CN116066123A - Automatic tracking control method for shield tunneling track based on model predictive control - Google Patents

Automatic tracking control method for shield tunneling track based on model predictive control Download PDF

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CN116066123A
CN116066123A CN202211095173.7A CN202211095173A CN116066123A CN 116066123 A CN116066123 A CN 116066123A CN 202211095173 A CN202211095173 A CN 202211095173A CN 116066123 A CN116066123 A CN 116066123A
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shield
pose
control
tunneling
model
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袁大军
王旭阳
金大龙
陆平
金慧
韩冰宇
罗维平
王小宇
段怿欣
耿哲
郭海鹏
杨引尊
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Beijing Jiaotong University
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21D—SHAFTS; TUNNELS; GALLERIES; LARGE UNDERGROUND CHAMBERS
    • E21D9/00—Tunnels or galleries, with or without linings; Methods or apparatus for making thereof; Layout of tunnels or galleries
    • E21D9/06—Making by using a driving shield, i.e. advanced by pushing means bearing against the already placed lining
    • E21D9/093—Control of the driving shield, e.g. of the hydraulic advancing cylinders
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

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  • Mining & Mineral Resources (AREA)
  • Environmental & Geological Engineering (AREA)
  • Life Sciences & Earth Sciences (AREA)
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  • Geochemistry & Mineralogy (AREA)
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Abstract

The invention provides a shield tunneling track automatic tracking control method based on model predictive control, which adopts a state space model based on a shield tunneling dynamics model as a predictive model, uses the thrust of an oil cylinder of a shield propulsion system as a control quantity, and uses the predictive model to predict the pose state of a shield machine at each sampling moment in a prediction time domain at the current sampling moment; on the basis of predicting the shield pose state, calculating an optimal control sequence which minimizes the error between the predicted shield pose state and the reference shield pose state based on the tunnel design axis, wherein the optimal control sequence needs to meet all control conditions; finally, the first component of the sequence is used as the optimal thrust control quantity of the input oil cylinder at the current moment to be applied to the shield propulsion system; the method overcomes the defects of the existing pose control technology, can realize accurate intelligent control of the shield pose, and ensures accurate automatic tracking of the tunneling track of the shield machine on the tunnel design axis in the tunneling process.

Description

Automatic tracking control method for shield tunneling track based on model predictive control
Technical Field
The invention belongs to the field of shield construction, and particularly relates to an automatic tracking control method for a shield tunneling track based on model predictive control.
Background
The consistency of the actual forming axis of the tunnel and the design axis of the tunnel is the key point of the construction quality control of the shield tunnel. For shield tunneling engineering, shield tunneling pose (position and pose) is difficult to accurately control due to factors such as difference constraint of surrounding rock, unreasonable operation parameter setting and the like in the shield tunneling process, so that a shield tunneling track inevitably deviates from a tunnel design axis. The improper control of the shield pose easily causes the problems of segment staggering, breakage, leakage and the like of the segment due to the extrusion of the shield tail, and meanwhile, the quality of the formed tunnel axis can be greatly reduced due to the fact that the shield tunneling track deviates from the tunnel design axis, so that potential safety hazards are buried for future operation of the tunnel. Therefore, in the shield tunneling process, the position and the posture of the shield are accurately controlled, and the precise tracking of the tunnel design axis of the shield tunneling track is ensured to have important significance for guaranteeing the safety and the efficiency of tunnel construction.
At present, most of shield pose control is feedback control. The shield driver or the automatic control system adjusts the parameters of the shield propulsion system by means of manual experience or a certain control strategy according to the shield pose deviation measured by the shield guiding system, adjusts the shield pose, and realizes the tracking of the shield tunneling track to the tunnel design axis, but the pose control method based on feedback control has great hysteresis due to large inertia caused by the self mass of the shield machine and the time lag of the control of the hydraulic system, so that the snakelike motion of the shield is very easy to cause. In the shield tunneling process, if the shield is biased or unbiased, the predicted shield pose deviation can be lifted and controlled, and the mode of the predicted control on the shield pose can effectively eliminate the control hysteresis and improve the control precision of the shield pose.
Disclosure of Invention
The invention aims to provide a shield tunneling track automatic tracking control method based on model predictive control, which is used for solving the problems.
