A method for on-line identification of damping characteristics of a hemispherical resonator using active standing wave precession

Abstract

The application discloses an on-line identification method for damping characteristics of a hemispherical resonator, which is realized by active standing wave precession and belongs to the technical field of inertia.The application solves the problem that the damping characteristics of a hemispherical resonator in the working process of a hemispherical resonator gyro cannot be identified in real time at present.The application drives the standing wave active precession of the resonator by using the additional driving force of the control electrode of the hemispherical resonator gyro, and the damping characteristics of the resonator can be detected in real time in the working process of the hemispherical resonator gyro system by solving each part of the control quantity.The error of the damping characteristics of the hemispherical resonator gyro system caused by the change of the external environment and the service life of the components is overcome, and the problem that the damping characteristics of the gyro are difficult to accurately determine in a long time working process is solved.Compared with the traditional off-line determination identification method by using a turntable when leaving the factory, the method of the application can stably determine the damping characteristics for a long time.The method of the application can be applied to on-line identification of the damping characteristics of the hemispherical resonator.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of inertia, and particularly relates to a method for on-line identification of damping characteristics of a hemispherical resonator by using active standing wave precession. BACKGROUND

[0002] The hemispherical resonator gyroscope is a rate integrating gyroscope based on the Coriolis effect, which senses the angular rate of motion by detecting the precession effect of the hemispherical resonator vibration standing wave relative to the base, and has the advantages of simple structure, high reliability, wide detection range, etc.

[0003] Since the position of the vibration standing wave is not fixed under the rate integrating mode, the system has higher requirements for the isotropy in the circumferential direction. However, during the processing and assembly of the hemispherical resonator, the non-uniform distribution of damping and other characteristics is inevitably generated, which affects the symmetry of the gyroscope structure and generates measurement errors. Therefore, identifying the damping characteristics of the hemispherical resonator is an important means to further eliminate damping errors and improve the accuracy of the hemispherical resonator gyroscope.

[0004] However, the identification of the damping characteristics of the hemispherical resonator gyroscope currently stays in the stage of experimental determination on the turntable, that is, the identification of the damping characteristics can only be performed before the hemispherical resonator gyroscope starts to work, and the damping characteristics of the hemispherical resonator during the working process of the hemispherical resonator gyroscope cannot be identified in real time. Therefore, it is an urgent problem to be solved to propose a method for real-time on-line identification of the damping characteristics of the hemispherical resonator. SUMMARY

[0005] The purpose of the application is to solve the problem that the damping characteristics of the hemispherical resonator during the working process of the hemispherical resonator gyroscope cannot be identified in real time, and a method for on-line identification of the damping characteristics of the hemispherical resonator by using active standing wave precession is proposed.

[0006] The technical scheme adopted by the application to solve the above technical problem is: a method for on-line identification of the damping characteristics of a hemispherical resonator by using active standing wave precession, which specifically comprises the following steps:

[0007] Step 1: establishing the equation of the first derivative of the standing wave energy of the hemispherical resonator gyroscope and the first derivative of the quadrature error, and performing closed-loop control on the hemispherical resonator gyroscope in the rate integrating control mode to obtain the required quadrature control force of the resonator under the stable state of the hemispherical resonator gyroscope;

[0008] Step 2: introducing the active driving force f v to drive the standing wave precession, and using the spindle amplitude control quantity d a , the quadrature control quantity d q and the additional driving control quantity d v to superimpose on the driving electrode of the hemispherical resonator gyroscope to drive the hemispherical resonator gyroscope to vibrate;

[0009] At each data sampling moment in the vibration process of the hemispherical resonator gyroscope, the combined signal S, the combined signal R, the main shaft amplitude control quantity and the quadrature control quantity are collected, and the standing wave rotation angle at each sampling moment is calculated according to S and R;

[0010] Step three, based on the quadrature control force required by the resonator in step one and the data collected in step two, the damping distribution characteristics of the hemispherical resonator gyroscope are identified.

[0011] The beneficial effects of the present application are:

[0012] The method of the present application utilizes the additional driving force of the control electrode of the hemispherical resonator gyroscope to drive the active precession of the standing wave of the resonator, and through the calculation of each part of the control quantity, the damping characteristics of the resonator can be detected in real time during the operation of the hemispherical resonator gyroscope system. The error caused by the change of the external environment and the service life of the components to the damping characteristics of the hemispherical resonator gyroscope system is overcome, and the problem that the damping characteristics of the gyroscope are difficult to accurately determine in a long time operation is solved. Compared with the traditional offline identification method using the turntable at the time of delivery, the damping characteristics can be stably determined for a long time by the method of the present application. And it can be realized only by matching the control circuit, and the application range is wider. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The mechanical equivalent model of the hemispherical resonator;

[0014] In the figure, represents the force of the hemispherical resonator on the intrinsic damping axis x τ represents the force of the hemispherical resonator on the intrinsic damping axis y τ

[0015] Figure 2 The signal flow diagram of the control loop of the hemispherical resonator gyroscope. DETAILED DESCRIPTION

[0016] Detailed implementation one: the hemispherical resonator damping characteristic online identification method using active standing wave precession realized by the embodiment, the method specifically includes the following steps:

[0017] Step one, establish the equation of the first derivative of the standing wave energy and the first derivative of the quadrature error of the hemispherical resonator gyroscope, and adopt the rate integral control mode to carry out closed loop control on the hemispherical resonator gyroscope, so as to obtain the quadrature control force required by the resonator under the stable state of the hemispherical resonator gyroscope;

[0018] Step two, introduce the active driving force f v to drive the standing wave precession, utilize the main shaft amplitude control quantity d a , the quadrature control quantity d q and the additional driving control quantity d​​v The driving electrode acts on the hemispherical resonator gyroscope to drive the hemispherical resonator gyroscope to vibrate;

[0019] At each data sampling moment in the vibration process of the hemispherical resonator gyroscope, the combined signal S, the combined signal R, the main axis amplitude control quantity and the quadrature control quantity are collected, and the standing wave rotation angle at each sampling moment is calculated according to S and R;

[0020] Step three, based on the quadrature control force required by the resonator in step one and the data collected in step two, the damping distribution characteristics of the hemispherical resonator gyroscope are identified.

