A shield tunneling trajectory automatic tracking control method based on model predictive control

Abstract

This invention provides an automatic tracking control method for tunnel boring machine (TBM) trajectory based on model predictive control. It employs a state-space model based on the TBM tunneling dynamics model as the prediction model and uses the thrust of the TBM propulsion system cylinders as the control variable. At the current sampling moment, the prediction model is used to predict the TBM's pose state at each sampling moment within the prediction time domain. Based on the predicted TBM pose state, the optimal control sequence is calculated to minimize the error between the predicted TBM pose state and the reference TBM pose state based on the tunnel design axis. This optimal control sequence must satisfy all control conditions. Finally, the first component of the sequence is applied to the TBM propulsion system as the optimal input cylinder thrust control variable at the current moment. This method overcomes the shortcomings of existing pose control technologies, enabling precise and intelligent control of the TBM pose and ensuring accurate automatic tracking of the TBM's tunneling trajectory to the tunnel design axis during tunneling.

Description

Technical Field

[0001] This invention belongs to the field of tunnel boring machine (TBM) construction, specifically relating to an automatic tracking control method for TBM tunneling trajectory based on model predictive control. Background Technology

[0002] Maintaining consistency between the actual tunnel axis and the designed tunnel axis is crucial for quality control in shield tunnel construction. During shield tunneling, factors such as varying surrounding rock constraints and inappropriate operating parameters make precise control of the shield's position and attitude difficult, inevitably causing its trajectory to deviate from the designed tunnel axis. Improper shield posture control can easily lead to tail-end compression of tunnel segments, resulting in misalignment, damage, and leakage. Furthermore, deviations from the designed tunnel axis significantly reduce the quality of the formed tunnel axis, creating safety hazards for future operation. Therefore, precise control of the shield's posture during tunneling, ensuring its accurate tracking of the designed tunnel axis, is of paramount importance for ensuring both construction safety and efficiency.

[0003] Currently, most shield tunneling machine (TBM) posture control relies on feedback control. The TBM operator or the automatic control system adjusts the TBM propulsion system parameters based on the shield's posture deviation measured by the shield's guidance system, using manual experience or certain control strategies to adjust the shield's posture and achieve tracking of the tunnel's design axis. However, due to the large inertia caused by the TBM's own mass and the time lag in the hydraulic system control, feedback-based posture control methods suffer from significant lag, easily leading to serpentine shield movement. If the shield's posture deviation could be predicted and controlled before it deviates during tunneling, this predictive control approach could effectively eliminate control lag and improve the accuracy of shield posture control. Summary of the Invention

[0004] The present invention aims to provide an automatic tracking control method for shield tunneling trajectory based on model predictive control, in order to solve the above problems.

[0005] The technical solution of this invention is:

[0006] An automatic tracking control method for tunnel boring machine (TBM) trajectory based on model predictive control, characterized by the following steps:

[0007] S1: Construct the shield coordinate system and determine the shield pose transformation matrix based on the shield pose information;

[0008] S2: Construct a complete multi-rigid-body dynamics model of the tunnel boring machine propulsion system based on its structural characteristics;

[0009] S3: Constructing constraints during the tunnel boring machine (TBM) excavation process;

[0010] S4: Construct the state-space model of the tunnel boring machine propulsion system;

[0011] S5: Construct an equivalent load estimation model for the tunnel boring machine process;

[0012] S6: Construct a shield tunneling posture prediction model based on the load estimation model and the state space model;

[0013] S7: Construct the objective function based on the shield tunneling trajectory control target;

[0014] S8: Based on the shield tunneling posture prediction model, the optimal thrust control sequence is generated by combining the constraints and objective function. The optimal thrust control sequence is then input into the shield propulsion system to control the shield posture, thereby achieving precise automatic tracking of the shield tunneling trajectory to the tunnel design axis.

[0015] Preferably, S1 specifically includes:

[0016] The shield coordinate system is constructed by: a dynamic coordinate system {B-xByBzB} fixed on the shield machine and a base coordinate system {A-xyz} fixed on the segment ring;

[0017] a. Construct a dynamic coordinate system {B-xByBzB}, which is fixed to the back plate of the shield machine. The origin B is the distribution center of the front ball joint of the hydraulic cylinder. In the initial state, the xB axis points along the central axis of the shield machine in the direction of shield tunneling, the zB axis is perpendicular to the central axis of the shield machine and vertically upward, and the direction of the yB axis is determined according to the right-hand rule.

