A hierarchical adaptive disturbance suppression control method for drilling systems under unbounded disturbances

Abstract

This invention discloses a hierarchical adaptive disturbance suppression control method for drilling systems under unbounded disturbances, belonging to the field of intelligent control methods. It establishes a dynamic model of a multi-drilling system containing unbounded disturbances; designs a first-order observer with low computational complexity to estimate leader information; constructs a novel disturbance observer with dynamic changes, removing the constraint that traditional disturbance observers require the assumption that the lumped disturbance is differentiable and its derivative is bounded; and designs an adaptive backstepping sliding mode controller based on the novel disturbance observer and radial basis function neural network to suppress the influence of unbounded disturbances. This invention can ensure the safe and reliable operation of multi-drilling systems under complex operating conditions such as unbounded disturbance derivatives, thereby effectively improving coal mining in thin coal seams.

Description

Technical Field

[0001] This invention relates to the field of intelligent control methods, specifically a hierarchical adaptive disturbance suppression control method for drilling systems under unbounded disturbances. Background Technology

[0002] Thin coal seams are rich in resources, and their efficient mechanized mining is a key research focus. To improve mining efficiency, multi-drilling systems have been proposed to solve the challenges of directional drilling in complex geological conditions. However, the harsh mining environment (faults, unbounded interference, etc.) poses significant challenges to the centralized control and stability of the system. Furthermore, with limited sensors, leader information can only be partially propagated, requiring estimation through distributed observers. Therefore, designing distributed observers for complex multi-drilling systems under conditions where some followers can obtain leader information, and constructing a hierarchical control framework to compensate for unbounded lumped interference, is extremely challenging.

[0003] However, in actual drilling, systems face various disturbances (such as wellbore reaction forces, gravity, and friction). While existing research on disturbance rejection control (such as disturbance estimators, active disturbance rejection control, and robust learning model prediction) has yielded results, it generally suffers from a key limitation: it requires the assumption that the derivative of the unbounded disturbance is bounded or that the unbounded disturbance error of neighboring agents is bounded. This means that these methods require that the rate of change of the unbounded disturbance cannot be too large. This assumption limits their application scope, making them ineffective in dealing with disturbances where the derivative itself is unbounded (i.e., the rate of change can be very large and unconstrained in real-world situations).

[0004] Furthermore, the unbounded disturbance of the unbounded derivative directly leads to serious consequences:

[0005] (1) The measurement output produces a very large deviation;

[0006] (2) This renders traditional interference observer design methods ineffective, making it impossible to reliably and accurately estimate this type of interference.

[0007] Therefore, designing novel disturbance observers to accurately estimate unbounded disturbances with unbounded derivatives has become a key challenge in ensuring the overall anti-interference control performance of multi-drilling systems. Hence, a hierarchical adaptive disturbance suppression control method for drilling systems under unbounded disturbances is proposed to address the above issues. Summary of the Invention

[0008] In view of this, the technical problem to be solved by the present invention is to propose a layered adaptive disturbance suppression control method for drilling systems under unbounded disturbances, so as to solve the problems mentioned in the background art.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a layered adaptive disturbance suppression control method for drilling systems under unbounded disturbance, comprising the following steps:

[0010] S1: Establish a dynamic model of the deviation control mechanism for a multi-drilling system containing unbounded disturbances;

[0011] S2: Based on the dynamic model described in S1, a low-computational-complexity first-order observer is designed to estimate leader information, thereby achieving fully distributed control;

[0012] S3: Construct a novel disturbance observer with a dynamically changing function, removing the assumptions of disturbance differentiability and bounded derivative;

[0013] S4: Based on the disturbance observer and radial basis function (RBF) neural network described in S3, an adaptive backstepping sliding mode controller is designed to suppress unbounded disturbances.

[0014] Preferably, the multi-drilling system described in S1 includes N drilling agents, which locate and track a preset desired trajectory signal y0, and each agent is equipped with a novel deviation control mechanism; wherein a single novel deviation control mechanism consists of a dual-chamber deflection control cylinder, a servo valve and a control unit.

[0015] The relationship between the servo valve spool displacement and the control voltage of a single novel deviation control mechanism is considered to be a linear proportional relationship, as expressed by the following formula:

[0016] x v =k xv u#(1)

[0017] In the formula, x v This represents the spool displacement of the servo valve; k xv The value indicates a positive constant, and u indicates the control voltage.

