CN110067550A - It is a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method - Google Patents
It is a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method Download PDFInfo
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- E—FIXED CONSTRUCTIONS
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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
Technical field
The present invention relates to a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, belongs to drill string
Control field.
Background technique
China is resources and energy consumption big country, and occupancy volume per person is in that the world is lowly horizontal, and resource exploration is exploited work and carved
Do not allow to delay.As the continuous exploration of shallow-layer energy resource is exploited, shallow-layer easy production of resources in China's is gradually decreased, and develops deep ground resource
Have become the important directions of Science in Future in China development in science and technology.According to mineral resources exploration depth 500m or more, oil-gas mining depth
4500m or more defines deep drilling, and China's deep petroleum resource and natural gas resource account for residual petroleum resource and remaining respectively
40% of natural gas resource and 60% or so.Therefore, the exploitation and utilization for increasing the deep resource energy continue the realization energy
Supply is of great significance.
During deep ground resources exploration, be continuous thousands of rice even tens of kms, drill string of DRILL-STRING SYSTEM length is equivalent
Torsion stiffness constantly reduces, and DRILL-STRING SYSTEM dynamics gradually changes.Meanwhile entire DRILL-STRING SYSTEM be faced with it is complicated and changeable
Geological environment, damped including the effect of shaft bottom Bit-rock, drill string-borehole wall CONTACT WITH FRICTION, drilling fluid etc..In DRILL-STRING SYSTEM
Under portion's factor and ground environment bring external factor collective effect, entire DRILL-STRING SYSTEM is difficult to keep constant on gyratory directions
Rotation speed, cause to have a certain difference on well with underground revolving speed, system occur twisting vibration even stick slip vibration.Drill string
The violent torsion of system, stick-slip can accelerate drill string fatigue, the aging for leading to drilling tool and failure, reduce drilling efficiency, increase
Drilling cost, it is serious when even damage drill string, seriously threaten drilling safety.
In recent years, many scholars and related drilling company are devoted to be understood using various methods and techniques, grasp brill
The underground moving situation of column system controls underground state.Although the available downhole data of measurement while drilling device, in deep
Under complicated, severe ground environment, the real-time and accuracy of measurement while drilling device are difficult to ensure, and have high cost；
Measurement based on data on well simultaneously, analysis are difficult to Accurate Prediction downhole conditions again.Therefore, DRILL-STRING SYSTEM rotary motion is carried out to build
Mould is a kind of effective means.On the one hand, DRILL-STRING SYSTEM rotary motion model is established, can predict that underground becomes in real time based on model
Amount, while can help to understand drill string torsion, stick-slip phenomenon, its mechanism of production is disclosed, provides preanalysis for drilling process；
On the other hand, DRILL-STRING SYSTEM rotary motion model can instruct the design of controller on well, realize the consistent of underground revolving speed,
Guarantee efficient drilling.
Summary of the invention
The invention proposes a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, for reality
The DRILL-STRING SYSTEM of the elongated degree in border is simplified, and the simplification system described by multiple degrees of freedom spring-damper is obtained；Based on this,
It is expressed based on vibration equation, and is translated into state space equation；In combination with drill string length time-varying characteristics, derive
DRILL-STRING SYSTEM variable parameter model, obtaining Linear Fractional by linear fraction transformation technology indicates；Finally using Karnopp friction mould
Pattern intends Bit-rock effect, in conjunction with drill string model, completes the modeling to DRILL-STRING SYSTEM rotary motion.
