A local fault-tolerant control method for a rotary steerable drilling tool platform

Abstract

The application discloses a kind of local fault-tolerant control methods of rotary steerable drilling tool platform, belong to the field of fault-tolerant control, comprising the following steps: step 1, obtain the random high-order full-drive system model of rotary steerable drilling tool platform with local fault;Step 2, design equivalent control law based on high-order operator, build equivalent system;Step 3, pre-division state domain, design observer based on adaptive gain;Step 4, design output feedback fault-tolerant control law, realize the stable rotary steerable drilling tool platform system under the probability sense.The application realizes the efficient fault-tolerant control for the local fault of rotary steerable drilling tool platform, ensures the stability of rotary steerable drilling tool platform.

Description

Technical Field

[0001] This invention belongs to the field of fault-tolerant control, specifically relating to a local fault-tolerant control method for a rotary steerable drilling tool platform. Background Technology

[0002] In production practice, rotary steerable drilling tool platforms are equipped with several components. Due to manufacturing defects and assembly precision issues of these components, local faults may occur when the rotary steerable drilling tool platform operates in a certain angle, angular velocity, or other state range. However, the faults will disappear when the rotary steerable drilling tool platform leaves this state range, making it difficult for the controller to accurately and effectively perform fault tolerance. Summary of the Invention

[0003] To address the aforementioned issues, this invention proposes a local fault-tolerant control method for rotary steerable drilling tool platforms. For rotary steerable drilling tool platforms containing random signals, a novel fault-tolerant control law is developed based on a stochastic high-order full-drive system model. Under different pre-divided state domains, efficient fault-tolerant control for local faults is achieved, ensuring the stability of the rotary steerable drilling tool platform system.

[0004] The technical solution of the present invention is as follows:

[0005] A local fault-tolerant control method for a rotary steerable drilling tool platform includes the following steps:

[0006] Step 1: Obtain a stochastic high-order all-drive system model of a rotary steerable drilling tool platform with localized faults;

[0007] Step 2: Design equivalent control laws based on higher-order operators and construct equivalent systems;

[0008] Step 3: Pre-divide the state domain and design an observer based on adaptive gain;

[0009] Step 4: Design an output feedback fault-tolerant control law to achieve a stable rotary steerable drilling tool platform system in a probabilistic sense.

[0010] Furthermore, the specific process of step 1 is as follows:

[0011] Step 1.1: Establish the platform dynamic equations driven by the permanent magnet synchronous motor, as follows:

[0012]

[0013] Among them, i q It is the q-axis current, θ is the tool face angle; R s It is the stator winding impedance, L q It is the q-axis stator winding inductance, n pIt is the number of pole pairs of the motor, Φ a J is the magnetic flux of the permanent magnet, B is the total inertia, and U is the damping coefficient. q It is the q-axis voltage. It is a local fault; ζ is random interference;

[0014] Step 1.2: Obtain the platform parameters R through direct measurement or identification methods. s L q n p , Φ a J, B;

[0015] Step 1.3: Model the random disturbance as a probability space A standard Brownian motion in , where Ω is the sampling space, It is a σ-domain on the sampling space Ω. yes A probability measure on;

[0016] Step 1.4: Define the following higher-order integral operators as follows:

[0017]

[0018] in, Here, is a higher-order integral operator, where n is the order of the operator, typically an integer greater than 1; t, t i All are integrand time elements, i = 1, ..., n; f is a general dynamic function;

[0019] Step 1.5: Based on the platform's dynamic equations, convert the platform dynamic equations in Step 1.1 into a higher-order integral equation form as shown in equation (3);

[0020]

[0021] Where z(t) is the r-dimensional system state variable, z(t0) is the value of the system state variable at the initial moment, g is the input channel gain, and u(t) is the controller input, i.e., the q-axis voltage u. q h is the gain of the interference channel. Integral for Lebesgue, for integral, This is a local area failure.

[0022] Step 1.6: It is agreed that equation (3) is expressed as the differential form of equation (4), that is, the stochastic high-order all-drive system model.