The technical scheme of the invention is as follows:
the automatic tracking control method for the shield tunneling track based on model predictive control is characterized by comprising the following steps of:
s1: constructing a shield coordinate system, and determining a shield pose transformation matrix according to shield pose information;
s2: constructing a complete multi-rigid-body dynamic model of the shield propulsion system according to the structural characteristics of the shield propulsion system;
s3: constructing constraint conditions in the shield tunneling process;
s4: constructing a state space model of the shield propulsion system;
s5: constructing an equivalent load estimation model in the shield tunneling process;
s6: constructing a shield tunneling pose prediction model according to the load estimation model and the state space model;
s7: constructing an objective function according to the shield tunneling track control target;
s8: and carrying out optimization solution according to the shield tunneling pose prediction model and combining constraint conditions and an objective function to generate an optimal thrust control sequence, and inputting the optimal thrust control sequence into a shield propulsion system to control the shield pose so as to realize accurate and automatic tracking of the shield tunneling track on the tunnel design axis.
Preferably, S1 specifically includes:
the construction of the shield coordinate system comprises the following steps: a dynamic coordinate system { B-xByBzB } fixedly connected to the shield machine and a basic coordinate system { A-xyz } fixedly connected to the segment ring;
a. constructing a dynamic coordinate system { B-xByBzB }, wherein the coordinate system is fixedly connected to a middle shield backboard of the shield machine, an origin B is a distribution center of a spherical hinge in front of an oil cylinder, an xB axis points to a shield tunneling direction along a central axis of the shield machine in an initial state, a zB axis is vertical to the central axis of the shield machine and vertically upwards, and a yB axis direction is determined according to a right-hand principle;
b. and constructing a base coordinate system { A-xyz }, wherein the coordinate system is fixedly connected to a segment ring providing a counterforce for the thrust cylinder, an origin A is a distribution center of a spherical hinge behind the cylinder, and in an initial state, coordinate axes of the base coordinate system { A-xyz } and the movable coordinate system { B-xByBzB } are correspondingly parallel.
The shield pose information is formed by a pose vector q= [ x y z psi theta phi ]] T A representation, wherein (x, y, z) represents the position coordinates of the origin of a dynamic coordinate system { B-xByBzB } consolidated on the shield machine; (ψ, θ, φ) represents three attitude angles of the shield machine: roll angle, pitch angle and yaw angle;
the shield pose transformation matrix is determined according to the shield pose information, and the calculation formula of the shield pose transformation matrix is as follows:
Figure BDA0003832853770000031
wherein ,
Figure BDA0003832853770000032
and />
Figure BDA0003832853770000033
Respectively representing the attitude matrix and the position vector of the shield, wherein the calculation formula is as follows
Figure BDA0003832853770000034
Figure BDA0003832853770000035
Wherein c represents a cosine function cos; s represents a sine function sin.
Preferably, S2 specifically includes:
determining structural parameters of the shield propulsion system according to engineering data: rear spherical hinge coordinate B of thrust cylinder i The method comprises the steps of carrying out a first treatment on the surface of the Shield constitution heart position vector r G The method comprises the steps of carrying out a first treatment on the surface of the Shield mass M G The method comprises the steps of carrying out a first treatment on the surface of the Shield body inertial tensor A I M The method comprises the steps of carrying out a first treatment on the surface of the Propulsion force vector F of shield propulsion system d ＝[F 1 F 2 …F n ] T N is the total number of the propulsion cylinders;
establishing a complete multi-rigid-body dynamic model of the shield propulsion system based on a kane method:
Figure BDA0003832853770000036
wherein ,FT Equivalent load applied in the shield tunneling process is realized; other coefficient calculation formulas are:
Figure BDA0003832853770000041
wherein ,E3 Is a third-order identity matrix; A u i i=1, 2,3, … … n for the i-th thrust cylinder unit direction vector; g= [0 0-9.8] T Is a gravity acceleration vector; omega is the shield angular velocity; A u i ，T 0 ，
Figure BDA0003832853770000042
and ω is calculated as:
Figure BDA0003832853770000043
Figure BDA0003832853770000044
Figure BDA0003832853770000045
Figure BDA0003832853770000046
preferably, the constraint conditions in the shield tunneling process in S3 include: kinematic and kinetic constraints; the two constraints specifically comprise the maximum stroke constraint of the thrust cylinder; constraint of shield tail clearance; the elongation speed of the oil cylinder is restrained; and (5) oil cylinder thrust constraint.
