Redundant active fault-tolerant control method for rotary steerable drilling tool sensor failure

Abstract

The present invention discloses a redundant active fault-tolerant control method for sensor faults of rotary steerable drilling tools, which belongs to the field of fault diagnosis and fault-tolerant control, and includes the following steps: Step 1: Obtain a high-order full-drive system model of the rotary steerable drilling tool; Step 2: Decouple the redundant observability of the full-drive system model, and give a redundant observable full-drive system structure; Step 3: Design a fault detection strategy; Step 4: Design an active fault-tolerant tracking controller to perform trajectory tracking control on the rotary steerable drilling. Starting from the high-order full-drive system model of the rotary steerable drilling tool, the present invention designs a sensor fault detection and active fault-tolerant control technology based on redundant observation, and realizes high-precision trajectory tracking of the rotary steerable drilling tool. The method of the present invention fully extracts the inherent redundant characteristics of the drilling tool, and the designed engineering controller is easy to design, and has significant advantages in handling novel and catastrophic sensor failures.

Description

Technical Field

[0001] The invention belongs to the field of fault diagnosis and fault-tolerant control, and in particular relates to a redundant active fault-tolerant control method for a rotary steering drilling tool sensor fault. Background Art

[0002] Rotary steerable drilling tools are important equipment for the development of deep-earth and deep-sea oil and gas resources. Drilling tools that work in complex and changing environments for a long time are very likely to encounter unknown, sudden, and catastrophic sensor failures.

[0003] The existing trajectory tracking control methods for rotary steerable drilling tools mostly use PID control and H ∞ These control methods are particularly dependent on the measurement accuracy of sensors. Once a sensor fails, these control methods will lose their original effects. However, most of the existing fault-tolerant control methods for sensor failures are robust and can only tolerate sensor failures with small amplitudes or slow changes. These methods often result in reduced accuracy or even system divergence when dealing with sudden large-amplitude sensor failures. Summary of the invention

[0004] In order to solve the above problems, the present invention starts from the high-order full-drive system model of the rotary steerable drilling tool, designs a sensor fault detection and active fault-tolerant control technology based on redundant observation, and realizes high-precision trajectory tracking of the rotary steerable drilling tool.

[0005] The technical solution of the present invention is as follows:

[0006] A redundant active fault-tolerant control method for a rotary steerable drilling tool sensor failure comprises the following steps:

[0007] Step 1: Obtain a high-order all-wheel drive system model of a rotary steerable drilling tool;

[0008] Step 2: Decouple the redundant observability of the all-wheel drive system model and give the redundant observability all-wheel drive system structure;

[0009] Step 3: Design a fault detection strategy;

[0010] Step 4: Design an active fault-tolerant tracking controller to perform trajectory tracking control on rotary steerable drilling.

[0011] Furthermore, the specific steps of step 1 are:

[0012] Step 1.1: Build a dynamic model of a rotary steerable drilling tool with a permanent magnet synchronous motor as the driving mechanism, as follows:

[0013]

[0014] Among them, iq is the stator q-axis current component, Indicates i q The first derivative of , θ is the tool face angle, represents the first-order derivative of θ, represents the second-order derivative of θ, L is the stator q-axis inductance component, R is the stator resistance, u represents the stator q-axis voltage component, n0 is the number of motor pole pairs, J is the total moment of inertia, φ is the permanent magnet flux, is the damping coefficient;

[0015] Step 1.2: Build the sensor measurement equation,

[0016]

[0017] Where y is the four-dimensional measurement value, s1, s2, s3, s4 are possible time-varying sensor faults, and v1, v2, v3, v4 are bounded measurement noises;

[0018] Step 1.3: Obtain the parameters L, R, n0, J, φ, according to the mechanism or actual measurement Specific value of

[0019] Step 1.4: Define a new variable z and transform the model (1) (2) into a high-order all-wheel drive system model (3).

[0020]

[0021] Among them, z(n) is the nth order derivative of z, F(·),G(·),H j (·) is the function after variable transformation; the model transformation form is general and corresponds to the dynamic model of drilling tools, that is,

[0022] Furthermore, the specific steps of step 2 are:

[0023] Step 2.1: Consider the system model corresponding to each sensor measurement output,

[0024]

[0025] Among them, x j,1 =H j (z (0～n-1) ), x j The dimension is r j , for each measured output y j , the relative order of the system is r j , the dimension of the observable subspace is r j , x′ j For nrj dimensional unobservable subspace, is the corresponding function;

[0026] Step 2.2: Define a bi-Lipschitz mapping T based on the full sensor index set and a bi-Lipschitz mapping based on the sensor index set I, corresponding to formula (5) and formula (6) respectively.