DRILL-STRING SYSTEM rotary motion modeling method of the invention, mainly comprises the steps of:
Step 1: DRILL-STRING SYSTEM is abstract and simplifies: being directed to actual DRILL-STRING SYSTEM, according to DRILL-STRING SYSTEM component units, establishes
Corresponding multiple degrees of freedom spring-damper system；
Step 2: building vibration equation: vibration mechanics is based on, by multiple degrees of freedom spring-damper system with the 2 rank differential equations
Form description, and derive corresponding quality, damping, stiffness matrix expression formula；
Step 3: model state space is realized, and constructs linear variation parameter (LPV) model: it is each to choose spring-damper system
It is state variable that differential seat angle is rotated between unit angular velocity of rotation and each unit, derives that the state space equation of vibration equation is real
It is existing；According to drill string length time-varying property, calculate drill string each unit rotary inertia, rigidity and institute be dampened and the pass of drill string length
It is formula, and is based on state space equation, derives the LPV model relied on drill string length；
The Linear Fractional of step 4:LPV model indicates: expression is normalized in drill string length, and is become by Linear Fractional
(LFT) technology is changed, is linearly invariant part and uncertain block portion point, the above linear fraction transformation form by LPV model separation
Description；
Step 5: introducing Bit-rock action model, complete DRILL-STRING SYSTEM rotary motion model: introducing Karnopp friction
Model describes Bit-rock effect, in conjunction with drill string LFT model, completes the Dynamic Modeling of DRILL-STRING SYSTEM rotary motion.
The technical effects of the invention are that: practical DRILL-STRING SYSTEM is described using many-degrees of freedom system and state space equation,
Meet drill string multiple-unit combined characteristic, improves drill string modeling accuracy；Meanwhile the drill string length and LFT technology of time-varying are introduced, benefit
It is analyzed in the rotary motion to entire drilling process DRILL-STRING SYSTEM, improves the scope of application of model.Finally, introduce
Karnopp model is suitble to describe Bit-rock effect, for simulating practical DRILL-STRING SYSTEM rotary motion there is preferably simulation to make
With.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is the flow chart with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method of the invention；
Fig. 2 is DRILL-STRING SYSTEM structure chart of the invention；
Fig. 3 is multiple degrees of freedom simplified model of the invention；
Fig. 4 is the LFT form of rotary motion model of the invention；
Fig. 5 is the frequency response of rotary motion model of the invention；
Fig. 6 is the step response of rotary motion model of the invention；
Fig. 7 is DRILL-STRING SYSTEM rotating simulation-torsion and stick slip vibration of the invention.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
It is of the invention with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method with reference to Fig. 1, Fig. 1
Flow chart, the present invention specifically include the following steps:
Step 1: the foundation of DRILL-STRING SYSTEM
Practical DRILL-STRING SYSTEM is as shown in Fig. 2, it constitutes complexity, comprising various machinery, electric power, driving unit, in order to capture
Its dominant dynamic characteristic, the present invention is according to the chief component of DRILL-STRING SYSTEM, the i.e. motor, turntable of well-surface part, in well
The drill bit and rock of partial multistage drilling rod, heavy weight drill pipe, drill collar and drilling fluid and underground part.Based on these component parts,
It establishes DRILL-STRING SYSTEM and simplifies knot ,-multiple degrees of freedom spring-damper system is specific as shown in Figure 3.Set the total freedom degree of the system as
N+3, wherein drilling rod includes n freedom degree, and turntable, heavy weight drill pipe and drill collar respectively include 1 freedom degree.Wherein n value can pass through brill
Bar and the ratio of drill collar (or heavy weight drill pipe) length are determined.
Step 2: building vibration equation
In conjunction with Fig. 2, it is based on vibration mechanics, simplifies mould using the DRILL-STRING SYSTEM of 2 n+3 freedom degrees of rank differential equation
Type, by shown in following formula (vibration equation):
Wherein θ=[θr,θdp1,…,θdpn,θhdp,θdc]T∈Rn+3The angular displacement for representing the unit of n+3 respectively corresponds and turns
The subscript of disk, n unit drilling rod, heavy weight drill pipe and drill collar, θ indicates first derivative, indicates second dervative, i.e.,Table
Show angular speed,Indicate angular acceleration.Tr∈ R is the input torque acted on turntable, i.e. the output torque of motor, Tb∈ R is
Torque is contacted from bottom Bit-rock, the coefficient of the two is respectively Sr=[1,0 ..., 0]T∈Rn+3And Sb=[0,0 ... ,-
1]T∈Rn+3.Coefficient J, K, CdThe respectively moment of inertia matrix of n+3 unit of DRILL-STRING SYSTEM, stiffness matrix and viscous damping square
Battle array, is provided by formula (2)-(4):
J=diag (Jr,Jdp1,…,Jdpn,Jhdp,Jdc)∈Rn+3 (2)
Cd=diag (dr,ddp1,…,ddpn,dhdp,ddc)∈Rn+3 (3)
Wherein Jr,drFor top rotatable disc rotary inertia and dampened, Jdpi,kdpi,ddpi, i ∈ 1,2 ..., n } be respectively
The rotary inertia of i-th of drilling rod unit, corresponding drilling rod torsion stiffness and the damping of suffered drilling fluid bring, Jhdp,dhdp,khdp
The respectively rotary inertia of heavy weight drill pipe, torsion stiffness and the damping of suffered drilling fluid bring, Jdc,ddc,kdcRespectively drill collar
Rotary inertia, torsion stiffness and the damping of suffered drilling fluid bring.
