CN110067550A - It is a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method - Google Patents

Abstract

The invention discloses a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, the following steps are included: DRILL-STRING SYSTEM is abstract and simplifies, construct vibration equation, it realizes in model state space, construct Linear parameter-varying modeling of turbo, the Linear Fractional of LPV model indicates, constructs DRILL-STRING SYSTEM rotary motion model.Method of the invention describes practical DRILL-STRING SYSTEM using many-degrees of freedom system and state space equation, meets drill string multiple-unit combined characteristic, improves drill string modeling accuracy；Meanwhile the drill string length and LFT technology of time-varying are introduced, it is analyzed conducive to the rotary motion to entire drilling process DRILL-STRING SYSTEM, improves the scope of application of model.In addition, the Karnopp model introduced is suitble to describe Bit-rock effect, there is preferable dummy activity for simulating practical DRILL-STRING SYSTEM rotary motion.

Description

A Modeling Method for Rotary Motion of Drill String System with Multiple Degrees of Freedom and Variable Parameters

technical field

The invention relates to a rotary motion modeling method of a drill string system with multiple degrees of freedom and variable parameters, and belongs to the field of drill string control.

Background technique

my country is a country with a large consumption of resources and energy, and its per capita possession is at a low level in the world. Therefore, the exploration and exploitation of resources cannot be delayed. With the continuous exploration and exploitation of shallow resources and energy, my country's shallow easy-to-exploit resources are gradually decreasing, and the development of deep resources has become an important direction for China's scientific and technological development in the future. Deep drilling is defined according to the mineral resources exploration depth of more than 500m and the oil and gas exploitation depth of more than 4500m. my country's deep oil resources and natural gas resources account for about 40% and 60% of the remaining oil resources and remaining natural gas resources, respectively. Therefore, increasing the exploitation and utilization of deep resources and energy is of great significance to realize the continuous supply of energy.

In the process of deep resource exploration and development, the length of the drill string system extends for thousands or even tens of kilometers, the equivalent torsional stiffness of the drill string is continuously reduced, and the dynamics of the drill string system gradually changes. At the same time, the entire drill string system is faced with complex and changeable geological environment, including bottom hole bit-rock interaction, drill string-well wall friction contact, drilling fluid damping, etc. Under the combined action of the internal factors of the drill string system and the external factors brought by the formation environment, it is difficult for the entire drill string system to maintain a constant rotational speed in the direction of rotation, resulting in a certain difference in the rotational speed between the uphole and downhole, and the system may experience torsional vibration or even stick-slip vibration. Violent torsion and stick-slip motion of the drill string system will accelerate the fatigue of the drill string, cause the aging and failure of the drilling tools, reduce the drilling efficiency, increase the drilling cost, and even damage the drill string in severe cases, which seriously threatens the drilling safety.

In recent years, many scholars and related drilling companies have devoted themselves to using various methods and technologies to understand and master the downhole motion of the drill string system and control the downhole state. Although the MWD device can obtain downhole data, in the deep complex and harsh formation environment, the real-time and accuracy of the MWD device is difficult to guarantee, and has a very high cost; at the same time, the measurement and analysis based on the uphole data are also It is difficult to accurately predict downhole conditions. Therefore, modeling the rotary motion of the drill string system is an effective method. On the one hand, establishing a rotary motion model of the drill string system can predict downhole variables in real time based on the model, and at the same time, it can help to understand the phenomenon of drill string torsion and stick-slip motion, reveal its generation mechanism, and provide pre-analysis for the drilling process; on the other hand, drilling The rotary motion model of the column system can guide the design of the uphole controller, realize the consistency of the uphole and downhole rotational speeds, and ensure high-efficiency drilling.

SUMMARY OF THE INVENTION

The present invention proposes a rotary motion modeling method of a drill string system with multiple degrees of freedom and variable parameters, and simplifies the actual variable length drill string system to obtain a simplified system described by multiple degrees of freedom spring-damping; At the same time, combined with the time-varying characteristics of the drill string length, the variable parameter model of the drill string system is derived, and the linear fractional representation is obtained by means of the linear fractional transformation technique; finally, Karnopp is used. The friction model simulates the bit-rock interaction, and combined with the drill string model, the modeling of the rotary motion of the drill string system is completed.

