A method, system and medium for calibrating jerk error coefficient of PIGA

Abstract

The present invention discloses a calibration method, system and medium for the acceleration error term coefficient of PIGA, which belongs to the field of rocket launch technology. The uniform acceleration stage of a centrifuge is used to stimulate the output of the acceleration error term to calibrate. The calibration accuracy of the acceleration error coefficient is simulated and analyzed by taking the PIGA output as the observed quantity. Through analysis, it is known that in the specific application of rocket launch, the circular probability error CEP of the rocket landing point during calibration is two orders of magnitude smaller than the circular probability error CEP without calibration, which improves the accuracy and practicality.

Description

Technical Field

[0001] The invention belongs to the technical field of rocket launching, and in particular relates to a calibration method, system and medium for calibrating a jerk error term coefficient of a PIGA. Background Art

[0002] During the use of the pendulum integrating gyro accelerometer (PIGA), it was found that the missile's hit accuracy is closely related to the PIGA's jerk term. In order to solve this problem, a method of calibrating the jerk term using an existing precision centrifuge was proposed. Since the existing large-arm centrifuge has a large moment of inertia of about 7000 and a working radius of 2.5m, the maximum angular acceleration generated by the main shaft can only reach 5° / s2. Whether it is possible to stimulate the jerk error term to output effectively and achieve a certain calibration accuracy.

[0003] The existing PIGA calibration method basically does not involve this item. The present invention elaborates in detail how to further improve the accuracy of PIGA and reduce the circular error probability CEP of the rocket landing point. Summary of the invention

[0004] In view of the above defects in the prior art, the present invention provides a method for calibrating the jerk error coefficient of PIGA.

[0005] The present invention provides a calibration method for the acceleration error term coefficient of PIGA, which is applied in rocket launch, and comprises the following steps: adding an error term related to the acceleration motion parameter to the error model of the pendulum integrating gyro accelerometer (PIGA), and determining the PIGA error model as: ,in, is the PIGA precession angular rate, is zero bias, is the calibration factor, is the quadratic error coefficient, is the cubic error coefficient, is the coefficient of the cross axis quadratic term, is the acceleration error coefficient, is the specific force on the PIGA input shaft, is the specific force on the PIGA output shaft, is the specific force on the PIGA balance shaft, for The derivative with respect to time, i.e. the jerk, is a random error; calculate the rotation angle of the centrifuge spindle: ,in, is the rotation angle of the centrifuge main shaft, is the initial angle of the centrifuge, is the initial rotation angular velocity of the spindle, is the spindle angular acceleration, t is the spindle rotation time; the instantaneous angular velocity is , the centripetal acceleration at the working radius R is , g is the acceleration due to gravity, and the time derivative of the centripetal acceleration at the working radius R is , the tangential acceleration at the working radius R is , the radial Coriolis acceleration at the working radius R is , L is the local latitude, is the angular velocity of the earth's rotation. The input parameters for calculating each axis of PIGA include: the platform installation error angle is , the two-dimensional parallelism error between the platform outer ring axis and the centrifuge main axis is , since the centrifuge main shaft inclination angle is small and has little effect on the calibration accuracy, it is ignored, and the input of each axis of PIGA is calculated according to the following formula:

[0006] ;

[0007] in is the specific force on the PIGA balance shaft.

[0008] The uniform rotation process of the centrifuge with 5 speeds was used for calibration, and the multi-rate calibration test was carried out to select the appropriate centrifuge speed so that the PIGA would not produce precession error. Through the multi-rate calibration method, the calibration coefficient was identified by the least square method.

[0009] When rotating at a constant speed, we get:

[0010] ;

[0011] in is the uniform rotation angular velocity of the centrifuge,

[0012] in, ,make Substituting the five angular velocity values, we get:

[0013] ,

[0014] ,

[0015] ,

[0016] in is 5 angular velocities, is the observation matrix, , The angular velocity of the centrifuge is The corresponding PIGA output;

[0017] Using least squares identification, we get: ,

[0018] ;

[0019] in is the structural matrix. Calibrate and substitute the above formula into the error model. When the centrifuge starts to rotate from a standstill, Substituting into the formula and ignoring the second-order small quantity, we get:

[0020] , integrating both sides simultaneously, we get:

[0021] ,

[0022] Written in matrix form:

[0023] ,

[0024] in is the structure matrix, is the coefficient matrix,

[0025] ,

[0026] ,

[0027] ;

