Estimation method of unknown failure roll target angular velocity based on electromagnetic induction torque

Abstract

The application discloses an estimation method of an unknown failure tumbling target angular velocity based on an electromagnetic induction torque, which is composed of the following steps: obtaining historical data of the unknown failure tumbling target, wherein the historical data comprises angular velocity historical data and electromagnetic induction torque historical data; performing dimension increasing on the historical data through nonlinear transformation to obtain dimension-increased data; performing dynamic mode decomposition on the dimension-increased data to obtain a system matrix, an output matrix and a prediction matrix; constructing a linear predictor model of the unknown failure tumbling target in the electromagnetic despinning process according to the system matrix, the output matrix and the prediction matrix; and solving the linear predictor model as a constraint condition of an optimal estimation problem to obtain a real-time accurate estimation value of the angular velocity of the unknown failure tumbling target. In the electromagnetic despinning process of a close-range space target, the application realizes real-time accurate estimation of the target angular velocity by using electromagnetic despinning torque data, thereby solving the problem that the target angular velocity is difficult to measure in a close-range despinning task.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aerospace, and particularly relates to an estimation method for the angular velocity of an unknown failed tumbling target based on an electromagnetic induction torque. BACKGROUND

[0002] Space debris is considered as a serious threat to future space missions. However, space debris often appears in a tumbling motion due to passivation, collision, environmental torque, etc. According to the ground measurement results, the maximum angular velocity of a retired satellite in geosynchronous orbit is that of the INTELSAT 4-F7 (1973-058A) satellite, which is 139.1 (° / s); and the maximum angular velocity of a retired rocket body is that of the BREEZE-M R / B (2015-075B), which is 409.6 (° / s). High-speed and even irregular rotation makes active removal of space debris a complex problem. Therefore, it is necessary to use electromagnetic despinning technology (such as application numbers 201611039166.X and 201810821276.4) to reduce the speed of space debris before removal.

[0003] When electromagnetic despinning is performed on a target, the size and direction of the angular velocity of the target greatly affect the despinning effect. The angular velocity of the target not only determines the safe corridor for the service spacecraft to control the target, but also affects the optimal despinning position and attitude. If the angular velocity of the target is unknown or inaccurate, it may cause the service spacecraft to collide with the target or fail to achieve the desired despinning effect. Therefore, the angular velocity of the target needs to be measured in real time when electromagnetic despinning is performed. However, when performing close-range despinning tasks, it is difficult to accurately measure the angular velocity of the target using conventional attitude measurement methods such as cameras due to the small field of view, lack of characteristic markers, and tumbling motion of the target. SUMMARY

[0004] The purpose of the present application is to provide an estimation method for the angular velocity of an unknown failed tumbling target based on an electromagnetic induction torque, which can solve the problem of inaccurate measurement of the angular velocity of a target during close-range electromagnetic despinning of a space target.

[0005] The present application adopts the following technical solution: an estimation method for the angular velocity of an unknown failed tumbling target based on an electromagnetic induction torque, which is composed of the following steps:

[0006] Step S1: obtaining historical data of an unknown failed tumbling target, the historical data including angular velocity historical data and electromagnetic induction torque historical data,

[0007] Step S2: performing dimensionality increasing on the historical data through nonlinear transformation to obtain dimensionality increased data,

[0008] Step S3: performing dynamic mode decomposition on the dimensionality increased data to obtain a system matrix, an output matrix, and a prediction matrix,

[0009] Step S4: constructing a linear predictor model of the unknown failure tumbling target in the electromagnetic despinning process according to the system matrix, the output matrix and the prediction matrix,

[0010] Step S5: solving the real-time accurate estimation value of the angular velocity of the unknown failure tumbling target by taking the linear predictor model as the constraint condition of the optimal estimation problem.

[0011] Further, the linear predictor model of step S4 is:

[0012] z(k+1) = Az(k)

[0013] T b (k) = Cz(k)

[0014]

[0015] In the formula, z(k) is the state variable of the predictor model at time k, z(k+1) is the state variable of the predictor model at time k+1, is the target angular velocity generated by the predictor at time k, T b (k) represents the electromagnetic induction torque at time k, A is the system matrix, C is the output matrix, and C x is the prediction matrix.