[0027]

[0028]

[0029] Among them, the number of sensors in the indicator set I is m I ,m I <m,

[0030] Step 2.3: Solve the inverse mapping of the above two mappings and use the saturation function Sat(·) to constrain the range of its independent variables.

[0031]

[0032]

[0033] Among them, x and z are constants given in practical engineering, x,x I They respectively represent the observable state corresponding to the full sensor indicator set and the observable state corresponding to the sensor indicator set I.

[0034] Furthermore, the specific steps of step 3 are:

[0035] Step 3.1: Consider a continuously updated sensor index set Γ(σ(t)), σ(0) = 1, which is projected onto all sensors m by the integer σ(t) I The indicator set,

[0036]

[0037] Step 3.2: Define the fault detection metrics,

[0038]

[0039] in, is the observed value given by formula (17);

[0040] Step 3.3: If the detection index (10) satisfies formula (11), it is determined that at least one sensor failure occurs in the index set Γ(σ(t)).

[0041]

[0042] in, represents the Lipschitz constant of the mapping, represents the multiplication of two mappings, id represents the identity mapping, and ε(t) is the observation error function when the system is fault-free. The maximum value on the right side of equation (11) is obtained based on Monte Carlo simulation and used for fault detection.

[0043] Step 3.4: If the detection index (11) is established, find the next sensor index set Γ according to formula (12) until (11) is not established; the sensor index set determined at this time is used for subsequent tracking control,

[0044]

[0045] Among them, t + The next number after time t represents the calculation time, and mod is the modulo operator.

[0046] Furthermore, the specific steps of step 4 are:

[0047] Step 4.1: Design parameterization matrix Φ

[0048]

[0049] So that it satisfies the existence of a positive definite matrix Q so that formula (14) holds true,

[0050] Φ T Q+QΦ≤-I n (14)

[0051] Among them, I n is the n-dimensional identity matrix;

[0052] Step 4.2: Design m parameterization matrices K j ,j=1,2,…,m

[0053]

[0054] So that it satisfies the existence of a positive definite matrix P j So that formula (16) holds true,

[0055]

[0056] in, For r j dimensional identity matrix;

[0057] Step 4.3: Let A 0～n-1 =[A0,A1,…,A n-1], design an integrated structure that integrates observer and fault-tolerant controller,

[0058]

[0059] Among them, z r is the reference signal to be tracked, l j ,j=1,2,…,m is the parameter greater than 1 to be designed;

[0060] Step 4.4: For the rotary steerable drilling tool model, j The design standards are as follows:

[0061] make

[0062]

[0063] l j Needs to be satisfied

[0064]

[0065] Step 4.5: When the parameters of the fault-tolerant controller meet the above requirements, the observation and tracking errors of the original system are eventually uniformly bounded and stable; when the measurement equations of the rotary steerable drilling tool are noise-free, the observation and tracking error dynamics are globally asymptotically stable.

[0066] Beneficial technical effects brought by the present invention:

[0067] Starting from the high-order full-drive system model of the rotary steerable drilling tool, the present invention designs a sensor fault detection and active fault-tolerant control method based on redundant observation, and realizes high-precision trajectory tracking of the rotary steerable drilling tool. The method can fully extract the inherent redundant characteristics of the drilling tool, and the designed engineering controller is easy to design, and has significant advantages in handling novel and catastrophic sensor failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of the redundant active fault-tolerant control method of the rotary steerable drilling tool sensor failure of the present invention;

[0069] Figure 2 The result diagram of the fault-tolerant control of the technical solution of the present invention, wherein (a) is the observation and tracking effect of the rotation speed value of the drilling tool during the fault-tolerant control, and (b) is the corresponding fault residual signal;

[0070] Figure 3 Result diagram when the prior art does not perform fault-tolerant control, where (a) is the observation and tracking effect of the drilling tool rotation speed value when fault-tolerant control is not performed, and (b) is the corresponding fault residual signal. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0072] like Figure 1 As shown, a redundant active fault-tolerant control method for sensor failure of a rotary steerable drilling tool, the technical process is as follows:

