mode control system is suppressed by improving the switching function. The sliding mode buffeting suppression controller based on the state feedback accurate linearization can effectively decouple the gas-water-coal lifting system, not only remove the unstable influence of the system caused by time lag, but also effectively suppress buffeting of the centrifugal pump, and has good control performance.

Description

Control method and system for lifting underground mixture of gas of coal seam
Technical Field
The invention relates to the field of underground mixture lifting control in a coal bed methane exploitation process, in particular to a method and a system for controlling underground mixture lifting of a coal bed methane.
Background
The coalbed methane in China is rich in resources and has wide development prospect. As a part of found coal resources in China, the constructed coal has the characteristics of rich gas, low permeability, softness and the like, is mostly coal and gas outburst coal beds, and is difficult to mine and utilize. The development of the coalbed methane at the present stage mainly surrounds two aspects of resource exploration and the development of a coalbed methane ground well. With the development of coalbed methane, the problem of coal dust has gradually become an important problem restricting the development of coalbed methane. Mainly shows that coal dust migration causes drainage faults on reservoir damage and coal dust blockage.
Experiments of coal dust generation and migration show that coal dust in the production process has a remarkable influence on coal bed permeability. The gas-liquid-solid three-phase experiment shows that the coal powder particle size, the liquid flow and the gas flow have obvious influence on the coal powder lifting height, and the influence on the coal particle mass concentration is negligible. For the control of the lifting device, the mature control mode in petroleum and natural gas exploitation is used as a reference in the current stage, and the artificial lifting system is optimized by adopting machine learning. By designing a new pipeline, the sedimentation of coal dust in the coal water suspension is reduced.
Because of the high structural deformation degree of the coal, the underground pulverized coal concentration is higher than that of other raw coal, and the average grain diameter is smaller. In the actual exploitation process, the horizontal well induces the cave-building coal dust to collapse, the fluid mainly produced by the coalbed methane after the stress of the reservoir is released and the water pumped into the well form a gas-water-high concentration coal dust multiphase mixture, and the mixture needs to be lifted through the vertical well. If the lifting flow is insufficient or the lifting is not in time, the problems of coal powder clamping pump, pump leakage, difficult opening of a pump valve and the like are easily caused. And when the flow is too large or the pressure is too large, the damage of a gas production channel is easy to cause, the subsequent gas production is reduced, and the economic benefit of coal bed gas exploitation is reduced. Therefore, the control of the flow stabilization in the lifting process of the gas-water-coal mixture has important significance for realizing the efficient lifting of the mixture.
Disclosure of Invention
The invention aims to solve the technical problem of providing a control method and a system for lifting a downhole mixture of a coal layer gas by constructing aiming at the defects in the prior art.
The technical scheme adopted for solving the technical problems is as follows:
the invention provides a control method for lifting a downhole mixture of a coal seam gas, which comprises the following steps:
step 1: deducing a mathematical model under the control of a pump valve control system according to the lifting process of the gas-water coal mixture in the coal seam gas exploitation control system, and establishing a state space expression of the pump valve control system;
step 2: based on the state space expression, adopting state feedback linearization to directly decouple and control a lifting system formed by a pump valve;
step 3: based on the direct decoupling control of the state feedback linearization, the system instability caused by time lag is removed by adopting an improved Smith predictor;
step 4: based on the direct decoupling control with the state feedback linearization of the improved Smith predictor, the robustness of the pump valve control system is further improved by using sliding mode control;
step 5: based on the feedback linearization sliding mode control, utilizing an improved switching function to inhibit buffeting of a pump valve control system, and determining a control rate of lifting of a coal layer gas downhole mixture;
step 6: and controlling the gas-water-coal mixture lifting system based on the control rate.