The rotary motion modeling method of the drill string system of the present invention mainly comprises the following steps:

Step 1: Abstraction and simplification of drill string system: For the actual drill string system, according to the drill string system constituent units, establish the corresponding multi-degree-of-freedom spring-damping system;

Step 2: Construct the vibration equation: Based on vibration mechanics, describe the multi-degree-of-freedom spring-damper system in the form of a second-order differential equation, and derive the corresponding mass, damping, and stiffness matrix expressions;

Step 3: Realize the state space of the model, and build a linear variable parameter (LPV) model: select the rotational angular velocity of each element of the spring-damper system and the rotational angle difference between the elements as state variables, and derive the state space equation implementation of the vibration equation; The time-varying property of the string length is used to calculate the relationship between the moment of inertia, stiffness and damping of each element of the drill string and the length of the drill string, and based on the state space equation, the LPV model with the dependence of drill string length is derived;

Step 4: Linear Fractional Representation of the LPV Model: Normalize the drill string length, and separate the LPV model into a linear time-invariant part and an uncertain block part through the Linear Fractional Transform (LFT) technology. Fractional transformation form description;

Step 5: Introduce the bit-rock interaction model to complete the rotary motion model of the drill string system: Introduce the Karnopp friction model to describe the bit-rock interaction, and combine the LFT model of the drill string to complete the dynamic modeling of the rotary motion of the drill string system.

The technical effect of the invention is that: the multi-degree-of-freedom system and state space equation are used to describe the actual drill string system, which conforms to the multi-unit combination characteristics of the drill string and improves the modeling accuracy of the drill string; at the same time, the time-varying drill string length and LFT technology are introduced. , which is beneficial to analyze the rotary motion of the drill string system during the whole drilling process, and improves the applicable scope of the model. Finally, the introduced Karnopp model is suitable for describing the bit-rock interaction, and has a good simulation effect on simulating the rotary motion of the actual drill string system.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

Fig. 1 is the flow chart of the rotary motion modeling method of drill string system with multi-degree-of-freedom-variable parameters of the present invention;

Fig. 2 is the drill string system structure diagram of the present invention;

Fig. 3 is the multi-degree-of-freedom simplified model of the present invention;

Fig. 4 is the LFT form of the rotary motion model of the present invention;

Fig. 5 is the frequency response of the rotary motion model of the present invention;

Fig. 6 is the step response of the rotary motion model of the present invention;

FIG. 7 is a simulation of the rotary motion of the drill string system of the present invention—torsion and stick-slip vibration.

Detailed ways

In order to have a clearer understanding of the technical features, objects and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

With reference to Fig. 1, Fig. 1 is the flow chart of the rotary motion modeling method of drill string system with multi-degree-of-freedom-variable parameters of the present invention, and the present invention specifically comprises the following steps:

Step 1: Establishment of the drill string system

The actual drill string system is shown in Figure 2, which has a complex structure and includes various mechanical, electrical, and driving units. In order to capture its main dynamic characteristics, the present invention is based on the main components of the drill string system, that is, the motor and turntable in the upper well. , the multi-section drill pipe, weighted drill pipe, drill collar and drilling fluid in the well part, and the drill bit and rock in the downhole part. Based on these components, a simplified knot of the drill string system, a multi-degree-of-freedom spring-damper system, is established, as shown in Figure 3. The total degree of freedom of the system is set to be n+3, in which the drill pipe contains n degrees of freedom, and the turntable, weighted drill pipe and drill collar each contain one degree of freedom. The n value can be determined by the ratio of the length of the drill pipe to the drill collar (or weighted drill pipe).

Step 2: Build the Vibration Equation

Combined with Fig. 2, based on vibration mechanics, a simplified model of the drill string system with n+3 degrees of freedom is described by a second-order differential equation, which is shown by the following formula (vibration equation):

where θ=[θ _r ,θ _dp1 ,…,θ _dpn ,θ _hdp ,θ _dc ] ^T ∈R ⁿ⁺³ represents the angular displacement of n+3 units, corresponding to the turntable, n unit drill pipes, and weighted drill pipes, respectively And the drill collar, the superscript of θ indicates the first derivative, and · indicates the second derivative, that is represents the angular velocity, represents the angular acceleration. T _r ∈ R is the input torque acting on the turntable, that is, the output torque of the motor, T _b ∈ R is the bottom bit-rock contact torque, and the coefficients of the two are S _r =[1,0,…,0] ^T ∈ R ⁿ⁺³ and S _b =[0,0,...,-1] ^T ∈ R ⁿ⁺³ . The coefficients J, K, C _d are the rotational inertia matrix, stiffness matrix and viscous damping matrix of n+3 elements of the drill string system, respectively, which are given by formulas (2)-(4):

