A method for controlling the feed force of a sliding directional drilling based on equivalent input disturbance

Abstract

This invention discloses a sliding directional drilling feed force control method based on equivalent input disturbances, comprising: establishing a mathematical model for pressure reducing valve control, obtaining the mapping relationship between electromagnet current and pressure reducing valve outlet pressure, and modeling and controlling the directional drilling rig feed system; modeling includes: constructing the transfer function of the directional drilling rig feed system and establishing the state-space equation of the directional drilling rig feed system; control includes: establishing a control structure based on equivalent input disturbance estimation and compensation, specifically designing a state feedback controller, a state observer, and an equivalent input disturbance estimator, to achieve stable operation of the sliding directional drilling feed force closed-loop control system, enabling the system to have good tracking and disturbance suppression functions, and providing a control research foundation for ensuring the working performance of the directional drilling rig and the safe and efficient construction of directional drilling holes.

Description

Technical Field

[0001] This invention belongs to the field of underground sliding directional drilling control in coal mines, and particularly relates to a sliding directional drilling feed control method based on equivalent input disturbance. Background Technology

[0002] As the scale, intensity, and depth of coal mining in my country gradually increase, mine disasters are becoming more diversified and complex. Underground tunnel drilling in coal mines has become an indispensable and important part of the disaster prevention, mitigation, and control technology system for deep coal mining, and is widely used in the prevention and control of gas, water hazards, and rock bursts.

[0003] Conventional rotary drilling suffers from drawbacks such as slow construction speed, uncontrollable borehole trajectory, inability to adapt to undulating coal seam roof and floor, high ineffective drilling depth, low borehole utilization rate, and small gas extraction capacity per borehole, making it difficult to meet the needs of efficient gas extraction, water drainage, and geological anomaly detection in coal mines. Compared with traditional rotary drilling, directional drilling offers advantages such as controllable trajectory, high target stratum encounter rate, and long single-hole drainage distance. It can also be used for multi-branch borehole construction, achieving multi-purpose functionality and ensuring uniform coverage of the required exploration area, thus effectively improving drilling efficiency and economic benefits.

[0004] The underground measurement-while-drilling (MWD) directional drilling technology in coal mines mainly uses screw motors as the directional drilling tool. It primarily includes two modes: composite directional drilling and sliding directional drilling. Composite directional drilling is used when the deviation between the borehole trajectory and the designed trajectory is within the allowable error range. In this mode, the power head and screw motor rotate together, providing axial feed power to the feed system. When the borehole trajectory deviates from the designed trajectory to a certain extent, sliding directional drilling is used. In this mode, the power head does not rotate, but the screw motor rotates, providing axial sliding power to the feed system. The borehole trajectory is changed by adjusting the tool face angle of the screw motor. The borehole trajectory parameters are transmitted to an explosion-proof computer at the borehole opening via the MWD device. By manually analyzing the deviation between the actual drilling trajectory and the designed trajectory, and combining this with borehole trajectory control experience, the tool face angle of the screw motor is adjusted to control the borehole trajectory and ensure that it extends within the predetermined strata.

[0005] Because the geological and mechanical environment of coal-bearing strata in underground coal mines is complex, the load resistance is generally random and difficult to measure accurately. Therefore, the directional drilling process is a nonlinear, time-varying and uncertain process, which can easily cause fluctuations in drilling parameters and lead to instability in the operation of the feed system.

[0006] As the main actuator in directional drilling, the feed system's stable tracking and control of the feed force is one of the key technologies in directional drilling, playing a crucial role in ensuring drilling quality and efficiency. The feed system employs hydraulic feeding, where a hydraulic pump supplies high-pressure oil to the hydraulic cylinders. The hydraulic cylinders output feed force, which is then driven by an intermediate transmission device (slide) to move the drill string connected to the power head, achieving feeding or pulling. The feed force is controlled by a pressure reducing valve, enabling pressurized or depressurized drilling. Summary of the Invention

[0007] The purpose of this invention is to provide a sliding directional drilling feed control method based on equivalent input disturbance, which can effectively solve the problem that the uncertainty disturbance of complex underground strata in coal mines affects the working performance of directional drilling rigs and the construction quality and efficiency of directional drilling.