Further, in the step 1 of the present invention, according to the lifting process of the gas-water-coal mixture in the coal seam gas exploitation control system, a mathematical model controlled by the pump valve control system is deduced, and a state space expression of the pump valve control system is established, and the specific method comprises:
the construction coal seam gas exploitation control system comprises six major parts: the system comprises a coal measure stratum structure reconstruction and similar material subsystem, a horizontal well bidirectional reciprocating drilling and cave completion subsystem, a horizontal well cave excitation pressure relief and fluid migration subsystem, a vertical well gas-water coal powder mixture lifting and output subsystem, a ground gas-water coal separation, collection and water recycling subsystem, an instrument system information and an automatic control subsystem;
the system is used for exploring and developing theory and technical equipment of the in-situ coal bed gas of the construction coal; the method is used for researching and controlling a vertical well gas-water pulverized coal mixture lifting and output subsystem; the vertical well gas-water pulverized coal mixture lifting and producing subsystem controls lifting equipment and a pulverized coal crushing and disturbing device through a pump valve control system, so that the timely crushing and hydraulic conveying of bottom pulverized coal are realized, and the purposes of no blockage of a pipeline by pulverized coal and stable collection of produced liquid are achieved; the pump valve control system consists of a power liquid tank, a centrifugal pump, a pneumatic control valve, an equipment pipeline, lifting equipment and a production liquid tank;
the pump valve control system is simplified from the power fluid tank to the output fluid tank by Bernoulli equation:
Figure BDA0003100483380000031
wherein Q is the flow in the pipeline, A is the cross-sectional area of the pipeline, ρ is the fluid density, and L is the total length of the pipeline; ΔP e Pressure, ΔP, provided to the pump v For pressure loss caused by valves, ΔP c Pressure loss for the mixture lifting equipment;
the flow rate Q, the control valve opening gamma and the centrifugal pump rotation speed n are used as state variables, and the valve opening gamma is set set And centrifugal pump rotational speed setting n set As input variables, with flow Q and control valve differential pressure ΔP v For output variables, the state space equation of the pump valve control system is deduced as follows:
Figure BDA0003100483380000032
wherein:
Figure BDA0003100483380000033
Figure BDA0003100483380000034
Figure BDA0003100483380000035
/>
Figure BDA0003100483380000036
wherein T is γ And T n Time constants of the control valve and the centrifugal pump, respectively.
Further, in the step 2 of the present invention, based on the state space expression, a state feedback linearization is adopted to directly decouple and control the lifting system formed by the pump valve, and the specific method is as follows:
deriving the output y in the state equation until the control u appears explicitly;
Figure BDA0003100483380000037
wherein:
Figure BDA0003100483380000041
wherein b is a valve pressure loss fitting coefficient, and K (gamma) is a valve flow fitting curve;
when the control rate is selected as
Figure BDA0003100483380000042
When the control rate is substituted into the linearization model, the original model is described as:
Figure BDA0003100483380000043
Figure BDA0003100483380000044
direct decoupling of precise linearization can be achieved.
Further, in the step 3 of the present invention, based on the direct decoupling control of the state feedback linearization, the improved Smith predictor is adopted to remove the system instability caused by time lag, and the specific method is as follows:
after the time lag system is subjected to time lag balance, a first-order filtering link G is added on the basis of the design of an original Smith predictor in a main feedback loop f And(s) reducing the influence of model errors and interference.
Further, in the step 4 of the present invention, based on the direct decoupling control with the state feedback linearization of the improved Smith predictor, the robustness of the pump valve control system is further improved by using sliding mode control, which specifically comprises the following steps:
defining a sliding die surface:
Figure BDA0003100483380000045
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient;
then
Figure BDA0003100483380000046
In the middle of
Figure BDA0003100483380000051
The coefficient alpha is such that the polynomial meets the Hulvitz stability criterion;
the control law is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function;
Figure BDA0003100483380000052
in the middle of
Figure BDA0003100483380000053
And k is 1 >0,k 2 > 0; to sum up, it is obtained:
Figure BDA0003100483380000054
Figure BDA0003100483380000055
then
Figure BDA0003100483380000056
Thus s i Trending towards 0 for a limited time; when the track reaches the sliding mode surface, the error approaches 0, so that the system always moves near the sliding mode surface, the tracking of the target signal is realized, and the system has certain disturbance rejection capability.
Further, in the step 5 of the present invention, based on the feedback linearization sliding mode control, the control rate of lifting the underground mixture of the gas of the coal layer is determined by utilizing an improved switching function to restrain the buffeting of the system, and the specific method is as follows:
considering that the buffeting problem in the sliding mode control is caused by a sign function sgn (S) in the control rate, a continuously smooth hyperbolic tangent function is selected as a substitute, so that the buffeting problem in the sliding mode control is reduced:
Figure BDA0003100483380000057
the improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
The invention provides a control system for lifting a downhole mixture for constructing coal bed gas, which comprises the following components:
the state space expression building module is used for building a state space expression of the pump valve control system according to a mathematical model under the pump valve control system; the pump valve control system comprises a power liquid tank, a centrifugal pump, a pneumatic control valve, lifting equipment and a production liquid tank which are connected in sequence, wherein the middle of each part of the pump valve control system is connected by a pipeline and a flange;
the state feedback linearization decoupling module is used for acquiring a state feedback linearization decoupling control rate based on the state space expression;
the improved Smith predictor module is used for removing system instability caused by time lag based on the direct decoupling control of the state feedback linearization;
the sliding mode control module is used for obtaining the sliding mode control rate based on the direct decoupling control of the state feedback linearization of the improved Smith predictor;
and the sliding mode buffeting suppression module is used for suppressing buffeting of the system by utilizing an improved switching function based on the feedback linearization sliding mode control.
