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

Abstract

The application provides a random fault-tolerant control method for a rotary steerable drilling tool platform, comprising the following steps: S1, establishing a random high-order full-drive system equation based on the rotary steerable drilling tool platform according to rotary steerable drilling tool platform parameters; S2, designing an equivalent control law according to the random high-order full-drive system structure to obtain a pre-closed-loop rotary steerable drilling platform system with a linear drift term; S3, designing a gain observer on the basis of the pre-closed-loop system to obtain an estimated value of high-order states of the rotary steerable drilling platform; and S4, designing an output feedback control law of the rotary steerable drilling platform system to realize fault-tolerant control. The technical scheme of the application overcomes the problem that the rotary steerable drilling platform system is unstable after a sensor fault occurs in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault-tolerant control, and particularly relates to a random fault-tolerant control method for a rotary steerable drilling tool platform. BACKGROUND

[0002] The rotary steerable drilling tool platform is an advanced device for oil and gas exploitation, and needs to work stably for a long time in a harsh downhole environment. In actual engineering, strong process noise is generated when rocks are broken, and the impact is easy to cause sensor failure, thereby causing the rotary steerable drilling platform system to be unstable. Therefore, a control method is needed to ensure the stability of the rotary steerable drilling tool platform system when the sensor has a partial failure fault. SUMMARY

[0003] The main purpose of the present application is to provide a random fault-tolerant control method for a rotary steerable drilling tool platform, so as to solve the problem that the rotary steerable drilling platform system is unstable after the sensor fails in the prior art.

[0004] To achieve the above-mentioned purpose, the present application provides a random fault-tolerant control method for a rotary steerable drilling tool platform, comprising the following steps:

[0005] S1, establishing a random high-order full-drive system equation based on the rotary steerable drilling tool platform according to the rotary steerable drilling tool platform parameters;

[0006] S2, designing an equivalent control law according to the random high-order full-drive system structure to obtain a pre-closed-loop rotary steerable drilling platform system with a linear drift term;

[0007] S3, designing a gain observer on the basis of the pre-closed-loop system to obtain an estimated value of the high-order state of the rotary steerable drilling platform;

[0008] S4, designing an output feedback control law of the rotary steerable drilling platform system to realize fault-tolerant control.

[0009] Further, step S1 specifically comprises the following steps:

[0010] S1.1, establishing a platform dynamics equation driven by a permanent magnet synchronous motor

[0011]

[0012] where i q is the q-axis current, u q is the q-axis voltage, θ is the tool face angle, R s is the stator winding impedance, L q is the q-axis stator winding inductance, n p is the number of motor pole pairs, and Φ ais the permanent magnet flux, J is the total inertia, B is the damping coefficient, ζ is the random disturbance;

[0013] S12, establish tool face angle measurement equation

[0014]

[0015] where y is the measured value, sensor fault gain is time-varying unknown, under the condition of no fault and satisfy

[0016]

[0017] where, is the boundary of the sensor fault gain variation range, and

[0018] S1.3, obtain the following platform parameters R s , L q , n p , Φ a , J, B, by historical redundant measurement data to obtain fault boundary

[0019] S1.4, model the random disturbance as a standard Brownian motion in the probability space , where Ω is the sample space, is a σ-field on the sample space Ω, is a probability measure on ;

[0020] S1.5, define the following high-order integral operator

[0021]

[0022] S1.6, according to the dynamic equation of the system, convert the physical system (1) into a high-order integral equation form as shown in equation (5)

[0023]

[0024] where f(z(t)) is the drift term of the system dynamics, g(z(t)) is the controller channel, h(z(t)) is the diffusion term of the system dynamics, u(t) is the control input signal, is the Lebesgue integral, is the integral;

[0025] S1.7, at this time (2) is written as:

[0026]

[0027] S1.8, the equation (5) can be written as the differential form as shown in equation (7)

[0028]

[0029] S1.9, the lower bound of the absolute value of g(z) is calculated, denoted as and needs to satisfy The upper bound of the absolute value of the derivative of f i (z), i = 1, 2,..., n is calculated, denoted as p f ; the upper bound of the absolute value of the derivative of g(z) is calculated, denoted as p g ; the upper bound of the absolute value of the derivative of h(z) is calculated, denoted as p h .