In this modeling method, it is contemplated that the internal torsion of drilling rod, heavy weight drill pipe and drill collar is damped to drilling string dynamics
Influence is smaller, therefore is omitted in vibration equation (1).Meanwhile drilling rod is by n equal part, i.e. ldpi=ldp/n,i∈{1,2,…,
N }, and assume that drill string integral material attribute is identical, therefore rotary inertia corresponding to n drilling rod unit and suffered viscous damping are equal
It is identical.More, since drill bit is connected directly in drill collar, and movement is driven by drill collar, in addition compared with drill collar, bit body
Product, weight all very littles, therefore reasonable setting drill speed is equal to drill collar revolving speed, i.e.,
Step 3-1: building vibration equation.
By state space techniques, state variable is chosenM=2n+5 comes reconstruction formula (1),
The DRILL-STRING SYSTEM dynamics described with state space equation is obtained, as shown in formula (5):
Wherein u (t), d (t) are control input and disturbance input, correspond to Tr,Tb, and control input channel and disturbance input
Channel is respectively Bu=Sr,Bd=Sb.Y (t) is system output, in this modeling method, the variable paid close attention to the most i.e. well top rotary table
Revolving speed and downhole drill bit revolving speed, therefore y (t)=[x1 xn+3]T, correspond to [θr θb]T.Matrix A, Bu,Bd, C pushes away by appropriate
It leads, can be described by following Formula Series:
Step 3-2: building linear variation parameter (LPV) model
For practical DRILL-STRING SYSTEM, length composition is mainly run of steel ldp, heavy weight drill pipe length lhdpAnd drill collar length
ldc, i.e. l ≈ ldp+lhdp+ldc.It with the intensification of drilling depth, is constantly increasing drilling rod and run of steel is constantly lengthened, and add
The length for being redrilled bar and drill collar is typically maintained in 100~200m.Therefore, in medium and deep probing, the length of drilling rod, which changes, to be determined
The variation of entire drill string length.Meanwhile drilling rod, the torsion stiffness of heavy weight drill pipe and drill collar, rotary inertia and suffered viscous
Damping all relies on the length of itself.It is available by the mechanics of materials:
Wherein α ∈ { dp1 ..., dpn, hdp, dc }, ρ are drill string density of material, IαFor polar moment of inertia, G is modulus of shearing,For unit viscous damping, Douter_αAnd douter_αIndicate corresponding material outer diameter and inner diameter.
For the l of regular lengthhdpAnd ldc, corresponding attribute is constant value.The rotary inertia of turntable and institute are dampened
For constant value.Therefore, observing system matrix A depends on run of steel ldp.In conjunction with formula (2)-(4) and (5)-(6), Ke Yijin
One step abbreviation matrix A, it can be found thatFor constant value
Matrix.
Therefore, formula (5) can be described by linear variation parameter's (linear parameter varying, LPV) model, it may be assumed that
Wherein B=[Bu Bd], ω (t)=[u (t) d (t)]T,i∈{1,2,…,n}。
The Linear Fractional of step 4:LPV model indicates
Consideration run of steel variation range is ldp∈[ldp_min,ldp_max], expression is normalized and is obtained:
And
It, can be by l by linear fraction transformation (linear fractional transformation, LFT) technologydpPoint
Solution is certainty part and uncertain part, and is connected by upper linear fraction transformation, as shown in formula (9):
Wherein, a11、a12、a21、a22Respectively indicate a11=0, a12=1,Meanwhile it being based onIt can also be described as LFT form:
In conjunction with formula (9), LPV model (6) can be described by LFT form:
With
Δ p=Δ q, Δ=diag (δ I(2×n+2)×(2×n+2)),|δ|≤1 (12)
Wherein p, q are respectively outputting and inputting for uncertain block.Each constant value matrix is described by a series of following formula:
Oi×jIndicate 0 matrix of i row j column.