[0018] b. Construct a base coordinate system {A-xyz}, which is fixed to the segment ring that provides the reaction force to the propulsion cylinder. The origin A is the distribution center of the rear ball joint of the cylinder. In the initial state, the coordinate axes of the base coordinate system {A-xyz} and the moving coordinate system {B-xByBzB} are parallel to each other.

[0019] The shield tunneling machine's pose information is derived from the pose vector q = [xyz ψ θ φ]. T Let (x, y, z) represent the position coordinates of the origin of the moving coordinate system {B-xByBzB} fixed on the tunnel boring machine; (ψ, θ, φ) represent the three attitude angles of the tunnel boring machine: roll angle, pitch angle, and yaw angle.

[0020] The shield orientation transformation matrix is ​​determined based on the shield orientation information. The formula for calculating the shield orientation transformation matrix is ​​as follows:

[0021]

[0022] in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows:

[0023]

[0024]

[0025] Where c represents the cosine function cos; s represents the sine function sin.

[0026] Preferably, S2 specifically includes:

[0027] Based on engineering data, determine the structural parameters of the tunnel boring machine propulsion system: coordinate B of the ball joint behind the propulsion cylinder. i ; Shield body centroid position vector r G Shield mass M G Shield body inertial tensor A I M ; Shield propulsion system propulsion force vector F d =[F1 F2…F n ] T n is the total number of hydraulic cylinders;

[0028] A complete multi-rigid-body dynamics model of the tunnel boring machine propulsion system is established based on the Kane method:

[0029]

[0030] Among them, F T The equivalent load experienced during shield tunneling; the formulas for calculating other coefficients are:

[0031]

[0032] Where E3 is a third-order identity matrix; A u i Let g be the unit direction vector of the i-th propulsion cylinder, i = 1, 2, 3, ..., n; g = [0 0 -9.8] T ω is the gravitational acceleration vector; ω is the angular velocity of the shield. A u i T0 The formula for calculating ω is:

[0033]

[0034]

[0035]

[0036]

[0037] Preferably, the constraints in the shield tunneling process in S3 include: kinematic constraints and dynamic constraints; these two constraints specifically include: maximum stroke constraint of the propulsion cylinder; tail clearance constraint; cylinder extension speed constraint; and cylinder thrust constraint.

[0038] Preferably, the state-space model of the shield tunneling propulsion system in S4 is as follows:

[0039]

[0040] Y = X1 = HX (11)

[0041] Among them, X1=q=[xyz ψ θ φ] T This represents the pose vector of the tunnel boring machine. This represents the rate of change of the shield tunneling propulsion system's posture. U represents the state vector of the tunnel boring machine propulsion system; U = F d =[F1F2…F n ] T This represents the control quantity of the tunnel boring machine propulsion system; C = [E60] 6×6 [] represents the output matrix of the tunnel boring machine propulsion system; Y = [x yz ψ θ φ] T Let h1(X) represent the output pose vector of the tunnel boring machine propulsion system; where h1(X) and h2(X) are calculated using the following formulas:

[0042] h1(X)=M -1 (F T -CX2-G) (12)

[0043] h2(X)=M -1 J T (13).

[0044] Preferably, the equivalent load estimation model during the shield tunneling process in S5 includes:

[0045] By performing backward difference on formula (4), the equivalent load of the tunnel boring machine can be estimated by the following formula:

[0046]

[0047] Among them, F T (k) represents the equivalent load of the shield at time k; U(k) represents the control input of the shield propulsion system at time k; M(k), C(k), G(k) and J(k) represent the values ​​of parameters M, C, G and J in formula (5) at time k, respectively; X(k) represents the state vector of the shield propulsion system at time k; X(k-1) represents the state vector of the shield propulsion system at time k-1; T s D1 = [0] is the sampling interval time of the tunnel boring machine propulsion system; 6×6E6],D2=[E6 0 6×6 ].

