CN119045557A - Torsional drill string vibration suppression method and device based on model reference adaptive control - Google Patents
Torsional drill string vibration suppression method and device based on model reference adaptive control Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B17/00—Drilling rods or pipes; Flexible drill strings; Kellies; Drill collars; Sucker rods; Cables; Casings; Tubings
- E21B17/02—Couplings; joints
- E21B17/04—Couplings; joints between rod or the like and bit or between rod and rod or the like
- E21B17/07—Telescoping joints for varying drill string lengths; Shock absorbers
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D19/00—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase
- G05D19/02—Control of mechanical oscillations, e.g. of amplitude, of frequency, of phase characterised by the use of electric means
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Abstract
The invention provides a torsional drill string vibration suppression method and device based on model reference self-adaptive control, which relate to the technical field of resource exploration and comprise the steps of establishing a torsional drill string vibration model according to the multi-degree-of-freedom theory of drill string movement and combining action torque between a drill bit and rock; the method comprises the steps of converting a torsional drill string vibration model into a state space form, observing state variables of the torsional drill string vibration model through a state observer, performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model, analyzing the target torsional drill string vibration model and a reference model through a Lyapunov stability analysis method, determining a model self-adaption rate, and determining a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model self-adaption rate. The modeling and the control are carried out based on the actual condition of the site, so that the vibration of the torsion drill string under the condition of stratum change is effectively restrained, and the safety of the drilling process is improved.
Description
Technical Field
The invention relates to the technical field of resource exploration, in particular to a torsional drill string vibration suppression method and device based on model reference self-adaptive control.
Background
The guarantee of resource energy supply is one of the keys for realizing the sustainable development of various industries of society. Deep geological resources and unconventional oil and gas resources in China are rich in accumulation, and the development potential is high. However, the mineral resource exploration depth in China is only 500m on average, and according to the mineral resource exploration depth of more than 500m, the deep natural gas resource accounts for about 60% of the rest natural gas resources, and the external dependence of minerals such as petroleum, iron ore, copper and the like is estimated to be about 70%, 85% and 80% respectively in 2030, so geological prospecting is still a main task of geological work. With the increasing exhaustion of shallow mineral resources and the development of deep mining theory, the exploration of a large number of deep mineral resources at home and abroad makes deep geological exploration and development necessary. With the increase of drilling depth, the stratum environment becomes more and more complex, the stratum is different from shallow drilling, the stratum needing to be traversed in deep drilling is more and more, the stratum with different structures such as alternating hardness, fault accompaniment, steep and gentle production are faced, the rock breaking process of the drill bit is more severe, the problems of uncertainty, strong interference, nonlinearity and the like in the deep drilling process are caused to be prominent, the length of a drill string required by deep drilling is extremely long, the vibration of the drill string is extremely easy to occur under the action of intense drill bit-rock, the fatigue of the drilling tool is caused, the quality of a borehole is reduced, and serious safety problems are caused. The complex and changeable geological environment and the severe construction conditions of drill string vibration frequently give new requirements to geological drilling equipment and technology and new challenges to geological drilling process control. During drilling, as the drilling depth increases, the formation environment becomes more and more complex, which increases the difficulty of vibration suppression of the drill string.
Disclosure of Invention
The invention aims to solve the problem that in the current drilling process, as the drilling depth increases, the stratum environment becomes more and more complex, so that the vibration of a drill string is difficult to suppress.
The technical scheme of the embodiment of the application is realized as follows:
An embodiment of the present application provides a torsional drill string vibration suppression method based on model reference adaptive control, including:
According to the theory of multiple degrees of freedom of drill string movement, combining the action torque between the drill bit and rock to establish a torsional drill string vibration model;
converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model through a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model;
Analyzing the target torsion drill string vibration model and a reference model by using a Lyapunov stability analysis method to determine a model self-adaptation rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock;
A torsional drill string vibration suppression strategy is determined based on the target torsional drill string vibration model and the model adaptation rate.
Optionally, the creating a torsional drill string vibration model according to the multiple degrees of freedom theory of drill string movement and combining the action torque between the drill bit and the rock includes:
discretizing the drill string system into a plurality of rigid body segments connected by elastic means;
Determining a corresponding torsional vibration dynamics equation based on the motion parameters of each rigid body segment;
And optimizing the torsional vibration dynamics equation by utilizing the action torque between the drill bit and the rock of the drill string system, and establishing the torsional drill string vibration model.