At this point, DRILL-STRING SYSTEM fromTransmission function It indicates
Upper linear fraction transformation.
Step 5: introducing Bit-rock action model, complete DRILL-STRING SYSTEM rotary motion model
Step 1-5 completes the foundation of drill string multiple degrees of freedom-variable parameter model, finally, we introduce Disturbance Model, i.e. d
(t) it is acted on to describe Bit-rock.Bit-rock contact is process most violent in entire drilling process, is DRILL-STRING SYSTEM institute
The most important external disturbance received, suitable, reasonable d (t) are extremely important for simulating practical DRILL-STRING SYSTEM rotary motion.
The effect of the drill bit rock is described using Karnopp model, is shown below:
Wherein Dv> 0, static friction torque T2=WobRbμsb, Rb> 0 is drill bit radius, Wob> 0 is torque on drill bit
(weight on bit, WoB),For very small preset positive value constant, it can use [10-6, 10-5] number in range, such as 10-6, θb
Indicate drill speed, μbIt is dry friction coefficient, is described by formula (12):
Wherein μsb,μcb∈ (0,1) indicates static friction and static friction coefficient, 0 < γb< 1, vf> 0.T1For contact force
Square:
The drill bit-rock action model (13) is combined together with drill string LFT model (10), obtains complete drill string system
System rotary motion model, shown in model structure Fig. 4.
The meaning of involved parameter in step 1-5 can be shown in Table 1.
Parameter involved in one modeling method of table
Finally, considering that DRILL-STRING SYSTEM length variation range is 3000m-6000m, -1≤δ≤1 is corresponded to；Consider drilling rod packet
Containing 20 units, i.e. n=20.In conjunction with drill string LFT model (10), it can successively obtain DRILL-STRING SYSTEM amplitude response and step is rung
It answers, respectively as shown in Figures 5 and 6.Fig. 5 is observed it is found that DRILL-STRING SYSTEM has larger at multiple resonant frequencies under same δ value
Amplitude；Under different drill string lengths, the amplitude response of system is had a certain difference.Fig. 6 is observed it is found that in different brills
Under column length, DRILL-STRING SYSTEM overshoot, regulating time and in terms of there is larger difference.Therefore, different brill
Column length largely affects drilling string dynamics.
Then, binding model (10) and model (13) give bit pressure 60KN, motor output torque 8500Nm, emulate drill string
Bit pressure is increased to 80KN in Bit-rock effect and the response under drilling fluid damping, and in t=30s by system.Emulation knot
Fruit is as shown in Figure 7.Image is observed it is found that under 60KN bit pressure, occurs twisting vibration, and the length of drill string at DRILL-STRING SYSTEM drill bit
Degree is longer, and corresponding drill speed is lower；In t=30s, due to the increase of bit pressure, the corresponding DRILL-STRING SYSTEM in δ=0 and δ=1 is
Through becoming stick slip vibration from twisting vibration.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (10)
1. a kind of with multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, which is characterized in that including following step
It is rapid:
Step 1: the foundation of DRILL-STRING SYSTEM: being established corresponding more for actual DRILL-STRING SYSTEM according to DRILL-STRING SYSTEM component units
Freedom degree spring-damper system；
Step 2: building vibration equation: vibration mechanics is based on, by the multiple degrees of freedom spring-damper system with the 2 rank differential equations
Form description, and obtain corresponding quality, damping, stiffness matrix expression formula；
Step 3: vibration equation state space realization, and construct LPV model: choose spring-damper system each unit rotation angle speed
Rotation differential seat angle is state variable between degree and each unit, derives that the state space equation of vibration equation is realized；It is long according to drill string
Time-varying property is spent, calculates the rotary inertia of drill string each unit, rigidity and the institute relational expression dampened with drill string length, and based on shape
State space equation obtains the LPV model relied on drill string length；
The Linear Fractional of step 4:LPV model indicates: expression is normalized in drill string length, and passes through linear fraction transformation side
LPV model separation is linearly invariant part and uncertain block portion point, the above linear fraction transformation form description by method；
Step 5: introducing Bit-rock action model, complete DRILL-STRING SYSTEM rotary motion model: introducing Karnopp friction model
Bit-rock effect is described, in conjunction with drill string LFT model, completes the Dynamic Modeling of DRILL-STRING SYSTEM rotary motion.