Further, the state feedback linearization decoupling module of the present invention specifically includes:
based on the state space expression, the obtained state feedback linearization decoupling control rate is as follows:
Figure BDA0003100483380000061
substituting the control rate into the linearization model, the original model is described as:
Figure BDA0003100483380000062
Figure BDA0003100483380000063
the direct decoupling of accurate linearization can be realized;
the improved Smith predictor module specifically comprises: based on the instituteThe state feedback linearization direct decoupling control is adopted to remove system instability caused by time lag; after the time lag system is subjected to time lag balance, a first-order filtering link G is added on the basis of the design of an original Smith predictor in a main feedback loop f And(s) reducing the influence of model errors and interference.
Further, the sliding mode control module of the present invention specifically includes:
based on the direct decoupling control with the state feedback linearization of the improved Smith predictor, the sliding mode control rate is obtained;
defining a sliding die surface:
Figure BDA0003100483380000064
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient;
then
Figure BDA0003100483380000071
In the middle of
Figure BDA0003100483380000072
The coefficient alpha is such that the polynomial meets the Hulvitz stability criterion;
the control law is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function;
Figure BDA0003100483380000073
in the middle of
Figure BDA0003100483380000074
And k is 1 >0,k 2 >0。
Further, the sliding mode buffeting suppression module of the invention specifically comprises:
based on the feedback linearization sliding mode control, utilizing an improved switching function to inhibit buffeting of the system; considering that the buffeting problem in the sliding mode control is caused by a sign function sgn (S) in the control rate, a continuously smooth hyperbolic tangent function is selected as a substitute, so that the buffeting problem in the sliding mode control is reduced:
Figure BDA0003100483380000075
the improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
The invention has the beneficial effects that: the sliding mode control based on the state feedback accurate linearization design can have the advantage of state feedback accurate linearization and has good decoupling effect. (2) The sliding mode control has stronger robustness aiming at uncertainty of model parameters. The flow regulating time can be obviously shortened, and meanwhile, the frequent start and stop of the centrifugal pump are avoided. (3) The hyperbolic tangent function is used for replacing the sign function, so that the buffeting problem of the sliding mode is obviously improved, the service life of the pump body is prolonged, and the rotating speed of the centrifugal pump is regulated more stably.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a schematic flow chart of a method for controlling lifting of a downhole mixture for constructing a coal bed gas according to the present invention;
FIG. 2 is a block diagram of an improved Smith predictor in accordance with the present invention;
FIG. 3 is a graph comparing the response curves of the direct control and the improved Smith predictor control of the present invention;
FIG. 4 is a graph comparing response curves of direct decoupling and sliding mode control according to the present invention;
FIG. 5 is a graph comparing the response curves of the slip mode control and slip mode buffeting suppression of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, the control method for lifting the underground mixture of the gas of the coal layer comprises the following steps:
step 1: and deducing a mathematical model under a pump valve control system according to the lifting process of the gas-water coal mixture in the coal seam gas exploitation control system, and establishing a state space expression of the pump valve control system. The specific process is as follows:
for the whole system, the power liquid tank is set as a, the output liquid tank is set as b, and neglecting friction loss of the inner wall of a pipeline is obtained by Bernoulli equation:
Figure BDA0003100483380000081
where ρ is the fluid density, g is the gravitational acceleration, h is the horizontal height, P is the fluid pressure, v is the flow rate, and l is the length along the pipeline.