[0028] At the n centrifuge rotation moments, The output of PIGA is sampled. The output of PIGA is, ,……, , The coefficients do not need to be calibrated, because only the coefficients before the square term of t need to be calibrated , all other items are used express,

[0029] ;

[0030] In the formula The coefficient of

[0031] ;

[0032] During the uniform rotation phase, The calibration results have been obtained. The magnitude of the error is large, and its influence As a result, only the uniform rotation stage is used. The calibration results are Perform secondary identification and Separation, The calibration error will not affect ,because Known,

[0033] make , About The polynomial of

[0034] ,

[0035] ,

[0036] ,

[0037] in, are the angular accelerations of the three centrifuges, The angular acceleration of the centrifuge is hour The value of

[0038] Using the following formula, the least squares identification is used to identify Identify:

[0039] , ,

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] Where B is the observation matrix, is the structure matrix, is the coefficient matrix.

[0045] In this method, when the centrifuge angular acceleration PIGA Calibration accuracy reaches Order of magnitude.

[0046] The present invention does not involve the existing PIGA calibration method. The problem of the jerk term was solved by calibrating the jerk term coefficient of PIGA. When PIGA is used on a rocket, the landing point accuracy on the rocket can be improved after calibrating the jerk term coefficient of PIGA and compensating it. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of centrifuge speed.

[0048] Figure 2 exist When sampling between The fitting process with time t.

[0049] Figure 3 exist When sampling between The fitting process with time t. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clear, optional embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0051] Embodiment 1

[0052] During the use of PIGA, it does not accelerate directly from 0g to 10g, but will experience an acceleration time of more than 100 seconds. Assuming that PIGA is uniformly accelerated, it is assumed that the error term related to the acceleration motion parameter is added to the original error model. The error model of PIGA becomes:

[0053] ;

[0054] In the formula, is the PIGA precession angular rate, in "rad / s"; is zero bias, unit is "rad / s"; is the calibration factor, the unit is "rad / s / g"; is the quadratic error coefficient, the unit is "rad / s / g2"; is the cubic error coefficient, the unit is "rad / s / g3"; is the cross-axis quadratic term coefficient, the unit is "rad / s / g2"; is the acceleration error coefficient, and its unit is "rad / g". is the specific force on the PIGA input shaft, in "g"; is the specific force on the PIGA output shaft, in "g"; is the specific force on the PIGA pendulum shaft, in "g"; for The derivative with respect to time, i.e. jerk, is expressed in "g / s", is a random error;

[0055] The centrifuge spindle performs angular position movement:

[0056] ;

[0057] In the formula, is the rotation angle of the centrifuge main shaft, is the initial angle of the centrifuge, is the initial rotation angular velocity of the spindle, is the spindle angular acceleration, and t is the spindle rotation time. Then the instantaneous angular velocity is:

[0058] ;

[0059] The centripetal acceleration at the working radius R (the working radius is the distance from the center of mass of PIGA to the axis of the centrifuge spindle) is:

[0060] ;

[0061] Where g is the acceleration due to gravity.

[0062] The time derivative of the centripetal acceleration at the working radius R is:

[0063] ;

[0064] The tangential acceleration at the working radius R is:

[0065] ;

[0066] The radial Coriolis acceleration at the working radius R is:

[0067] ;

[0068] Where L is the local latitude, is the angular velocity of the Earth's rotation.

[0069] The platform installation error angle is , the two-dimensional parallelism error between the platform outer ring axis and the centrifuge main axis is , since the centrifuge main shaft inclination angle is small and has little effect on the calibration accuracy, it can be ignored. Then the input of each axis of PIGA is:

[0070] ;

[0071] in is the specific force on the PIGA balance shaft.

[0072] The following introduces Calibration method.

[0073] The centrifuge rotation process Figure 1 As shown, the centrifuge is calibrated using a uniform rotation process at 5 speeds. , a multi-rate calibration test can be performed to select the appropriate centrifuge speed so that PIGA produces almost no precession error.

[0074] ;

[0075] The speed at which PIGA produces almost no precession error is as follows:

[0076] Table 1 The speed at which PIGA produces almost no precession error

[0077]

[0078] Through the multi-rate calibration method, the calibration coefficients are identified by the least squares method. There is already a mature calibration method, which is briefly introduced below.