[0023]

[0024] Step 1.7: Model the local fault as follows:

[0025]

[0026] Where λ(t) is the unknown time-varying fault amplitude, I f It is an unknown local fault characteristic function, Ω f It is the fault occurrence region, and α(z) is an unknown fault structure function;

[0027] Step 1.8: Verify that the local area fault meets the conditions:

[0028] |λ(t)α(z)|≤ρ|z| (7);

[0029] Where ρ is a finite but unknown constant.

[0030] Furthermore, the specific process of step 2 is as follows:

[0031] Step 2.1: Using the operator as shown in equation (9), for any random variable x satisfying equation (8) and a quadratic differentiable function V, we have equation (9).

[0032]

[0033] Where b represents the drift term; s represents the integrand time element; σ represents the diffusion term; ω s It is a standard Brownian motion; It is a newly defined operator; Tr(·) represents the trace of the matrix;

[0034] Step 2.2: Design a higher-order operator as shown in equation (10), and define the following conventions.

[0035]

[0036] in, To represent a first-order operator, Represents higher-order operators;

[0037] Step 2.3: Design the equivalent control law as shown in equation (11).

[0038]

[0039] Where u represents the final control variable; u ＊ Indicates auxiliary control quantity; parameter v is the intermediate control signal;

[0040] Step 2.4: Substitute the equivalent control law (11) into (4) to obtain the equivalent system as shown in (12).

[0041]

[0042] Furthermore, the specific process of step 3 is as follows:

[0043] Step 3.1, let the observer variable...

[0044] Step 3.2: Design the parameter matrix

[0045]

[0046] To satisfy the condition that for a certain positive definite symmetric matrix P, we have

[0047] Φ T P+PΦ≤-2I n (14);

[0048] Among them, I n Represents an n-order identity matrix;

[0049] Step 3.3: Pre-divide n into the state region. Ω n regions Ω >1, respectively denoted as

[0050] Step 3.4: Design the dynamic adaptive gain L c ,

[0051]

[0052] in, This is the observation error; The indicative function of the i-th fault domain; This represents the gain of the i-th fault domain;

[0053] Step 3.5: Design the observer as follows:

[0054]

[0055] in, This indicates that for the observer variable The estimated value, Let be the derivative of the estimated value, i = 1, ..., n.

[0056] Furthermore, the specific process of step 4 is as follows:

[0057] Step 4.1: Design the parameter matrix

[0058]

[0059] To satisfy the condition that for a certain positive definite symmetric matrix Q, we have

[0060] Γ T Q+QΓ≤-2I n (18);

[0061] Where, k i It is the control gain, i = 1,...,n;

[0062] Step 4.2, Introduce transformation

[0063]

[0064] Where, ζ i Let i be the variable of the intermediate control signal, i = 1, ..., n;

[0065] Step 4.3: Design the auxiliary control quantity v′ of the intermediate control signal v as follows:

[0066]

[0067] At this point, for a fault that satisfies formula (7), the equivalent control law (11) designed by output feedback fault-tolerant control law (19) and (20) can make it achieve global asymptotic stability in a probabilistic sense.

[0068] The beneficial technical effects of this invention are as follows:

[0069] This invention develops a novel fault-tolerant control law based on a stochastic high-order all-drive system model. Under different pre-divided state domains, it achieves efficient fault-tolerant control for localized faults in rotary steerable drilling tool platforms, ensuring the platform's stability. Compared to traditional fault-tolerant control methods, this invention has lower control costs and more precise fault tolerance. Attached Figure Description

[0070] Figure 1 This is a flowchart of the local fault-tolerant control method for the rotary steerable drilling tool platform of the present invention.

[0071] Figure 2 This is an example diagram illustrating the precise pre-division of a two-dimensional state region according to the present invention.

[0072] Figure 3 This is an example diagram illustrating the rough pre-division of the three-dimensional state region according to the present invention.

[0073] Figure 4 This is a schematic diagram of the control output results of the controller in the simulation experiment of this invention.