[0018] The load flow of the servo valve in the new deviation control mechanism is Q. L The formula is defined as follows:

[0019]

[0020] In the formula, C d ω and P represent the flow coefficient and area gradient of the servo valve, respectively; s This refers to the system oil pressure supplied; p1 and p2 are the oil pressures of the inlet and outlet chambers, respectively; p L =p1-p2; ρ is the hydraulic oil density; the sign function definition of sgn is as follows:

[0021]

[0022] The load flow rate of the two chambers within the control cylinder by the new deviation control mechanism is expressed as follows:

[0023]

[0024] In the formula, Q1 and Q2 represent the load flow rates in the inlet and outlet oil chambers, respectively, and x p and the valve core displacement of the servo valve These represent the displacement signal and speed signal of the control cylinder valve core of the new deviation control mechanism, respectively; A p Represented as the effective area of ​​the control cylinder; β e V is expressed as the effective bulk modulus. t C represents the total volume of the inlet and outlet oil chambers. ip and C ep These are the internal leakage coefficient and external leakage coefficient of the control cylinder, respectively;

[0025] Based on the equivalent load elastic deformation during drilling, the force balance equation for a single deflection control cylinder is expressed as follows:

[0026]

[0027] In the formula, m p and B p These represent the total mass of the control cylinder and the load, and the viscous damping coefficient, k, respectively. s and F L These represent the equivalent elastic stiffness coefficient of the drilling load and the external load force acting on the deflection control cylinder, respectively.

[0028] according to Combining (4) and (6), we can obtain the following expression:

[0029]

[0030] Among them, C tp =(C ip +2C ep ) / 2 is the total leakage coefficient of the control cylinder;

[0031] External load force in the formula The derivative expression is as follows:

[0032]

[0033] In the formula, And x a and F represents the valve core displacement acceleration signal of the control cylinder of the new deviation control mechanism (6). b and F c These represent the separation friction and Coulomb friction of the deflection control cylinder, respectively. sThis represents the velocity threshold, and e represents the natural constant.

[0034] According to equations (6)-(8), the force balance equation of a single novel deviation control mechanism control cylinder is rewritten as follows:

[0035]

[0036] In the formula, C d This is expressed as the flow coefficient of the servo valve; k xv It is a positive constant; P s This represents the system oil pressure supplied by the servo valve; C tp This is expressed as the total leakage coefficient of the control cylinder.

[0037] Preferably, the multi-drilling system comprises N drilling systems to achieve consistent anti-interference control, where x is defined. i,1 =x p x i,2 =x v and x i,3 =x a x i,1 x i,2 and x i,3 Let $\mathbf{i}$ represent the displacement signal, velocity signal, and acceleration signal of the control cylinder valve core of the novel deviation control mechanism (6) of the i-th drilling system, respectively. Based on the expression (8) of the control cylinder of the novel deviation control mechanism (6), the state-space equation expression of the i-th drilling system is calculated as follows:

[0038]

[0039] In the formula, d i θ represents the unknown term of the system. i This indicates the external interference experienced by the system. This is represented as model uncertainty; Represented as a nonlinear function of the system;

[0040] Due to the nonlinear characteristics of the control system and unbounded disturbances, including friction during drilling, friction between the control cylinder and piston rod, and cutting loads, the model uncertainties and unbounded disturbances are combined into a single unbounded lumped disturbance term. The new system state-space equation expression is then:

[0041]

[0042] In the formula, It is the unbounded lumped disturbance of the deflection control system, Represented as a known nonlinear function of the system; These are represented as known system parameters.

[0043] Preferably, the low-computational-complexity first-order observer estimation of leader information described in S2 includes the following:

[0044] Each agent is designed with the following first-order observer to estimate the desired trajectory information, defined as y0, with the specific expression as follows:

[0045]

[0046] In the formula, and θ i These are the observer's output and input, respectively;

[0047] The observer's input θ i The design expression is:

[0048]

[0049] In the formula, w i b represents the observation error between neighboring agents; i Node information representing the leader agent; This is represented as the derivative information of the desired trajectory;

[0050] The following expression for the error variable is defined as:

[0051]

[0052] Therefore, we can conclude that:

[0053]

[0054] In the formula,

[0055] Define the following symbols respectively:

[0056]

[0057] w = [w1, ..., w N ] T (17)

[0058] ξ=[ξ1,…,ξ N ] T (18)

[0059] In the formula, For γ i ξ is the vector representation of the error variable; w is the vector representation of the observation error between agents; ξ is the vector representation of the error variable.