Since the pump valve system pressure in this arrangement is not great, it can be approximately considered that the water is not compressible and the density is constant. Let the pressure provided by the pump be DeltaP e The pressure loss caused by the valve is delta P v The pressure loss caused by the mixture lifting device is delta P c . And the height of the power liquid water tank is not greatly different from that of the output liquid water tank, and the pressure and the flow rate are basically consistent. Thus, it is obtained:
Figure BDA0003100483380000082
wherein L is the total length of the pipeline, A is the cross-sectional area of the pipeline, and Q is the flow in the pipeline. If the pump is a centrifugal pump, a quadratic polynomial can be adopted for fitting, and the fitting relation of the centrifugal pump lift H, the rotating speed n and the flow Q is H=a 1 Q 2 +a 2 nQ+a 3 n 2 Wherein a is 1 、a 2 、a 3 Fitting coefficients for the lift curve of the centrifugal pump, the pressure provided by the centrifugal pump is:
ΔP e =ρgH=ρg(a 1 Q 2 +a 2 nQ+a 3 n 2 )
the regulating valve is a pneumatic ball valve, and the pressure loss delta P of fluid passing through the valve v v Depending on the installation, fluid type, flow Q and valve flow coefficient K (γ). The fitting curve relation of the valve pressure loss measured by the experiment is as follows:
Figure BDA0003100483380000091
where b is the valve pressure loss fitting coefficient. K (γ) =b 1 γ 2 +b 2 γ+b 3 ,b 1 、b 2 、b 3 Fitting coefficients for the valve flow coefficient curve.
Pressure loss delta P brought by gas-water-coal mixture lifting device c The fitting relation is formed by a quadratic relation with the flow Q, and the fitting relation is as follows:
ΔP c =ρgK c Q 2
k in the formula c Fitting coefficients for the pressure loss curve of the lifting device.
The pneumatic control valve and variable frequency centrifugal pump can be characterized by a first order linear system:
Figure BDA0003100483380000092
Figure BDA0003100483380000093
t in γ And T n Respectively is controlled byTime constant, gamma of valve and centrifugal pump set And n set The valve opening of the control valve and the rotational speed set value of the centrifugal pump are respectively set. The flow rate Q, the control valve opening gamma and the centrifugal pump rotation speed n are used as state variables, and the valve opening gamma is set set And centrifugal pump rotational speed setting n set As input variables, with flow Q and control valve differential pressure ΔP v For output variables, the state space equation of the system is deduced as follows:
Figure BDA0003100483380000094
in the middle of
Figure BDA0003100483380000101
Figure BDA0003100483380000102
Figure BDA0003100483380000103
/>
Figure BDA0003100483380000104
Step 2: based on the state space expression, a state feedback linearization is adopted to directly decouple and control a lifting system formed by the pump valves. The specific process is as follows:
for a typical multiple-input multiple-output affine nonlinear system, the goal of this system's exact linearization problem is to transform the system into a fully controllable linear system. The relative order is calculated below, and the output y in the state equation is derived for the relative order until the control u appears explicitly.
Is provided with
Figure BDA0003100483380000105
For output y 1
Figure BDA0003100483380000106
For output y 2
Figure BDA0003100483380000107
So the relative order of the system is r=r 1 +r 2 =2+1=3, and satisfies the requirement of accurate linearization.
And (3) finishing to obtain:
Figure BDA0003100483380000108
in the middle of
Figure BDA0003100483380000111
It can be seen that the differentiation of the output y is linearly related to the input u, and the purpose of controlling the output y can be achieved by controlling the differentiation of the output y.
And adopting state feedback control, wherein when the control rate is selected as follows:
Figure BDA0003100483380000112
when the control rate is substituted into the linearization model, the original model can be described as:
Figure BDA0003100483380000113
/>
Figure BDA0003100483380000114
setting the error e of the target signal and the tracking signal i The method comprises the following steps:
Figure BDA0003100483380000115
in which y 1set ,y 2set For the target signal, a new input v is selected i The method comprises the following steps:
Figure BDA0003100483380000116
according to the Routh stability criterion, when k 12 ,k 11 ,k 21 All feature roots of the equation lie in the left half plane when they are all greater than 0, and:
Figure BDA0003100483380000117
thus, tracking of the controlled variable to the target signal is achieved.
Step 3: based on the direct decoupling control of the state feedback linearization, the system instability caused by time lag is removed by adopting an improved Smith predictor. The specific process is as follows:
the key idea of the Smith predictor is to design a prediction compensator for a system containing hysteresis, so as to compensate a controlled object, and a first-order filtering link G is added in a main feedback loop based on the original Smith predictor f And(s) the influence caused by model errors and interference is obviously reduced. The first-order filtering link can be selected as follows:
Figure BDA0003100483380000121
t in f =τ/2。
Step 4: based on the direct decoupling control with the state feedback linearization of the improved Smith predictor, the robustness of the control system is further improved by using sliding mode control. The specific process is as follows:
in consideration of the fact that a large amount of approximate simplification exists in the modeling process, and the actual lifting system is changed at any time due to multiphase mixing of gas, water and coal, uncertainty exists in system parameters, and robustness of a control system needs to be improved. On the basis of the accurate linearization of the original state feedback, in order to improve the robustness of the system, the most common method is to adopt sliding mode control. Defining a sliding die surface:
Figure BDA0003100483380000122
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient.