[0030] Further, the equivalent control law is designed in step S2, specifically including the following steps:

[0031] S2.1, for any random variable x satisfying

[0032]

[0033] and a quadratic differentiable function V, the operator is denoted as

[0034]

[0035] In equation (8), b(x(s)) is the drift term, and σ(x(s)) is the diffusion term;

[0036] S2.2, a high-order operator as shown in equation (10) is designed

[0037]

[0038] and it is agreed that

[0039] S2.3, an equivalent control law as shown in equation (11) is designed

[0040]

[0041] Wherein, the estimation of the high-order state z will be given in step 3, and the parameter and the intermediate control signal v will be designed in step S3.2 and step S4.3 respectively;

[0042] S2.4, the equivalent control law (11) is substituted into (5) to obtain the equivalent system as shown in equation (12)

[0043]

[0044] wherein, Ξ0 is the error due to observation.

[0045] Further, the step S3 of designing the observer comprises the following steps:

[0046] S3.1, let

[0047] S3.2, design the parameter matrix

[0048]

[0049] such that for some positive definite symmetric matrix P, there is

[0050] Φ T P+PΦ≤-2I n (14)

[0051] Meanwhile, let ρ a = nmax 1≤i≤n a i ;

[0052] S3.3, design the parameter matrix

[0053]

[0054] such that for some positive definite symmetric matrix Q, there is

[0055] Γ T Q+QΓ≤-2I n (16)

[0056] S3.4, let

[0057] S3.5, let the eigenvalue

[0058]

[0059] S3.6, design the gain L c satisfying

[0060] S3.7, design the observer

[0061]

[0062] S3.8, let

[0063] Further, the step S4 of designing the output feedback control law comprises the following steps:

[0064] S4.1, let design the gain

[0065]

[0066] S4.2, introducing transformation

[0067]

[0068] where σ is a constant appropriately selected, 0 < σ < 1;

[0069] S4.3, the intermediate control variable v' in the design is

[0070]

[0071] At this time, for the fault satisfying According to the fault-tolerant control law formula (20), formula (21), it can achieve global asymptotic stability in the sense of probability.

[0072] The present application has the following advantages:

[0073] The present application is aimed at a rotary steerable drilling tool platform containing random signals, and a new fault-tolerant control method is developed based on a random high-order full-drive system model, which can realize the stabilization of the system when a sensor partial failure fault occurs. Compared with the method without fault-tolerant control design, the convergence speed of the present method is faster, the observation error is smaller, and the control effect is better. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the specific embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor. In the drawings:

[0075] Figure 1 A flow chart of a random fault-tolerant control method of a rotary steerable drilling tool platform of the present application is shown;

[0076] Figure 2 A comparison chart of the rotational speed amplitude of the rotary steerable drilling platform changing with time using the present method and the fault-tolerant control design is shown;

[0077] Figure 3 A comparison chart of the observation error of the observer changing with time using the present method and the fault-tolerant control design is shown. DETAILED DESCRIPTION

[0078] The technical solutions of the present application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0079] As shown in a random fault-tolerant control method of a rotary steerable drilling tool platform, comprising the following steps: Figure 1

[0080] S1, according to the rotary steerable drilling tool platform parameters, establish a random high-order full-drive system equation based on the rotary steerable drilling tool platform;

[0081] S2, according to the random high-order full-drive system structure, design equivalent control law, obtain the pre-closed-loop rotary steerable drilling platform system with linear drift term;

[0082] S3, on the basis of the pre-closed-loop system, design gain observer, obtain the estimation value of the high-order state of the rotary steerable drilling platform;

[0083] S4, design the output feedback control law of the rotary steerable drilling platform system, realize the fault-tolerant control.

[0084] Specifically, step S1 specifically includes the following steps:

[0085] S1.1, establish the platform dynamics equation driven by permanent magnet synchronous motor

[0086]

[0087] Where i q is the q-axis current, u q is the q-axis voltage, θ is the tool face angle, R s is the stator winding impedance, L q is the q-axis stator winding inductance, n p is the number of motor pole pairs, Φ a is the permanent magnet flux, J is the total inertia, B is the damping coefficient, ζ is the random disturbance;

[0088] S1.2, establish the tool face angle measurement equation

[0089]

[0090] Where y is the measured value, the sensor fault gain is time-varying unknown, and under the condition of no fault and satisfies

[0091] ​

[0092] where, is the bound of sensor fault gain variation range, and

[0093] S1.3, obtain the following platform parameters R s , L q , n p , Φ a , J, B, by historical redundant measurement data

[0094] S1.4, model the random disturbance as a standard Brownian motion in the probability space , where Ω is the sample space, is a σ-field on the sample space Ω, is a probability measure on ;