Preferably, the state space model of the shield propulsion system in S4 is:
Figure BDA0003832853770000047
Y＝X 1 ＝HX (11)
wherein ,X1 ＝q＝[x y z ψ θ φ] T Represents the pose vector of the shield tunneling machine,
Figure BDA0003832853770000048
representing the pose change rate of the shield propulsion system; />
Figure BDA0003832853770000049
Representing a state vector of the shield propulsion system; u=f d ＝[F 1 F 2 …F n ] T Representing the control quantity of the shield propulsion system; c= [ E 6 0 6×6 ]Representing an output matrix of the shield propulsion system; y= [ x Y z ψθphi ]] T The output pose vector of the shield propulsion system is represented; wherein h is 1(X) and h2 The calculation formula of (X) is: />
h 1 (X)＝M -1 (F T -CX 2 -G) (12)
h 2 (X)＝M -1 J T (13)。
Preferably, the equivalent load estimation model in the shield tunneling process in S5 includes:
and (3) carrying out backward difference on the formula (4), wherein the shield equivalent load estimation can be carried out according to the following formula:
Figure BDA0003832853770000051
wherein ,FT (k) The shield equivalent load at the moment k is represented; u (k) represents a shield propulsion system control input at time k; m (k), C (k), G (k) and J (k) respectively represent values of M, C, G and J parameters in the formula (5) at the moment k; x (k) represents a state vector of the shield propulsion system at the moment k; x (k-1) represents a state vector of the shield propulsion system at the moment k-1; t (T) s Sampling interval time for a shield propulsion system; d (D) 1 ＝[0 6×6 E 6 ]，D 2 ＝[E 6 0 6×6 ]。
Preferably, the shield tunneling pose prediction model in S6 includes:
(1) One-step prediction
The shield equivalent load estimation at the moment k is as follows:
Figure BDA0003832853770000052
the system state vector at the time k predicting future time k+1 is:
X p (k+1|k)＝X(k)+T s f(X(k),U(k),F T (k)) (16)
(2) Two-step prediction
The shield equivalent load at time k+1 is estimated as:
Figure BDA0003832853770000053
the system state vector at the time k predicting future time k+2 is:
X p (k+2k)＝X p (k+1k)+T s f(X p (k+1k),U(k+1),F T (k+1)) (18)
(3)N p step prediction
k+N p The shield equivalent load estimation at time-1 is:
Figure BDA0003832853770000061
wherein Np To predict the time domain;
predicting future k+N at time k p The time system state vector is:
Figure BDA0003832853770000062
from equation (11), k+1 to k+N can be predicted at time k p The output quantity of the shield pose state is as follows:
Figure BDA0003832853770000063
preferably, constructing the objective function in S7 includes:
Figure BDA0003832853770000064
wherein ,Yr The method comprises the steps of representing target output pose reference quantity determined by a shield tunneling target track, namely a tunnel design axis; delta U is the thrust control increment of the shield propulsion system; n (N) c To control the time domain; q and R are weight matrices.
Preferably, S8 specifically includes:
according to the shield pose output measured value and the prediction model of k moment acquired by the shield guiding system, predicting N in the prediction time domain p Outputting the position and the posture of the shield in the shield;
by solving for satisfying an objective functionAnd various constraint optimization problems, solving and obtaining a control time domain N c And (3) a series of shield thrust control input quantity sequences in the control sequence at the moment is used as the actual control quantity of the controlled object, and the process is repeated when the next moment k+1 is reached, namely, the optimization problem of each strip constraint is completed in a rolling way, so that the continuous control of the shield pose is realized, and the accurate tracking of the shield tunneling track to the tunnel design axis is completed.
The invention has the beneficial effects that:
(1) The invention provides a model predictive control-based shield tunneling track automatic tracking control method, which is an optimization control algorithm based on a model, rolling implementation and combined feedback correction, and has feedback correction and rolling optimization links in the control process, so that the method has the advantages of good control effect, strong robustness and low requirement on model accuracy.
(2) The method is predictive control, can perform intervention control in advance when the shield tunneling track is not biased, can effectively eliminate the hysteresis of shield pose and track tracking control, avoids the occurrence of snaking of the shield, and ensures accurate and automatic tracking of the shield tunneling track on the tunnel design axis.
Drawings
FIG. 1 is a flow chart of a method for automatically tracking and controlling shield tunneling track based on model predictive control according to an embodiment of the invention;
fig. 2 is an effect schematic diagram of a method for automatically tracking and controlling a shield tunneling track based on model predictive control according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples so that those skilled in the art may better understand the present invention and practice it, and the embodiments of the present invention are not limited thereto.
Example 1
As shown in fig. 1, the method for automatically tracking and controlling the shield tunneling track based on model predictive control comprises the following steps:
step one: and establishing a shield coordinate system, and determining a shield pose transformation matrix according to the shield pose information.