Optionally, the creating a torsional drill string vibration model according to the multiple degrees of freedom theory of drill string movement and combining the action torque between the drill bit and the rock includes:
Dividing the drill string system into an uphole rotary table, a plurality of drill rods in the well, a weighted drill rod, a drill collar and drilling fluid, and the drill bit-rock action of a downhole part, and establishing a multi-degree-of-freedom torsional drill string vibration model:
;
Wherein, therein The angular displacement of the units representing n+3 is respectively a rotary table, a drill rod (n units), a weighted drill rod and a drill collar,The angular velocity is indicated as such,Representing angular acceleration;,; For the torque of the rotary disk, For bit torque, coefficient,,The moment of inertia matrix, the rigidity matrix and the viscous damping matrix of n+3 units of the drill string system are respectively:
;
;
;
Based on material mechanics, matrix The units in (2) are calculated by the following formula:
;
Wherein, Respectively represent the firstThe drill rod units, the weighting drill rod units and the drill collars; And Representing the density and shear modulus of the drill string; And Respectively represent aboutThe outer diameter, inner diameter and polar moment of inertia of the cell.Is the damping coefficient of drilling fluid received by each unit length of drill rod, and the inertia of the top driveIs a constant value;
the drill bit-rock action model adopts a torsion Karnopp drill bit-rock action model:
;
Wherein, For the bit torque to be the same,Indicating the radius of the drill bit,Is the static moment of force, and the static moment of force,Is a very small positive value that is used,For the maximum static friction torque to be the maximum,For the rotation speed of the drill collar,Is the rotation speed of the drill bit.
Optionally, the converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model through a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model, including:
converting the torsional drill string vibration model into a state space form to obtain a state equation;
Determining observer gain and state feedback gain of the state equation by a state observer and linear quadratic regulator method respectively;
And optimizing the torsional drill string vibration model by using the observer gain and the state feedback gain to obtain a target torsional drill string vibration model.
Optionally, the converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model through a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model, including:
acquiring a state space equation corresponding to the torsional drill string vibration model, and selecting a state quantity:
;
obtaining a state space equation of the drill string system:
;
Wherein, ,In order for the control input and the disturbance input,For outputting a vibration model of the drill string, a matrix、、AndCan be expressed as:
Wherein, Representing a 0 matrix;
the internal model controller is expressed as: =0,=1;
neglecting bit-rock action disturbances, the step response comprising the drill string vibration model and the internal model is:
;
Wherein,
;
Optimizing performance indexes of the drill string system:
;
based on design matrix AndDetermining a state feedback control matrixAnd。
Optionally, the analyzing the target torsion drill string vibration model and a reference model by using a lyapunov stability analyzing method to determine a model self-adapting rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock, and comprises the following steps:
Analyzing the target torsion drill string vibration model and the reference model through a Lyapunov stability analysis method, and determining a model self-adaption rate by combining the current state of a drill string system and the torque disturbance.
Optionally, the analyzing the target torsion drill string vibration model and a reference model by using a lyapunov stability analyzing method to determine a model self-adapting rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock, and comprises the following steps:
Obtaining a reference model:
;
Wherein, As a matrix of states of the reference model,For the input matrix of the reference model,The output matrix for the reference model can be obtained by the following formula:
The control input of the system is the sum of the model reference adaptive and state feedback control rate, and can be obtained by the following formula:
;
Wherein, For the system control input(s),For the state feedback control input,For the state feedback control input,;
A tracking error is defined and the tracking error is,Deriving a tracking error:
;
Order the ,The above formula can be simplified as:
;
The lyapunov function of the defined system is:
;
Wherein, AndA positive constant greater than 0;
deriving Lyapunov functions
;
If it is to makeNeeds to meet
;
The lyapunov function becomes:
;
Solving through a Linear Matrix Inequality (LMI) toolbox to enable 。
The second aspect of the embodiment of the application provides a torsional drill string vibration suppression device based on model reference adaptive control, which comprises a building module, a configuration module, an analysis module and a determination module, wherein,
The building module is configured to build a torsional drill string vibration model according to the theory of multiple degrees of freedom of drill string movement and combining action torque between a drill bit and rock;
The configuration module is configured to convert the torsional drill string vibration model into a state space form, observe state variables of the torsional drill string vibration model through a state observer, and perform pole configuration on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model;
The analysis module is configured to analyze the target torsion drill string vibration model and a reference model through a Lyapunov stability analysis method to determine a model self-adaptation rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock;
The determination module is configured to determine a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model adaptation rate.