[0060] As a preferred embodiment, the novel interference observer described in S3 is expressed as follows:

[0061]

[0062] In the formula, Auxiliary variable The estimated value, It is the function to be designed for the new interference observer, s i It is a sliding mode switching function; Represented as disturbance estimates;

[0063] Define the following form of variable as:

[0064] s i =e i,2 +e i,3 (20)

[0065]

[0066] In the formula, e i,2 and e i,3 These represent the displacement velocity and acceleration tracking error of the valve core of the new deviation control mechanism (6), respectively. and For intermediate dummy variables;

[0067] For auxiliary variable η i By performing differentiation and combining it with the system state-space equations (11) and (19), the formula expression is obtained as follows:

[0068]

[0069] In the formula, Y i Indicates error design;

[0070] Adaptive rate The specific formula is expressed as follows:

[0071]

[0072] In the formula, It is η i The estimated value is used to design the interference observer function. The expression is:

[0073]

[0074] In the formula, k0 is any positive constant. It is a positive function and satisfies the condition.

[0075] The following definitions are given:

[0076]

[0077] in Indicates the disturbance value Di and disturbance estimates The difference.

[0078] As a preferred embodiment, the adaptive backstepping sliding mode controller based on a novel disturbance observer and radial basis function neural network design described in S4 includes the following:

[0079] The value of the DCM control displacement input of the i-th drilling system is used to track the reference displacement, and an adaptive backstepping sliding mode controller is designed to effectively suppress the influence of unbounded disturbances.

[0080] Define variables in the following form:

[0081]

[0082] Where, α i,1 and α i,2 Represents a virtual control law;

[0083] The controller design process includes:

[0084] Step 1:

[0085] Define the tracking error variable for the valve core displacement of the novel deviation control mechanism (6):

[0086]

[0087] Subsequently, by combining differential formula (29) with formulas (11), (12), and (27), we obtain:

[0088]

[0089] In the formula, the virtual control variable α i,1 =-e i,1 +θ i ; This is expressed as the derivative information of the valve core displacement error;

[0090] Step 2:

[0091]

[0092] In the formula, It is represented as the derivative of an intermediate dummy variable.

[0093] The formula for designing virtual control variables is as follows:

[0094]

[0095] Step 3:

[0096]

[0097] In the formula, The derivative is represented as an intermediate dummy variable; This represents the system's control input information;

[0098] Because of the unbounded lumped interference D in equation (32) i Therefore, the system control law u i The design is as follows:

[0099]

[0100] because The variables are related to the parameters of the DCM-controlled cylinder, therefore the denominator of the designed controller (33) is not zero, which ensures its non-singularity; however, the unbounded lumped disturbance D in the controller... i The combined disturbance term D directly affects the system's output performance and jitter characteristics; therefore, a disturbance observer is used to estimate the combined disturbance term D. i Simultaneously, a radial basis function neural network is used to approximate the known nonlinear function of the system. And disturbance error estimation To avoid control errors and jitter;

[0101] New system control law u i The design is as follows:

[0102]

[0103] In the formula, Γ represents the ideal weight estimate of the neural network; Γ represents the kernel function vector of the radial basis function neural network. The estimation of the known nonlinear function of the system.

[0104] Compared with the prior art, the layered adaptive disturbance suppression control method for drilling systems under unbounded disturbance provided by the present invention has the following beneficial effects:

[0105] 1. Innovative Observer Design: This invention first designs a first-order observer with low computational complexity, specifically for estimating leader information. This observer design not only improves the system's flexibility and availability, but its hierarchical architecture with the controller also enables fully distributed control of multi-drilling systems. A key advantage of this design is its ability to effectively isolate the effects of unbounded disturbances on individual drilling systems, preventing the propagation of adverse factors throughout the system, thereby significantly enhancing system robustness.

[0106] 2. Overcoming the limitations of traditional observers: Unlike traditional disturbance observers that require assumptions that the lumped disturbance is differentiable and its derivative is bounded, this invention removes these constraints. More importantly, traditional observers can typically only estimate bounded disturbances, while this invention innovatively constructs a new type of disturbance observer. This observer introduces a state-dependent dynamic change function, giving it a unique ability—to accurately estimate unbounded lumped disturbances with unbounded rates of change (i.e., unbounded derivatives).