[0048] Preferably, the shield tunneling pose prediction model in S6 includes:

[0049] (1) One-step prediction

[0050] The equivalent load of the tunnel boring machine at time k is estimated as follows:

[0051]

[0052] The predicted system state vector at time k+1 is:

[0053] X p (k+1|k)=X(k)+T s f(X(k),U(k),F T (k)) (16)

[0054] (2) Two-step prediction

[0055] The equivalent load of the tunnel boring machine at time k+1 is estimated as follows:

[0056]

[0057] The system state vector predicted at time k+2 is:

[0058] X p (k+2k)=X p (k+1k)+T s f(X p (k+1k),U(k+1),F T (k+1)) (18)

[0059] (3)N p Step prediction

[0060] k+N p The estimated equivalent load on the tunnel boring machine at time -1 is:

[0061]

[0062] Where N p For prediction in the time domain;

[0063] Predict the future k+N at time k. p The system state vector at time t is:

[0064]

[0065] According to formula (11), it is possible to predict k+1 to k+N at time k. p The shield tunneling machine's pose state output is:

[0066]

[0067] Preferably, constructing the objective function in S7 includes:

[0068]

[0069] Among them, Y r The output pose reference value is determined by the target trajectory of the tunnel boring machine, i.e., the tunnel design axis; ΔU is the thrust control increment of the tunnel boring machine propulsion system; N c To control the time domain; Q and R are weight matrices.

[0070] Preferably, S8 specifically includes:

[0071] Based on the shield posture output measurement value at time k obtained by the shield guidance system and the prediction model, the prediction in the prediction time domain N is made. p The shield's position and posture output is within the tunnel.

[0072] By solving the optimization problem that satisfies the objective function and various constraints, the control time-domain N is obtained. c A series of shield thrust control inputs are used, and the first element in the control series at that moment is taken as the actual control quantity of the controlled object. When the next moment k+1 arrives, the above process is repeated, that is, the constraint-laden optimization problem is completed in a rolling manner, so as to achieve continuous control of the shield posture and complete the accurate tracking of the shield tunneling trajectory to the tunnel design axis.

[0073] The beneficial effects of this invention are as follows:

[0074] (1) This invention provides an automatic tracking control method for shield tunneling trajectory based on model predictive control. It is an optimized control algorithm based on model, rolling implementation and combined with feedback correction. In the control process, it has feedback correction and rolling optimization links, thus having the advantages of good control effect, strong robustness and low requirements for model accuracy.

[0075] (2) The method of the present invention is a predictive control that can intervene and control the shield tunneling trajectory in advance when it is about to deviate. It can effectively eliminate the lag in shield posture and trajectory tracking control, avoid shield serpentine behavior, and ensure the shield tunneling trajectory accurately and automatically tracks the tunnel design axis. Attached Figure Description

[0076] Figure 1 A flowchart of an automatic tracking control method for shield tunneling trajectory based on model predictive control provided in an embodiment of the present invention;

[0077] Figure 2This is a schematic diagram illustrating the effect of an automatic tracking control method for shield tunneling trajectory based on model predictive control provided in an embodiment of the present invention. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. The embodiments of the present invention are not limited thereto.

[0079] Example 1

[0080] like Figure 1 As shown, an automatic tracking control method for tunnel boring machine (TBM) trajectory based on model predictive control includes the following steps:

[0081] Step 1: Establish the shield coordinate system and determine the shield pose transformation matrix based on the shield pose information.

[0082] Step 2: Establish a complete multi-rigid-body dynamics model of the tunnel boring machine (TBM) propulsion system based on its structural characteristics;

[0083] Step 3: Obtain the constraints during the tunnel boring machine (TBM) excavation process based on the characteristics of the TBM propulsion mechanism;

[0084] Step 4: Based on the nonlinear dynamic model, obtain the state-space model of the tunnel boring machine propulsion system;

[0085] Step 5: Establish an equivalent load estimation model for the tunnel boring process;

[0086] Step 6: Establish a shield tunneling pose prediction model based on the load estimation model and the state-space model;

[0087] Step 7: Construct the objective function based on the shield tunneling trajectory control target;

[0088] Step 8: Based on the shield tunneling posture prediction model, and in combination with the constraints and objective function, perform optimization to generate the optimal thrust control sequence. The optimal thrust control sequence is then input into the shield propulsion system to control the shield posture, thereby achieving precise and automatic tracking of the shield tunneling trajectory to the tunnel design axis.