Then
Figure BDA0003100483380000123
In the middle of
Figure BDA0003100483380000124
/>
The coefficient alpha should be such that the polynomial satisfies the helvetz stability criterion.
The control law is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function, as shown in the following equation.
Figure BDA0003100483380000125
In the middle of
Figure BDA0003100483380000126
And k is 1 >0,k 2 > 0. The method can be summarized as follows:
Figure BDA0003100483380000127
Figure BDA0003100483380000128
then
Figure BDA0003100483380000129
Thus s i And tends to 0 for a finite period of time. When the track reaches the sliding mode surface, the error approaches 0, so that the system always moves near the sliding mode surface, the tracking of the target signal is realized, and the system has certain disturbance rejection capability.
Selecting Lyapunov function as
Figure BDA0003100483380000131
The stable sliding mode control can be proved:
Figure BDA0003100483380000132
step 5: and determining the control rate of lifting the underground mixture of the gas of the coal layer by utilizing an improved switching function to inhibit buffeting of the system based on the feedback linearization sliding mode control. The specific process is as follows:
in the actual process, the buffeting of the sliding mode brings great hidden danger, seriously affects the service life of the actuator, and is optimized to reduce the amplitude. The buffeting problem in the sliding mode control is considered to be caused by a sign function sgn (S) in the control rate. The continuous smooth hyperbolic tangent function can be used as a substitute to reduce the buffeting problem in the sliding mode control.
Figure BDA0003100483380000133
The improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
Step 6: and controlling the gas-water-coal mixture lifting system based on the control rate.
Fig. 2 is a block diagram of an improved Smith predictor in accordance with the present invention. The method comprises the steps of designing a pre-estimation compensator aiming at a system containing hysteresis, further compensating a controlled object, adding a first-order filtering link G in a main feedback loop on the basis of an original Smith pre-estimation compensator f And(s) the influence caused by model errors and interference is obviously reduced. The first-order filtering link can be selected as follows:
Figure BDA0003100483380000134
t in f =τ/2。
The embodiment of the invention discloses a control system for lifting a downhole mixture for constructing coal bed gas, which comprises the following components:
the state space expression building module is used for building a state space expression of the pump valve control system according to a mathematical model under the pump valve control system;
the state feedback linearization decoupling module is used for acquiring a state feedback linearization decoupling control rate based on the state space expression;
the improved Smith predictor module is used for removing system instability caused by time lag based on the direct decoupling control of the state feedback linearization;
the sliding mode control module is used for obtaining the sliding mode control rate based on the direct decoupling control of the state feedback linearization of the improved Smith predictor;
and the sliding mode buffeting suppression module is used for suppressing buffeting of the system by utilizing an improved switching function based on the feedback linearization sliding mode control.
As a specific embodiment, in the control system for constructing the lifting of the underground mixture of the coal bed gas, the state feedback linearization decoupling module specifically comprises:
based on the state space expression, the obtained state feedback linearization decoupling control rate is as follows:
Figure BDA0003100483380000141
substituting the control rate into the linearization model, the original model can be described as:
Figure BDA0003100483380000142
Figure BDA0003100483380000143
direct decoupling of precise linearization can be achieved.
As a specific embodiment, in the control system for constructing the lifting of the downhole mixture of the coal bed gas, the improved Smith predictor module specifically comprises: and removing system instability caused by time lag based on the direct decoupling control of the state feedback linearization. After the time lag system is subjected to time lag balance, a first-order filtering link G is added on the basis of the design of an original Smith predictor in a main feedback loop f And(s) reducing the influence of model errors and interference.
As a specific embodiment, in the control system for lifting the underground mixture of the coal layer gas, the sliding mode control module specifically comprises:
and obtaining the sliding mode control rate based on the direct decoupling control with the state feedback linearization of the improved Smith predictor.
Defining a sliding die surface:
Figure BDA0003100483380000144
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient.
Then
Figure BDA0003100483380000145
In the middle of
Figure BDA0003100483380000151
The coefficient alpha should be such that the polynomial satisfies the helvetz stability criterion.
The control law is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function.