Step two: establishing a complete multi-rigid-body dynamic model of the shield propulsion system according to the structural characteristics of the shield propulsion system;
step three: obtaining constraint conditions in the shield tunneling process according to the characteristics of the shield tunneling mechanism;
step four: according to the nonlinear dynamics model, a state space model of the shield propulsion system is obtained;
step five: establishing an equivalent load estimation model in the shield tunneling process;
step six: establishing a shield tunneling pose prediction model according to the load estimation model and the state space model;
step seven: constructing an objective function according to the shield tunneling track control target;
step eight: and carrying out optimization solution according to the shield tunneling pose prediction model and combining constraint conditions and an objective function to generate an optimal thrust control sequence, and inputting the optimal thrust control sequence into a shield propulsion system to control the shield pose so as to realize accurate and automatic tracking of the shield tunneling track on the tunnel design axis.
The method for establishing the shield coordinate system in the first step comprises the steps of:
establishing two coordinate systems according to the shield propulsion mechanism, including: a dynamic coordinate system { B } fixedly connected to the shield machine and a basic coordinate system { A } fixedly connected to the segment ring;
constructing a dynamic coordinate system { B-xByBzB }, wherein the coordinate system is fixedly connected to a shield back plate in the shield machine, an origin B is a distribution center of a spherical hinge in front of an oil cylinder, an xB axis points to a shield tunneling direction along a central axis of the shield machine in an initial state, a zB axis is vertical to the central axis of the shield machine and vertically upwards, and a yB axis direction is determined according to a right-hand principle;
and constructing a base coordinate system { A-xyz }, wherein the coordinate system is fixedly connected to a segment ring providing a counterforce for the thrust cylinder, an origin A is a distribution center of a spherical hinge behind the cylinder, and in an initial state, coordinate axes of the base coordinate system { A-xyz } and the movable coordinate system { B-xByBzB } are correspondingly parallel.
The shield pose information can be obtained by a pose vector q= [ x y z ψ theta phi ]] T Description.
Wherein (x, y, z) represents the position coordinates of the origin of a dynamic coordinate system { B } fixed on the shield machine; (ψ, θ, φ) represents three attitude angles of the shield machine: roll angle, pitch angle and yaw angle.
The shield pose transformation matrix is determined according to the shield pose information, and the calculation formula of the shield pose transformation matrix is as follows:
Figure BDA0003832853770000081
wherein ,
Figure BDA0003832853770000091
and />
Figure BDA0003832853770000092
Respectively representing the attitude matrix and the position vector of the shield, wherein the calculation formula is as follows
Figure BDA0003832853770000093
Figure BDA0003832853770000094
Wherein c represents a cosine function cos; s represents a sine function sin.
In the second step, a complete multi-rigid-body dynamic model of the shield propulsion system is established according to the structural characteristics of the shield propulsion system, and the method comprises the following steps:
determining structural parameters of the shield propulsion system according to engineering data: rear spherical hinge coordinate B of thrust cylinder i The method comprises the steps of carrying out a first treatment on the surface of the Shield constitution heart position vector r G The method comprises the steps of carrying out a first treatment on the surface of the Shield mass M G The method comprises the steps of carrying out a first treatment on the surface of the Shield body inertial tensor A I M The method comprises the steps of carrying out a first treatment on the surface of the Propulsion force vector F of shield propulsion system d ＝[F 1 F 2 …F n ] T N is propulsion oilTotal number of cylinders.
And establishing a complete multi-rigid-body dynamic model of the shield propulsion system based on a kane method, wherein the multi-rigid-body dynamic model is as follows:
Figure BDA0003832853770000095
/>
wherein ,FT Equivalent load applied in the shield tunneling process is realized; other coefficient calculation formulas are:
Figure BDA0003832853770000096
wherein ,E3 Is a third-order identity matrix; A u i i=1, 2,3, … … n for the i-th thrust cylinder unit direction vector; g= [0 0-9.8] T Is a gravity acceleration vector; omega is the shield angular velocity; A u i ，T 0 ，
Figure BDA0003832853770000097
and ω is calculated as:
Figure BDA0003832853770000098
Figure BDA0003832853770000099
Figure BDA0003832853770000101
Figure BDA0003832853770000102
in the third step, constraint conditions in the shield tunneling process are obtained according to the characteristics of the shield tunneling mechanism, and the method comprises the following steps: kinematic and kinetic constraints; the method comprises the steps of pushing the maximum stroke constraint of the oil cylinder; constraint of shield tail clearance; the elongation speed of the oil cylinder is restrained; and (5) oil cylinder thrust constraint. The following are listed below
(1) Maximum stroke constraint of thrust cylinder
In the tunneling process of the shield, the shield machine overcomes the slow extension of an external load cylinder under the action of the thrust of a thrust system cylinder, so that the forward propulsion of the shield is realized. However, the length of the piston rod of the oil cylinder is a fixed value, so that the maximum stroke of the length of the shield thrust oil cylinder is a basic constraint condition. The shield propulsion mechanism is required to meet the maximum travel constraint condition of each propulsion cylinder, and is expressed as follows in a mathematical form:
l min ≤l i ≤l max (32)
wherein ,lmin ,l max The minimum stroke and the maximum stroke of the propulsion cylinder are respectively; l (L) i For the travel of the ith thrust cylinder, the following equation can be solved:
Figure BDA0003832853770000103
wherein L is the length of the cylinder body of the propulsion cylinder.