[0008] The technical solution adopted in this invention is:

[0009] A method for controlling the feed force in sliding directional drilling based on equivalent input disturbances, characterized in that it includes:

[0010] A mathematical model for pressure reducing valve control is established to obtain the mapping relationship between electromagnet current and pressure reducing valve outlet pressure. Based on the clear feed force driving mode, the feed system of directional drilling rig is modeled and controlled. The control input of the feed system of directional drilling rig is electromagnet current u(t), and the control output of the feed system of directional drilling rig is the actual feed force y(t) at the borehole.

[0011] Modeling includes: constructing the transfer function of the directional drilling rig feed system and establishing the state-space equations of the directional drilling rig feed system;

[0012] The control includes: establishing a control structure based on equivalent input disturbance estimation and compensation, specifically designing a state feedback controller, a state observer, and an equivalent input disturbance estimator.

[0013] Optionally, the mathematical model for controlling the pressure reducing valve is:

[0014]

[0015] V is the volume of the controlled cavity at the outlet of the pressure reducing valve, in cm³. 3 E is the bulk modulus of the oil, in N·m. -2 ;k I Here, b is the current-to-force proportional gain coefficient, and k is the friction coefficient. Q For flow gain, k c A is the flow-pressure coefficient. out The bottom area of ​​the pressure reducing valve core is in cm². 2 K0 = k + k s k sis the stiffness of the hydrodynamic spring, N·m; k is the spring stiffness, N·m; s is the complex frequency, in Hz.

[0016] Optionally, the transfer function F(s) of the directional drilling rig feed system is:

[0017]

[0018] In the formula, η is the transmission efficiency of the directional drilling rig's feed system.

[0019] Optionally, the state-space equation of the directional drilling rig feed system is:

[0020]

[0021] In the formula, x(t) is defined as the state of the feed system, u(t) is the electromagnet current, d(t) is the load disturbance, and y(t) is the actual feed force at the orifice.

[0022] C = [1 K] AQ ], B d =B, T3=kk c +k Q A out K IQ =k I k Q ,

[0023] Optionally, the state observer is:

[0024]

[0025] In equation (20), To provide the observed state of the system, the dot above the letter in the formula indicates differentiation, representing the rate of change of the variable with respect to time, u. f (t) represents the state feedback controller, and L represents the gain of the observer to be designed. y(t) is the output of the observer, and y(t) is the actual feed force at the orifice.

[0026] Optionally, the equivalent input interference estimator is:

[0027]

[0028] Among them, K e This represents the gain of the EID estimator.

[0029] Optionally, the state feedback controller u f (t) is:

[0030]

[0031] In the formula, K represents the observed state of the system. r With K c x is the gain of the state feedback controller. r (t) represents the state recommended by the orifice to the advance dynamics model, and the state-space equation of the orifice recommended to the advance dynamics model is:

[0032]

[0033] x r (t) represents the state recommended by the orifice to the infeed dynamics model. The dot above the letters in the formula indicates the differential calculation, representing the rate of change of this variable with respect to time. To track errors; when the recommended feed force r(t) at the orifice is precisely known, parameter A r and B r It can be determined directly.

[0034] The beneficial effects of this invention are:

[0035] (1) The sliding directional drilling feed force control method based on equivalent input interference of the present invention establishes a mathematical model of pressure reducing valve control according to the working principle of the feed system, obtains the mapping relationship between electromagnet current and pressure reducing valve outlet pressure, and models and controls the entire feed system based on the clear feed force driving mode.

[0036] (2) A directional drilling feed tracking control strategy based on the equivalent input disturbance method was proposed. The state space equation of the directional drilling rig feed system was established, and then the equivalent input disturbance estimator was constructed. The state feedback controller, state observer and equivalent input disturbance estimator gain were designed to enable the system to have good tracking and disturbance suppression functions. This provides a control research basis for ensuring the working performance of the directional drilling rig and the safe and efficient construction of directional drilling holes. Attached Figure Description

[0037] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the following detailed description to explain the present disclosure, but do not constitute a limitation thereof. In the drawings:

[0038] Figure 1 Directional drilling rigs are used to construct gas extraction holes;

[0039] Figure 2 Physical structure of pressure reducing valve;

[0040] Figure 3 Block diagram of the transfer function for current control of a pressure reducing valve;

[0041] Figure 4 Directional drilling rig feed tracking control system;

[0042] Figure 5 Fitting curve of field data for pressure reducing valve outlet pressure;

[0043] Figure 6 Results of feed force tracking control in the feed system of a directional drilling rig;

[0044] Figure 7 Tracking error and disturbance suppression error of the directional drilling rig feed system;