J=diag(J _r ,J _dp1 ,…,J _dpn ,J _hdp ,J _dc )∈R ⁿ⁺³ (2)

C _d =diag(d _r ,d _dp1 ,...,d _dpn ,d _hdp ,d _dc )∈R ⁿ⁺³ (3)

where J _r , d _r are the moment of inertia and damping of the top turntable, J _dpi , k _dpi , d _dpi , i∈{1,2,…,n} are the moment of inertia of the i-th drill pipe unit, the corresponding The torsional stiffness of the drill pipe and the damping caused by the drilling fluid, J _hdp , d _hdp , and k _hdp are the moment of inertia, torsional stiffness of the aggravated drill pipe and the damping caused by the drilling fluid, J _dc , d _dc , k _dc are the moment of inertia, torsional stiffness of the drill collar and the damping caused by the drilling fluid, respectively.

In this modeling method, considering that the internal torsional damping of drill pipe, weighted drill pipe and drill collar has little effect on drill string dynamics, it is ignored in the vibration equation (1). At the same time, the drill pipe is equally divided by n, that is, l _dpi =l _dp /n,i∈{1,2,...,n}, and it is assumed that the overall material properties of the drill string are the same, so the moment of inertia corresponding to the n drill pipe units and the viscous damping is the same. More, since the drill bit is directly connected to the drill collar and is driven by the drill collar, and compared with the drill collar, the volume and weight of the drill bit are very small, so it is reasonable to set the speed of the drill bit equal to the speed of the drill collar, that is,

Step 3-1: Construct the vibration equation.

With the help of state space techniques, state variables are selected m=2n+5 to reconstruct formula (1), and obtain the drill string system dynamics described by the state space equation, as shown in formula (5):

Where u(t), d(t) are the control input and the disturbance input, corresponding to Tr, _Tb , and the control input channel and the disturbance input channel are B _u =S _r , _{B d} =S _b , respectively. y(t) is the system output. In this modeling method, the most concerned variables are the rotational speed of the uphole rotary table and the rotational speed of the downhole drill bit, so y(t)=[x ₁ x _n+3 ] ^T , corresponding to [θ _r θ _b ] ^T . The matrices A, B _u , B _d , C can be described by the following series of formulas after appropriate derivation:

Step 3-2: Build a Linear Variable Parameter (LPV) Model

For the actual drill string system, its length is mainly composed of drill pipe length l _dp , weighted drill pipe length l _hdp and drill collar length l _dc , that is, l≈l _dp +l _hdp +l _dc . With the deepening of the drilling depth, the length of the drill pipe is continuously increased by continuously increasing the drill pipe, while the length of the weighted drill pipe and the drill collar is generally maintained at 100-200m. Therefore, in mid-deep drilling, the variation in the length of the drill pipe determines the variation in the length of the entire drill string. At the same time, the torsional stiffness, moment of inertia and viscous damping of drill pipe, weighted drill pipe and drill collar all depend on their lengths. With the help of material mechanics, we can get:

where α∈{dp1,…,dpn,hdp,dc}, ρ is the drill string material density, I _α is the polar moment of inertia, G is the shear modulus, For element viscous damping, D _{outer_α} and d _{outer_α} represent the corresponding material outer and inner diameters.

For fixed-length l _hdp and l _dc , the corresponding attributes are constant values. The moment of inertia and damping of the turntable are also constant. Therefore, observe the system matrix A, which depends on the drill pipe length l _dp . Combining formulas (2)-(4) and (5)-(6), the matrix A can be further simplified, and it can be found that is a constant matrix.

Therefore, Equation (5) can be described by a linear parameter varying (LPV) model, namely:

where B=[B _u B _d ], ω(t)=[u(t) d(t)] ^T , i∈{1,2,...,n}.

Step 4: Linear Fractional Representation of the LPV Model

Considering that the variation range of drill pipe length is l _dp ∈[l _{dp_min} ,l _{dp_max} ], normalize it to get:

and

With the help of linear fractional transformation (LFT) technology, l _dp can be decomposed into a deterministic part and an uncertain part, and connected by the upper linear fractional transformation, as shown in formula (9):

Among them, a ₁₁ , a ₁₂ , a ₂₁ , and a ₂₂ represent that a ₁₁ =0, a ₁₂ =1, respectively, At the same time, based on It can also be described in LFT form:

Combined with Equation (9), the LPV model (6) can be described by the LFT form:

and

Δp=Δq,Δ=diag(δI _{(2×n+2)×(2×n+2)} ),|δ|≤1 (12)

where p and q are the input and output of the uncertain block, respectively. Each constant value matrix is described by the following series of formulas:

O _i×j represents a 0 matrix with i row and j column.