[0074] Figure 5 This is a schematic diagram showing the gain magnitude results in different state domains during the simulation experiment of this invention. Detailed Implementation

[0075] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0076] like Figure 1 As shown, a local fault-tolerant control method for a rotary steerable drilling tool platform includes the following steps:

[0077] Step 1: Obtain a stochastic high-order all-drive system model of a rotary steerable drilling tool platform with localized faults. The specific process is as follows:

[0078] Step 1.1: Establish the platform dynamic equations driven by the permanent magnet synchronous motor, as follows:

[0079]

[0080] Among them, i q R is the q-axis current, θ is the tool face angle, i.e., the angle between the plane formed by the drill bit axis and the borehole axis and the line along the high side; s It is the stator winding impedance, L q It is the q-axis stator winding inductance, n p It is the number of pole pairs of the motor, Φ a J is the magnetic flux of the permanent magnet, B is the total inertia, and U is the damping coefficient. q It is the q-axis voltage. It is a local fault; ζ is random interference;

[0081] Step 1.2: Obtain the platform parameters R through direct measurement or identification methods, such as the least squares method or the maximum likelihood method. s L q n p , Φ a J, B;

[0082] Step 1.3: Model the random disturbance as a probability space A standard Brownian motion in , where Ω is the sampling space, It is a σ-domain on the sampling space Ω. yes A probability measure on;

[0083] Step 1.4: Define the following higher-order integral operators as follows:

[0084]

[0085] in, Here, is a higher-order integral operator, where n is the order of the operator, typically an integer greater than 1; t, t i All are integrand time elements, i = 1, ..., n; f is a general dynamic function;

[0086] Step 1.5: Based on the platform's dynamic equations, convert the platform dynamic equations in Step 1.1 into a higher-order integral equation form as shown in equation (3);

[0087]

[0088] Where z(t) is the r-dimensional system state variable, z(t0) is the value of the system state variable at the initial moment, g is the input channel gain, and u(t) is the controller input, i.e., the q-axis voltage u. q h is the gain of the interference channel. Integral for Lebesgue, for integral, This is a local area failure.

[0089] Step 1.6, it is agreed that equation (3) is expressed in the differential form of equation (4), that is... Figure 1 The stochastic high-order all-drive system model in

[0090]

[0091] Step 1.7: Model the local fault as follows:

[0092]

[0093] Where λ(t) is the unknown time-varying fault amplitude, I f It is an unknown local fault characteristic function, Ω f It is the fault occurrence region, and α(z) is an unknown fault structure function;

[0094] Step 1.8: Verify that the local area fault meets the conditions:

[0095] |λ(t)α(z)|≤ρ|z| (7);

[0096] Where ρ is a finite but unknown constant.

[0097] Step 2: Design equivalent control laws based on higher-order operators and construct equivalent systems. This includes the following steps:

[0098] Step 2.1: Using the operator as shown in equation (9), for any random variable x satisfying equation (8) and a quadratic differentiable function V, we have equation (9).

[0099]

[0100] Where b represents the drift term; s represents the integrand time element; σ represents the diffusion term; ω s It is a standard Brownian motion; It is a newly defined operator; Tr(·) represents the trace of the matrix;

[0101] Step 2.2: Design a higher-order operator as shown in equation (10), and define the following conventions.

[0102]

[0103] in, To represent a first-order operator, Represents higher-order operators;

[0104] Step 2.3: Design the equivalent control law as shown in equation (11).

[0105]

[0106] Where u represents the final control variable, u ＊ Indicates auxiliary control quantity; parameter Both the intermediate control signal v and the intermediate control signal v will be designed in steps 3.2 and 4.3 respectively;

[0107] Step 2.4: Substitute the equivalent control law (11) into (4) to obtain the equivalent system as shown in (12).

[0108]

[0109] Step 3: Pre-divide the state domain and design an observer based on adaptive gain. This includes the following steps:

[0110] Step 3.1, let the observer variable... _

[0111] Step 3.2: Design the parameter matrix

[0112]

[0113] To satisfy the condition that for a certain positive definite symmetric matrix P, we have

[0114] Φ T P+PΦ≤-2I n (14);

[0115] Among them, I n Represents an n-order identity matrix;

[0116] Step 3.3: Pre-divide n into the state region. Ω n regions Ω >1, respectively denoted as

[0117] If prior knowledge about the fault exists, the state region can be finely divided. For example, if it is known that a rotary steered drilling platform is prone to failure when operating at a certain angle or within a certain angular velocity range, then the division should include more regions within that range. Figure 2 As shown, the two-dimensional state region is precisely pre-divided into 11 regions, with the horizontal coordinate z1 representing the tool face angle and the vertical coordinate z2 representing the angular velocity.