[0016] Further, the objective function of the linear prediction rolling horizon optimal estimation problem P k at time k in step S5 is:

[0017]

[0018] wherein N is the step length of the rolling horizon, represents the state decision variable of the optimization problem, respectively represent the state decision variables at times t-N, t-N+1,..., t-1, represents the prior state value of the optimization problem at time t-N, P(t-N) represents the prior state weight matrix at time t-N, represents the disturbance decision variable of the optimization problem respectively represent the disturbance decision variables at times t-N, t-N+1,..., t-1; R and Q are respectively the measurement noise weight matrix and the model disturbance weight matrix;

[0019] P k The constraint condition of the optimization problem is:

[0020]

[0021]

[0022]

[0023] Wherein, Z is the constraint set of state variables, and W is the constraint set of disturbances.

[0024] The beneficial effects of the present application are:

[0025] The present application considers that the electromagnetic reaction torque generated by the electromagnetic induction of the unknown failed tumbling target on the service spacecraft in the electromagnetic despinning process is measurable, and the smaller the relative distance and the greater the target angular velocity, the greater the torque, which can be used to accurately estimate the angular velocity of the unknown failed tumbling target.

[0026] The present application considers that the unknown failed tumbling target is mostly a non-cooperative target, and its physical parameters such as structural distribution and electrical conductivity are often unknown, and the present application can accurately estimate the angular velocity of the unknown failed tumbling target while performing close-range electromagnetic despinning, thereby providing safety and efficiency for the electromagnetic despinning process of the unknown failed tumbling target.

[0027] The present application adopts a data-driven method of Koopman operator to obtain a linear predictor model of the electromagnetic despinning process of the unknown failed tumbling target, and compared with existing state estimation techniques, the present application does not require prior model information and is suitable for electromagnetic despinning tasks of unknown targets.

[0028] The present application constructs a rolling horizon optimal estimation problem of the data-driven linear predictor, and compared with existing nonlinear estimation techniques, the present application can ensure that the optimization problem is in the form of quadratic programming, thereby reducing the calculation amount of the optimization problem, ensuring the global optimality of the angular velocity estimation value in the electromagnetic despinning process, and facilitating the acquisition of more accurate angular velocity estimation values.

[0029] The present application realizes real-time accurate estimation of the target angular velocity by using electromagnetic despinning torque data in the close-range space target electromagnetic despinning process, thereby solving the problem of difficult measurement of the target angular velocity in the close-range despinning task. BRIEF DESCRIPTION OF DRAWINGS

[0030] Fig. 1 The actual value and the estimated value of the target angular velocity x-axis in the embodiment 1 of the present application;

[0031] Fig. 2 The actual value and the estimated value of the target angular velocity y-axis in the embodiment 1 of the present application;

[0032] Fig. 3 The actual value and the estimated value of the target angular velocity z-axis in the embodiment 1 of the present application. DETAILED DESCRIPTION

[0033] The present application will be described in detail below in combination with specific embodiments.

[0034] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0035] This invention discloses a method for estimating the angular velocity of an unknown failed tumbling target based on electromagnetic induction torque, comprising the following steps:

[0036] Step S1:

[0037] Acquire historical data of an unknown failed rolling target, including historical angular velocity data and historical electromagnetic induction torque data.

[0038] Record the target angular velocity ω in time series form d The historical data from time t=0 to t=T-1 is X. c =[ω d (0),ω d (1),...,ω d [(T-1)], the historical data of the target angular velocity from t=1 to t=T is X p =[ω d (1),ω d (2),...,ω d [(T)]; where the dimension of the target angular velocity ωd is n, and the electromagnetic induction torque T from t=0 to t=T-1 is recorded. d For Y c =[T d (0),...,T d [(T-1)], where T represents the total number of historical data collected.

[0039] Step S2:

[0040] Up-dimensional data is obtained by upscaling historical data through nonlinear transformation.