[0089] Step one, establishing the shield coordinate system and determining the shield pose transformation matrix based on the shield pose information, includes:

[0090] Two coordinate systems are established based on the shield tunneling mechanism: a moving coordinate system {B} fixed on the shield machine and a base coordinate system {A} fixed on the segment ring.

[0091] Construct a dynamic coordinate system {B-xByBzB}, which is fixed to the shield back plate of the tunnel boring machine. The origin B is the distribution center of the front ball joint of the hydraulic cylinder. In the initial state, the xB axis points along the central axis of the tunnel boring machine in the direction of shield tunneling, the zB axis is perpendicular to the central axis of the tunnel boring machine and vertically upward, and the direction of the yB axis is determined according to the right-hand rule.

[0092] A base coordinate system {A-xyz} is constructed, which is fixed to the segment ring that provides the reaction force to the propulsion cylinder. The origin A is the distribution center of the rear ball joint of the cylinder. In the initial state, the coordinate axes of the base coordinate system {A-xyz} and the moving coordinate system {B-xByBzB} are parallel to each other.

[0093] The shield tunneling machine's pose information can be obtained from the pose vector q = [xyz ψ θ φ]. T describe.

[0094] Where (x,y,z) represents the position coordinates of the origin of the moving coordinate system {B} fixed on the tunnel boring machine; (ψ,θ,φ) represents the three attitude angles of the tunnel boring machine: roll angle, pitch angle and yaw angle.

[0095] The shield orientation transformation matrix is ​​determined based on the shield orientation information. The formula for calculating the shield orientation transformation matrix is ​​as follows:

[0096]

[0097] in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows:

[0098]

[0099]

[0100] Where c represents the cosine function cos; s represents the sine function sin.

[0101] Step two involves establishing a complete multi-rigid-body dynamics model of the tunnel boring machine (TBM) propulsion system based on its structural characteristics, including:

[0102] Based on engineering data, determine the structural parameters of the tunnel boring machine propulsion system: coordinate B of the ball joint behind the propulsion cylinder. i ; Shield body centroid position vector r G Shield mass M G Shield body inertial tensor A I M ; Shield propulsion system propulsion force vector F d =[F1 F2…F n ] T , where n is the total number of hydraulic cylinders.

[0103] A complete multi-rigid-body dynamics model of the tunnel boring machine propulsion system is established based on the Kane method, as follows:

[0104]

[0105] Among them, F T The equivalent load experienced during shield tunneling; the formulas for calculating other coefficients are:

[0106]

[0107] Where E3 is a third-order identity matrix; A u i Let g be the unit direction vector of the i-th propulsion cylinder, i = 1, 2, 3, ..., n; g = [0 0 -9.8] T ω is the gravitational acceleration vector; ω is the angular velocity of the shield. A u i T0 The formula for calculating ω is:

[0108]

[0109]

[0110]

[0111]

[0112] Step three involves obtaining the constraints during the tunnel boring machine (TBM) excavation process based on the characteristics of the TBM propulsion mechanism. These constraints include kinematic and dynamic constraints; specifically, the maximum stroke constraint of the propulsion cylinder; the tail clearance constraint; the cylinder extension speed constraint; and the cylinder thrust constraint. (See below.)

[0113] (1) Maximum stroke constraint of hydraulic cylinder

[0114] During tunneling, the tunnel boring machine (TBM) overcomes external loads by the thrust of its propulsion system's hydraulic cylinders, which slowly extend to advance the shield. However, since the piston rod length of the hydraulic cylinders is a fixed value, the maximum stroke of the TBM's propulsion cylinders is a fundamental constraint. The TBM propulsion mechanism must satisfy the maximum stroke constraint of each propulsion cylinder, which can be expressed mathematically as follows:

[0115] l min ≤l i ≤l max (32)

[0116] Among them, l min ,l max These represent the minimum and maximum strokes of the hydraulic cylinder, respectively; iThe stroke of the i-th hydraulic cylinder can be calculated using the following formula:

[0117]

[0118] Where L is the length of the propulsion cylinder body.