[0118] Without prior knowledge of the fault, a rough division of the state region is possible, for example, as... Figure 3 As shown, the three-dimensional state region is roughly pre-divided into 3 regions.

[0119] Step 3.4: Design the dynamic adaptive gain L c ,

[0120]

[0121] in, For observation error, Defined in the next step; The indicative function of the i-th fault domain; This represents the gain of the i-th fault domain;

[0122] Step 3.5: Design the observer as follows:

[0123]

[0124] in, This indicates that for the observer variable The estimated value, Let be the derivative of the estimated value, i = 1, ..., n.

[0125] Step 4: Design an output feedback fault-tolerant control law to achieve a probabilistically stable rotary steerable drilling tool platform system. This includes the following steps:

[0126] Step 4.1: Design the parameter matrix

[0127]

[0128] To satisfy the condition that for a certain positive definite symmetric matrix Q, we have

[0129] Γ T Q+QΓ≤-2I n (18);

[0130] Where, k i It is the control gain, i = 1, ..., n;

[0131] Step 4.2, Introduce transformation

[0132]

[0133] Where ζ is a component variable of the intermediate control signal, i = 1, ..., n;

[0134] Step 4.3: Design the auxiliary control quantity v of the intermediate control signal v as follows:

[0135]

[0136] At this point, for a fault that satisfies formula (7), the equivalent control law (11) designed by output feedback fault-tolerant control law (19) and (20) can make it achieve global asymptotic stability in a probabilistic sense.

[0137] To demonstrate the feasibility and superiority of this invention, the following simulation experiments were conducted.

[0138] Consider a rotary steerable drilling tool platform, the parameters of which are shown in Table 1.

[0139] Table 1 Parameters of Rotary Steering Drilling Tool Platform

[0140]

[0141] Substituting the parameters from Table 1 into equation (1) of step 1, the equations for the stochastic high-order all-drive system model can be obtained through the transformation in equation (3) as follows:

[0142]

[0143] Where f0 = -716z and f1 = -24218z.

[0144] The simulated local fault caused by the drill bit position is as follows:

[0145]

[0146] It has been verified that condition (7) is met, where At this point, the method of the present invention can perform fault-tolerant control for the local fault.

[0147] Based on step 2, design the equivalent control law:

[0148]

[0149] Where a1 = 1, a2 = 3.

[0150] Based on step 3, four state domains are pre-divided as follows: Ω1=(-∞,-5),Ω2=[-5,0),Ω3=[0,5),Ω=[5,+∞). The observer is designed as follows:

[0151]

[0152] Among them, L c As shown in equation (16).

[0153] Based on step 4, the output feedback control law is designed as follows:

[0154]

[0155] Where k1 = 1, k2 = 0.2.

[0156] The initial conditions for the simulation were designed as follows: The numerical method used is the Euler-Maruyama method. The simulation results of the method of this invention are as follows: Figure 4 and Figure 5 As shown, where, Figure 4 For the control output of the controller, Figure 5 This represents the gain magnitude in different state domains. From Figure 4 and Figure 5 As can be seen, the gain of the method of the present invention increases rapidly only within the fault domain Ω3=[0,5), thus achieving precise and efficient control of the fault.