A third aspect of the embodiments of the present application provides an electronic device, comprising a processor and a memory, the memory having a stored computer program, wherein the computer program when executed by the processor implements the model reference adaptive control-based torsional drill string vibration suppression method of the first aspect.
A fourth aspect of the embodiments of the present application provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method of the first aspect.
Compared with the prior art, the technical scheme provided by the application has the beneficial effects that:
The invention provides a torsional drill string vibration suppression method and device based on model reference self-adaptive control. According to the theory of multiple degrees of freedom of drill string movement, the action torque between the drill bit and rock is combined, and a torsional drill string vibration model is built. And optimizing the torsional drill string vibration model through a state observer and a linear quadratic regulator method to obtain the target torsional drill string vibration model. And analyzing the vibration model and the reference model of the target torsion drill string by using a Lyapunov stability analysis method, and determining the model self-adaption rate. And determining a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model self-adaption rate, so that the torsional drill string vibration under the condition of stratum change is effectively suppressed, and the safety of the drilling process is improved.
Drawings
FIG. 1 is a schematic flow chart of a torsional drill string vibration suppression method based on model reference adaptive control according to an embodiment of the present application;
FIG. 2 is a schematic structural diagram of a torsional drill string vibration suppression device based on model reference adaptive control according to an embodiment of the present application;
fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
Hereinafter, embodiments of the present application will be described with reference to the accompanying drawings. It should be understood that the description is only illustrative and is not intended to limit the scope of the application. In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the embodiments of the application. However, it will be apparent that one or more embodiments may be practiced without these specific details. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the present application.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The terms "comprises," "comprising," and/or the like, as used herein, specify the presence of stated features, steps, operations, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, or components.
All terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art unless otherwise defined. It should be noted that the terms used herein should be construed to have meanings consistent with the context of the present specification and should not be construed in an idealized or overly formal manner.
Some of the block diagrams and/or flowchart illustrations are shown in the figures. It will be understood that some blocks of the block diagrams and/or flowchart illustrations, or combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the instructions, when executed by the processor, create means for implementing the functions/acts specified in the block diagrams and/or flowchart.
In some embodiments, referring to fig. 1, fig. 1 is a flow chart of a torsional drill string vibration suppression method based on model reference adaptive control according to an embodiment of the present application, where the torsional drill string vibration suppression method based on model reference adaptive control according to an embodiment of the present application includes:
S110, according to the theory of multiple degrees of freedom of drill string movement, combining action torque between a drill bit and rock to establish a torsional drill string vibration model.
During drilling of the drill string, complex torsional vibrations can occur due to the rotation of the drill bit and the resistance of the rock. According to the multi-degree of freedom theory, the drill string can be regarded as being composed of a plurality of elastically connected rigid bodies, and each rigid body has own moment of inertia and elastic coefficient. The torque acting between the drill bit and the rock is one of the main factors causing torsional vibrations of the drill string. This torque can be expressed as a function of parameters related to bit rotational speed, rock hardness, etc. Based on this, a torsional vibration dynamics equation of the drill string can be established. This equation may include the rotational inertia of the drill string, the coefficient of elasticity, the damping coefficient, and the applied torque between the drill bit and the rock.
In some embodiments, S110, according to the multiple degree of freedom theory of drill string motion, in combination with the applied torque between the drill bit and the rock, creates a torsional drill string vibration model, comprising:
discretizing the drill string system into a plurality of rigid body segments connected by elastic means;
determining a corresponding torsional vibration dynamics equation based on the motion parameters of each rigid body segment;
and optimizing a torsional vibration dynamics equation by utilizing the action torque between the drill bit and the rock of the drill string system, and establishing a torsional drill string vibration model.
In this embodiment, the drill string is discretized into a series of rigid body segments connected by elastic connections (e.g., drill pipe joints). Each rigid body segment has its own moment of inertia and elastic coefficient. For each rigid body segment, a kinetic equation of its torsional vibration can be written. The torque applied between the drill bit and the rock is complex and depends on various factors such as the type of drill bit, the rotational speed, the hardness and strength of the rock, the properties of the drilling fluid, etc. The torque may be expressed as a function of these parameters, or approximated by experimental data, when modeling.