[0079] When rotating at a constant speed, ;

[0080] ;

[0081] ;

[0082] ;

[0083] Ignore the second-order small quantities, and because as well as is smaller in magnitude than the other coefficients. , as well as In Just take the nominal value.

[0084] have:

[0085] ;

[0086] in is the uniform rotation angular velocity of the centrifuge.

[0087] ;

[0088] make , substitute the five angular velocity values ​​into:

[0089] ;

[0090] ;

[0091] ;

[0092] in There are 5 angular velocities, among which is the observation matrix, , The angular velocity of the centrifuge is The corresponding PIGA output;

[0093] Using least squares identification:

[0094] ,

[0095] ;

[0096] in is the structural matrix.

[0097] The present invention utilizes the uniform acceleration stage of the centrifuge to The centrifuge speed diagram is as follows: Figure 1 shown.

[0098] Substituting the above formula into the error model, when the centrifuge starts to rotate from a standstill ,in:

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] ;

[0105] because as well as is smaller in magnitude than the other coefficients. , as well as In Just take the nominal value. So, can be written as:

[0106] ;

[0107] ;

[0108] ;

[0109] Will Substitute into the formula and ignore the second-order small quantity:

[0110] ;

[0111] is the observation matrix, , The time when the centrifuge rotates The corresponding PIGA output is,

[0112] Integrating both sides simultaneously, we get:

[0113] ;

[0114] Written in matrix form:

[0115] ;

[0116] in is the structure matrix, is the coefficient matrix,

[0117] ,

[0118] ,

[0119] ;

[0120] At the n centrifuge rotation moments, The output of PIGA is sampled. The output of PIGA is , The coefficients do not need to be calibrated, because only the coefficients before the square term of t need to be calibrated , all other items are used express,

[0121] ;

[0122] In the formula The coefficient of

[0123] ;

[0124] During the uniform rotation phase, The calibration results have been obtained. The magnitude of the error is large, and its influence As a result, only the uniform rotation stage is used. The calibration results are Perform secondary identification and Separation, The calibration error will not affect ;

[0125] ;

[0126] ;

[0127] ;

[0128] because Known,

[0129] make , About The polynomial of

[0130] ;

[0131] ;

[0132] ;

[0133] in, are the angular accelerations of the three centrifuges, The angular acceleration of the centrifuge is hour The value of

[0134] Using least squares identification Identify:

[0135] , ,

[0136] ,

[0137] ,

[0138] ,

[0139] ,

[0140] Where B is the observation matrix, is the structure matrix, is the coefficient matrix.

[0141] Embodiment 2

[0142] The following is an error analysis to explain the calibration The necessity of this item to improve the accuracy of rocket landing.

[0143] Set the PIGA simulation parameters according to Table 2 below:

[0144] Table 2 PIGA simulation parameters

[0145]

[0146] Set some parameters of the centrifuge according to Table 3 below:

[0147] Table 3 Partial parameters of centrifuge

[0148]

[0149] In the first stage the centrifuge Start to rotate with uniform acceleration, angular acceleration ;

[0150] ;

[0151] ;

[0152] Setting PIGA precession angle error Standard Deviation ;

[0153] ;

[0154] calculate When PIGA produces Proportional to the precession angle , the corresponding time is , 181 precession angles can be collected.

[0155] ;

[0156] ;

[0157] There is an error in the output of PIGA, generating a standard deviation for 181 random error angles , the total output after adding the random error angle is ;

[0158] ;

[0159] ;

[0160] Figure 2 for The scatter diagram of time t is as follows: Figure 2 As shown, the black dots are , the curve is the fitting function ;

[0161] According to the computer fitting, the fitting results are obtained ;

[0162] ;

[0163] ;

[0164] right The calibration accuracy is poor because when the centrifuge starts to rotate, the PIGA precession error angle is smaller than the added output error, and the error accounts for a large proportion, which affects the curve fitting accuracy. The calibration accuracy is low.

[0165] In order to solve the problem under the existing centrifuge conditions, try to collect when the PIGA precession angle is large. Sampling is performed between the centrifuge speeds corresponding to ;

[0166] ;

[0167] ;

[0168] and The process is the same, generating the standard deviation for 181 random error angles , the total output after adding the random error angle is ;

[0169] ;

[0170] ;

[0171] Figure 3 for The scatter diagram of time t is as follows: Figure 3 As shown, the black dots are , the curve is the fitting function ; According to the computer fitting, the fitting results are obtained ;

[0172] ;

[0173] Calibration accuracy ;

[0174] Compared to Collect, in Collection pair The calibration accuracy is higher, which is improved by about 2 orders of magnitude.