[0157] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A local fault-tolerant control method for a rotary steerable drilling tool platform, characterized in that, Includes the following steps: Step 1: Obtain a stochastic high-order all-drive system model of a rotary steerable drilling tool platform with localized faults; Step 2: Design equivalent control laws based on higher-order operators and construct equivalent systems; Step 3: Pre-divide the state domain and design an observer based on adaptive gain; the specific process is as follows: Step 3.1, let the observer variable... Integral for Lebesgue; parameters i = 0, 1, ..., n-1; z is an r-dimensional system state variable; Step 3.2: Design the parameter matrix To satisfy the condition that for a certain positive definite symmetric matrix P, we have Φ T P+PΦ≤-2I n (14); Among them, I n Represents an n-order identity matrix; Step 3.3: Pre-divide n into the state region. Ω n regions Ω >1, respectively denoted as Step 3.4: Design the dynamic adaptive gain L c , in, This is the observation error; The indicative function of the i-th fault domain; This represents the gain of the i-th fault domain; Step 3.5: Design the observer as follows: in, This indicates that for the observer variable The estimated value, Let i be the derivative of the estimated value, i = 1, ..., n; Step 4: Design an output feedback fault-tolerant control law to achieve a probabilistically stable rotary steerable drilling tool platform system; the specific process is as follows: Step 4.1: Design the parameter matrix To satisfy the condition that for a certain positive definite symmetric matrix Q, we have Γ T Q+QΓ≤-2I n (18); Where, k i It is the control gain, i = 1,...,n; Step 4.2, Introduce transformation Where, ζ i Let i be the variable of the intermediate control signal, i = 1, ..., n; Step 4.3: Design the auxiliary control quantity v′ of the intermediate control signal v as follows: At this point, for a fault that meets the conditions for a local fault, the equivalent control law designed by output feedback fault-tolerant control law (19) and (20) can enable it to achieve global asymptotic stability in a probabilistic sense.

2. The local fault-tolerant control method for a rotary steered drilling tool platform according to claim 1, characterized in that, The specific process of step 1 is as follows: Step 1.1: Establish the platform dynamic equations driven by the permanent magnet synchronous motor, as follows: Among them, i q It is the q-axis current, θ is the tool face angle; R s It is the stator winding impedance, L q It is the q-axis stator winding inductance, n p It is the number of pole pairs of the motor, Φ a J is the magnetic flux of the permanent magnet, B is the total inertia, and U is the damping coefficient. q It is the q-axis voltage. It is a local fault; ζ is random interference; Step 1.2: Obtain the platform parameters R through direct measurement or identification methods. s L q n p , Φ a J, B; Step 1.3: Model the random disturbance as a probability space A standard Brownian motion in , where Ω is the sampling space, It is a σ-domain on the sampling space Ω. yes A probability measure on; Step 1.4: Define the following higher-order integral operators as follows: in, Here, is a higher-order integral operator, where n is the order of the operator, typically an integer greater than 1; t, t i All are integrand time elements, i = 1, ..., n; f is a general dynamic function; Step 1.5: Based on the platform's dynamic equations, convert the platform dynamic equations in Step 1.1 into a higher-order integral equation form as shown in equation (3); Where z(t) is the r-dimensional system state variable, z(t0) is the value of the system state variable at the initial moment, g is the input channel gain, and u(t) is the controller input, i.e., the q-axis voltage u. q h is the gain of the interference channel. for integral, This is a local area failure. Step 1.6: It is agreed that equation (3) is expressed as the differential form of equation (4), that is, the stochastic high-order all-drive system model. Step 1.7: Model the local fault as follows: Where λ(t) is the unknown time-varying fault amplitude, I f It is an unknown local fault characteristic function, Ω f It is the fault occurrence region, and α(z) is an unknown fault structure function; Step 1.8: Verify that the local area fault meets the conditions: |λ(t)α(z)|≤ρ|z| (7); Where ρ is a finite but unknown constant.

3. The local fault-tolerant control method for rotary steered drilling tool platforms according to claim 2, characterized in that, The specific process of step 2 is as follows: Step 2.1: Using the operator as shown in equation (9), for any random variable x satisfying equation (8) and a quadratic differentiable function V, we have equation (9). Where b represents the drift term; s represents the integrand time element; σ represents the diffusion term; ω s It is a standard Brownian motion; It is a newly defined operator; Tr(·) represents the trace of the matrix; Step 2.2: Design a higher-order operator as shown in equation (10), and define the following conventions. in, To represent a first-order operator, Represents higher-order operators; Step 2.3: Design the equivalent control law as shown in equation (11). Where u represents the final control variable; This represents the auxiliary control quantity; v is the intermediate control signal. Step 2.4: Substitute the equivalent control law (11) into (4) to obtain the equivalent system as shown in (12).

Images