Hypersonic flight vehicle reference trajectory storage and recovery method

Abstract

The invention discloses a hypersonic aircraft reference trajectory storage and recovery method, which comprises the following steps: firstly, considering that a Gibbs phenomenon appears at a node end point in a Lagrange interpolation method, and eliminating the phenomenon by adopting Chebyshev sampling; secondly, in order to solve the problem that the calculation precision of a missile-borne computer is limited, a self-adaptive scaling method is adopted to carry out reasonable scaling on the interpolation calculation process, so that the stage error of the calculation process is within an acceptable range; and finally, performing integral operation on differential terms of the original data to construct interpolation nodes, and ensuring smoothness of trajectory information. According to the method, the node number of a traditional linear interpolation algorithm is greatly reduced, the compression rate is lower than 1%, the nominal instruction is smooth, and the inner ring response is stable.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft, and in particular relates to a method for preserving and restoring a reference trajectory of a hypersonic aircraft. Background Art

[0002] In order to reduce the demand for storage space on the missile-borne computer and ensure the stability of the measurement, launch and control device in transmitting reference trajectory information, it is necessary to adopt high-fidelity compression and decompression of the trajectory information to effectively achieve the low cost of the missile-borne computer and the accuracy of various metadata.

[0003] According to the Nyquist sampling theorem, traditional reference trajectory information storage usually adopts the method of high-frequency sampling of trajectory points, followed by linear interpolation. Since linear interpolation has poor smoothness, a large number of trajectory nodes need to be saved to generate smooth trajectory instructions. When the missile-borne computer needs to store a large amount of reference trajectory information, it will take up a lot of storage space, thereby increasing the missile design cost. During the testing phase, the reference trajectory information is usually uploaded through the test, launch and control device. A large amount of reference trajectory information will also congest the channel, significantly reducing the upload speed, and it is also easy to cause data packet loss and create safety risks. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a method for preserving and restoring the reference trajectory of a hypersonic aircraft. First, the Lagrange interpolation method is considered to have the Gibbs phenomenon at the node endpoints, and Chebyshev sampling is used to eliminate the phenomenon; secondly, in view of the problem of limited calculation accuracy of the missile-borne computer, the interpolation calculation process is reasonably scaled by an adaptive scaling method, so that the stage error of the calculation process is within an acceptable range; finally, the interpolation node is constructed by performing an integral operation on the differential term of the original data to ensure the smoothness of the trajectory information. The method of the present invention greatly compresses the number of nodes of the traditional linear interpolation algorithm, with a compression rate of less than 1%, and the nominal instruction is smooth and the inner loop response is stable.

[0005] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0006] Step 1: Lagrange interpolation time allocation;

[0007] Set to save only The range and altitude are used as the reference trajectory, and the time interval Assigned as nodes, recorded as:

[0008] (1)

[0009] set up are the functions that need to be approximated by Lagrange interpolation, which are range and elevation, expressed as time Function of

[0010] According to the definition of Lagrange interpolation, the minimization of the remainder is approximated by minimizing the maximum remainder, that is, ;make For the Order Chebyshev polynomial, then the sampling nodes For The interval is The zeros of the Chebyshev polynomial of order , that is Root;

[0011] and The following conversion relationship exists:

[0012] (2)

[0013] Step 2: Lagrange interpolation differential matrix calculation;

[0014] The Lagrange polynomial expression is as follows:

[0015] (3)

[0016] in is the Lagrange interpolation function in The interpolated value at the point, is the basis function of the Lagrange polynomial;

[0017] set up:

[0018] (4)

[0019] Considering the requirements of truncation error and division-by-zero protection of the missile-borne computer, the following expression is obtained:

[0020] (5)

[0021] in Protection limit for denominator division by zero;

[0022] Loss calculation accuracy The denominator of is adaptively scaled, and the scaling factor is:

[0023] (6)

[0024] therefore:

[0025] (7)

[0026] Use matrix multiplication to differentiate equation (3), the differential matrix The expression is:

[0027] (8)

[0028] According to formula (2), the differential matrix has a similar transformation relationship, that is, :

[0029] (9)

[0030] Step 3: Range and elevation interpolation node construction;

[0031] The construction of the nodes in formula (3) is generated by integrating its differential terms:

[0032] (10)

[0033] in , is the initial range and initial elevation; , is the range and elevation point differential, i.e. heading and longitudinal flight speed; are the range and elevation generated by integrating the differential terms;