2. according to claim 1 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, in step 1, the foundation of DRILL-STRING SYSTEM includes following sub-step:
(1) motor and turntable for extracting the well-surface part of DRILL-STRING SYSTEM, in well the multistage drilling rod, heavy weight drill pipe, drill collar of part and
The drill bit and rock of drilling fluid and underground part, the component units based on extraction are established with the description of multiple degrees of freedom spring-damper
DRILL-STRING SYSTEM simplified model；
(2) the setting total freedom degree of DRILL-STRING SYSTEM simplified model is n+3, and wherein drilling rod includes n freedom degree, turntable, heavy weight drill pipe
It respectively include 1 freedom degree with drill collar；N value is carried out true by the ratio or drilling rod of drilling rod and drill collar length and the ratio of drill collar length
It is fixed.
3. according to claim 2 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, in step 2, building vibration equation includes following sub-step:
(1) it is based on vibration mechanics, uses the DRILL-STRING SYSTEM simplified model of 2 n+3 freedom degrees of rank differential equation, differentiation element
For rotation speed corresponding to turntable, drilling rod, heavy weight drill pipe and drill collar；System input is the output of the motor acted on turntable
Torque contacts torque with from bottom Bit-rock；
(2) moment of inertia matrix, stiffness matrix and viscous damping square of n+3 unit of DRILL-STRING SYSTEM in vibration equation are calculated
The expression formula of battle array；
Wherein, in DRILL-STRING SYSTEM, drilling rod is by n equal part, and drill string integral material attribute is identical, drill speedEqual to drill collar revolving speed
4. according to claim 1 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, in step 2:
Based on vibration mechanics, simplified using the DRILL-STRING SYSTEM simplified model DRILL-STRING SYSTEM of 2 n+3 freedom degrees of rank differential equation
Model is as shown in following vibration equations:
Wherein θ=[θr,θdp1,…,θdpn,θhdp,θdc]T∈Rn+3The angular displacement for representing the unit of n+3 respectively corresponds turntable, n
Unit drilling rod, heavy weight drill pipe and drill collar；The subscript of θ indicates first derivative, indicates second dervative, i.e.,Indicate angle speed
Degree,Indicate angular acceleration；Tr∈ R is the input torque acted on turntable, i.e. the output torque of motor, Tb∈ R is the bottom of from
Portion's Bit-rock contacts torque, and the coefficient of the two is respectively Sr=[1,0 ..., 0]T∈Rn+3And Sb=[0,0 ..., -1]T∈Rn +3；Coefficient J, K, CdThe respectively moment of inertia matrix of n+3 unit of DRILL-STRING SYSTEM, stiffness matrix and viscous damping matrix, specifically
Are as follows:
J=diag (Jr,Jdp1,…,Jdpn,Jhdp,Jdc)∈Rn+3；
Cd=diag (dr,ddp1,…,ddpn,dhdp,ddc)∈Rn+3；
Wherein, Jr、drFor top rotatable disc rotary inertia and dampened, Jdpi,kdpi,ddpi, i ∈ 1,2 ..., and n } it is respectively i-th
The rotary inertia of a drilling rod unit, corresponding drilling rod torsion stiffness and the damping of suffered drilling fluid bring, Jhdp,dhdp,khdpRespectively
For the damping of the rotary inertia of heavy weight drill pipe, torsion stiffness and suffered drilling fluid bring, Jdc,ddc,kdcThe respectively rotation of drill collar
Inertia, torsion stiffness and the damping of suffered drilling fluid bring；
Wherein, it is 0 in vibration equation that the internal torsion of drilling rod, heavy weight drill pipe and drill collar, which is damped,；Meanwhile drilling rod is by n equal part, i.e.,
ldpi=ldp/ n, i ∈ { 1,2 ..., n }, and drill string integral material attribute is identical, rotary inertia corresponding to n drilling rod unit and
Suffered viscous damping is all the same, and drill speed is equal to drill collar revolving speed, i.e.,
5. according to claim 1 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, in step 3, vibration equation state space realization, and constructing LPV model includes following sub-step:
(1) choosing rotation differential seat angle between spring-damper system each unit angular velocity of rotation and each component units is state variable, will
Vibration equation is described as standard state space equation；It chooses well top rotary table revolving speed and downhole drill bit revolving speed to export as system, together
When obtain the expression formula of state matrix, input matrix, output matrix；
(2) by the mechanics of materials, torsion stiffness, rotary inertia and the suffered viscous resistance of drilling rod, heavy weight drill pipe and drill collar are calculated
Buddhist nun constructs LPV model to obtain the dependence of state matrix and run of steel；Wherein, the variation of entire drill string length by
The length variation of drilling rod determines.