[0095] S1.5, define the following high-order integral operator

[0096]

[0097] S1.6, convert the physical system (1) into a high-order integral equation form as (5) according to the dynamic equation of the system

[0098]

[0099] where f(z(t)) is the drift term of the system dynamics, g(z(t)) is the controller channel, h(z(t)) is the diffusion term of the system dynamics, u(t) is the control input signal, is the Lebesgue integral, is the integral;

[0100] S1.7, at this time (2) is written as:

[0101]

[0102] S1.8, (5) can be written as the differential form as (7)

[0103]

[0104] S1.9, calculate the lower bound of the absolute value of g(z), denoted as and need to satisfy calculate the upper bound of the absolute value of the derivative of f i (z), i = 1, 2,..., n, denoted as ρ f ; calculate the upper bound of the absolute value of the derivative of g(z); denoted as ρ g; compute an upper bound of the derivative absolute value of h(z), denoted as p h .

[0105] Specifically, the equivalent control law in step S2 is designed, specifically including the following steps:

[0106] S2.1, for any random variable x satisfying

[0107]

[0108] For a quadratic differentiable function V, the operator is

[0109]

[0110] In formula (8), b(x(s)) is the drift term, and σ(x(s)) is the diffusion term;

[0111] S2.2, design a high-order operator as shown in formula (10)

[0112]

[0113] And it is agreed that

[0114] S2.3, design an equivalent control law as shown in formula (11)

[0115]

[0116] Wherein, the estimation of high-order state z Will be given in step 3, and the parameter And the intermediate control signal v will be designed in step S3.2 and step S4.3 respectively;

[0117] S2.4, substitute the equivalent control law (11) into (5) to obtain the equivalent system as shown in formula (12)

[0118]

[0119] Wherein, Ξ0 is the error due to observation.

[0120] Specifically, the observer in step S3 is designed, specifically including the following steps:

[0121] S3.1, let

[0122] S3.2, design the parameter matrix

[0123]

[0124] So that it satisfies for a certain positive definite symmetric matrix P

[0125] Φ T P+PΦ≤-2I n (14)

[0126] Meanwhile, let ρ a = nmax 1≤i≤n a i ;

[0127] S3.3, design parameter matrix

[0128]

[0129] such that for some positive definite symmetric matrix Q, there exists

[0130] Γ T Q+QΓ≤-2I n (16)

[0131] S3.4, let

[0132] S3.5, let eigenvalue

[0133]

[0134] S3.6, design gain L c such that

[0135] S3.7, design observer

[0136]

[0137] S3.8, let

[0138] Specifically, the output feedback control law is designed in step S4, which specifically includes the following steps:

[0139] S4.1, let design gain

[0140]

[0141] S4.2, introduce transformation

[0142]

[0143] where σ is a constant appropriately selected, 0 < σ < 1;

[0144] S4.3, design intermediate control v' as

[0145]

[0146] At this time, for the fault satisfying According to the fault-tolerant control law (20), (21), it can be made to achieve global asymptotic stability in the sense of probability.

[0147] Preferred embodiments

[0148] Consider a rotary steerable drilling tool platform, the system parameters are obtained as shown in Table 1 in step 1. At the same time, from the historical data, the boundary of the sensor fault gain variation range is Substitute the parameters in Table 1 into equation (1), and through conversion, the random high-order full-drive system equation can be obtained

[0149]

[0150] Where f0=-716z, f1=-24218z, at this time ρ f = 24218, ρ g = 0, ρ h = 16. The simulation fault variation is

[0151] Parameter Value Unit [R s ]] 1.52 Ω [[ L q ]]> 2.1383 x 10 -3 ]] H n p ]] 4 - Φ a ]] 0.02148 Wb J 1.449 x 10 -5 ]]> Kg·m 2 ]]> B 8 x 10 -5 ]] N·m·s

[0152] Table 1: Rotary steerable drilling tool platform parameters

[0153] According to step 2, the equivalent control law is designed

[0154]

[0155] Where a1=1, a2=1.5, at this time

[0156] According to step 3, the observer is designed

[0157]

[0158] Where L c = 3.

[0159] According to step 4, the output feedback control law is designed

[0160]

[0161] Where

[0162] The initial conditions of the simulation are designed as The numerical method uses the Euler-Maruyama method. Compared with the method without fault-tolerant control design, the simulation results are shown in Figure 2 and Figure 3 From Figures 2 and​Figure 3 It can be seen that the convergence speed is faster, the observation error is smaller, and the control effect is better by using the method.