[0045] Figure 8 Comparison results between the feed force tracking control of the feed system and the PID control method;

[0046] Figure 9 Comparison of feed system tracking error with PID control method. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0048] This invention presents a sliding directional drilling feed force control method based on equivalent input disturbances. Addressing the problem of uncertain disturbances in complex formations affecting the performance of directional drilling rigs and the quality and efficiency of directional drilling, this method analyzes the structural composition and drilling process of the directional drilling rig. Based on the working principle of its feed system, a mathematical model for pressure reducing valve control is established, obtaining the mapping relationship between the electromagnet current and the outlet pressure of the pressure reducing valve. The entire feed system is modeled and controlled based on a clear understanding of the feed force driving method. Then, a directional drilling rig feed force tracking control system is designed. The state of the controlled object is reconstructed using a Luenburger full-dimensional state observer, and an equivalent input disturbance estimator is established. A state feedback controller, a state observer, and an equivalent input disturbance estimator are designed to achieve a stable feed force closed-loop control system with satisfactory tracking and disturbance suppression performance.

[0049] Specifically:

[0050] A mathematical model for pressure reducing valve control is established to obtain the mapping relationship between electromagnet current and pressure reducing valve outlet pressure. Based on the clear feed force driving mode, the feed system of directional drilling rig is modeled and controlled. The control input of the feed system of directional drilling rig is electromagnet current u(t), and the control output of the feed system of directional drilling rig is the actual feed force y(t) at the borehole.

[0051] Modeling includes: constructing the transfer function of the directional drilling rig feed system and establishing the state-space equations of the directional drilling rig feed system;

[0052] The control includes: establishing a control structure based on equivalent input disturbance estimation and compensation, specifically designing a state feedback controller, a state observer, and an equivalent input disturbance estimator.

[0053] 1. Analysis of the directional drilling process

[0054] Directional drilling rigs mainly consist of a feeding system, a slewing system, a control panel, a pole-mounting manipulator, a pole-addition device, a mining explosion-proof and intrinsically safe controller, a hydraulic pump station, a cooling system, a stabilizing device, and a tracked vehicle body.

[0055] In directional drilling, drilling efficiency and drilling safety are the two primary considerations. Drilling efficiency is determined by drilling speed, while drilling safety refers to the directional drilling rig's feed force and rotation torque operating within rated conditions regardless of borehole depth and formation conditions. Based on analysis of actual drilling processes in coal mines, feed force is a key decision variable determining drilling speed. The directional drilling rig optimizes the feed force value corresponding to the target drilling speed by real-time monitoring of drilling conditions and parameters. During drilling operations, the controller sends a current control signal to change the opening of the pressure reducing valve, adjusting the pressure in the feed cylinder's inlet chamber, thereby changing the output feed force of the feed system. This force is then transmitted through the drill rod and drill bit, ensuring the feed system can adapt to changes in coal seam load and achieve safe and efficient drilling. Figure 1 The diagram shows a directional drilling rig constructing a gas extraction hole.

[0056] 2. Feed system modeling

[0057] When drilling in complex geological conditions, the feed system of a directional drilling rig experiences significant impacts, which can easily lead to system instability. Therefore, modeling the feed system is necessary. The control and execution components of the directional drilling rig feed system mainly consist of a pressure reducing valve, a hydraulic cylinder, and an intermediate transmission device. The feed force output by the hydraulic cylinder is controlled by the pressure reducing valve, and energy is consumed when passing through the intermediate transmission device. Therefore, the pressure reducing valve is first dynamically modeled to clarify the driving method of the feed force, and then the entire feed system is modeled and controlled.

[0058] 2.1 Dynamic Modeling of Pressure Reducing Valve (In the following formulas, the unit of pressure is MPa and the unit of force is N)

[0059] like Figure 2 The diagram shows the physical structure of a pressure reducing valve. During the dynamic control of the valve outlet pressure, the pressure reducing valve's spring-damping structure affects the spring pre-compression x0 and the outlet flow rate Q. out It will affect the outlet pressure P of the pressure reducing valve out The magnitude of the pressure, plus the influence of the load during drilling (the reaction force generated by the drill string system drilling into the formation), affects the outlet pressure P of the pressure reducing valve. out Fluctuations will occur.