In some embodiments, S110, according to the multiple degree of freedom theory of drill string motion, in combination with the applied torque between the drill bit and the rock, creates a torsional drill string vibration model, comprising:
dividing a drill string system into an uphole rotary table, a plurality of drill rods in a well, a weighted drill rod, a drill collar and drilling fluid, and the drill bit-rock action of a downhole part, and establishing a multi-degree-of-freedom torsional drill string vibration model:
;
Wherein, therein The angular displacement of the units representing n+3 is respectively a rotary table, a drill rod (n units), a weighted drill rod and a drill collar,The angular velocity is indicated as such,Representing angular acceleration;,; For the torque of the rotary disk, For bit torque, coefficient,,The moment of inertia matrix, the rigidity matrix and the viscous damping matrix of n+3 units of the drill string system are respectively:
;
;
;
Based on material mechanics, matrix The units in (2) are calculated by the following formula:
;
Wherein, Respectively represent the firstThe drill rod units, the weighting drill rod units and the drill collars; And Representing the density and shear modulus of the drill string; And Respectively represent aboutThe outer diameter, inner diameter and polar moment of inertia of the cell.Is the damping coefficient of drilling fluid received by each unit length of drill rod, and the inertia of the top driveIs a constant value;
the drill bit-rock action model adopts a torsion Karnopp drill bit-rock action model:
;
Wherein, For the bit torque to be the same,Indicating the radius of the drill bit,Is the static moment of force, and the static moment of force,Is a very small positive value that is used,For the maximum static friction torque to be the maximum,For the rotation speed of the drill collar,Is the rotation speed of the drill bit.
S120, converting the torsional drill string vibration model into a state space form, observing state variables of the torsional drill string vibration model through a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain the target torsional drill string vibration model.
Here, the torsional drill string vibration model is converted into a state space form, i.e., defining state variables (e.g., angular displacement and angular velocity of various portions of the drill string) and input variables (e.g., torque experienced by the drill bit). The purpose of the state observer is to estimate some state variables that are not directly measurable. For a twisted drill string, if the angular displacement or angular velocity of certain segments cannot be measured directly, a state observer may be used to estimate. The linear quadratic regulator LQR is an optimal control method that finds the optimal control law by minimizing a quadratic cost function consisting of state variables and control inputs.
In some embodiments, S120, converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model by a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model, including:
converting the torsional drill string vibration model into a state space form to obtain a state equation;
The observer gain and the state feedback gain of the state equation are respectively determined by a state observer and a linear quadratic regulator method;
and optimizing the torsional drill string vibration model by using the observer gain and the state feedback gain to obtain the target torsional drill string vibration model.
In some embodiments, S120, converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model by a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model, including:
acquiring a state space equation corresponding to a torsional drill string vibration model, and selecting a state quantity:
;
obtaining a state space equation of the drill string system:
;
Wherein, ,In order for the control input and the disturbance input,For outputting a vibration model of the drill string, a matrix、、AndCan be expressed as:
Wherein, Representing a 0 matrix;
the internal model controller is expressed as: =0,=1;
neglecting bit-rock action disturbances, the step response comprising the drill string vibration model and the internal model is:
;
Wherein,
;
Optimizing performance indexes of the drill string system:
;
based on design matrix AndDetermining a state feedback control matrixAnd。
S130, analyzing a target torsion drill string vibration model and a reference model through a Lyapunov stability analysis method to determine a model self-adaption rate, wherein the reference model is a drill string vibration control model which does not consider action torque disturbance between a drill bit and rock.
For the target torsional drill string vibration model and the reference model, a suitable lyapunov function needs to be constructed. This function can reflect changes in system state and satisfies positive qualitative and radial unbounded properties. Since drill string systems typically contain multiple state variables (e.g., displacement, velocity, acceleration, etc.), the lyapunov function may be a quadratic or higher order function of these state variables. Substituting the state equation of the drill string system into the Lyapunov function and applying the chain rule to conduct derivation. For the target torsional drill string vibration model, the equation of state will contain more nonlinear terms, as the active torque disturbances between the drill bit and the rock are considered. Whereas for the reference model the state equation is relatively simple.