[0041] Given historical data, it is necessary to determine the data-driven Koopman operator characteristic function for the electromagnetic derotation process and increase the dimensionality of the historical dataset.

[0042] The characteristic function of the Koopman operator, consisting of M radial basis functions of thin plate splines, is given:

[0043] Φ(x)=[φ1(x),φ2(x),...,φ M (x)] T

[0044] Where the superscript T denotes the transpose operation, Φ(x) represents the characteristic function of the Koopman operator, x is the independent variable of the function, and φ i (x)=||xc i || 2 ln(xc i ||), c i Let represent the center point of the i-th radial basis function, where i is an integer between 1 and M, and M represents the dimension of the Koopman operator characteristic function and is an integer greater than n.

[0045] Therefore, by performing a nonlinear transformation to increase the dimensionality of the original historical data, the following increased-dimensional data can be obtained:

[0046] X c,l =[ω d,l (0),ω d,l (1),...,ω d,l (T-1)]

[0047] X p,l =[ω d,l (1),ω d,l (2),...,ω d,l (T)]

[0048] Y c,l =[T d,l (0),...,T d,l (T-1)]

[0049] Where ω d,l (k)=Φ(ω d (k)), T d,l (j)=Φ(T d (j)), k represents an integer between 0 and T, and j represents an integer between 0 and T-1.

[0050] Step S3: Perform dynamic pattern decomposition on the upgraded data to obtain the system matrix, output matrix, and prediction matrix; obtain the system matrix A, output matrix C, and prediction matrix Ct of the linear predictor by solving the following optimization problems 1, 2, and 3. x .

[0051] Optimization issue 1: Among them ||·|| F The F-norm of a matrix is ​​denoted by .

[0052] Optimization issue 2: Among them ||·|| F The F-norm of a matrix is ​​denoted by .

[0053] Optimization issue 3: Among them ||·||F The F-norm of a matrix is ​​denoted by .

[0054] Step S4:

[0055] A linear predictor model of an unknown failure tumbling target in the electromagnetic despinning process is constructed based on the system matrix, output matrix, and prediction matrix.

[0056] Solving the above optimization problem and combining it with the properties of pseudoinverse, we can obtain:

[0057]

[0058] superscript This represents the pseudo-inverse operation of a matrix.

[0059] Therefore, a linear predictor model for the target electromagnetic despinning process can be constructed as follows:

[0060] z(k+1)=Az(k)

[0061] T b (k)=Cz(k)

[0062]

[0063] In the formula, z(k) is the state variable of the predictor model at time k, and z(k+1) is the state variable of the predictor model at time k+1. Let T be the target angular velocity generated by the predictor at time k. b (k) represents the electromagnetic induced torque at time k, A is the system matrix, C is the output matrix, and Ck is the output matrix. x This is the prediction matrix.

[0064] Step S5: Using the linear predictor model as the constraint condition for the optimal estimation problem, solve to obtain the real-time accurate estimate of the angular velocity of the unknown failed rolling target.

[0065] The linear prediction rolling time-domain optimal estimation problem at time k P k The objective function is:

[0066]

[0067] Where N is the step size in the rolling time domain, Represents the state decision variables of the optimization problem. Let N, t-N+1, ..., t-1 represent the state decision variables at times tN, t-N+1, ..., t-1, respectively. Let P(tN) represent the prior state values ​​of the optimization problem at time tN, and let P(tN) represent the prior state weight matrix at time tN. The perturbation decision variables represent the optimization problem. respectively represent the disturbance decision variables at time t-N, t-N+1,..., t-1; R and Q are respectively the measurement noise weight matrix and the model disturbance weight matrix;

[0068] P k The constraint condition is:

[0069]

[0070]

[0071]

[0072] Wherein, Z is the constraint set of state variables, and W is the constraint set of disturbance.

[0073] The input real-time measured electromagnetic reaction torque is used to solve the optimal estimation problem above to obtain the real-time accurate estimation value of the target angular velocity.