[0060] Based on the working principle of a pilot-operated proportional pressure reducing valve, during dynamic movement, the electromagnetic force drives the valve core to move, generating inertial force, frictional damping force, and spring elastic force. This force can be controlled by adjusting the current I of the pressure reducing valve. m Controlling the outlet pressure P out Size. Ignoring the weight of the valve core itself, the dynamic equation of the pressure reducing valve can be expressed as:

[0061]

[0062] In the formula, m is the mass of the valve core; b is the coefficient of friction; k is the spring stiffness (N·m); x0 is the pre-compression of the pressure reducing valve spring (m); x is the valve core displacement (valve opening degree) (m); k s The stiffness of the hydrodynamic spring is expressed in N·m; A out The bottom area of ​​the pressure reducing valve core is in cm². 2 ;I m The current of the pressure reducing valve electromagnet is mA; k I This is the current-to-force proportional gain coefficient.

[0063] The output pressure of the pressure reducing valve is related to the inlet and outlet flow rates. During dynamic operation, the flow rate relationship within the controlled chamber is as follows:

[0064]

[0065] In the formula, the dot above the letters indicates differentiation, representing the rate of change of these variables with respect to time; V is the volume of the controlled cavity at the outlet of the pressure reducing valve, in cm³. 3 E is the bulk modulus of the oil, in N·m. -2 Q in The flow rate entering the load is measured in L / min; Q out The pressure reducing valve spool outlet flow rate, with the unit of flow rate being L / min, can be expressed as:

[0066]

[0067] C d Valve spool flow coefficient, D is the valve spool diameter in meters; ρ represents the oil density in kg·m⁻³; P in This represents the inlet pressure of the pressure reducing valve. Since the outlet flow rate and pressure of the pressure reducing valve are non-linear functions, when the valve is in a certain equilibrium position, the following can be obtained using the linearization formula:

[0068] ΔQ out =k Q Δx+k c Δ(P in -P out (4);

[0069] In the formula, k Q For flow gain, k c Flow-pressure coefficient;

[0070]

[0071]

[0072] Therefore, the outlet pressure P of the pressure reducing valve can be obtained. out The relationship between the valve core displacement x and the valve core displacement x:

[0073]

[0074] 2.2 Feed System Control Model

[0075] In the feed system of a directional drilling rig, the pressure reducing valve, hydraulic cylinder, and intermediate transmission device are connected in series. To facilitate analysis, the force transmission problem of each module is analyzed separately first, and then the control model of the feed system is established.

[0076] Since the outlet flow rate in the pressure reducing valve model is coupled with the state variable x, it is difficult to establish the outlet pressure P solely from formula (5). out With input current I m The controllable state equations between the two are determined. By selecting a transfer function, the control input and output of the pressure reducing valve can be separated, revealing the relationship between them. Therefore, the Laplace transform is used to separate the input and output variables, where s is the complex frequency in the Laplace transform, measured in Hz.

[0077] After performing a Laplace transform on formula (1), we get:

[0078] k I I m (s)-A out P out (s)=[ms 2 +bs+(k+k s )]X(s)+K s X0(s) (6);

[0079] The movement of the pressure reducing valve is a gradual process. The acceleration generated by the spring is very small, and the mass of the pressure reducing valve is relatively small. Therefore, the inertial force generated is very small compared to the spring force and the electromagnetic force. During the control process of the solenoid valve, the initial spring force is much smaller than the electromagnetic force. For control purposes, we ignore the inertial force generated by the spring and the spring force generated by the spring pre-compression, and thus we get:

[0080] k I I m (s)-A out P out (s)=[bs+(k+k s)]X(s) (7);

[0081] After performing a Laplace transform on formula (5), we get:

[0082]

[0083] From formula (8), we can obtain:

[0084]

[0085] Substituting (9) into (7) will eliminate the valve opening;

[0086]

[0087] According to formulas (6), (8), and (10), the block diagram of the current control transfer function of the pressure reducing valve can be drawn, as follows: Figure 3 As shown.