[0107] 3. Advanced Controller Enables Reliable Control: Based on the aforementioned novel observer capable of handling unbounded disturbances, this invention further integrates Radial Basis Function Neural Networks (RBFNN) to design an adaptive backstepping sliding mode controller. The core advantage of this controller lies in its ability to effectively suppress and compensate for unbounded disturbances with unbounded derivatives (something traditional disturbance-based observer methods cannot achieve). This powerful anti-interference capability fundamentally ensures the reliable and safe operation of multi-drilling systems, ultimately improving the efficiency of thin coal seam mining. Attached Figure Description

[0108] Figure 1 This is a schematic diagram simulating the structure of the multi-drilling system of the present invention;

[0109] Figure 2 This is a schematic diagram of the layered adaptive interference suppression control method for drilling systems under unbounded interference according to the present invention. Detailed Implementation

[0110] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0111] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0112] For an example, please refer to... Figures 1 to 2 As shown:

[0113] To address the problems mentioned in the technical solutions, this application provides a layered adaptive disturbance suppression control method for drilling systems under unbounded disturbances.

[0114] like Figure 2 As shown, this invention proposes a layered adaptive disturbance suppression control method for drilling systems under unbounded disturbances, comprising:

[0115] A dynamic model of a multi-drilling system incorporating unbounded disturbances is established, specifically including the following:

[0116] The multi-drilling system comprises N drilling agents. To accurately locate and track the preset desired trajectory signal y0, each agent is equipped with a novel deviation control mechanism (DCM). The model structure of a single DCM is as follows: Figure 1 As shown, it consists of a dual-chamber deflection control cylinder, a servo valve, and a control unit.

[0117] Ideally, the relationship between the servo valve spool displacement and the control voltage for each DCM can be considered a linear proportional relationship. This means that the spool displacement is directly proportional to the applied voltage signal, enabling the servo valve to precisely control the hydraulic cylinder's movement. Therefore, an approximation can be expressed as follows:

[0118] x v =k xv u#(1)

[0119] Where, x v This refers to the valve spool displacement of the servo valve. We define the rightward displacement of the servo valve spool as positive, k xv It is a positive constant, and u is the control voltage.

[0120] The load flow Q of the DCM servo valve L The definition is as follows:

[0121]

[0122] Among them, C d ω and P s These represent the servo valve's flow coefficient, area gradient, and supplied system oil pressure, respectively; p L =p1-p2, where p1 and p2 are the oil pressures in the inlet and outlet chambers, respectively; ρ is the hydraulic oil density. Furthermore, sgn is a symbolic function defined as follows:

[0123]

[0124] To describe the load flow rates of the two chambers within the DCM control cylinder, considering external leakage, the continuity equation from fluid mechanics is applied, and the load flow rates of the two chambers are as follows:

[0125]

[0126] Where Q1 and Q2 are the load flow rates (m³) in the inlet and outlet oil chambers, respectively. 3 / s); A p To control the effective area of ​​the cylinder; C ip C ep and β e These are the internal leakage coefficient, external leakage coefficient, and effective bulk modulus of the control cylinder, respectively; Vt This refers to the total volume of the oil inlet chamber and the oil outlet chamber.

[0127] Due to the load flow Q of the DCM servo valve L It can be expressed again by the average load flow rate of the inlet and outlet oil chambers, according to Combining (2) and (5), we can obtain the following expression:

[0128]

[0129] Among them, C tp The total leakage coefficient of the control cylinder can be expressed as C. tp =(C ip +2C ep ) / 2.

[0130] refer to Figure 1 The schematic diagram of the DCM system shown can be interpreted as follows: Based on the equivalent load elastic deformation during drilling, the force balance equation for a single deflection control cylinder can be written as:

[0131]

[0132] Where, m p and B p These represent the total mass of the control cylinder and the load, and the viscous damping coefficient, respectively; k s and F L Represent the equivalent elastic stiffness coefficient of the drilling load and the external load force acting on the deflection control cylinder, respectively, where the external load force F L The derivative expression is as follows:

[0133]

[0134] in, and F represents the valve core displacement velocity and acceleration signal of the DCM control cylinder, respectively. b and F c These represent the separation friction and Coulomb friction of the deflection control cylinder, respectively. s This represents the velocity threshold, where e is a natural constant.

[0135] According to equations (8)-(10), the force balance equations for a single DCM control cylinder can be rewritten as follows:

[0136]

[0137] In the formula, C d This is expressed as the flow coefficient of the servo valve; k xv It is a positive constant; P s This represents the system oil pressure supplied by the servo valve; C tpThis is expressed as the total leakage coefficient of the control cylinder.