Figure BDA0003100483380000152
In the middle of
Figure BDA0003100483380000153
And k is 1 >0,k 2 >0。
As a specific embodiment, in the control system for lifting the underground mixture of the gas of the coal formation, the sliding mode buffeting suppression module of the invention specifically comprises:
based on the feedback linearization sliding mode control, the buffeting of the system is restrained by utilizing an improved switching function. The buffeting problem in the sliding mode control is considered to be caused by a sign function sgn (S) in the control rate.
The continuous smooth hyperbolic tangent function can be used as a substitute to reduce the buffeting problem in the sliding mode control.
Figure BDA0003100483380000154
The improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
Fig. 3-5 are partial graphs of this embodiment, illustrating the following:
from fig. 3, it can be seen that the improved Smith predictor is used to remove the time lag effect, the system is stable, and decoupling can be realized well after linearization of state feedback, namely, only the flow signal is changed when t=40s, the flow signal in the actual signal is changed and tracked rapidly, the differential pressure signal has a certain amplitude and is restored rapidly, and it is presumed that the pump rotation speed suddenly increases to cause the control valve to fail to adjust in time; only the differential pressure signal is changed at t=80 s, and only the differential pressure signal is changed and tracked rapidly in the actual signal. Therefore, decoupling can be well realized after the state feedback is linearized.
It can be seen from fig. 4 that the sliding mode control is added on the basis of the original state feedback precise linearization, the system still has good decoupling effect, and the system is stable. After the sliding mode control is adopted, the stability of flow regulation is improved, and the speed of flow regulation is accelerated. Because slip mode control is introduced, buffeting still exists after the system is stabilized, and further optimization is needed.
It can be seen from fig. 5 that after the slip-form buffeting suppression is adopted, the system still has a good decoupling effect and is stable. The effect on flow regulation is very small and still has good flow regulation performance. After the slip form buffeting inhibition is adopted, buffeting of the rotation speed of the centrifugal pump is obviously inhibited, and the condition that the rotation speed of the centrifugal pump in direct decoupling control is 0 is avoided.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.

Claims (9)

1. A control method for lifting a downhole mixture for constructing a coal seam, the method comprising the steps of:
step 1: deducing a mathematical model under the control of a pump valve control system according to the lifting process of the gas-water coal mixture in the coal seam gas exploitation control system, and establishing a state space expression of the pump valve control system;
in the step 1, according to the lifting process of the gas-water-coal mixture in the coal seam gas exploitation control system, a mathematical model controlled by a pump valve control system is deduced, and a state space expression of the pump valve control system is established, wherein the specific method comprises the following steps:
the construction coal seam gas exploitation control system comprises six major parts: the system comprises a coal measure stratum structure reconstruction and similar material subsystem, a horizontal well bidirectional reciprocating drilling and cave completion subsystem, a horizontal well cave excitation pressure relief and fluid migration subsystem, a vertical well gas-water coal powder mixture lifting and output subsystem, a ground gas-water coal separation, collection and water recycling subsystem, an instrument system information and an automatic control subsystem;
the system is used for exploring and developing theory and technical equipment of the in-situ coal bed gas of the construction coal; the method is used for researching and controlling a vertical well gas-water pulverized coal mixture lifting and output subsystem; the vertical well gas-water pulverized coal mixture lifting and producing subsystem controls lifting equipment and a pulverized coal crushing and disturbing device through a pump valve control system, so that the timely crushing and hydraulic conveying of bottom pulverized coal are realized, and the purposes of no blockage of a pipeline by pulverized coal and stable collection of produced liquid are achieved; the pump valve control system consists of a power liquid tank, a centrifugal pump, a pneumatic control valve, an equipment pipeline, lifting equipment and a production liquid tank;
the pump valve control system is simplified from the power fluid tank to the output fluid tank by Bernoulli equation:
Figure FDA0004137873070000011
wherein Q is the flow in the pipe, A is the cross-sectional area of the pipe, ρ isFluid density, L is the total length of the pipeline; ΔP e Pressure, ΔP, provided to the pump v For pressure loss caused by valves, ΔP c Pressure loss for the mixture lifting equipment;
the flow rate Q, the control valve opening gamma and the centrifugal pump rotation speed n are used as state variables, and the valve opening gamma is set set And centrifugal pump rotational speed setting n set As input variables, with flow Q and control valve differential pressure ΔP v For output variables, the state space equation of the pump valve control system is deduced as follows:
Figure FDA0004137873070000021
wherein:
Figure FDA0004137873070000025
Figure FDA0004137873070000026
Figure FDA0004137873070000022
Figure FDA0004137873070000023
/>
wherein T is γ And T n Time constants of the control valve and the centrifugal pump respectively;
step 2: based on the state space expression, adopting state feedback linearization to directly decouple and control a lifting system formed by a pump valve;
step 3: based on the direct decoupling control of the state feedback linearization, the system instability caused by time lag is removed by adopting an improved Smith predictor;
step 4: based on the direct decoupling control of the state feedback linearization of the improved Smith predictor, the robustness of a pump valve control system is further improved by utilizing sliding mode control;
step 5: based on the state feedback linearization sliding mode control, utilizing an improved switching function to inhibit buffeting of a pump valve control system, and determining a control rate of lifting of a gas downhole mixture of a coal seam;
step 6: and controlling the gas-water-coal mixture lifting system based on the control rate.