[0088] As can be seen from the transfer function block diagram, given the electromagnet current I(s) as a controllable input, the pressure reducing valve outlet pressure P... out (s) To control the output, the pressure P at the inlet of the pressure reducing valve is... in (s) and inflow load flow Q in (s) represents the external disturbance quantity. Compared with formula (1), the control quantity of the pressure reducing valve is well separated from the external disturbance quantity. Therefore, when P in (s)=0, Q in When (s) = 0, the transfer function of the control system is:

[0089]

[0090] Let K0 = k + k s Therefore, the closed-loop transfer function of the control system is:

[0091]

[0092] After obtaining the outlet pressure of the pressure reducing valve, the feed force is provided to the feed system by driving the intermediate transmission device through the hydraulic cylinder. However, during the process of the hydraulic cylinder driving the intermediate transmission device, energy loss occurs, and the feed force provided by the feed system will decrease. This paper takes the ZDY4500LFK electric drilling rig as an example to calculate the transmission efficiency of its feed system. Considering the transmission efficiency of the feed system from the theoretical maximum input feed force, its theoretical maximum input feed force is:

[0093] F max0 =p max A2 (13);

[0094] In the formula, p maxThe maximum feed pressure of the hydraulic cylinder (corresponding to the outlet pressure P of the pressure reducing valve) out (Maximum value), A2 is the area of ​​the rod-side chamber of the hydraulic cylinder, cm² 2 .

[0095] The maximum output feed force F of the hydraulic cylinder max It can be represented as:

[0096] F max =η max (F max0 -p 21 A1) (14);

[0097] In the formula, η max p represents the mechanical efficiency of the hydraulic cylinder. 21 A1 is the return oil back pressure of the feed system, and A1 is the area of ​​the rodless chamber of the hydraulic cylinder (cm²). 2 .

[0098] However, friction is generated when the hydraulic cylinder drives the intermediate transmission device (slide plate):

[0099]

[0100] In the formula, u0 is the friction coefficient between the slide plate and the feed machine body guide rail, l is the length of the slide plate (m), h1 is the distance from the center of the power head to the contact surface between the slide plate and the feed machine body guide rail (m), and h2 is the distance from the feed cylinder to the contact surface between the slide plate and the feed machine body guide rail (m).

[0101] Therefore, the transmission efficiency η of the feed system can be calculated as follows:

[0102]

[0103] The theoretical transmission efficiency of the feed system, calculated using the parameters of the ZDY4500LFK electric drilling rig, is 77%, while the actual measured transmission efficiency of the drilling rig is 76%, which is very close.

[0104] Therefore, considering the transmission efficiency factor of the feed system during the directional drilling process, the transfer function F(s) of the directional drilling rig feed system can be obtained as follows:

[0105]

[0106] 3. Description of the feed tracking control problem

[0107] During directional drilling, the opening of the pressure reducing valve is changed by controlling the current of the pressure reducing valve, thereby adjusting the outlet pressure (oil pressure) of the pressure reducing valve, which is the inlet pressure of the hydraulic cylinder in the feed system. In the actual feed system, the outlet pressure of the pressure reducing valve can be measured, and the actual feed force at the borehole can be calculated through the hydraulic cylinder and intermediate transmission device.

[0108] Furthermore, the drill string is subjected to the combined effects of feed force and load disturbance during drilling. Due to limitations of sensors, the state of the feed system cannot be directly measured, and disturbance suppression cannot be achieved through state feedback.

[0109] Therefore, by establishing an observer based on the actual feed force at the orifice and state feedback, the state of the feed system is reconstructed, and a feed force tracking control strategy for directional drilling rigs based on the equivalent input disturbance method is designed.

[0110] like Figure 4 As shown, the feed force tracking control system of a directional drilling rig consists of a feed system, a dynamic model of the recommended feed force at the orifice, a state feedback controller, a state observer, and an equivalent input disturbance (EID) estimator. The outer loop of the feed force tracking control system comprises the dynamic model of the recommended feed force at the orifice, the state feedback controller, and the feed system, achieving tracking control of the recommended feed force. The inner loop of the feed force tracking control system comprises the feed system, the state observer, and the equivalent input disturbance estimator, achieving suppression of load disturbances experienced by the feed system. Specifically, the dynamic model of the recommended feed force at the orifice is used to track the recommended feed force, the state feedback controller is used for stabilizing the feed force tracking control system, the state observer is used to reconstruct the state of the feed system, and the EID estimator is used to compensate for the total disturbance experienced by the feed system.

[0111] 3.1 Control System Description:

[0112] Based on the transfer function F(s) of the feed system, let K IQ =k I k Q , T3=kk c +k Q A out Y(s) = P out (s), and by introducing intermediate variables x1(t) and x2(t), the state-space equations of the system are constructed as follows:

[0113]

[0114] In the formula, x(t) = [x1(t) x2(t)] T Let u(t) represent the state of the feed system, d(t) represent the electromagnet current, d(t) represent the load disturbance, and y(t) represent the actual feed force at the orifice.