At this point, the drill string system starts from transfer function of Represents the upper linear fractional transformation.

Step 5: Introduce the bit-rock interaction model to complete the rotary motion model of the drill string system

Steps 1-5 complete the establishment of the multi-degree-of-freedom-variable parameter model of the drill string. Finally, we introduce a disturbance model, namely d(t), to describe the bit-rock interaction. Bit-rock contact is the most violent process in the whole drilling process, and is the most important external disturbance to the drill string system. Appropriate and reasonable d(t) is very important for simulating the rotary motion of the actual drill string system.

The Karnopp model is used to describe the rock action of the bit, as follows:

where D _v >0, the static friction torque T ₂ =W _ob R _b μ _sb , R _b > 0 is the drill bit radius, W _ob > 0 is the weight on bit (WoB), is a very small preset positive constant, which can be a number in the range of [10 ^-6 , 10 ^-5 ], such as 10 ^-6 , θ _b is the drill speed, μ _b is the dry friction coefficient, which is described by the formula (12) :

where μ _sb , μ _cb ∈(0,1) represent static friction and Coulomb friction coefficient, 0<γ _b <1, v _f >0. T1 is the contact moment _:

The drill-rock interaction model (13) is combined with the drill string LFT model (10) to obtain a complete rotary motion model of the drill string system. The model structure is shown in FIG. 4 .

The meanings of the parameters involved in steps 1-5 can be seen in Table 1.

Table 1 Parameters involved in the modeling method

Finally, consider that the length of the drill string system varies from 3000m to 6000m, which corresponds to -1≤δ≤1; consider that the drill pipe contains 20 units, that is, n=20. Combined with the drill string LFT model (10), the amplitude response and step response of the drill string system can be obtained in turn, as shown in Figures 5 and 6, respectively. Observing Fig. 5, it can be seen that under the same δ value, the drill string system has large amplitudes at multiple resonance frequencies; under different drill string lengths, there are certain differences in the amplitude responses of the system. Observing Fig. 6, it can be seen that under different drill string lengths, the drill string system has great differences in overshoot, adjustment time and steady-state value. Therefore, different drill string lengths affect drill string dynamics to a large extent.

Next, combined with model (10) and model (13), given the WOB of 60KN and the motor output torque of 8500Nm, the response of the drill string system under the bit-rock action and drilling fluid damping was simulated, and at t=30s, the WOB was set to Increase to 80KN. The simulation results are shown in Figure 7. Observing the image, it can be seen that under 60KN WOB, there is torsional vibration at the drill bit of the drill string system, and the longer the drill string is, the lower the corresponding bit rotation speed; at t=30s, due to the increase of WOB, δ=0 The drill string system corresponding to δ=1 has changed from torsional vibration to stick-slip vibration.

The embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the inspiration of the present invention, without departing from the scope of protection of the present invention and the claims, many forms can be made, which all belong to the protection of the present invention.

Claims (10)