(2) Shield tail clearance constraint
In the tunneling process of the shield, the position and the posture of the shield are adjusted by adjusting the pressure of the oil cylinders in different subareas, so that the oil cylinders in different subareas generate travel differences, and further the functions of left and right deflection, up and down deflection and the like of the shield machine are realized. In the process, the gap between the outer wall of the duct piece and the inner wall of the shield tail, namely the shield tail gap, can be correspondingly changed. When the gap between the shield tail is too small, the shield brush is easy to squeeze and deform, so that the duct piece and the shield tail are in hard contact, and even the duct piece in the shield tail can be damaged, and the duct piece is damaged. When the gap between the shield tail is too large, the contact pressure between the shield tail brush and the duct piece is reduced, and the seal of the shield tail is possibly invalid, so that water, soil and slurry flow into the tunnel. Therefore, the shield tail clearance in the shield tunneling process is required to be within a reasonable range, and the following formula is shown:
Δ TVmin ≤Δ TV ≤Δ TVmax (34)
wherein ,ΔTVmin ,Δ TVmax Respectively the minimum and maximum shield tail gaps delta for ensuring the normal propulsion of the shield TV For the shield tail clearance, the following can be solved:
Figure BDA0003832853770000111
wherein ,xso Is the abscissa of any point S on the shield tail inner shell under the dynamic coordinate system { B }; eta is the point S and the dynamic coordinate system x B An included angle of the shaft; r is R r Is the inner radius of the shield tail; d (D) S Is the outer diameter of the duct piece; c represents a cosine function cos; s represents a sine function sin.
(4) Oil cylinder elongation speed constraint
In the shield tunneling process, because of the limitation of the characteristics of the hydraulic system and the limitation of construction factors, the elongation speed of the oil cylinder generally does not exceed a limit value, and the elongation speed can be represented by the following formula:
Figure BDA0003832853770000112
wherein ,vmax The maximum extension speed of the oil cylinder is set;
Figure BDA0003832853770000113
the extension speed of the ith oil cylinder.
(5) Thrust constraint of oil cylinder
Due to the self-characteristics of the hydraulic system of the thrust cylinder and the safety requirements, the thrust force of the cylinder generally does not exceed a certain limit value.
0≤F i ≤F max (37)
wherein ,Fmax Is a thrust threshold value of the hydraulic cylinder; f (F) i The thrust of the ith oil cylinder.