[0138] Considering a multi-drilling system comprising N drilling systems, achieving consistent and interference-resistant control, x i,1 =x p x i,2 =x v and x i,3 =x a Let represent the displacement signal, velocity signal, and acceleration signal of the DCM control cylinder valve core of the i-th drilling system, respectively. According to the DCM control cylinder expression (7), the state-space equation of the i-th drilling system can be expressed as:

[0139]

[0140] Among them, state variables

[0141] d i θ represents the unknown term of the system. i This indicates the external interference experienced by the system; This is represented as model uncertainty; Represented as a nonlinear function of the system;

[0142] Considering the nonlinear characteristics of the control system and unbounded disturbances, including friction during drilling, friction between the control cylinder and piston rod, and cutting loads, the model uncertainties and unbounded disturbances are combined into a single unbounded lumped disturbance term. The new state-space equations of the drilling system can then be expressed as:

[0143]

[0144] in, It is the unbounded lumped disturbance of the deflection control system. Represented as a known nonlinear function of the system; Indicates known system parameters;

[0145] Design a first-order observer with low computational complexity to estimate leader information, specifically including the following:

[0146] This invention designs a first-order observer for each agent to estimate the desired trajectory information y0, specifically in the following form:

[0147]

[0148] in, and θ i These are the observer's output and input, respectively.

[0149] The observer's input is designed as follows:

[0150]

[0151] in,

[0152] In the formula, w i b represents the observation error between neighboring agents; i Node information representing the leader agent; This is represented as the derivative information of the desired trajectory;

[0153] The following expression for the error variable is defined as:

[0154]

[0155] Therefore, we can conclude that:

[0156]

[0157] In the formula,

[0158] Define the following symbols respectively:

[0159]

[0160] w = [w1, ..., w N ] T (17)

[0161] ξ=[ξ1,…,ξ N ] T (18)

[0162] In the formula, For γ i ξ is the vector representation of the error variable; w is the vector representation of the observation error between agents; ξ is the vector representation of the error variable.

[0163] According to equations (12)-(18), we get:

[0164] w=(L+B)ξ (20)

[0165]

[0166] Choose the Lyapunov function as follows:

[0167]

[0168] In the formula, w T Pw represents the product term of the error vector matrix;

[0169] Where P is a non-singular N-dimensional matrix, and combining (13), (20), (21), the derivative of V0(t) can be expressed as

[0170]

[0171] In the formula, L represents the Laplace matrix; B represents the information interaction between the leader and the agent.

[0172] Where Q = P(L+B) + (L+B) T Since P is a non-singular matrix, we can obtain...

[0173]

[0174] In the formula, cλ min (Q) represents the smallest eigenvalue of matrix Q; λ max It is represented by the largest eigenvalue of matrix Q; For γ i Vector representation of;

[0175] Further deduction:

[0176]

[0177] In the formula, and Represented as positive constants; where Clearly, V0(t) is bounded for any finite initial state.

[0178] A novel type of dynamic disturbance observer is constructed, removing the constraint that traditional disturbance observers require the assumption that the lumped disturbance is differentiable and its derivative is bounded. Specifically, this includes the following:

[0179] This invention designs a novel disturbance observer for multi-drilling systems. Compared to most existing decoupling methods where the disturbance observer's parameters are designed as constants, the novel disturbance observer utilizes a neural network to estimate coupling terms and disturbance error information in the system to adjust the sliding mode switching function and the disturbance observer's parameter design function. Finally, based on the disturbance observer information, a controller is designed to decompose the system and avoid error jitter, achieving decoupled control without relying on precise parameters. This design method significantly expands the application range of disturbance observers and can be used in a wider range of disturbance control systems. The specific form of the novel disturbance observer is as follows:

[0180]

[0181] In the formula, Auxiliary variable The estimated value, It is the function to be designed for the new interference observer, si It is a sliding mode switching function; Represented as disturbance estimates;

[0182] Define the following form of variable as:

[0183] s i =e i,2 +e i,3 (20)

[0184]

[0185] In the formula, e i,2 and e i,3 These represent the displacement velocity and acceleration tracking error of the valve core of the new deviation control mechanism (6), respectively. and For intermediate dummy variables;

[0186] Subsequently, the auxiliary variable η i By performing differentiation and combining it with the system state-space equations (13) and (32), we obtain:

[0187] In the formula, Y i Indicates error design;

[0188] Adaptive rate The specific formula is expressed as follows:

[0189]

[0190] In the formula, It is η i The estimated value is used to design the interference observer function. The expression is:

[0191]

[0192] In the formula, k0 is any positive constant. It is a positive function and satisfies the condition.