1. a drill string system rotary motion modeling method with multiple degrees of freedom-variable parameters, is characterized in that, comprises the following steps: Step 1: Establishment of drill string system: For the actual drill string system, according to the drill string system constituent units, establish the corresponding multi-degree-of-freedom spring-damping system; Step 2: Constructing a vibration equation: Based on vibration mechanics, describe the multi-degree-of-freedom spring-damping system in the form of a second-order differential equation, and obtain the corresponding mass, damping, and stiffness matrix expressions; Step 3: Realize the state space of the vibration equation and build the LPV model: Select the rotational angular velocity of each unit of the spring-damper system and the rotational angle difference between the units as state variables, and derive the state space equation realization of the vibration equation; according to the time-varying length of the drill string properties, calculate the relationship between the moment of inertia, stiffness and damping of each unit of the drill string and the length of the drill string, and based on the state space equation, obtain the LPV model with the dependence of drill string length; Step 4: Linear fractional representation of the LPV model: normalize the drill string length, and separate the LPV model into a linear time-invariant part and an uncertain block part through the linear fractional transformation method. The above linear fractional transformation formal description; Step 5: Introduce the bit-rock interaction model to complete the rotary motion model of the drill string system: Introduce the Karnopp friction model to describe the bit-rock interaction, and combine the LFT model of the drill string to complete the dynamic modeling of the rotary motion of the drill string system. 2. The method for modeling the rotary motion of a drill string system with multiple degrees of freedom-variable parameters according to claim 1, wherein in step 1, the establishment of the drill string system comprises the following substeps: (1) Extract the motor and turntable of the uphole part of the drill string system, the multi-segment drill pipe, weighted drill pipe, drill collar and drilling fluid in the middle part of the well, and the drill bit and rock of the downhole part. Simplified model of drill string system described by spring-damper; (2) Set the total degree of freedom of the simplified model of the drill string system to n+3, in which the drill pipe contains n degrees of freedom, and the turntable, the weighted drill pipe and the drill collar each contain 1 degree of freedom; the value of n is determined by the length of the drill pipe and the drill collar. The ratio of drill pipe to drill collar length is determined. 3. The rotary motion modeling method of drill string system with multiple degrees of freedom-variable parameters according to claim 2, is characterized in that, in step 2, constructing vibration equation comprises the following substeps: (1) Based on vibration mechanics, a simplified model of the drill string system with n+3 degrees of freedom is described by a second-order differential equation. The differential unit is the rotation speed corresponding to the turntable, drill pipe, weighted drill pipe and drill collar; the system input is the action The output torque of the motor on the turntable and the bit-rock contact torque from the bottom; (2) Calculate the expressions of the moment of inertia matrix, stiffness matrix and viscous damping matrix of the n+3 elements of the drill string system in the vibration equation; Among them, in the drill string system, the drill pipe is divided into n equal parts, and the overall material properties of the drill string are the same, and the drill bit speed Equal to drill collar speed 4. the rotary motion modeling method of drill string system with multiple degrees of freedom-variable parameters according to claim 1, is characterized in that, in step 2: Based on vibration mechanics, a simplified model of drill string system with n+3 degrees of freedom is described using 2nd order differential equations. The simplified model of drill string system is shown by the following vibration equation: where θ=[θ _r ,θ _dp1 ,…,θ _dpn ,θ _hdp ,θ _dc ] ^T ∈R ⁿ⁺³ represents the angular displacement of n+3 units, corresponding to the turntable, n unit drill pipes, and weighted drill pipes, respectively and drill collar; the superscript of θ represents the first derivative, and the second derivative, that is represents the angular velocity, represents the angular acceleration; T _r ∈ R is the input torque acting on the turntable, that is, the output torque of the motor, T _b ∈ R is the contact torque from the bottom bit-rock, and the coefficients of the two are S _r = [1,0, …,0] ^T ∈ R ⁿ⁺³ and S _b =[0,0,…,-1] ^T ∈ R ^{n +3} ; the coefficients J, K, C _d are the rotations of n+3 units of the drill string system, respectively Inertia matrix, stiffness matrix and viscous damping matrix, specifically: J=diag(J _r , J _dp1 ,...,J _dpn ,J _hdp ,J _dc )∈R ⁿ⁺³ ; C _d =diag(d _r ,d _dp1 ,...,d _dpn ,d _hdp ,d _dc )∈R ⁿ⁺³ ; Among them, J _r , d _r are the moment of inertia and damping of the top turntable, J _dpi , k _dpi , d _dpi , i∈{1,2,…,n} are the moment of inertia of the i-th drill pipe unit, the corresponding The torsional stiffness of the drill pipe and the damping caused by the drilling fluid, J _hdp , d _hdp , k _hdp are the moment of inertia, torsional stiffness of the aggravated drill pipe and the damping caused by the drilling fluid, J _dc , d _dc , k _dc are the moment of inertia, torsional