[0119] (2) Shield tail gap constraint

[0120] During tunneling, the shield's position is adjusted by regulating the pressure of different hydraulic cylinders in different zones, creating a stroke difference between them, thus enabling the shield to yaw left and right, and up and down. During this process, the gap between the outer wall of the tunnel segments and the inner wall of the shield tail, i.e., the tail gap, will change accordingly. When the tail gap is too small, the shield brush is prone to compression deformation, causing hard contact between the tunnel segments and the shield tail, potentially damaging the segments inside the shield tail and causing them to break. When the tail gap is too large, the contact pressure between the tail brush and the tunnel segments decreases, potentially causing the shield tail seal to fail, allowing water, soil, and grout to enter the tunnel. Therefore, the tail gap during shield tunneling must be within a reasonable range, as shown in the following formula:

[0121] Δ TVmin ≤Δ TV ≤Δ TVmax (34)

[0122] Where, Δ TVmin ,Δ TVmax These are the minimum and maximum tail clearances that ensure normal tunnel boring machine (TBM) advancement, Δ TV The shield tail clearance can be calculated using the following formula:

[0123]

[0124] Where, x so Let η be the x-coordinate of any point S on the inner shell of the shield tail in the moving coordinate system {B}; η is the x-coordinate of point S and the moving coordinate system {B}. B Angle between axes; R r D is the inner radius of the shield tail; S denoted as the outer diameter of the tube segment; c represents the cosine function cos; s represents the sine function sin.

[0125] (4) Limitation of cylinder extension speed

[0126] During tunnel boring machine (TBM) excavation, due to limitations imposed by the hydraulic system itself and construction factors, the cylinder extension speed generally does not exceed a certain limit, which can be expressed by the following formula:

[0127]

[0128] Among them, v max This is the maximum extension speed of the hydraulic cylinder; Let be the extension speed of the i-th cylinder.

[0129] (5) Cylinder thrust constraint

[0130] Due to the inherent characteristics and safety requirements of the hydraulic system of the propulsion cylinder, the cylinder thrust generally does not exceed a certain limit.

[0131] 0≤F i ≤F max (37)

[0132] Among them, F max F is the hydraulic cylinder thrust threshold; i Let be the thrust of the i-th cylinder.

[0133] Based on the nonlinear dynamic model in step four, the state-space model of the tunnel boring machine propulsion system is obtained as follows:

[0134]

[0135] Y = X1 = HX (39)

[0136] Among them, X1=q=[xyz ψ θ φ] T This represents the pose vector of the tunnel boring machine. This represents the rate of change of the system's pose. U represents the state vector of the tunnel boring machine propulsion system; U = F d =[F1 F2…F n ] T Represents the system's control input; C = [E6 0 6×6 [] represents the system's output matrix; Y = [xyz ψ θ φ] T This represents the system's output pose vector. The formulas for calculating h1(X) and h2(X) are:

[0137] h1(X)=M -1 (F T -CX2-G) (40)

[0138] h2(X)=M -1 J T (41)

[0139] Step five involves establishing an equivalent load estimation model for the tunnel boring process, including...

[0140] By performing backward difference on formula (4), the equivalent load of the tunnel boring machine can be estimated by the following formula:

[0141]

[0142] Among them, F T(k) represents the shield equivalent load at time k; U(k) represents the shield propulsion system control input at time k; M(k), C(k), G(k) and J(k) represent the values ​​of parameters M, C, G and J in formula (5) at time k, respectively; X(k) represents the system state vector at time k; X(k-1) represents the system state vector at time k-1; T s The system sampling interval time; D1 = [0 6×6 E6],D2=[E6 0 6×6 ]

[0143] Step six involves establishing a shield tunneling pose prediction model based on the load estimation model and the state-space model, including...

[0144] (1) One-step prediction

[0145] The equivalent load of the tunnel boring machine at time k is estimated as follows:

[0146]

[0147] The system state vector at time k is predicted to be at time k+1 in the future.

[0148] X p (k+1|k)=X(k)+T s f(X(k),U(k),F T (k)) (44)

[0149] (2) Two-step prediction

[0150] The equivalent load of the tunnel boring machine at time k+1 is estimated as follows:

[0151]

[0152] The system state vector at time k is predicted to be the state vector at time k+2.