2. The method for controlling the lifting of the underground mixture of the gas of the coal seam according to claim 1, wherein in the step 2, based on the state space expression, the lifting system formed by the pump valve is directly decoupled and controlled by adopting state feedback linearization, and the specific method comprises the following steps:
deriving the output y in the state equation until the control rate u appears clearly;
Figure FDA0004137873070000024
wherein:
Figure FDA0004137873070000031
wherein b is a valve pressure loss fitting coefficient, and K (gamma) is a valve flow fitting curve;
when the control rate is selected as
Figure FDA0004137873070000032
When the control rate is substituted into the linearization model, the original model is described as:
Figure FDA0004137873070000033
Figure FDA0004137873070000034
direct decoupling of precise linearization can be achieved.
3. The method for controlling lifting of the underground mixture of the coal seam gas according to claim 2, wherein in the step 3, based on the direct decoupling control of the state feedback linearization, the system instability caused by time lag is removed by adopting an improved Smith predictor, and the specific method comprises the following steps:
after time-lag balancing is carried out on a time-lag system, a first-order filtering link G is added on the basis of the design of an original Smith predictor in a main feedback loop f And(s) reducing the influence of model errors and interference.
4. The method for controlling lifting of the underground mixture of the gas of the coal seam according to claim 3, wherein in the step 4, the robustness of the pump valve control system is further improved by using sliding mode control based on the direct decoupling control of the state feedback linearization of the improved Smith predictor, and the specific method comprises the following steps:
defining a sliding die surface:
Figure FDA0004137873070000035
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient;
then
Figure FDA0004137873070000036
In the middle of
Figure FDA0004137873070000041
The coefficient alpha is such that the polynomial meets the Hulvitz stability criterion;
the control rate is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function;
Figure FDA0004137873070000042
in the middle of
Figure FDA0004137873070000047
And k is 1 >0,k 2 > 0; to sum up, it is obtained:
Figure FDA0004137873070000043
Figure FDA0004137873070000044
then
Figure FDA0004137873070000045
Thus s i Trending towards 0 for a limited time; when the track reaches the sliding mode surface, the error approaches 0, so that the system always moves near the sliding mode surface, the tracking of the target signal is realized, and the system has certain disturbance rejection capability.