[0074] The iteration formula is used to calculate P(t-N) and

[0075] P(t-N) = (I - K(t-N)C)P'(t-N)

[0076]

[0077] Wherein, I is the unit matrix, K(t-N) = P'(t-N)C T [S -1 (t-N)], S(t-N) = CP'(t-N)C T + R, P'(t-N) = AP(t-N-1)A T + Q, is the estimation value of the predictor state variable at time t-N-1.

[0078] The electromagnetic racemization torque T b from time t-N to t-1 and the P(t-N) and calculated by iteration are input into the optimal estimation problem, and k = t is set, so that the estimation value of the target angular velocity at the current time k can be obtained by solving the problem P

[0079] Example 1

[0080] The numerical simulation takes the Xinnuo No. 2 satellite launched in China in 2006 as an example, and the specific parameters are: mass m t = 2086.3 kg, moment of inertia J c = diag(4513.2, 4138.1, 3282.5) kg·m 2Historical data on the angular velocity and electromagnetic induction torque of an unknown failed rolling target at 200 time points (T=200) are obtained to generate time-series historical data X. c X p Y c After increasing the dimensionality of the data, X can be obtained. c,l X p,l Y c,l By solving optimization problems 1, 2, and 3, matrices A, C, and C0 can be obtained. x Finally, solve the optimal estimation problem P. k To obtain an estimate of the target state, the actual values ​​and estimated values ​​of each dimension are as follows: Figs. 1-3 As shown. From Figs. 1-3 As can be seen, this invention achieves angular velocity estimation for the three axes of the target, and can also achieve angular velocity estimation for various cases such as large-amplitude angular velocity and sinusoidal angular velocity.

[0081] from Fig. 1 It can be seen that, under the case of large angular velocity, the maximum absolute estimation error of the target angular velocity is 0.1101° / s, the mean absolute estimation error is 0.0741° / s, and the absolute estimation accuracy is 99.43%.

[0082] from Fig. 2 It can be seen that, under the condition of sinusoidal angular velocity variation, the maximum absolute estimation error is 0.1360° / s, the mean absolute estimation error is 0.0898° / s, and the absolute estimation accuracy is 96.18%.

[0083] from Fig. 3 It can be seen that, under normal circumstances, the maximum absolute estimation error is 0.1085° / s, the mean absolute estimation error is 0.0716° / s, and the absolute estimation accuracy is 95.47%.

[0084] In summary, this method can effectively estimate the target angular velocity under various conditions.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for estimating the angular velocity of an unknown failed rolling target based on electromagnetic induction torque, characterized in that, Comprise the following steps: Step S1: obtaining the historical data of the unknown failure rollover target, the historical data including angular velocity historical data and electromagnetic induction torque historical data, Step S2: dimensionality increasing the historical data through nonlinear transformation to obtain dimensionality increased data, Step S3: dynamically mode decomposing the dimensionality increased data to obtain system matrix, output matrix and prediction matrix, Step S4: constructing a linear predictor model of the unknown failure rollover target in the electromagnetic despinning process according to the system matrix, the output matrix and the prediction matrix, Step S5: taking the linear predictor model as the constraint condition of the optimal estimation problem, and solving to obtain the real-time accurate estimation value of the angular velocity of the unknown failure rollover target; The linear predictor model of step S4 is: ， wherein is the state variable of the time k predictor model, is the state variable of the time k predictor model, is the target angular velocity generated by the time k predictor, denotes the electromagnetic induction torque at the time k, is the system matrix, is the output matrix, is the prediction matrix; In step S5 Linear prediction rolling horizon optimal estimation problem at time instant The objective function is where, is the step size of the rolling horizon, denotes the state decision variable of the optimization problem, denotes the state decision variable of the optimization problem, denotes the state decision variable of the optimization problem, denotes the state decision variable of the optimization problem, denotes the prior state value of the optimization problem at time denotes the prior state value of the optimization problem at time denotes the prior state weight matrix at time denotes the disturbance decision variable of the optimization problem denotes the disturbance decision variable of the optimization problem, denotes the disturbance decision variable of the optimization problem; and are the measurement noise weight matrix and the model disturbance weight matrix, respectively. with the constraint that: ， wherein, is a constraint set of state variables, is a constraint set of disturbances.

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