[0073] Step 1: Obtain a high-order all-wheel drive system model of the rotary steerable drilling tool. The specific steps are as follows:

[0074] Step 1.1: Build a dynamic model of a rotary steerable drilling tool with a permanent magnet synchronous motor as the driving mechanism, as follows:

[0075]

[0076] Among them, i q is the stator q-axis current component, Indicates i q The first derivative of , θ is the tool face angle, represents the first-order derivative of θ, represents the second-order derivative of θ, L is the stator q-axis inductance component, R is the stator resistance, u represents the stator q-axis voltage component, n0 is the number of motor pole pairs, J is the total moment of inertia, φ is the permanent magnet flux, is the damping coefficient.

[0077] Step 1.2: Build the sensor measurement equation,

[0078]

[0079] Where y is the four-dimensional measurement value, s1, s2, s3, s4 are possible time-varying sensor faults, the sensor fault signal may be unbounded or non-differentiable, and v1, v2, v3, v4 are bounded measurement noise.

[0080] Step 1.3: Obtain the parameters L, R, n0, J, φ, according to the mechanism or actual measurement The specific value of .

[0081] Step 1.4: Define a new variable z and transform the model (1) (2) into a high-order all-wheel drive system model (3).

[0082]

[0083] Among them, z (n) is the nth-order derivative of z, F(·),G(·),H j (·) is the function after variable transformation. The model transformation form is general and corresponds to the dynamic model of drilling tools, that is,

[0084] Step 2: Decouple the redundant observability of the all-wheel drive system model and give the redundant observability all-wheel drive system structure. The specific steps are:

[0085] Step 2.1: Consider the system model corresponding to each sensor measurement output,

[0086]

[0087] Among them, x j,1 =H j (z (0～n-1) ), x j The dimension is r j , that is, for each measured output y j , the relative order of the system is r j , the dimension of the observable subspace is r j , x′ j For nr j dimensional unobservable subspace, is the corresponding function.

[0088] A specific analysis of the redundant observability structure of the rotary steerable drilling tool shows that it can tolerate at most one sensor failure. The number of tolerable sensor failures comes from the redundant observability analysis of the system. When q sensors are arbitrarily selected to measure the dynamic system, the system is still observable. At this time, the dynamic system is called q redundant observable. If the system is 2q redundant observable, then the original system can tolerate at most q sensor failures. The rotary steerable drilling tool model (1)(2) is 2 redundant observable, so it can tolerate at most one sensor failure. Naturally, the more drilling tool sensors there are, the more sensor failures it can tolerate.

[0089] Step 2.2: Define a bi-Lipschitz mapping T based on the full sensor index set and a bi-Lipschitz mapping based on the sensor index set I, corresponding to formula (5) and formula (6) respectively.

[0090]

[0091]

[0092] Among them, the number of sensors in the indicator set I is m I ,m I <m,

[0093] Step 2.3: Solve the inverse mapping of the above two mappings and use the saturation function Sat(·) to constrain the range of its independent variables, because the system state in actual engineering has a certain working range, that is,

[0094]

[0095]

[0096] Among them, x and z are constants given in practical engineering, x,x I They respectively represent the observable state corresponding to the full sensor indicator set and the observable state corresponding to the sensor indicator set I.

[0097] Step 3: Design a fault detection strategy. The specific steps are as follows:

[0098] Step 3.1: Consider a continuously updated sensor index set Γ(σ(t)), σ(0) = 1, which can be projected to all sensors m by the integer σ(t) I The indicator set is

[0099]

[0100] Step 3.2: Define the fault detection metrics,

[0101]

[0102] in, is the observed value given by formula (17).

[0103] Step 3.3: If the detection index (10) satisfies formula (11), it is determined that at least one sensor failure occurs in the index set Γ(σ(t)).

[0104]

[0105] in, represents the Lipschitz constant of the mapping, represents the multiplication of two mappings, id represents the identity mapping, and ε(t) is the observation error function when the system is fault-free. In general, the maximum value on the right side of equation (11) can be obtained based on Monte Carlo simulation for fault detection.

[0106] Step 3.4: If the detection index (11) is established, find the next sensor index set Γ according to formula (12) until (11) is not established. The sensor index set determined at this time is used for subsequent tracking control.

[0107]

[0108] Among them, t + The next number after time t represents the calculation time, and mod is the modulo operator.