In some embodiments, S130, analyzing the target torsional drill string vibration model and a reference model by a Lyapunov stability analysis method to determine a model adaptation rate, wherein the reference model is a drill string vibration control model which does not consider an action torque disturbance between a drill bit and rock, and comprises:
and analyzing the vibration model and the reference model of the target torsion drill string by using a Lyapunov stability analysis method, and determining the model self-adaption rate by combining the current state of the drill string system and torque disturbance.
In this embodiment, in order to cope with torque disturbance and maintain stability of the system, an adaptive controller needs to be designed. The adaptation rate (i.e., the regulation of the controller parameters) may be determined from the results of the lyapunov stability analysis. When the time derivative of the lyapunov function along the system trajectory approaches or becomes positive, the controller parameters change to decrease the value of the time derivative, thereby maintaining the stability of the system.
In some embodiments, S130, analyzing the target torsional drill string vibration model and a reference model by a Lyapunov stability analysis method to determine a model adaptation rate, wherein the reference model is a drill string vibration control model which does not consider an action torque disturbance between a drill bit and rock, and comprises:
Obtaining a reference model:
;
Wherein, As a matrix of states of the reference model,For the input matrix of the reference model,The output matrix for the reference model can be obtained by the following formula:
The control input of the system is the sum of the model reference adaptive and state feedback control rate, and can be obtained by the following formula:
;
Wherein, For the system control input(s),For the state feedback control input,For the state feedback control input,;
A tracking error is defined and the tracking error is,Deriving a tracking error:
;
Order the ,The above formula can be simplified as:
;
The lyapunov function of the defined system is:
;
Wherein, AndA positive constant greater than 0;
deriving Lyapunov functions
;
If it is to makeNeeds to meet
;
The lyapunov function becomes:
;
Solving through a Linear Matrix Inequality (LMI) toolbox to enable 。
S140, determining a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model adaptation rate.
Here, the validity of the designed adaptive control law can be verified through simulation or experimentation, including applying the adaptive control law to a target torsional drill string vibration model and observing the response of the drill string system at different torque disturbances. If the drill string system is capable of maintaining stable operation and meeting performance requirements, it is stated that the designed adaptive control law is effective.
According to the embodiment of the application, a torsional drill string vibration model is established by combining the action torque between a drill bit and rock according to the multi-degree-of-freedom theory of drill string movement, and then the state observer and linear quadratic regulator method optimize the torsional drill string vibration model to obtain a target torsional drill string vibration model, the target torsional drill string vibration model and a reference model are analyzed by the Lyapunov stability analysis method, the model self-adaptation rate is determined, and the torsional drill string vibration suppression strategy is determined based on the target torsional drill string vibration model and the model self-adaptation rate, so that the torsional drill string vibration under the condition of stratum change is effectively suppressed, and the safety of the drilling process is improved.
In some embodiments, referring to fig. 2, fig. 2 is a schematic structural diagram of a torsional drill string vibration suppression device based on model reference adaptive control according to an embodiment of the present application. The torsional drill string vibration suppression device 200 based on model reference adaptive control provided by the embodiment of the application comprises an establishing module 210, a configuring module 220, an analyzing module 230 and a determining module 240, wherein,
A build-up module 210 configured to build a torsional drill string vibration model based on the multiple degree of freedom theory of drill string movement, in combination with the applied torque between the drill bit and the rock;
The configuration module 220 is configured to convert the torsional drill string vibration model into a state space form, observe a state variable of the torsional drill string vibration model through a state observer, and perform pole configuration on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model;
An analysis module 230 configured to analyze the target torsional drill string vibration model by a Lyapunov stability analysis method and a reference model, which is a drill string vibration control model that does not take into account torque disturbances acting between the drill bit and the rock, to determine a model adaptation rate;
a determination module 240 is configured to determine a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model adaptation rate.
In some embodiments, the setup module 210 is specifically configured to:
discretizing the drill string system into a plurality of rigid body segments connected by elastic means;
determining a corresponding torsional vibration dynamics equation based on the motion parameters of each rigid body segment;
and optimizing the torsional vibration dynamics equation by utilizing the action torque between the drill bit and the rock of the drill string system, and establishing the torsional drill string vibration model.