And step four, obtaining a state space model of the shield propulsion system according to the nonlinear dynamics model, wherein the state space model is as follows:
Figure BDA0003832853770000114
Y＝X 1 ＝HX (39)
wherein ,X1 ＝q＝[x y z ψ θ φ] T Represents the pose vector of the shield tunneling machine,
Figure BDA0003832853770000115
representing the pose change rate of the system; />
Figure BDA0003832853770000116
Representing a state vector of the shield propulsion system; u=f d ＝[F 1 F 2 …F n ] T Representing a control amount of the system; c= [ E 6 0 6×6 ]Representing an output matrix of the system; y= [ x Y z ψθphi ]] T Representing the output pose vector of the system. h is a 1(X) and h2 The calculation formula of (X) is: />
h 1 (X)＝M -1 (F T -CX 2 -G) (40)
h 2 (X)＝M -1 J T (41)
Establishing an equivalent load estimation model in the shield tunneling process, wherein the equivalent load estimation model comprises the following steps of
And (3) carrying out backward difference on the formula (4), wherein the shield equivalent load estimation can be carried out according to the following formula:
Figure BDA0003832853770000121
wherein ,FT (k) The shield equivalent load at the moment k is represented; u (k) represents a shield propulsion system control input at time k; m (k), C (k), G (k) and J (k) respectively represent values of M, C, G and J parameters in the formula (5) at the moment k; x (k) represents a state vector of the system at time k; x (k-1) represents a state vector of the system at time k-1; t (T) s Sampling interval time for the system; d (D) 1 ＝[0 6×6 E 6 ]，D 2 ＝[E 6 0 6×6 ]
In the sixth step, a shield tunneling pose prediction model is established according to the load estimation model and the state space model, which comprises
(1) One-step prediction
The shield equivalent load at the moment k is estimated as
Figure BDA0003832853770000122
Predicting the future k+1 time at the k time as the system state vector
X p (k+1|k)＝X(k)+T s f(X(k),U(k),F T (k)) (44)
(2) Two-step prediction
The shield equivalent load at time k+1 is estimated to be
Figure BDA0003832853770000123
Predicting the future k+2 time at the k time as the system state vector
X p (k+2|k)＝X p (k+1|k)+T s f(X p (k+1|k),U(k+1),F T (k+1)) (46)
(3)N p Step prediction
k+N p The shield equivalent load at the moment-1 is estimated to be
Figure BDA0003832853770000131
wherein Np To predict the time domain.
Predicting future k+N at time k p The moment system state vector is
Figure BDA0003832853770000132
According to equation (11), k+ can be predicted at time k1 to k+N p The output quantity of the shield pose state is as follows:
Figure BDA0003832853770000133
in the seventh step, an objective function is constructed according to the control objective of the shield tunneling track, which comprises the following steps:
Figure BDA0003832853770000134
wherein ,Yr The method comprises the steps of representing target output pose reference quantity determined by a shield tunneling target track, namely a tunnel design axis; delta U is the thrust control increment of the shield propulsion system; n (N) c To control the time domain; q and R are weight matrices.
And step eight, according to the shield tunneling pose prediction model, carrying out optimization solution by combining constraint conditions and an objective function to generate an optimal thrust control sequence, and inputting the optimal thrust control sequence into a shield propulsion system to control the shield pose so as to realize accurate and automatic tracking of a shield tunneling track on a tunnel design axis.
As shown in FIG. 2, the relation diagram between the shield control track and the target track by adopting the shield tunneling track automatic tracking control method of the invention is shown.
According to the shield pose output measured value and the prediction model of k moment acquired by the shield guiding system, predicting N in the prediction time domain p And outputting the position and the pose of the shield in the shield system.
Solving the optimization problem meeting the objective function and various constraints to obtain a control time domain N c And a series of shield thrust control input quantity sequences in the control system, and inputting the first element in the time control sequence as the actual control quantity of the controlled object into the shield propulsion system.
When the next moment k+1 comes, the process is repeated, namely the rolling is completed, namely the optimization problem with constraint is solved, so that the continuous control of the shield pose is realized, and the precise tracking of the shield tunneling track to the tunnel design axis is completed. Therefore, the shield control track adopting the shield tunneling track automatic tracking control method is close to the target track in height.
Those of ordinary skill in the art will appreciate that: the drawings are schematic representations of one embodiment only and the flow in the drawings is not necessarily required to practice the invention.

Claims (9)

1. The automatic tracking control method for the shield tunneling track based on model predictive control is characterized by comprising the following steps of:
s1: constructing a shield coordinate system, and determining a shield pose transformation matrix according to shield pose information;
s2: constructing a complete multi-rigid-body dynamic model of the shield propulsion system according to the structural characteristics of the shield propulsion system;
s3: constructing constraint conditions in the shield tunneling process;
s4: constructing a state space model of the shield propulsion system;
s5: constructing an equivalent load estimation model in the shield tunneling process;
s6: constructing a shield tunneling pose prediction model according to the load estimation model and the state space model;
s7: constructing an objective function according to the shield tunneling track control target;
s8: and carrying out optimization solution according to the shield tunneling pose prediction model and combining constraint conditions and an objective function to generate an optimal thrust control sequence, and inputting the optimal thrust control sequence into a shield propulsion system to control the shield pose so as to realize accurate and automatic tracking of the shield tunneling track on the tunnel design axis.