[0115] C = [1 K] AQ ], B d =B.

[0116] A dynamic model of the orifice feed force is established to achieve accurate tracking of the orifice feed force. The state-space equation of the orifice feed force is:

[0117]

[0118] In equation (19), x r (t) represents the state recommended by the orifice to the advance dynamics model. To track errors. When the orifice feed force r(t) is precisely known, parameter A... r and B r It can be determined directly.

[0119] Since the actual feed force at the orifice cannot be measured, a Luenberger full-dimensional state observer is used.

[0120]

[0121] Reconstruct the state of the controlled object. In equation (20), For the observed state of the system, u f (t) represents the state feedback, and L represents the gain of the observer to be designed. This is the output of the observer.

[0122] The state feedback controller is designed as follows:

[0123]

[0124] In the formula, K r With K c This is the gain of the state feedback controller.

[0125] Considering the load disturbance of the controlled object, a control structure based on estimation and compensation is established to achieve high-precision feed force tracking control.

[0126] 3.2 Design of Equivalent Input Disturbance Estimator:

[0127] First, we will explain the existence of EID.

[0128] Definition 1: Let the control input u(t) = 0, and the initial state satisfy x(0) = x o (t). If for The outputs y(t) and y of the controlled object o (t) satisfies y(t)≡y o (t), then the disturbance d e (t) is called the equivalent input disturbance of the disturbance d(t).

[0129] Based on the concept of stable inverses, we give a definition of the existence of equivalent input disturbances.

[0130] Definition 2: Under the influence of disturbance d(t), if the system output y o (t) satisfies y o If (t)∈Φ, then there exists an equivalent input disturbance d(t) at the input end of the controlled object. e (t), and d e (t)∈Φ, the set is defined as:

[0131]

[0132] In the formula, α i (t) is a polynomial function of time t, ω i (≥0) and Let i be a constant, i = 1, 2, ..., n.

[0133] According to the definition of EID, the controlled object (18) is rewritten as:

[0134]

[0135] Based on the literature, the EID estimate is constructed as follows:

[0136]

[0137] Since the estimated disturbance is easily affected by output measurement noise, a first-order low-pass filter is used to limit the bandwidth of the disturbance estimation, i.e., the disturbance estimation is:

[0138]

[0139] for s-domain expression, for The s-domain expression for the low-pass filter is:

[0140]

[0141] In the formula, x f (t) represents the state of the low-pass filter. This is the estimated disturbance value after filtering. When the cutoff frequency ω of the low-pass filter... f When the exact value is known, parameter A f B f and C f It can be determined directly. The cutoff frequency ω of a typical low-pass filter is... f Greater than the highest frequency of the disturbance ω d 5-10 times.

[0142] The filtered disturbance estimate Reverse compensation is applied to the system input:

[0143] The control input u(t) of the feed system is obtained.

[0144] The drilling rig feed tracking control problem is described as follows: Design the gain {K} of the state feedback controller. r ,K c The gain L of the state observer and the gain K of the EID estimator e This ensures that the feed system is stable under the action of the electromagnet current u(t), while also providing satisfactory tracking and disturbance suppression performance.

[0145] 4. Controller Design and Optimization:

[0146] To simplify the system stability analysis, consider external signals r(t) = 0 and d(t) = 0. Definition To account for the state observation error, the state-space equations of the feed force tracking control system are obtained from equations (19), (20), (23), (26), and (27) as follows:

[0147]

[0148] In the formula,

[0149]

[0150] The controller design involves two steps: First, assuming that all external disturbances are compensated by the EID estimator of the inner loop of the feed tracking control system, the gain {K} of the state feedback controller of the outer loop of the feed tracking control system is calculated. r ,K c Design; then, based on the designed state feedback controller, calculate the gain L of the state observer and the gain K of the EID estimator. e The design.