5. The method for controlling lifting of the downhole mixture of the gas layer of the construction coal according to claim 4, wherein in the step 5, based on the feedback linearization sliding mode control, the control rate of lifting of the downhole mixture of the gas layer of the construction coal is determined by utilizing an improved switching function to suppress buffeting of the system, and the method specifically comprises the following steps:
considering that the buffeting problem in the sliding mode control is caused by a sign function sgn (S) in the control rate, a continuously smooth hyperbolic tangent function is selected as a substitute, so that the buffeting problem in the sliding mode control is reduced:
Figure FDA0004137873070000046
the improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
6. A control system for constructing a coal seam gas downhole mixture lift, the system comprising:
the state space expression building module is used for building a state space expression of the pump valve control system according to a mathematical model under the pump valve control system; the pump valve control system comprises a power liquid tank, a centrifugal pump, a pneumatic control valve, lifting equipment and a production liquid tank which are connected in sequence, wherein the middle of each part of the pump valve control system is connected by a pipeline and a flange;
in the state space expression building module, a state space expression of the pump valve control system is built, and the specific method comprises the following steps:
the construction coal seam gas exploitation control system comprises six major parts: the system comprises a coal measure stratum structure reconstruction and similar material subsystem, a horizontal well bidirectional reciprocating drilling and cave completion subsystem, a horizontal well cave excitation pressure relief and fluid migration subsystem, a vertical well gas-water coal powder mixture lifting and output subsystem, a ground gas-water coal separation, collection and water recycling subsystem, an instrument system information and an automatic control subsystem;
the system is used for exploring and developing theory and technical equipment of the in-situ coal bed gas of the construction coal; the method is used for researching and controlling a vertical well gas-water pulverized coal mixture lifting and output subsystem; the vertical well gas-water pulverized coal mixture lifting and producing subsystem controls lifting equipment and a pulverized coal crushing and disturbing device through a pump valve control system, so that the timely crushing and hydraulic conveying of bottom pulverized coal are realized, and the purposes of no blockage of a pipeline by pulverized coal and stable collection of produced liquid are achieved;
the pump valve control system is simplified from the power fluid tank to the output fluid tank by Bernoulli equation:
Figure FDA0004137873070000051
wherein Q is the flow in the pipeline, A is the cross-sectional area of the pipeline, ρ is the fluid density, and L is the total length of the pipeline; ΔP e Pressure, ΔP, provided to the pump v For pressure loss caused by valves, ΔP c Pressure loss for the mixture lifting equipment;
the flow rate Q, the control valve opening gamma and the centrifugal pump rotation speed n are used as state variables, and the valve opening gamma is set set And centrifugal pump rotational speed setting n set As input variables, with flow Q and control valve differential pressure ΔP v For output variables, the state space equation of the pump valve control system is deduced as follows:
Figure FDA0004137873070000052
wherein:
Figure FDA0004137873070000066
Figure FDA0004137873070000067
Figure FDA0004137873070000061
Figure FDA0004137873070000062
wherein T is γ And T n Time constants of the control valve and the centrifugal pump respectively;
the state feedback linearization decoupling module is used for acquiring a state feedback linearization decoupling control rate based on the state space expression;
the improved Smith predictor module is used for removing system instability caused by time lag based on the direct decoupling control of the state feedback linearization;
the sliding mode control module is used for obtaining the sliding mode control rate based on the direct decoupling control of the state feedback linearization of the improved Smith predictor;
and the sliding mode buffeting suppression module is used for controlling the sliding mode based on the state feedback linearization and utilizing an improved switching function to suppress buffeting of the system.
7. The control system for lifting the underground mixture of the coal seam gas is constructed according to claim 6, wherein the state feedback linearization decoupling module specifically comprises:
based on the state space expression, the obtained state feedback linearization decoupling control rate is as follows:
Figure FDA0004137873070000063
substituting the control rate into the linearization model, the original model is described as:
Figure FDA0004137873070000064
Figure FDA0004137873070000065
the direct decoupling of accurate linearization can be realized;
the improved Smith predictor module specifically comprises: based on the direct decoupling control of the state feedback linearization, system instability caused by time lag is removed; after time-lag balancing is carried out on a time-lag system, a first-order filtering link G is added on the basis of the design of an original Smith predictor in a main feedback loop f And(s) reducing the influence of model errors and interference.
8. The control system for lifting the underground mixture of the coal seam gas is constructed according to claim 7, wherein the sliding mode control module specifically comprises:
based on the direct decoupling control of the state feedback linearization of the improved Smith predictor, the sliding mode control rate is obtained;
defining a sliding die surface:
Figure FDA0004137873070000071
in the formula e 1 =y 1set -y 1 ,e 2 =y 2set -y 2 Alpha is a constant coefficient;
then
Figure FDA0004137873070000072
In the middle of
Figure FDA0004137873070000073
The coefficient alpha is such that the polynomial meets the Hulvitz stability criterion;
the control rate is selected as follows:
u=G -1 [d+k·sgn(S)-F]
in sgn(s) i ) Is a sign function;
Figure FDA0004137873070000074
/>
in the middle of
Figure FDA0004137873070000075
And k is 1 >0,k 2 >0。
9. The control system for lifting the underground mixture of the coal seam gas is constructed according to claim 8, wherein the sliding mode buffeting suppression module specifically comprises:
based on the feedback linearization sliding mode control, utilizing an improved switching function to inhibit buffeting of the system; considering that the buffeting problem in the sliding mode control is caused by a sign function sgn (S) in the control rate, a continuously smooth hyperbolic tangent function is selected as a substitute, so that the buffeting problem in the sliding mode control is reduced:
Figure FDA0004137873070000081
the improved sliding mode control does not influence the performance of the original sliding mode control, and has stronger robustness.
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