2. The automatic tracking control method for the shield tunneling track based on model predictive control according to claim 1, wherein S1 specifically comprises:
the construction of the shield coordinate system comprises the following steps: a dynamic coordinate system { B-xByBzB } fixedly connected to the shield machine and a basic coordinate system { A-xyz } fixedly connected to the segment ring;
a. constructing a dynamic coordinate system { B-xByBzB }, wherein the coordinate system is fixedly connected to a middle shield backboard of the shield machine, an origin B is a distribution center of a spherical hinge in front of an oil cylinder, an xB axis points to a shield tunneling direction along a central axis of the shield machine in an initial state, a zB axis is vertical to the central axis of the shield machine and vertically upwards, and a yB axis direction is determined according to a right-hand principle;
b. and constructing a base coordinate system { A-xyz }, wherein the coordinate system is fixedly connected to a segment ring providing a counterforce for the thrust cylinder, an origin A is a distribution center of a spherical hinge behind the cylinder, and in an initial state, coordinate axes of the base coordinate system { A-xyz } and the movable coordinate system { B-xByBzB } are correspondingly parallel.
The shield pose information is formed by a pose vector q= [ x y z psi theta phi ]] T A representation, wherein (x, y, z) represents the position coordinates of the origin of a dynamic coordinate system { B-xByBzB } consolidated on the shield machine; (ψ, θ, φ) represents three attitude angles of the shield machine: roll angle, pitch angle and yaw angle;
the shield pose transformation matrix is determined according to the shield pose information, and the calculation formula of the shield pose transformation matrix is as follows:
Figure FDA0003832853760000021
wherein ,
Figure FDA0003832853760000022
and />
Figure FDA0003832853760000023
Respectively representing the attitude matrix and the position vector of the shield, wherein the calculation formula is as follows
Figure FDA0003832853760000024
Figure FDA0003832853760000025
Wherein c represents a cosine function cos; s represents a sine function sin.
3. The method for automatically tracking and controlling the shield tunneling track based on model predictive control according to claim 1, wherein S2 specifically comprises:
determining structural parameters of the shield propulsion system according to engineering data: rear spherical hinge coordinate B of thrust cylinder i The method comprises the steps of carrying out a first treatment on the surface of the Shield constitution heart position vector r G The method comprises the steps of carrying out a first treatment on the surface of the Shield mass M G The method comprises the steps of carrying out a first treatment on the surface of the Shield body inertial tensor A I M The method comprises the steps of carrying out a first treatment on the surface of the Propulsion force vector F of shield propulsion system d ＝[F 1 F 2 …F n ] T N is the total number of the propulsion cylinders;
establishing a complete multi-rigid-body dynamic model of the shield propulsion system based on a kane method:
Figure FDA0003832853760000026
wherein ,FT Equivalent load applied in the shield tunneling process is realized; other coefficient calculation formulas are:
Figure FDA0003832853760000031
wherein ,E3 Is a third-order identity matrix; A u i i=1, 2,3, … … n for the i-th thrust cylinder unit direction vector; g= [0 0-9.8] T Is a gravity acceleration vector; omega is the shield angular velocity; A u i ，T 0 ，
Figure FDA0003832853760000032
and ω is calculated as:
Figure FDA0003832853760000033
Figure FDA0003832853760000034
Figure FDA0003832853760000035
Figure FDA0003832853760000036
4. the automatic tracking control method for shield tunneling tracks based on model predictive control according to claim 1, wherein the constraint conditions in the shield tunneling process in S3 include: kinematic and kinetic constraints; the two constraints specifically comprise the maximum stroke constraint of the thrust cylinder; constraint of shield tail clearance; the elongation speed of the oil cylinder is restrained; and (5) oil cylinder thrust constraint.