[0151] 4.1 Design of State Feedback Controller

[0152] To account for the fact that all load disturbances are compensated by the EID estimator of the inner loop of the system, the state-space equations of the outer loop of the feed tracking control system are established as follows:

[0153]

[0154] In the formula,

[0155] Theorem 1: Given adjustment parameters α and β, if there exists a scalar δ, a positive definite symmetric matrix and a matrix of appropriate dimension Make the linear matrix inequality Θ<0 (30);

[0156] Established, in the formula:

[0157] The outer loop system (29) is asymptotically stable, and the gain of the state feedback controller is:

[0158]

[0159] 4.2 Stabilization of the feed tracking control system

[0160] Theorem 2: Given adjustment parameters γ and μ, and a set of state feedback controllers {K} r ,K c If there exists a scalar ε, a positive definite symmetric matrix And a matrix of suitable dimension such that the linear matrix inequality Ξ<0(32) holds, where,

[0161]

[0162]

[0163]

[0164] The closed-loop system (23) is asymptotically stable, and the state observer gain and EID estimator gain are:

[0165]

[0166] I n This represents an n-dimensional identity matrix.

[0167] 4.3 Design and Optimization Steps

[0168] The tracking and disturbance suppression performance of the feed tracking control system is jointly adjusted by the parameter combination {α,β,δ,γ,μ,ε}. The specific design steps are as follows:

[0169] Step 1: Based on the highest frequency ω of the disturbance d Choose the cutoff frequency ω of the low-pass filter f ;

[0170] Step 2: Adjust the parameters {α,β,δ,γ,μ,ε} to make Theorem 1 and Theorem 2 hold;

[0171] Step 3: Solve for the control gain {K} according to equations (31) and (33). r ,K c ,L,K e}

[0172] To achieve better control performance, the differential evolution algorithm can be used to find the optimal combination of control parameters {α,β,δ,γ,μ,ε}.

[0173] 5. Simulation Verification

[0174] The simulation parameters of the pressure reducing valve model for directional drilling rigs are shown in Table 1.

[0175] Table 1 Simulation parameters of pressure reducing valve model

[0176]

[0177] Based on the parameters given in Table 1, the simulation model is as follows:

[0178]

[0179]

[0180] C = [1 4.9596 × 10 -5 ],

[0181] B d =B.

[0182] To ensure safe mining operations in underground coal mines, a coal mine designed boreholes with a depth of 60m to 120m along the working face for pre-drainage of gas. During construction, a ZDY4500LFK electrically controlled drilling rig was used with pressurized drilling, and the feed pressure was controlled in real time by a pressure reducing valve. This paper takes one borehole as an example. The borehole was designed with an azimuth of 189.1° and an inclination of -11.5°. Due to the soft coal seam, the measured feed pressure during drilling was 1-2 MPa. To verify the applicability of the proposed method in the control of underground coal mine drilling processes, the selected input parameters and interference functions were determined based on the actual drilling conditions.

[0183] During actual drilling operations in a soft coal seam in the return airway of a coal mine, the feed force was 5-7 kN. Therefore, the reference signal was given as follows:

[0184]

[0185] Choose A r =-0.001, B r =1.

[0186] The measured feed pressure fitting curve is as follows: Figure 5 As shown, the calculated field pressure data fluctuates around 10% of the fitted curve. The data fluctuation is mainly caused by external interference. Therefore, this fluctuation amplitude ratio is used as the amplitude ratio of the given disturbance signal.

[0187] Therefore, the given disturbance signal is designed as follows:

[0188] d(t)=5[sinπt+cos(t-5)][mA],10≤t≤50[s] (35);

[0189] Select a low-pass filter

[0190] Therefore A f =-101,B f =100,C f =1.

[0191] 5.1 Design and Simulation

[0192] Design adjustment parameters α = 1, β = 1 × 10 -24 δ=1×10 -1 γ = 1, μ = 1 × 10 -4 With ε = 1, the controller is obtained as follows:

[0193] K r =2.5810×10 -5 K c =10 -5 ×[-0.1893-0.0013] (37);

[0194] L = 10 4 ×[3.3241 0.0004] T K e =0.0024 (38);

[0195] Figure 6 The figure shows the control results of the directional drilling rig feed system based on the equivalent input disturbance method. It can be seen that the proposed method ensures stable system operation and achieves good tracking and disturbance suppression performance. Figure 7 It can be seen that the peak-to-peak value of the steady-state tracking error is 4 × 10⁻⁶. -5 The peak-to-peak value of the steady-state disturbance estimation error is 0.1 mA.

[0196] 5.2 Comparison with PID control method

[0197] A PID controller is used to stabilize the feed system. The PID controller is designed as follows:

[0198]

[0199] To obtain the same control input, the gains of the PID controllers are set as follows: K P =1×10 -5 ,K I =1×10 -4 ,K D =1×10-9 .