[0153] 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)

[0154] (3)N p Step prediction

[0155] k+N p The estimated equivalent load of the tunnel boring machine at time -1 is:

[0156]

[0157] Where N p For prediction in the time domain.

[0158] Predict the future k+N at time k. p The system state vector at time t is

[0159]

[0160] According to formula (11), it is possible to predict k+1 to k+N at time k. p The shield tunneling machine's pose state output is:

[0161]

[0162] Step seven, which involves constructing the objective function based on the shield tunneling trajectory control target, includes:

[0163]

[0164] Among them, Y r The output pose reference value is determined by the target trajectory of the tunnel boring machine, i.e., the tunnel design axis; ΔU is the thrust control increment of the tunnel boring machine propulsion system; N c To control the time domain; Q and R are weight matrices.

[0165] In step eight, the shield tunneling posture prediction model is used to perform optimization by combining constraints and objective functions to generate the optimal thrust control sequence. The optimal thrust control sequence is then input into the shield propulsion system to control the shield posture, thereby achieving precise and automatic tracking of the shield tunneling trajectory to the tunnel design axis.

[0166] like Figure 2 The diagram shown illustrates the relationship between the shield control trajectory and the target trajectory using the automatic tracking control method for shield tunneling trajectories of this invention.

[0167] Based on the shield posture output measurement value at time k obtained by the shield guidance system and the prediction model, the prediction in the prediction time domain N is made. p The shield position and posture output within the tunnel.

[0168] By solving the optimization problem that satisfies the objective function and various constraints, the control time-domain N is obtained. c A series of shield thrust control inputs are generated, and the first element in the control sequence at that moment is used as the actual control quantity of the controlled object and input into the shield propulsion system.

[0169] When the next time step k+1 is reached, the above process is repeated, that is, the constrained optimization problems are completed in a rolling manner, thereby achieving continuous control of the shield tunneling posture and completing the precise tracking of the shield tunneling trajectory to the tunnel design axis. It can be seen that the shield control trajectory using the automatic tracking control method of the present invention closely matches the target trajectory.

[0170] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the processes depicted in the drawings are not necessarily essential for implementing the present invention.