In some embodiments, the setup module 210 is specifically configured to:
dividing a drill string system into an uphole rotary table, a plurality of drill rods in a well, a weighted drill rod, a drill collar and drilling fluid, and the drill bit-rock action of a downhole part, and establishing a multi-degree-of-freedom torsional drill string vibration model:
;
Wherein, therein The angular displacement of the units representing n+3 is respectively a rotary table, a drill rod (n units), a weighted drill rod and a drill collar.The angular velocity is indicated as such,Representing angular acceleration;,; For the torque of the rotary disk, Is the bit torque. Coefficients of,,The moment of inertia matrix, the rigidity matrix and the viscous damping matrix of n+3 units of the drill string system are respectively:
;
;
;
Based on material mechanics, matrix The units in (2) are calculated by the following formula:
;
Wherein, Respectively represent the firstThe drill rod units, the weighting drill rod units and the drill collars; And Representing the density and shear modulus of the drill string; And Respectively represent aboutThe outer diameter, inner diameter and polar moment of inertia of the cell.Is the damping coefficient of drilling fluid received by each unit length of drill rod, and the inertia of the top driveIs a constant value.
The drill bit-rock action model adopts a torsion Karnopp drill bit-rock action model:
;
Wherein, For the bit torque to be the same,Indicating the radius of the drill bit,Is the static moment of force, and the static moment of force,Is a very small positive value that is used,For the maximum static friction torque to be the maximum,For the rotation speed of the drill collar,Is the rotation speed of the drill bit.
In some embodiments, the configuration module 220 is specifically configured to:
converting the torsional drill string vibration model into a state space form to obtain a state equation;
The observer gain and the state feedback gain of the state equation are respectively determined by a state observer and a linear quadratic regulator method;
and optimizing the torsional drill string vibration model by using the observer gain and the state feedback gain to obtain the target torsional drill string vibration model.
In some embodiments, the configuration module 220 is specifically configured to:
acquiring a state space equation corresponding to a torsional drill string vibration model, and selecting a state quantity:
;
obtaining a state space equation of the drill string system:
;
Wherein, ,In order for the control input and the disturbance input,For outputting a vibration model of the drill string, a matrix、、AndCan be expressed as:
Wherein, Representing a matrix of 0.
The internal model controller is expressed as:=0,=1;
neglecting bit-rock action disturbances, the step response comprising the drill string vibration model and the internal model is:
;
Wherein,
;
Optimizing performance indexes of the drill string system:
;
based on design matrix AndDetermining a state feedback control matrixAnd。
In some embodiments, the analysis module 230 is specifically configured to:
and analyzing the vibration model and the reference model of the target torsion drill string by using a Lyapunov stability analysis method, and determining the model self-adaption rate by combining the current state of the drill string system and torque disturbance.
In some embodiments, the analysis module 230 is specifically configured to:
Obtaining a reference model:
;
Wherein, As a matrix of states of the reference model,For the input matrix of the reference model,The output matrix for the reference model can be obtained by the following formula:
The control input of the system is the sum of the model reference adaptive and state feedback control rate, and can be obtained by the following formula:
;
Wherein, For the system control input(s),For the state feedback control input,For the state feedback control input,;
A tracking error is defined and the tracking error is,Deriving a tracking error:
;
Order the ,The above formula can be simplified as:
;
The lyapunov function of the defined system is:
;
Wherein, AndIs a positive constant greater than 0.
Deriving Lyapunov functions
;
If it is to makeNeeds to meet
;
The lyapunov function becomes:
;
Solving through a Linear Matrix Inequality (LMI) toolbox to enable 。
The torsional drill string vibration suppression device based on the model reference adaptive control provided by the embodiment of the application can realize each process in the embodiment corresponding to the torsional drill string vibration suppression method based on the model reference adaptive control, and in order to avoid repetition, the description is omitted.
It should be noted that, the torsional drill string vibration suppression device based on the model reference adaptive control provided by the embodiment of the present application and the torsional drill string vibration suppression method based on the model reference adaptive control provided by the embodiment of the present application are based on the same application conception, so that the specific implementation of the embodiment may refer to the implementation of the torsional drill string vibration suppression method based on the model reference adaptive control, and the repetition is omitted.
In some embodiments, referring to fig. 3, fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present application. The electronic device 300 provided by the embodiment of the application comprises a processor 310 and a memory 320, wherein the memory 320 stores a computer program, and the computer program realizes the torsional drill string vibration suppression method based on the model reference adaptive control when being executed by the processor.