[0163] Of course, the above description is not a limitation on the present application, and the present application is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present application should also be within the scope of the present application.

Claims

1. A method for stochastic fault-tolerant control of a rotary steerable drilling tool platform, characterized by, Comprising the following steps: S1, establishing a random high-order full-drive system equation based on a rotary steerable drilling tool platform according to rotary steerable drilling tool platform parameters; S2, designing an equivalent control law according to a random high-order full-drive system structure to obtain a pre-closed-loop rotary steerable drilling platform system with a linear drift term; S3, designing a gain observer on the basis of the pre-closed-loop system to obtain an estimated value of a high-order state of the rotary steerable drilling platform; S4, designing an output feedback control law of the rotary steerable drilling platform system to realize fault-tolerant control; The step S2 of designing the equivalent control law specifically comprises the following steps: S2.1, for any satisfying Let x be a random variable and V a twice differentiable function. Let be the operator The b(x(s)) in formula (8) is a drift term, and the σ(x(s)) is a diffusion term; S2.2, designing a high-order operator as shown in formula (10) and agreed S2.3, designing an equivalent control law as shown in formula (11) where the estimate of the higher order state z The parameters i = 0, 1,..., n - 1, and the intermediate control signal v will be designed in steps S3.2 and S4.3, respectively; S2.4, substituting the equivalent control law (11) into (5) to obtain an equivalent system as shown in formula (12) Wherein, Ξ0 is an error due to observation; The step S3 of designing the observer specifically comprises the following steps: S3.1, let S3.2, designing a parameter matrix So as to satisfy, for a certain positive definite symmetric matrix P, that Φ T P+PΦ≤-2I n (14) Meanwhile, the memory 130 stores data, a program, and the like. ρ a = nmax 1≤i≤n a i ; S3.3, designing a parameter matrix So as to satisfy, for a certain positive definite symmetric matrix Q, that Γ T Q+QΓ≤-2I n (16) S3.4, let S3.5, letting the characteristic value S3.6, design gain L c satisfies S3.7, designing an observer S3.8, let 2. The random fault-tolerant control method of a rotary steerable drilling tool platform of claim 1, wherein, The step S1 specifically comprises the following steps: S1.1, establishing a platform dynamics equation driven by a permanent magnet synchronous motor where i q is the q-axis current, u q is the q-axis voltage, θ is the tool face angle, R s is the stator winding resistance, L q is the q-axis stator winding inductance, n p is the number of motor pole pairs, Φ a is the permanent magnet flux, J is the total inertia, B is the damping coefficient, ζ is the random disturbance; S1.2, establishing a tool face angle measurement equation where y is the measured value, the sensor fault gain is time-varying and unknown, and under no fault condition and satisfies wherein, is a bound on the sensor fault gain variation range, and S1.3, obtain the following platform parameters R by direct measurement or recognition method s , L q , n p , Φ a , J, B, obtain the fault boundary by historical redundant measurement data S1.

4. Model the random perturbation as a standard Brownian motion in the probability space where Ω is the sample space, is a σ-field on the sample space Ω, is a probability measure on . S1.5, defining the following high-order integral operator S1.6, converting the physical system (1) into a high-order integral equation form as shown in formula (5) according to the dynamics equation of the system where f(z(t)) is the drift term of the system dynamics, g(z(t)) is the controller channel, h(z(t)) is the diffusion term of the system dynamics, u(t) is the control input signal, is the Lebesgue integral, is the integral; S1.7, at this time, (2) is written as: S1.8, it is agreed that (5) can be written as a differential form as shown in formula (7) S1.9, compute a lower bound of the absolute value of g(z), denoted by and satisfying Compute f i (z), i = 1, 2,..., n, denoted by p f ; compute an upper bound of the absolute value of the derivative of g(z); denoted by p g ; compute an upper bound of the absolute value of the derivative of h(z); denoted by p h .

3. The random fault-tolerant control method of a rotary steerable drilling tool platform of claim 1, wherein, The step S4 of designing the output feedback control law specifically comprises the following steps: S4.1, record Design gain S4.2, introducing a transformation Wherein, σ is a constant selected appropriately, and 0<σ<1; S4.3, designing an intermediate control amount v' as At this time, for the fault satisfying According to the fault-tolerant control law formula (20), formula (21) can make it globally asymptotically stable in the sense of probability.

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