Claims

1. A method for automatic tracking control of shield tunneling trajectory based on model predictive control, characterized in that, Includes the following steps: S1: Construct the shield coordinate system and determine the shield pose transformation matrix based on the shield pose information; S1 specifically includes: The shield coordinate system includes: a dynamic coordinate system {B-xByBzB} fixed on the shield machine and a base coordinate system {A-xyz} fixed on the segment ring; a. Construct a dynamic coordinate system {B-xByBzB}, which is fixed to the back plate of the shield machine. The origin B is the distribution center of the front ball joint of the hydraulic cylinder. In the initial state, the xB axis points along the central axis of the shield machine in the direction of shield tunneling, the zB axis is perpendicular to the central axis of the shield machine and vertically upward, and the direction of the yB axis is determined according to the right-hand rule. b. Construct a base coordinate system {A-xyz}, which is fixed to the segment ring that provides the reaction force to the propulsion cylinder. The origin A is the distribution center of the rear ball joint of the cylinder. In the initial state, the coordinate axes of the base coordinate system {A-xyz} and the moving coordinate system {B-xByBzB} are parallel to each other. The shield tunneling machine's pose information is derived from the pose vector. It means, among which, This represents the position coordinates of the origin of the moving coordinate system {B-xByBzB} fixed on the tunnel boring machine; The three attitude angles of a tunnel boring machine are: roll angle, pitch angle, and yaw angle. The shield orientation transformation matrix is ​​determined based on the shield orientation information. The formula for calculating the shield orientation transformation matrix is ​​as follows: （1） in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows: （2） （3） in, Represents the cosine function cos; Represents the sine function sin; S2: Construct a complete multi-rigid-body dynamic model of the tunnel boring machine (TBM) propulsion system based on its structural characteristics; whereby... S2 specifically includes: Based on engineering data, determine the structural parameters of the tunnel boring machine propulsion system: coordinate B of the ball joint behind the propulsion cylinder. i Shield body centroid position vector Shield mass M G Shield body inertial tensor ; Shield propulsion system thrust vector , To increase the total number of hydraulic cylinders; A complete multi-rigid-body dynamics model of the tunnel boring machine propulsion system is established based on the Kane method: （4） in, The equivalent load experienced during shield tunneling; the formulas for calculating other coefficients are: （5） in, It is a third-order identity matrix; Let i be the unit direction vector of the i-th propulsion cylinder. ; It is the vector of gravitational acceleration; The shield's angular velocity; , , and The calculation formula is: （6） （7） （8） （9）； Among them, the shield tunneling pose information is composed of pose vectors. express; and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows: （2） S3: Constructing constraints during the tunnel boring machine (TBM) excavation process; S4: Construct the state-space model of the tunnel boring machine propulsion system; S5: Construct an equivalent load estimation model for the tunnel boring machine process; S6: Construct a shield tunneling posture prediction model based on the load estimation model and the state space model; S7: Construct the objective function based on the shield tunneling trajectory control target; S8: Based on the shield tunneling posture prediction model, the optimal solution is obtained by combining the constraints and objective function to generate the optimal thrust control sequence. The optimal thrust control sequence is then input into the shield propulsion system to control the shield posture, thereby achieving precise automatic tracking of the shield tunneling trajectory to the tunnel design axis. The state-space model of the shield tunneling propulsion system in S4 is as follows: （10） （11） in, This represents the pose vector of the tunnel boring machine. This represents the rate of change of the shield tunneling propulsion system's posture. This represents the state vector of the tunnel boring machine propulsion system; This indicates the control parameters of the tunnel boring machine propulsion system; This represents the output matrix of the tunnel boring machine propulsion system; This represents the output pose vector of the tunnel boring machine propulsion system; where, and The calculation formula is: （12） （13）； The equivalent load estimation model for the shield tunneling process in S5 includes: For the formula After performing backward differential estimation, the equivalent load of the tunnel boring machine can be estimated using the following formula: （14） in, This represents the equivalent load on the tunnel boring machine at time k; This represents the control input of the tunnel boring machine propulsion system at time k; , , and They respectively represent the formula (5) The value of the parameter at time k; This represents the state vector of the tunnel boring machine propulsion system at time k; express The state vector of the tunnel boring machine propulsion system at any given moment; This refers to the sampling interval time of the tunnel boring machine propulsion system. .

2. The automatic tracking control method for shield tunneling trajectory based on model predictive control according to claim 1, characterized in that, The shield tunneling pose prediction model in S6 includes: (1) One-step prediction The equivalent load of the tunnel boring machine at time t is estimated as follows: （15） The predicted system state vector at time k+1 is: （16） (2) Two-step prediction The equivalent load of the tunnel boring machine at time t is estimated as follows: （17） Predicting the future The system state vector at time t is: （18） (3) Step prediction The equivalent load of the tunnel boring machine at time t is estimated as follows: （19） in For prediction in the time domain; Predicting the future The system state vector at time t is: （20） According to formula (11), it is possible to... Time Prediction to The shield tunneling machine's pose state output is: （21）。 3. The automatic tracking control method for shield tunneling trajectory based on model predictive control according to claim 2, characterized in that, The objective function in S7 includes: （22） in, This represents the target output pose reference value determined by the tunnel boring machine's target trajectory, i.e., the tunnel design axis. For the thrust control increment of the tunnel boring machine propulsion system; To control the time domain; Q and R are weight matrices.

4. The automatic tracking control method for shield tunneling trajectory based on model predictive control according to claim 1, characterized in that, S8 specifically includes: Based on the shield tunneling guidance system The shield tunneling machine's pose outputs measured values ​​and a prediction model at each moment, predicting the position in the prediction time domain. The shield's position and posture output is within the tunnel. By solving the optimization problem that satisfies the objective function and various constraints, the control time domain is obtained. A series of shield thrust control inputs are given, and the first element in the control series at that moment is taken as the actual control quantity of the controlled object. When the next moment arrives... The above process is repeated continuously, that is, the constraint-laden optimization problems are completed one by one in a rolling manner, so as to achieve continuous control of the shield posture and complete the precise tracking of the shield tunneling trajectory to the tunnel design axis.

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