6. according to claim 4 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, vibration equation state is obtained in step 3 and is specifically included:
State variable is chosen to reconstruct the vibration equation, obtains state space equation；
Wherein, the state of selection becomes:
Obtained DRILL-STRING SYSTEM kinetics equation are as follows:
Wherein u (t), d (t) are control input and disturbance input, correspond to Tr,Tb, and control input channel and disturbance input channel
Respectively Bu=Sr,Bd=Sb；Y (t) is system output, y (t)=[x1 xn+3]TCorrespond to [θr θb]T；Matrix A, Bu、BdAnd C by
Formula Series describe below:
O table
Show 0 matrix.
7. according to claim 4 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, vibration equation state is obtained in step 3 and is specifically included:
In DRILL-STRING SYSTEM:
Wherein α ∈ { dp1 ..., dpn, hdp, dc }, ρ are drill string density of material, IαFor polar moment of inertia, G is modulus of shearing,For
Unit viscous damping, Douter_αAnd douter_αIndicate corresponding material outer diameter and inner diameter；
LPV model are as follows:
Wherein B=[Bu Bd], ω (t)=[u (t) d (t)]T,i∈{1,2,…,n}。
8. according to claim 1 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, in step 4, the Linear Fractional of LPV model indicates to include following sub-step:
(1) expression is normalized in the run of steel variation range of setting；By LFT by run of steel be decomposed into certainty and
Uncertain part, and connected by upper linear fraction transformation；
(2) it brings the LFT form of run of steel into state matrix, obtains dividing description by LTI model part and uncertain block portion
LPV system, and connect to obtain ssystem transfer function by upper linear fraction transformation.
9. according to claim 7 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, feature
It is, step 4 specifically includes:
It is l by run of steel variation rangedp∈[ldp_min,ldp_max] it is normalized:
It and is fixed constant；
And
By LFT by ldpiIt is decomposed into certainty part and uncertain part, and is connected by upper linear fraction transformation:
Wherein, a11、a12、a21、a22Respectively indicate a11=0, a12=1,
According to about ldpAbove-mentioned formula obtain the LFT form of LPV model:
With p=Δ q, Δ=diag (δ I(2×n+2)×(2×n+2)),|δ|≤1；
Wherein p, q are respectively outputting and inputting for uncertain block；Each constant value matrix is described by a series of following formula:
Oi×jIndicate 0 matrix of i row j column.
At this point, DRILL-STRING SYSTEM fromTransmission function Indicate online
Property fraction transformation.
10. according to claim 1 have multiple degrees of freedom-variable element DRILL-STRING SYSTEM rotary motion modeling method, spy
Sign is, in step 5, introduces Bit-rock action model, completing DRILL-STRING SYSTEM rotary motion model includes following sub-step:
Bit-rock effect is described using Karnopp model, is shown below:
Wherein, Dv> 0, static friction torque T2=WobRbμsb, Rb> 0 is drill bit radius, Wob> 0 is torque on drill bit,Indicate pre-
If regime values, θbIndicate drill speed, μbIt is dry friction coefficient:
Wherein μsb、μcb∈ (0,1) indicates static friction and static friction coefficient, 0 < γb< 1, vf> 0；
T1To contact torque:
Karnopp model and the LFT form of LPV model are combined together, complete DRILL-STRING SYSTEM rotary motion model is obtained.
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