[0175] In actual application, PIGA is placed on a rocket to give the rocket a jerk during launch. , the error model of PIGA is converted into output Model, divide both sides of formula (1) by ,get:

[0176] ;

[0177] Since PIGA is installed on the rocket, when the rocket is launched Much greater than , so the above formula Ignore, and get:

[0178] ;

[0179] in, ;

[0180] set up If not Calibrate by The speed error caused The rocket then ran at a constant speed for 2000s, and the circular error probability CEP was .

[0181] If Through the above analysis, it is known that when hour, . You can get hour, .

[0182] because Speed ​​error caused by calibration error .

[0183] The rocket then ran at a constant speed for 2000s, and the circular error probability CEP was .

[0184] Table 4 is the calibration With no calibration Comparison of the circular error probability CEP of the rocket landing point in the two cases:

[0185] Table 4 Comparison of circular probability errors of rocket landing points in two cases

[0186]

[0187] It can be seen that the calibration of PIGA The circular error probability CEP of the rocket landing point after the term is higher than that of the uncalibrated PIGA. The CEP of the rocket landing point is much smaller when the rocket is in the same position. Therefore, the PIGA calibration This item can improve the rocket landing accuracy.

[0188] The following describes the improvement Calibration accuracy

[0189] Based on the existing centrifuge conditions, The calibration accuracy can only reach If you want to improve the calibration accuracy to , a dynamic centrifuge that can provide higher angular acceleration is needed.

[0190] Ensure calibration accuracy is ,Right now ,ensure Within the error range

[0191] ;

[0192] ;

[0193] Can get ,exist When Within the fitting error range, it can be achieved The calibration accuracy of . In the above inequality, the random error Set to , in fact ,so The calibration accuracy is The sufficient but not necessary conditions are as follows. The approximate , Table 5 shows the corresponding angular accelerations Calibration accuracy.

[0194] Table 5 Corresponding angular accelerations Calibration accuracy

[0195]

[0196] When the centrifuge angular acceleration PIGA The calibration accuracy can reach Order of magnitude.

[0197] The conditions of this simulation are shown in Table 1. If you want to continue to increase the calibration accuracy, you can start with the three parameters in Table 1 and the parameters of PIGA: ① Use a centrifuge with a larger working radius; ② Use a dynamic centrifuge that can provide higher angular acceleration; ③ Use a dynamic centrifuge that can provide higher angular velocity; ④ Use a PIGA with a smaller precession angle error.

[0198] The present invention introduces a calibration method for PIGA, using the uniform acceleration stage of a centrifuge to stimulate the output of the acceleration error term to calibrate . Taking the PIGA output as the observed quantity, the calibration accuracy of the acceleration error coefficient is simulated and analyzed. Through analysis, it is known that in the specific application of rocket launch, the circular probability error CEP of the rocket landing point during calibration is two orders of magnitude smaller than the circular probability error CEP without calibration, which verifies the correctness and practicality of the present invention. The present invention proposes specific measures to improve the calibration accuracy of the term.

[0199] It should be noted that the computer program code for performing the operations of the present disclosure may be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server; in the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0200] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some implementations as replacements, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0201] The units involved in the embodiments described in the present disclosure may be implemented by software or hardware, wherein the name of a unit does not, in some cases, limit the unit itself.

[0202] The above introduces the preferred embodiments of the present invention, which is intended to make the spirit of the present invention clearer and easier to understand, but is not intended to limit the present invention. All modifications, substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection outlined by the claims attached to the present invention.