[0193] The following definitions are given:

[0194]

[0195] in Indicates the disturbance value D i and disturbance estimates The difference, by differentiating (33) and combining (30) and (31), yields:

[0196]

[0197] Consider the following Lyapunov function

[0198]

[0199] Combining (34), V D The time derivative is:

[0200]

[0201] According to (36) and (11):

[0202]

[0203] It is easy to deduce that, in the formula, k0 represents a positive constant; if If it is true, then it exists. Therefore, there is

[0204]

[0205] Otherwise, the following inequality holds.

[0206]

[0207] Combining (11), it can be further rewritten as

[0208]

[0209] Obviously, the disturbance value D i and disturbance estimates The difference It is bounded.

[0210] S104. An adaptive backstepping sliding mode controller is designed based on a novel disturbance observer and radial basis function neural network to suppress the effects of unbounded disturbances, specifically including the following:

[0211] The objective of this invention in this part is to obtain the value of the DCM control displacement input of the i-th drilling system in order to track the reference displacement, while designing an adaptive backstepping sliding mode controller to effectively suppress the influence of unbounded disturbances.

[0212] Define variables in the following form:

[0213]

[0214]

[0215] Where α i,1 and α i,2 Represents the virtual control law, z i,1 and z i,2 This refers to the parameter representation in the sliding mode controller.

[0216] The controller design process can be divided into three steps.

[0217] Step 1:

[0218] Define the tracking error variable for the DCM valve spool displacement:

[0219]

[0220] Subsequently, by differentiating (43) and combining it with (12), (28), and (41), we obtain:

[0221]

[0222] Design virtual control variable α i,1 =-e i,1 +θ i To ensure displacement tracking error e i,1 As the function approaches zero, we can define a positive semi-definite Lyapunov function:

[0223]

[0224] Consider equation (44), V i,1 The time derivative can be given as follows:

[0225]

[0226] Step 2:

[0227]

[0228] Design virtual control variables To ensure system stability and convergence speed,

[0229] Therefore, e i,2 A new Lyapunov function is defined as:

[0230]

[0231] V i,2 The time derivative is as follows:

[0232]

[0233] Step 3:

[0234]

[0235] In the formula, The derivative is represented as an intermediate dummy variable; This represents the system's control input information;

[0236] Because of the unbounded lumped interference D in equation (32) i Therefore, the system control law u i The design is as follows:

[0237]

[0238] because The variables are related to the parameters of the DCM-controlled cylinder, therefore the denominator of the designed controller (51) is not zero, which ensures its non-singularity. However, the unbounded lumped disturbance D in the controller... i This directly affects the system's output performance and jitter characteristics. Therefore, a disturbance observer is used to estimate the composite disturbance term D. i Simultaneously, a radial basis function neural network is used to approximate the known nonlinear function of the system. And disturbance error estimation To avoid control errors and jitter.

[0239] New system control law u i The design is as follows:

[0240]

[0241] In the formula, This can be represented as an estimate of a known nonlinear function of a system by a neural network.

[0242] According to equations (50) and (52), we can obtain:

[0243]

[0244] Consider the following Lyapunov function:

[0245]

[0246] In the formula, It is expressed as the product of the neural network weights and the estimation difference; It is W i The estimate and In addition, r i,2 It is a positive constant. Based on assumption 3, we can obtain V. i,3 The time derivative is as follows:

[0247]

[0248] Combining (53) and (40), we can conclude that:

[0249]

[0250] Since Theorem 1 holds, we can approximate the approximation using a neural network. (64) Further transformed into:

[0251]

[0252] Design Adaptive Update Law for

[0253]

[0254] In the formula, Γ represents the kernel function vector of the radial basis function neural network; r i,1 Since it is a positive constant, combining (57) and (58), we have:

[0255]

[0256] Combining (27), (45), (48) and (54) we get

[0257]

[0258] Where β1=min{1,r i,1}, According to the above equations (45), (48) and (60), the system can be obtained as asymptotically stable.

[0259] Table 1 shows the values ​​of each parameter;

[0260]

[0261] Through the above embodiments, this solution has the following advantages over the prior art:

[0262] 1. Innovative Observer Design: This invention first designs a first-order observer with low computational complexity, specifically for estimating leader information. This observer design not only improves the system's flexibility and availability, but its hierarchical architecture with the controller also enables fully distributed control of multi-drilling systems. A key advantage of this design is its ability to effectively isolate the effects of unbounded disturbances on individual drilling systems, preventing the propagation of adverse factors throughout the system, thereby significantly enhancing system robustness.