In particular, processor 310 may include, for example, a general purpose microprocessor, an instruction set processor and/or an associated chipset and/or a special purpose microprocessor (e.g., an Application Specific Integrated Circuit (ASIC)), or the like. Processor 310 may also include on-board memory for caching purposes. Processor 310 may be a single processing unit or multiple processing units for performing the different actions of the method flows according to embodiments of the application.
Memory 320 may be, for example, any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory 320 may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. Specific examples of memory 320 include magnetic storage devices such as magnetic tape or hard disk (HDD), optical storage devices such as compact disk (CD-ROM), but also Random Access Memory (RAM) or flash memory, and/or wired/wireless communication links.
The application also provides a computer readable medium having stored thereon a computer program which when executed by a processor implements the above-described method of torsional drill string vibration suppression based on model reference adaptive control. The computer readable medium may be embodied in the apparatus/device/system described in the above embodiments or may exist alone without being assembled into the apparatus/device/system. The computer readable medium carries one or more programs which, when executed, implement methods in accordance with embodiments of the present application.
According to an embodiment of the present application, the computer readable medium may be a computer readable signal medium or a computer readable storage medium or any combination of the two. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples of a computer-readable storage medium may include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. In the present application, however, the computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, with the computer-readable program code embodied therein. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, radio frequency signal, etc., or any suitable combination of the foregoing.
Those skilled in the art will appreciate that the features recited in the various embodiments of the application and/or in the claims may be combined in various combinations and/or combinations even if such combinations or combinations are not explicitly recited in the application. In particular, the features recited in the various embodiments of the application and/or in the claims can be combined in various combinations and/or combinations without departing from the spirit and teachings of the application. All such combinations and/or combinations fall within the scope of the application. The scope of the application should, therefore, be determined not with reference to the above-described embodiments, but instead should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.
Claims (10)
1. A torsional drill string vibration suppression method based on model reference adaptive control, comprising:
According to the theory of multiple degrees of freedom of drill string movement, combining the action torque between the drill bit and rock to establish a torsional drill string vibration model;
converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model through a state observer, and performing pole allocation on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model;
Analyzing the target torsion drill string vibration model and a reference model by using a Lyapunov stability analysis method to determine a model self-adaptation rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock;
A torsional drill string vibration suppression strategy is determined based on the target torsional drill string vibration model and the model adaptation rate.
2. The method for suppressing vibration of a torsional drill string based on model reference adaptive control according to claim 1, wherein the creating a torsional drill string vibration model based on the theory of multiple degrees of freedom of drill string movement, in combination with an applied torque between a drill bit and rock, comprises:
discretizing the drill string system into a plurality of rigid body segments connected by elastic means;
Determining a corresponding torsional vibration dynamics equation based on the motion parameters of each rigid body segment;
And optimizing the torsional vibration dynamics equation by utilizing the action torque between the drill bit and the rock of the drill string system, and establishing the torsional drill string vibration model.
3. The method for suppressing vibration of a torsional drill string based on model reference adaptive control according to claim 1, wherein the creating a torsional drill string vibration model based on the theory of multiple degrees of freedom of drill string movement, in combination with an applied torque between a drill bit and rock, comprises:
Dividing the drill string system into an uphole rotary table, a plurality of drill rods in the well, a weighted drill rod, a drill collar and drilling fluid, and the drill bit-rock action of a downhole part, and establishing a multi-degree-of-freedom torsional drill string vibration model:
;
Wherein, therein The angular displacement of the units representing n+3 is respectively a rotary table, a drill rod (n units), a weighted drill rod and a drill collar,The angular velocity is indicated as such,Representing angular acceleration;,; For the torque of the rotary disk, For bit torque, coefficient,,The moment of inertia matrix, the rigidity matrix and the viscous damping matrix of n+3 units of the drill string system are respectively:
;
;
;
Based on material mechanics, matrix The units in (2) are calculated by the following formula:
;
Wherein, Respectively represent the firstThe drill rod units, the weighting drill rod units and the drill collars; And Representing the density and shear modulus of the drill string; And Respectively represent aboutThe outer diameter, inner diameter and polar moment of inertia of the cell.Is the damping coefficient of drilling fluid received by each unit length of drill rod, and the inertia of the top driveIs a constant value;
the drill bit-rock action model adopts a torsion Karnopp drill bit-rock action model:
;
Wherein, For the bit torque to be the same,Indicating the radius of the drill bit,Is the static moment of force, and the static moment of force,Is a very small positive value that is used,For the maximum static friction torque to be the maximum,For the rotation speed of the drill collar,Is the rotation speed of the drill bit.