[0200] Figure 8 The comparison results between the proposed control method and the PID control method are shown. In transient situations, the PID controller achieves faster tracking of the reference signal, but it uses a larger control force, which can easily lead to actuator saturation in practice. The PID controller is a single-degree-of-freedom control method that achieves satisfactory tracking performance when no disturbance is applied; however, it lacks disturbance estimation and compensation capabilities, thus limiting its disturbance suppression performance. Compared to the PID controller, the proposed method, based on a two-degree-of-freedom control structure with disturbance estimation and compensation, achieves better control performance.

[0201] Depend on Figure 9 It can be seen that the peak-to-peak value of the steady-state tracking error obtained by the PID controller is 0.4 kN, which is 10 times that of the proposed method. 5 Therefore, the proposed method has better tracking and perturbation estimation performance, which is twice as fast.

[0202] The performance of the proposed control method is quantified by selecting Integrated Square Error (ISE), Integrated Time and Absolute Error (ITAE), and Root Mean Square Value (RMSE).

[0203] Table 2 Comparison of error data between EID and PID control methods

[0204]

[0205] As shown in Table 2, the proposed EID control method has a smaller tracking error and can effectively solve the problem of the impact of uncertain disturbances in complex underground strata on the working performance of directional drilling rigs and the quality and efficiency of drilling construction.

[0206] The preferred embodiments of this disclosure have been described in detail above with reference to the accompanying drawings. However, this disclosure is not limited to the specific details of the above embodiments. Within the scope of the technical concept of this disclosure, various simple modifications can be made to the technical solutions of this disclosure, and these simple modifications all fall within the protection scope of this disclosure.

[0207] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, this disclosure will not describe the various possible combinations separately.

[0208] Furthermore, various different embodiments of this disclosure can be combined in any way, as long as they do not violate the spirit of this disclosure, they should also be regarded as the content disclosed in this disclosure.

Claims

1. A method for controlling the feed force in sliding directional drilling based on equivalent input disturbances, characterized in that, include: A mathematical model for pressure-reducing valve control is established to obtain the mapping relationship between electromagnet current and pressure-reducing valve outlet pressure. Based on a clear understanding of the feed force drive method, the feed system of the directional drilling rig is modeled and controlled. The control input of the directional drilling rig feed system is the electromagnet current. u ( t The control output of the directional drilling rig's feed system is the actual feed force at the borehole opening. y ( t ); Modeling includes: constructing the transfer function of the directional drilling rig feed system and establishing the state-space equations of the directional drilling rig feed system; Control includes: establishing a control structure based on equivalent input disturbance estimation and compensation, specifically designing a state feedback controller, a state observer, and an equivalent input disturbance estimator; The mathematical model for controlling the pressure reducing valve is as follows: （12）； The pressure reducing valve outlet pressure is in MPa. Given an electromagnet current mA, The controlled chamber volume at the outlet of the pressure reducing valve. ; Let be the bulk modulus of the oil. 2 ; This is the current-to-force proportional gain coefficient. The coefficient of friction, For flow gain, The flow-pressure coefficient, The bottom area of ​​the pressure reducing valve core is in cm². 2 ; , For the stiffness of the hydraulic spring, , For spring stiffness, ; s is a complex frequency, measured in Hz; The transfer function of the directional drilling rig feed system for: (17); where, The transmission efficiency of the feed system for directional drilling rigs; The state-space equation of the directional drilling rig feed system is as follows: ； In the formula, x ( t The state of the feed system is defined as follows: u ( t ) represents the current in an electromagnet. d ( t This represents load disturbance. y ( t The actual feed force at the orifice is 0. ， ， ， ， ， ， ， ， ； The state observer is: （20）； In equation (20), To provide the observed state of the system, the dot above the letter in the formula indicates the differential calculation, representing the rate of change of these variables with respect to time; It is a state feedback controller. For the gain of the observer to be designed, For the output of the observer, y ( t The actual feed force at the orifice is 0. The equivalent input interference estimator is: （24）； in, Indicates the gain of the EID estimator; The state feedback controller for: （21）； In the formula, For the system's observation state, and For the state feedback controller gain, The state recommended by the orifice to the advance dynamics model is given by the following state-space equations: ； The state recommended for the orifice in the advance dynamics model is represented by a dot above the letters in the formula, indicating the rate of change of these variables with respect to time. To track errors; when the orifice is recommended to provide advance force When the exact parameters are known, and It can be determined directly.

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