5. The automatic tracking control method for shield tunneling tracks based on model predictive control according to claim 1, wherein the state space model of the shield propulsion system in S4 is:
Figure FDA0003832853760000037
Y＝X 1 ＝HX (11)
wherein ,X1 ＝q＝[x y z ψ θ φ] T Represents the pose vector of the shield tunneling machine,
Figure FDA0003832853760000041
representing the pose change rate of the shield propulsion system; />
Figure FDA0003832853760000042
Representing a state vector of the shield propulsion system; u=f d ＝[F 1 F 2 …F n ] T Representing shield propulsion systemA control amount of the system; c= [ E 6 0 6×6 ]Representing an output matrix of the shield propulsion system; y= [ x Y z ψθphi ]] T The output pose vector of the shield propulsion system is represented; wherein h is 1(X) and h2 The calculation formula of (X) is:
h 1 (X)＝M -1 (F T -CX 2 -G) (12)
h 2 (X)＝M -1 J T (13)。
6. the automatic tracking control method for shield tunneling tracks based on model predictive control according to claim 1, wherein the equivalent load estimation model in the shield tunneling process in S5 comprises:
and (3) carrying out backward difference on the formula (4), wherein the shield equivalent load estimation can be carried out according to the following formula:
Figure FDA0003832853760000043
wherein ,FT (k) The shield equivalent load at the moment k is represented; u (k) represents a shield propulsion system control input at time k; m (k), C (k), G (k) and J (k) respectively represent values of M, C, G and J parameters in the formula (5) at the moment k; x (k) represents a state vector of the shield propulsion system at the moment k; x (k-1) represents a state vector of the shield propulsion system at the moment k-1; t (T) s Sampling interval time for a shield propulsion system; d (D) 1 ＝[0 6×6 E 6 ]，D 2 ＝[E 6 0 6×6 ]。
7. The automatic tracking control method for shield tunneling tracks based on model predictive control according to claim 1, wherein the model for predicting the shield tunneling pose in S6 comprises:
(1) One-step prediction
The shield equivalent load estimation at the moment k is as follows:
Figure FDA0003832853760000044
the system state vector at the time k predicting future time k+1 is:
X p (k+1|k)＝X(k)+T s f(X(k),U(k),F T (k)) (16)
(2) Two-step prediction
The shield equivalent load at time k+1 is estimated as:
Figure FDA0003832853760000051
the system state vector at the time k predicting future time k+2 is:
X p (k+2|k)＝X p (k+1|k)+T s f(X p (k+1|k),U(k+1),F T (k+1)) (18)
(3)N p step prediction
k+N p The shield equivalent load estimation at time-1 is:
Figure FDA0003832853760000052
wherein Np To predict the time domain;
predicting future k+N at time k p The time system state vector is:
Figure FDA0003832853760000053
from equation (11), k+1 to k+N can be predicted at time k p The output quantity of the shield pose state is as follows:
Figure FDA0003832853760000054
8. the automatic tracking control method for shield tunneling trajectories based on model predictive control according to claim 1, wherein the constructing of the objective function in S7 comprises:
Figure FDA0003832853760000055
wherein ,Yr The method comprises the steps of representing target output pose reference quantity determined by a shield tunneling target track, namely a tunnel design axis; delta U is the thrust control increment of the shield propulsion system; n (N) c To control the time domain; q and R are weight matrices.
9. The automatic tracking control method for the shield tunneling track based on model predictive control according to claim 1, wherein S8 specifically comprises:
according to the shield pose output measured value and the prediction model of k moment acquired by the shield guiding system, predicting N in the prediction time domain p Outputting the position and the posture of the shield in the shield;
solving the optimization problem meeting the objective function and various constraints to obtain a control time domain N c And (3) a series of shield thrust control input quantity sequences in the control sequence at the moment is used as the actual control quantity of the controlled object, and the process is repeated when the next moment k+1 is reached, namely, the optimization problem of each strip constraint is completed in a rolling way, so that the continuous control of the shield pose is realized, and the accurate tracking of the shield tunneling track to the tunnel design axis is completed.
CN202211095173.7A 2022-09-05 2022-09-05 Automatic tracking control method for shield tunneling track based on model predictive control Pending CN116066123A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117034664A (en) * 2023-10-10 2023-11-10 北京城建设计发展集团股份有限公司 Hydraulic cylinder stroke calculation method and device for shield tunneling machine propulsion system
CN117236072A (en) * 2023-11-10 2023-12-15 北京城建设计发展集团股份有限公司 Method and system for resolving pose of shield target based on tunnel design axis
CN117552796A (en) * 2024-01-11 2024-02-13 北京城建设计发展集团股份有限公司 Method, device, equipment and medium for controlling telescoping speed of oil cylinder of shield propulsion system

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117034664A (en) * 2023-10-10 2023-11-10 北京城建设计发展集团股份有限公司 Hydraulic cylinder stroke calculation method and device for shield tunneling machine propulsion system
CN117236072A (en) * 2023-11-10 2023-12-15 北京城建设计发展集团股份有限公司 Method and system for resolving pose of shield target based on tunnel design axis
CN117236072B (en) * 2023-11-10 2024-03-08 北京城建设计发展集团股份有限公司 Method and system for resolving pose of shield target based on tunnel design axis
CN117552796A (en) * 2024-01-11 2024-02-13 北京城建设计发展集团股份有限公司 Method, device, equipment and medium for controlling telescoping speed of oil cylinder of shield propulsion system
CN117552796B (en) * 2024-01-11 2024-04-16 北京城建设计发展集团股份有限公司 Method, device, equipment and medium for controlling telescoping speed of oil cylinder of shield propulsion system

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