[0263] 2. Overcoming the limitations of traditional observers: Unlike traditional disturbance observers that require assumptions that the lumped disturbance is differentiable and its derivative is bounded, this invention removes these constraints. More importantly, traditional observers can typically only estimate bounded disturbances, while this invention innovatively constructs a new type of disturbance observer. This observer introduces a state-dependent dynamic change function, giving it a unique ability—to accurately estimate unbounded lumped disturbances with unbounded rates of change (i.e., unbounded derivatives).

[0264] 3. Advanced Controller Enables Reliable Control: Based on the aforementioned novel observer capable of handling unbounded disturbances, this invention further integrates Radial Basis Function Neural Networks (RBFNN) to design an adaptive backstepping sliding mode controller. The core advantage of this controller lies in its ability to effectively suppress and compensate for unbounded disturbances with unbounded derivatives (something traditional disturbance-based observer methods cannot achieve). This powerful anti-interference capability fundamentally ensures the reliable and safe operation of multi-drilling systems, ultimately improving the efficiency of thin coal seam mining.

[0265] This invention proposes a nonlinear adaptive backstepping sliding mode control strategy based on a disturbance observer for multi-drilling systems. By constructing an error observer for each servo system, consistency between the desired trajectory signal and the observer's output signal is achieved. Based on this, a disturbance observer based on a dynamic function is proposed to estimate lumped disturbances. An adaptive backstepping sliding mode controller is designed and combined with a neural network to compensate for and eliminate the impact of compound disturbances on the system, thereby avoiding control errors and jitter. This invention can ensure the safe and reliable operation of multi-drilling systems under complex operating conditions such as unbounded disturbance derivatives, thus effectively improving coal mining in thin coal seams.