[0109] Step 4: Design an active fault-tolerant tracking controller to perform trajectory tracking control on rotary steerable drilling. The specific steps are as follows: Step 4.1: Design the parameterized matrix Φ

[0110]

[0111] So that it satisfies the existence of a positive definite matrix Q so that formula (14) holds true,

[0112] Φ T Q+QΦ≤-I n (14)

[0113] Among them, I n is the n-dimensional identity matrix.

[0114] Step 4.2: Design m parameterization matrices K j ,j=1,2,…,m

[0115]

[0116] So that it satisfies the existence of a positive definite matrix P j So that formula (16) holds true,

[0117]

[0118] Among them, I rj For r j dimensional identity matrix.

[0119] Step 4.3: Let A 0～n-1 =[A0,A1,…,A n-1 ], design an integrated structure that integrates observer and fault-tolerant controller,

[0120]

[0121] Among them, z r is the reference signal to be tracked, l j ,j=1,2,…,m is the parameter greater than 1 to be designed.

[0122] Step 4.4: For the rotary steerable drilling tool model, j The design standards are as follows:

[0123] make

[0124]

[0125] l j Needs to be satisfied

[0126]

[0127] Step 4.5: When the parameters of the fault-tolerant controller meet the above requirements, the observation and tracking errors of the original system are eventually uniformly bounded and stable, and the larger parameter l j A smaller tracking error can be given. In particular, when the measurement equations of the rotary steerable drilling tool are noise-free, the observation and tracking error dynamics are globally asymptotically stable.

[0128] In order to prove the feasibility and superiority of the present invention, the following simulation experiment was carried out.

[0129] The actual parameters of a rotary steerable drilling tool are L = 2.14mH, R = 1.52Ω, n0 = 4, J = 1.45×10 -5 Kg / m 2 ,φ=0.021Wb, Substitute into the dynamic model (1), and the all-wheel drive system model is obtained after transformation

[0130]

[0131] The noise in the simulation is uniformly distributed between [-0.01, 0.01].

[0132] According to step 2, the relative orders of the four sensor outputs are 2, 2, 1, 1, and the system is 2-redundant. The simulation experiment considers injecting a square wave sensor fault s2(t) with a high-frequency change at t=20s, with an amplitude of ±1. The mapping to be designed is:

[0133]

[0134] Design I =3, yes

[0135]

[0136]

[0137] According to engineering experience or experimental simulation, two constants Ξ are given x =200,Ξ z =100.

[0138] According to step 3, the maximum value of the right side of (11) is 10 obtained through Monte Carlo simulation when there is no fault. Then the simplified fault detection strategy is: If there is a sensor failure in the sensor indicator set, the system will keep searching for a new sensor indicator set until the detection indicator no longer generates an alarm.

[0139] According to step 4, select parameter A 0～1 =[5,2],K 11 =5,K 12=2,K 21 =5,K 22 =2, l1=l2=l3=l4=20, where sensors No. 3 and No. 4 do not need feedback gain to obtain observation values, and their own signals are considered to be the corresponding observation values.

[0140] The initial values ​​of the simulation experiment are all zero, and the reference signal is designed to be z r =5sint. The experimental results of the active fault-tolerant control method of the present invention are shown in Figure 2 The experimental results without fault-tolerant control are shown in Figure 3 .in, Figure 2 (a) is the observation and tracking effect of the rotation speed value of the drilling tool under the technical solution of the present invention, Figure 2 (b) is the corresponding fault residual signal. Figure 3 (a) is the observation and tracking effect of the drilling tool speed value when no fault-tolerant control is performed. Figure 3 (b) is the corresponding fault residual signal. It is obvious that the active fault-tolerant control technology of the present invention realizes the trajectory tracking of the rotary steerable drilling tool under sensor failure, while the system without fault-tolerant control completely diverges.