[0034] Correct and compensate equation (10):

[0035] (11)

[0036] in and They are The linear estimation of , that is, the integrated errors of range and elevation are evenly distributed to each node;

[0037] In summary, saving the baseline trajectory range and elevation only requires the initial and final time periods, as well as range and elevation interpolation points, namely:

[0038] (12)

[0039] Step 4: Range and elevation interpolation calculation;

[0040] Use step 1 to compare the time interval Divide the time ;

[0041] Scaling interpolation nodes and interpolation inputs:

[0042] (13)

[0043] Calculate the elevation at any time according to formula (3): and range :

[0044] (14)

[0045] Calculate the coefficient vector :

[0046] (15)

[0047] The design error is , the interpolation calculation formula is as follows:

[0048] (16).

[0049] The beneficial effects of the present invention are as follows:

[0050] The method of the present invention greatly compresses the number of nodes of the traditional linear interpolation algorithm, with a compression rate of less than 1%, and the nominal instructions are smooth and the inner loop response is stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of interpolation differential comparison according to an embodiment of the present invention.

[0052] Figure 2 Schematic diagram of trajectory data interpolation information according to an embodiment of the present invention.

[0053] Figure 3 Schematic diagram of the horizontal elevation estimation error of an embodiment of the present invention.

[0054] Figure 4 Schematic diagram of the horizontal elevation speed estimation error of an embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0056] In order to solve the problems of poor smoothness of existing trajectory linear interpolation and large amount of stored data, the present invention provides a hypersonic aircraft reference trajectory storage and recovery method, which can fully compress the smooth trajectory information into fewer nodes, thus greatly reducing the amount of information stored in the trajectory.

[0057] A method for preserving and restoring a hypersonic vehicle reference trajectory is described as follows:

[0058] Step 1, Lagrange interpolation time allocation;

[0059] Set to save only The range and altitude are used as the reference trajectory, and the time interval Assigned as nodes, recorded as:

[0060] (1)

[0061] set up The function that needs to be approximated for Lagrangian interpolation, namely range and elevation, can be expressed as time In order to make the best approximation of interpolation, it is obviously necessary to minimize the polynomial interpolation remainder. According to the definition of Lagrange interpolation, minimizing the remainder can be used to approximate the calculation by minimizing the maximum remainder, that is, When the approximation residuals are the same, the interpolation order is the smallest, which is obviously beneficial to reduce the number of nodes. For the Order Chebyshev polynomial, then the sampling nodes For The interval is The zeros of the Chebyshev polynomial of order , that is Root.

[0062] and The following conversion relationship exists:

[0063] (2)

[0064] Step 2: Lagrange interpolation differential matrix calculation;

[0065] The Lagrange polynomial expression is as follows:

[0066] (3)

[0067] in is the Lagrange interpolation function in The interpolated value at the point, is the basis function of the Lagrange polynomial. Let

[0068] (4)

[0069] For the onboard computer, The range of the denominator of is very large, so considering the requirements of truncation error and division by zero protection of the missile-borne computer, the following expression is used:

[0070] (5)

[0071] in This is the protection limit for the denominator being divided by zero, usually a very small number.

[0072] Loss calculation accuracy The denominator of is adaptively scaled, and the scaling factor is:

[0073] (6)

[0074] therefore:

[0075] (7)

[0076] To differentiate (3), we can use matrix multiplication. The differential matrix The expression is:

[0077] (8)

[0078] According to equation (2), the differential matrix has a similar transformation relationship, that is, :

[0079] (9)

[0080] Step 3: Construction of range and elevation interpolation nodes;

[0081] In the design of guidance control algorithms, the nominal trajectory usually uses the PD (proportional differential) link to generate an overload command as the input reference signal of the inner loop response. In order to ensure smooth control output response, the tracking reference signal must be smooth. Therefore, in order to eliminate the unevenness caused by the calculation error brought by the interpolation algorithm, the construction of the node in formula (3) is generated by its differential term integral:

[0082] (10)

[0083] in , is the initial range and initial elevation; , is the range and elevation point differential, i.e. heading and longitudinal flight speed; are ranges and elevations generated by integrating the differential terms, so their derivatives are accurate and smooth. and the true range elevation After a long period of integration, there is a large deviation in the final section. In order to eliminate the inconsistency, the formula (10) is corrected and compensated:

[0084] (11)

[0085] in and They are The linear estimate of is to distribute the integrated errors of range and elevation evenly to each node.