Claims

1. A calibration method for the jerk error term coefficient of PIGA, applied in rocket launch, comprises the following steps: The error term related to the acceleration motion parameters is added to the error model of PIGA, and the PIGA error model is determined as: in, is the PIGA precession angular rate, is zero bias, is the calibration factor, is the quadratic error coefficient, is the cubic error coefficient, is the coefficient of the quadratic term of the cross axis, is the acceleration error term coefficient, is the specific force on the PIGA input shaft, is the specific force on the PIGA output shaft, is the specific force on the PIGA balance shaft, for The derivative with respect to time, i.e. the jerk, is a random error; Calculate the rotation angle of the centrifuge spindle: ,in, is the rotation angle of the centrifuge main shaft, is the initial angle of the centrifuge, is the initial rotation angular velocity of the spindle, is the spindle angular acceleration, t is the spindle rotation time; Calculate the input parameters of each axis of PIGA; The uniform rotation process of the centrifuge at 5 speeds was used for calibration, and a multi-rate calibration test was performed to select the appropriate centrifuge speed so that PIGA would not produce precession errors. Through the multi-rate calibration method, the calibration coefficients are identified by the least square method; Using the following formula, the least squares identification algorithm is used to identify Calculate: ， ， ， ， ， Where B is the observation matrix, is the structure matrix, is the coefficient matrix, R is the working radius, g is the gravitational acceleration, L is the local latitude, is the Earth's rotation angular velocity, , , are the angular accelerations of the three centrifuges, The angular acceleration of the centrifuge is hour The value of For about The polynomial of For about The polynomial of For about The polynomial of .

2. The method for calibrating the jerk error term coefficient of PIGA according to claim 1, characterized in that: In the calculation of the rotation angle of the centrifuge main shaft, the instantaneous angular velocity is , the centripetal acceleration at the working radius R isThe centripetal acceleration at the working radius R is , g is the acceleration due to gravity, and the time derivative of the centripetal acceleration at the working radius R is , the tangential acceleration at the working radius R is , the radial Coriolis acceleration at the working radius R is , L is the local latitude, is the Earth's rotation angular velocity The angular accelerations for the three centrifuges.

3. The method for calibrating the jerk error term coefficient of PIGA according to claim 1, characterized in that: The input parameters for calculating each axis of PIGA include: the platform installation error angle is , the two-dimensional parallelism error between the platform outer ring axis and the centrifuge main axis is , then calculate the input of each axis of PIGA according to the following formula: ， in is the specific force on the PIGA balance shaft, is the time derivative of the centripetal acceleration at the working radius R, is the radial Coriolis acceleration at the working radius R.

4. The method for calibrating the jerk error term coefficient of PIGA as claimed in claim 1, characterized in that: The method of identifying the calibration coefficients by the multi-rate calibration method by the least square method includes: When rotating at a constant speed, we get: ， in is the uniform rotation angular velocity of the centrifuge, in, ,make , substituting the five angular velocity values, we get: ， in is 5 angular velocities, ， ， in is the observation matrix, , is the angular velocity of the centrifuge, The corresponding PIGA output; Using least squares identification, we get: , ， in is the structural matrix; Using the uniform acceleration stage of the centrifuge To calibrate, when the centrifuge starts to rotate from a standstill, Substituting into the formula and ignoring the second-order small quantity, we get: ， is the observation matrix, , The time when the centrifuge rotates The corresponding PIGA output is, Integrating both sides simultaneously, we get: ， Written in matrix form: ， in is the structure matrix, is the coefficient matrix, ， ， ， At the n centrifuge rotation moments, The output of PIGA is sampled. The output of PIGA is ,……, , It is a coefficient that does not need to be calibrated, because only the coefficient before the square term of t needs to be calibrated , all other items are used express, ， In the formula The coefficient of ， Where R is the working radius, g is the acceleration of gravity, L is the local latitude, is the Earth's rotation angular velocity, Install the error angle for the platform.

5. The method for calibrating the jerk error term coefficient of PIGA as claimed in claim 1, characterized in that: In the least squares identification algorithm, Before calculation, it also includes: During the uniform rotation phase, The calibration results have been obtained. The magnitude of the error is large, and its influence As a result, only the uniform rotation stage is used. The calibration results are Perform secondary identification and Separation, The calibration error will not affect ,because Known, make , For about The polynomial of , , , in are the angular accelerations of the three centrifuges, The angular acceleration of the centrifuge is hour The value of, R is the working radius, g is the acceleration of gravity, L is the local latitude, is the angular velocity of the Earth's rotation.

6. A calibration system for the jerk error coefficient of PIGA, characterized in that: The system comprises a processor and a memory, and the processor implements a method for calibrating the jerk error term coefficient of a PIGA according to any one of claims 1 to 5 by executing computer instructions in the memory.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions in the computer-readable storage medium are executed by a processor to implement a method for calibrating a jerk error term coefficient of a PIGA according to any one of claims 1 to 5.

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