4. The torsional drill string vibration suppression method based on model reference adaptive control according to claim 1, wherein the torsional drill string vibration model is converted into a state space form, state variables of the torsional drill string vibration model are observed through a state observer, and pole allocation is performed on the torsional drill string vibration model by using a linear quadratic regulator method, so as to obtain a target torsional drill string vibration model, and the method comprises the following steps:
converting the torsional drill string vibration model into a state space form to obtain a state equation;
Determining observer gain and state feedback gain of the state equation by a state observer and linear quadratic regulator method respectively;
And optimizing the torsional drill string vibration model by using the observer gain and the state feedback gain to obtain a target torsional drill string vibration model.
5. The method for suppressing torsional drill string vibration based on model reference adaptive control according to claim 1, wherein the converting the torsional drill string vibration model into a state space form, observing a state variable of the torsional drill string vibration model through a state observer, and performing pole configuration on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model comprises:
acquiring a state space equation corresponding to the torsional drill string vibration model, and selecting a state quantity:
;
obtaining a state space equation of the drill string system:
;
Wherein, ,In order for the control input and the disturbance input,For outputting a vibration model of the drill string, a matrix、、AndCan be expressed as:
Wherein, Representing a 0 matrix;
the internal model controller is expressed as: =0,=1;
neglecting bit-rock action disturbances, the step response comprising the drill string vibration model and the internal model is:
;
Wherein,
;
Optimizing performance indexes of the drill string system:
;
based on design matrix AndDetermining a state feedback control matrixAnd。
6. The torsional drill string vibration suppression method based on model reference adaptive control of claim 1, wherein the target torsional drill string vibration model and a reference model are analyzed by a lyapunov stability analysis method to determine a model adaptation rate, wherein the reference model is a drill string vibration control model that does not consider an applied torque disturbance between a drill bit and rock, comprising:
Analyzing the target torsion drill string vibration model and the reference model through a Lyapunov stability analysis method, and determining a model self-adaption rate by combining the current state of a drill string system and the torque disturbance.
7. The method for suppressing torsional drill string vibration based on model reference adaptive control according to claim 6, wherein the target torsional drill string vibration model and a reference model are analyzed by Lyapunov stability analysis method to determine a model adaptation rate, and the reference model is a drill string vibration control model that does not consider an action torque disturbance between a drill bit and rock, comprising:
Obtaining a reference model:
;
Wherein, As a matrix of states of the reference model,For the input matrix of the reference model,The output matrix for the reference model can be obtained by the following formula:
The control input of the system is the sum of the model reference adaptive and state feedback control rate, and can be obtained by the following formula:
;
Wherein, For the system control input(s),For the state feedback control input,For the state feedback control input,;
A tracking error is defined and the tracking error is,Deriving a tracking error:
;
Order the ,The above formula can be simplified as:
;
The lyapunov function of the defined system is:
;
Wherein, AndA positive constant greater than 0;
deriving Lyapunov functions
;
If it is to makeNeeds to meet
;
The lyapunov function becomes:
;
Solving through a Linear Matrix Inequality (LMI) toolbox to enable 。
8. A torsional drill string vibration suppression device based on model reference adaptive control is characterized by comprising a building module, a configuration module, an analysis module and a determination module, wherein,
The building module is configured to build a torsional drill string vibration model according to the theory of multiple degrees of freedom of drill string movement and combining action torque between a drill bit and rock;
The configuration module is configured to convert the torsional drill string vibration model into a state space form, observe state variables of the torsional drill string vibration model through a state observer, and perform pole configuration on the torsional drill string vibration model by using a linear quadratic regulator method to obtain a target torsional drill string vibration model;
The analysis module is configured to analyze the target torsion drill string vibration model and a reference model through a Lyapunov stability analysis method to determine a model self-adaptation rate, wherein the reference model is a drill string vibration control model which does not consider the action torque disturbance between a drill bit and rock;
The determination module is configured to determine a torsional drill string vibration suppression strategy based on the target torsional drill string vibration model and the model adaptation rate.
9. An electronic device comprising a processor and a memory, the memory having a stored computer program, wherein the computer program when executed by the processor implements the model reference adaptive control-based torsional drill string vibration suppression method of any one of claims 1 to 7.
10. A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method of any of claims 1 to 7.
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