[0266] It should be noted that in this invention patent, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0267] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A layered adaptive interference rejection control method for a drilling system under unbounded interference, characterized in that, Comprise the following steps: S1: establish a multi-drilling drilling system deviation control mechanism dynamics model containing unbounded disturbance; The multi-drilling drilling system described in S1 comprises N drilling intelligent agents, and the preset desired trajectory signal is positioned and tracked as A new deviation control mechanism is mounted for each intelligent agent; Wherein a single new type of deviation control mechanism is composed of a double-chamber deflection control cylinder, a servo valve and a control unit; The relationship between the servo valve spool displacement of a single new type of deviation control mechanism and the control voltage is regarded as a linear proportional relationship, and the specific formula is as follows: (1) In the formula, represents the spool displacement of the servo valve; represents a normal number, represents a control voltage; The load flow of the new bias control mechanism servo valve is , the formula is defined as follows: (2) wherein and represent the flow coefficient and the area gradient of the servo valve, respectively; is the supplied system oil pressure; and are the oil pressures of the inlet and outlet oil chambers, respectively; ; is the hydraulic oil density; The sign function of is defined as follows: (3) The load flow of the two chambers in the control cylinder of the new type of deviation control mechanism is represented as follows: (4) (5) wherein, and Qd and Qd represent the load flow in the inlet and outlet chambers, respectively, and the spool displacement of the servo valve Qd and Vd represent the new bias control mechanism control cylinder spool displacement signal and velocity signal, respectively; Aeff represents the control cylinder effective area; Veff represents the effective volume modulus; Vtot represents the total volume of the inlet and outlet chambers; and and represent the inner and outer leakage coefficients of the control cylinder, respectively; According to the equivalent load elastic deformation in the drilling process, the force balance equation of a single deflection control cylinder is expressed as: (6) wherein, and respectively represent the total mass of the control cylinder and the load and the viscous damping coefficient, and respectively represent the equivalent elastic stiffness coefficient of the drilling load and the external load force acting on the deflection control cylinder; According to , the expressions below can be obtained by integrating (4)-(6): (7) wherein Ktot is the total leakage coefficient of the cylinder; The derivative of the external load force in the equation is given by the following expression: (8) wherein , and and respectively represent the valve core displacement acceleration signal of the new type of deviation control mechanism (6) controlling the cylinder, and respectively represent the separation friction and coulomb friction of the deflection control cylinder, represents the speed threshold, and e represents the natural constant; According to formula (6)-(8), the force balance equation of the control cylinder of a single new type of deviation control mechanism is rewritten as the following expression: (9) In the formula, is a flow coefficient of the servo valve; is a normal number; is a system oil pressure supplied to the servo valve; is a total leakage coefficient of the control cylinder; S2: design a low-complexity first-order observer to estimate leader information based on the dynamics model described in S1, and realize fully distributed control; S3: build a new type of disturbance observer with dynamic change function, remove the disturbance differentiable and derivative bounded assumption; The specific form of the new type of disturbance observer described in S3 is expressed as: (19) wherein is an auxiliary variable is an estimate of is a function to be designed for the new disturbance observer, is a sliding mode switching function; is expressed as a disturbance estimate; Define the following form variables as: (20) (21) (22) wherein and respectively represent the displacement velocity and acceleration tracking error of the spool of the new bias control mechanism (6) valve; and are intermediate dummy variables; For the auxiliary variable Taking the differential and combining the system state space equations (11) and (19), the formula expression is obtained as follows: (23) In the formula, ; denotes error design; Adaptive rate The specific formula is expressed as follows: (24) wherein is an estimate of The expression is (25) wherein is any positive number, is a positive function satisfying the condition ; Give the following definitions: (26) wherein represents a disturbance value and a disturbance estimate value the difference value; S4: design an adaptive backstepping sliding mode controller based on the disturbance observer described in S3 and the radial basis neural network to suppress unbounded disturbance; The adaptive backstepping sliding mode controller designed based on the new type of disturbance observer and the radial basis neural network described in S4 comprises the following contents: No. The DCM control displacement input value of the drilling system is used to track the reference displacement, and an adaptive backstepping sliding mode controller is designed to effectively suppress the influence of unbounded disturbances. Define the following form variables: (27) (28) wherein and denotes the virtual control law; The design process of the controller comprises: Step 1: Define the tracking error variable of the spool displacement of the new type of deviation control mechanism (6) as follows: (29) Then, differential formula (29) is combined with formula (11), formula (12) and formula (27) to obtain: (30) wherein the virtual control variable ; is represented as derivative information of the spool displacement error; Step 2: (31) wherein denotes the derivative of the intermediate virtual variable; The virtual control variable formula is designed as follows: ； Step 3: (32) wherein the derivative expressed as an intermediate virtual variable; denotes the control input information of the system; Because of the presence of unbounded set total disturbance in (32) the system control rate is designed as follows: (33) Due to being the variables related to the parameters of the DCM controlled cylinder, the designed controller (33) has non-zero denominator, which ensures its nonsingularity; however, the unbounded set of disturbances directly affects the output performance and chattering characteristics of the system; therefore, the disturbance observer is employed to estimate the compound disturbance term while the radial basis neural network is utilized to approximate the known nonlinear functions of the system and disturbance error estimation to avoid control error and chattering; New system control rate The design is as follows: (34) wherein represents an ideal weight estimate of a neural network; represents a kernel function vector of a radial basis neural network; is an estimate of a known nonlinear function of the system.

2. The method of claim 1, wherein, The multi-drilling drilling system comprises The drilling system realizes consistent anti-interference control, and defines 、 and , , and respectively represent the new deviation control mechanism (6) of the first Drilling system control cylinder spool displacement signal, speed signal and acceleration signal; according to the new deviation control mechanism (6) control cylinder expression (8), the state space equation expression of the first Drilling system is calculated as: (10) wherein, represents an unknown term of the system, represents an external disturbance to the system, represents as a model uncertainty; represents as a nonlinear function of the system; Due to the nonlinear characteristics of the control system and the unbounded disturbance, including the friction in the drilling process, the friction between the control cylinder and the piston rod, and the cutting load; the model uncertainty and the unbounded disturbance are combined into an unbounded lumped disturbance term, and the new system state space equation expression is as follows: (11) wherein is an unbounded lumped disturbance of the deflection control system, which is expressed as a known nonlinear function of the system; is expressed as a known system parameter.

3. The method of claim 1, wherein, The low-complexity first-order observer to estimate leader information described in S2 comprises the following contents: Each agent designs a first-order observer to estimate the desired trajectory information as follows The specific expression is as follows: (12) wherein and are the output and input of the observer, respectively Inputs to the observer The design expression is: (13) wherein represents the observation error between neighboring agents; represents the node information of the leader agent; represents the derivative information of the desired trajectory; Define the error variable expression as follows: (14) Thus, we can get: (15) In the formulae, ; Define the following symbols respectively: (16) (17) (18) wherein is a vector representation of is a vector representation of the observation error between agents; is a vector representation of the error variable.​

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