stiffness of the drill collar and the damping caused by the drilling fluid, respectively; Among them, the internal torsional damping of drill pipe, weighted drill pipe and drill collar is 0 in the vibration equation; at the same time, the drill pipe is equally divided by n, that is, l _dpi =l _dp /n,i∈{1,2,…,n }, and the overall material properties of the drill string are the same, the moment of inertia and viscous damping corresponding to the n drill pipe units are the same, and the speed of the drill bit is equal to the speed of the drill collar, that is, 5. the rotary motion modeling method of drill string system with multi-degree-of-freedom-variable parameter according to claim 1, is characterized in that, in step 3, vibration equation state space is realized, and build LPV model comprises following substep: (1) Select the rotational angular velocity of each unit of the spring-damper system and the rotational angle difference between each component unit as state variables, and describe the vibration equation as a standard state space equation; select the rotational speed of the uphole turntable and the rotational speed of the downhole drill bit as the system output, and obtain the state matrix at the same time , the expression of input matrix and output matrix; (2) With the help of material mechanics, the torsional stiffness, moment of inertia and viscous damping of drill pipe, weighted drill pipe and drill collar are calculated to obtain the dependence of state matrix and drill pipe length, and the LPV model is constructed; among them, The variation in the length of the entire drill string is determined by the variation in the length of the drill pipe. 6. The rotary motion modeling method of drill string system with multi-degree-of-freedom-variable parameter according to claim 4, is characterized in that, obtaining vibration equation state in step 3 specifically comprises: Selecting state variables to reconstruct the vibration equation to obtain a state space equation; Among them, the selected state becomes: The obtained dynamic equation of the drill string system is: Among them, u(t), d(t) are the control input and disturbance input, corresponding to Tr, _Tb , and the control input channel and the disturbance input channel are respectively B _u =S _r , _{B d} =S _b ; y(t ) is the system output, y(t)=[x ₁ x _n+3 ] ^T corresponds to [θ _r θ _b ] ^T ; matrices A, B _u , B _d and C are described by the following series of formulas: O represents a 0 matrix. 7. the rotary motion modeling method of drill string system with multi-degree-of-freedom-variable parameter according to claim 4, is characterized in that, obtaining vibration equation state in step 3 specifically comprises: In a drill string system: where α∈{dp1,…,dpn,hdp,dc}, ρ is the drill string material density, I _α is the polar moment of inertia, G is the shear modulus, is the element viscous damping, D _{outer_α} and d _{outer_α} represent the corresponding material outer diameter and inner diameter; The LPV model is: where B=[B _u B _d ], ω(t)=[u(t) d(t)] ^T , i∈{1,2,...,n}. 8. The rotary motion modeling method of drill string system with multiple degrees of freedom-variable parameters according to claim 1, is characterized in that, in step 4, the linear fractional representation of LPV model comprises following substep: (1) Normalize the variation range of the set drill pipe length; decompose the drill pipe length into deterministic and uncertain parts by LFT, and connect them through the upper linear fractional transformation; (2) The LFT form of the drill pipe length is brought into the state matrix, and the LPV system described by the LTI model part and the uncertain block part is obtained, and the system transfer function is obtained by connecting the upper linear fractional transformation. 9. The method for modeling rotary motion of drill string system with multiple degrees of freedom-variable parameters according to claim 7, wherein step 4 specifically comprises: Normalize the drill pipe length variation range l _dp ∈ [l _{dp_min} ,l _{dp_max} ]: and is a fixed constant; and The l _dpi is decomposed into a deterministic part and an uncertain part by LFT, and connected by the upper linear fractional transformation: Among them, a ₁₁ , a ₁₂ , a ₂₁ , and a ₂₂ represent that a ₁₁ =0, a ₁₂ =1, respectively, The LFT form of the LPV model is obtained according to the above formula for l _dp : and p=Δq,Δ=diag(δI _{(2×n+2)×(2×n+2)} ),|δ|≤1; where p, q are the input and output of the uncertain block, respectively; each constant value matrix is described by the following series of formulas: O _i×j represents a 0 matrix with i row and j column. At this point, the drill string system starts from transfer function of Represents the upper linear fractional transformation. 10. The method for modeling the rotary motion of a drill string system with multiple degrees of freedom-variable parameters according to claim 1, wherein in step 5, a drill bit-rock action model is introduced, and the completed drill string system rotary motion model comprises the following: Substeps: The Karnopp model is used to describe the bit-rock interaction as follows: Among them, D _v >0, the static friction torque T ₂ =W _ob R _b μ _sb , R _b >0 is the radius of the drill bit, W _ob > 0 is the torque on the drill bit, Indicates the preset normal value, θ _b is the drill speed, and μ _b is the dry friction coefficient: where μ _sb , μ _cb ∈(0,1) represent static friction and Coulomb friction coefficient, 0 < γ _b <1, v _f >0; T1 is the contact moment _: The Karnopp model is combined with the LFT form of the LPV model to obtain a complete rotary motion model of the drill string system.