[0086] In summary, saving the baseline trajectory range and elevation only requires the initial and final time periods, as well as range and elevation interpolation points, namely:

[0087] (12)

[0088] Step 4: interpolation calculation of range and elevation;

[0089] First, we adopt the step of one time interval Divide the time .

[0090] To reduce calculation errors, scale the interpolation nodes and interpolation inputs:

[0091] (13)

[0092] Calculate the elevation at any time using formula (3) and range :

[0093] (14)

[0094] Calculate the coefficient vector :

[0095] (15)

[0096] The design error is , the interpolation calculation formula is as follows:

[0097] (16)

[0098] Example:

[0099] like Figure 1 As shown in Figure 2, in order to verify the effectiveness of the algorithm, the method is further explained by combining the hypersonic vehicle loading benchmark bounce trajectory curve. , the trajectory flight time is , the range and elevation of trajectory interpolation points are 100 respectively.

[0100] Step 1, Lagrange interpolation time allocation;

[0101] First, the time interval Perform time allocation and calculate 100 time difference nodes as follows:

[0102]

[0103] Step 2: Lagrange interpolation differential matrix calculation;

[0104] The calculated differential matrix is:

[0105]

[0106] Step 3: Construction of range and elevation interpolation nodes;

[0107] Calculate the 100 interpolation nodes that need to be saved:

[0108]

[0109] Step 4: Range and elevation interpolation calculation:

[0110] Calculate the Lagrange interpolation of 2000 equally divided moments in the time interval 0~465 to get the range and elevation The difference result is as follows Figure 2 As shown. Assume the relative error of interpolation is:

[0111]

[0112] in , , , They are respectively the range, elevation, directional velocity and longitudinal velocity in the original data. , are the difference between the direction velocity and the elevation velocity, that is, the interpolation coefficients are and Lagrange interpolation of .

[0113] Compared with the original data, the relative errors of the interpolated range and elevation of the trajectory data obtained by 100 interpolations and the baseline trajectory are as follows: Figure 3 As shown, the relative error of velocity interpolation calculation is as follows Figure 4 As shown in Figure 2, linear interpolation with similar calculation results requires no less than 10,000 points, so the trajectory data compression exceeds 1%.

Claims

1. A method for preserving and restoring a reference trajectory of a hypersonic vehicle, characterized in that: The steps include: Step 1: Lagrange interpolation time allocation; Set to save only The range and altitude are used as the reference trajectory, and the time interval Assigned as nodes, recorded as: （1） set up are the functions that need to be approximated by Lagrange interpolation, which are range and elevation, expressed as time Function of According to the definition of Lagrange interpolation, the minimization of the remainder is approximated by minimizing the maximum remainder, that is, ;make For the Order Chebyshev polynomial, then the sampling nodes For The interval is The zeros of the Chebyshev polynomial of order , that is Root; and The following conversion relationship exists: （2） Step 2: Lagrange interpolation differential matrix calculation; The Lagrange polynomial expression is as follows: （3） in is the Lagrange interpolation function in The interpolated value at the point, is the basis function of the Lagrange polynomial; set up: （4） Considering the requirements of truncation error and division-by-zero protection of the missile-borne computer, the following expression is obtained: （5） in Protection limit for denominator division by zero; The loss calculation accuracy is The denominator of is adaptively scaled, and the scaling factor is: （6） therefore: （7） Use matrix multiplication to differentiate equation (3), the differential matrix The expression is: （8） According to formula (2), the differential matrix has a similar transformation relationship, that is, : （9） Step 3: Range and elevation interpolation node construction; The construction of the nodes in formula (3) is generated by integrating its differential terms: （10） in , are the initial range and initial elevation; , is the range and elevation point differential, i.e. heading and longitudinal flight speed; are the range and elevation generated by integrating the differential terms; Correct and compensate equation (10): （11） in and They are The linear estimation of , that is, the integrated errors of range and elevation are evenly distributed to each node; In summary, saving the baseline trajectory range and elevation only requires the initial and final time periods, as well as range and elevation interpolation points, namely: （12） Step 4: Range and elevation interpolation calculation; Use step 1 to compare the time interval Divide the time ; Scaling interpolation nodes and interpolation inputs: （13） Calculate the elevation at any time according to formula (3): and range : （14） Calculate the coefficient vector : （15） The design error is , the interpolation calculation formula is as follows: （16）。

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