[0141] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A redundant active fault-tolerant control method for sensor failure of a rotary steerable drilling tool, characterized in that: The steps include: Step 1: Obtain a high-order all-wheel drive system model of a rotary steerable drilling tool; Step 2: Decouple the redundant observability of the all-wheel drive system model and give the redundant observability all-wheel drive system structure; Step 3: Design a fault detection strategy; Step 4: Design an active fault-tolerant tracking controller to perform trajectory tracking control on the rotary steerable drilling; The specific steps of step 1 are: Step 1.1: Build a dynamic model of a rotary steerable drilling tool with a permanent magnet synchronous motor as the driving mechanism, as follows: Among them, i q is the stator q-axis current component, Indicates i q The first derivative of , θ is the tool face angle, represents the first-order derivative of θ, represents the second-order derivative of θ, L is the stator q-axis inductance component, R is the stator resistance, u represents the stator q-axis voltage component, n0 is the number of motor pole pairs, J is the total moment of inertia, φ is the permanent magnet flux, is the damping coefficient; Step 1.2: Build the sensor measurement equation, Where y is the four-dimensional measurement value, s1, s2, s3, s4 are possible time-varying sensor faults, and v1, v2, v3, v4 are bounded measurement noises; Step 1.3: Obtain the parameters L, R, n0, J, φ, according to the mechanism or actual measurement Specific value of Step 1.4: Define a new variable z and transform the model (1) (2) into a high-order all-wheel drive system model (3). Among them, z (n) is the nth-order derivative of z, F(·),G(·),H j (·) is the function after variable transformation; the model transformation form is general and corresponds to the dynamic model of drilling tools, that is, n=2,m=4.

2. The redundant active fault-tolerant control method for rotary steerable drilling tool sensor failure according to claim 1, characterized in that: The specific steps of step 2 are: Step 2.1: Consider the system model corresponding to each sensor measurement output, Among them, x j,1 =H j (z (0-n-1) ), x j The dimension is r j , for each measured output y j , the relative order of the system is r j , the dimension of the observable subspace is r j , x′ j For nr j dimensional unobservable subspace, is the corresponding function; Step 2.2: Define a bi-Lipschitz mapping T based on the full sensor indicator set and a bi-Lipschitz mapping T based on the sensor indicator set I I , corresponding to formula (5) and formula (6), respectively. Among them, the number of sensors in the indicator set I is m I ,m I <m, Step 2.3: Solve the inverse mapping of the above two mappings and use the saturation function Sat(·) to constrain the range of its independent variables. Among them, x and z are constants given in practical engineering, x,x I They respectively represent the observable state corresponding to the full sensor indicator set and the observable state corresponding to the sensor indicator set I.

3. The redundant active fault-tolerant control method for rotary steerable drilling tool sensor failure according to claim 2, characterized in that: The specific steps of step 3 are: Step 3.1: Consider a continuously updated sensor index set Γ(σ(t)), σ(0) = 1, which is projected onto all sensors m by the integer σ(t) I The indicator set, Step 3.2: Define the fault detection metrics, in, is the observed value given by formula (17); Step 3.3: If the detection index (10) satisfies formula (11), it is determined that at least one sensor failure occurs in the index set Γ(σ(t)). in, represents the Lipschitz constant of the mapping, represents the multiplication of two mappings, id represents the identity mapping, and ε(t) is the observation error function when the system is fault-free. The maximum value on the right side of equation (11) is obtained based on Monte Carlo simulation and used for fault detection. Step 3.4: If the detection index (11) is established, find the next sensor index set Γ according to formula (12) until (11) is not established; the sensor index set determined at this time is used for subsequent tracking control, Among them, t + The next number after time t represents the calculation time, and mod is the modulo operator.

4. The redundant active fault-tolerant control method for rotary steerable drilling tool sensor failure according to claim 3, characterized in that: The specific steps of step 4 are: Step 4.1: Design parameterization matrix Φ So that it satisfies the existence of a positive definite matrix Q so that formula (14) holds true, Φ T Q+QΦ≤-I n (14) Among them, I n is the n-dimensional identity matrix; Step 4.2: Design m parameterization matrices K j ,j=1,2,…,m So that it satisfies the existence of a positive definite matrix P j So that formula (16) holds true, in, For r j dimensional identity matrix; Step 4.3: Let A 0-n-1 =[A0,A1,…,A n-1 ], design an integrated structure that integrates observer and fault-tolerant controller, Among them, z r is the reference signal to be tracked, l j ,j=1,2,…,m is the parameter greater than 1 to be designed; Step 4.4: For the rotary steerable drilling tool model, j The design standards are as follows: make l j Needs to be satisfied Step 4.5: When the parameters of the fault-tolerant controller meet the above requirements, the observation and tracking errors of the original system are eventually uniformly bounded and stable; when the measurement equations of the rotary steerable drilling tool are noise-free, the observation and tracking error dynamics are globally asymptotically stable.

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