[0021] Specific implementation method two: the difference between this implementation method and the specific implementation method one is that the equations of the first derivative of the standing wave energy of the hemispherical resonator gyroscope and the first derivative of the quadrature error are respectively:

[0022]

[0023]

[0024] Wherein, E represents the standing wave energy, Q represents the quadrature error, represents the damping mismatch, represents the damping parameter, θ represents the standing wave rotation angle, a is the main standing wave amplitude, q is the quadrature wave amplitude, ω is the resonator vibration frequency, f qs represents the quadrature control force, f ac represents the amplitude control force, θ τ represents the resonator damping axis angle, θ ω represents the resonator stiffness axis angle, Δω is the frequency splitting.

[0025] Other steps and parameters are the same as those in the specific implementation method one.

[0026] In the field, and are defined as follows:

[0027]

[0028] Wherein, τ1 is the main standing wave axis damping time constant, τ2 is the quadrature axis damping time constant.

[0029] Specific implementation method three: the difference between this implementation method and the specific implementation method one or two is that the rate integral control mode is used to close-loop control the hemispherical resonator gyroscope to obtain the quadrature control force required by the resonator in the stable state of the hemispherical resonator gyroscope; specifically:

[0030] Through the amplitude and quadrature control loop, the rate integral control mode is used to close-loop control the hemispherical resonator gyroscope, and in the stable state of the hemispherical resonator gyroscope, E=a2 、 Q = 0, q = 0, according to the first order of the orthogonal error

[0031] derivative , the required orthogonal control force of the harmonic oscillator is obtained as:

[0032] f qs = aωΔωsin4(θ-θ ω )(9)

[0033] In formula (9), ωΔω is defined as formula (10);

[0034]

[0035] wherein, ω x is the vibration frequency on the main coordinate axis x, and ω y is the vibration frequency on the main coordinate axis y.

[0036] The other steps and parameters are the same as those in the first or second embodiment.

[0037] The fourth embodiment is different from one of the first to third embodiments in that the combined signal S, the combined signal R, the main axis amplitude control quantity and the orthogonal control quantity are collected at each data sampling moment in the vibration process of the hemispherical resonator gyroscope, and the standing wave rotation angle at each sampling moment is calculated according to S and R; the specific process is as follows:

[0038] Step two one, initializing the sampling moment i = 0;

[0039] Step two two, the standing wave rotation angle at the i-th sampling moment t i is recorded as θ(i), and the rotation speed at the moment t i is recorded as ω(i), then the standing wave rotation angle expected to be collected at the i+1-th sampling moment t i+1 is θ(i+1) = θ(i) + Δθ, and Δθ is a preset angle increment, then the i+1-th sampling moment t i+1 = t i + Δθ / ω(i);

[0040] Step two three, collecting S(i+1), R(i+1), the main axis amplitude control quantity d i+1 (i+1) and the orthogonal control quantity d a (i+1) at the i+1-th sampling moment t q ;

[0041] calculating the standing wave rotation angle θ(i+1) at the i+1-th sampling moment according to S(i+1) and R(i+1);

[0042] Step two four, judging whether i < N-1 is satisfied:

[0043] If not, let i=i+1, return to step two;

[0044] If yes, execute step two five;

[0045] Step two five, store the data collected at each sampling time in the form of array matrix in formula (13) in FPGA;

[0046]

[0047] Wherein, D a is the array matrix composed of the main axis amplitude control quantity data at each sampling time, D q is the array matrix composed of the quadrature control quantity data at each sampling time, and H is the coefficient array matrix related to the standing wave corner data at each sampling time.

[0048] The other steps and parameters are the same as one of the first to third embodiments.

[0049] The fifth embodiment is different from one of the first to fourth embodiments in that the specific process of the step three is:

[0050] Step three one, the quadrature control force applied to the resonator And the main axis control force Respectively:

[0051]

[0052] Wherein, is the phase delay error, f a is the main axis amplitude control force, f q is the quadrature control force;

[0053] In the quadrature control loop And f qs , then the actual quadrature control force output by the quadrature control loop is:

[0054]

[0055] Convert formula (15) into the quadrature control quantity equation of formula (16):

[0056]

[0057] Wherein, G c is the gain of the hemispherical resonator gyro driving signal to the resonator electrostatic excitation force;

[0058] Then, the quadrature control quantity equation of formula (16) is rewritten as:

[0059] dq =b1+p1sin4θ+q1cos4θ (17)

[0060] Where b1, p1, and q1 are all coefficients of the orthogonal control equation;

[0061] Let X1 = [p1 q1 b1] T D q =HX1, then

[0062] X1=(H T H) -1 H T D q (18)

[0063] The coefficients of the sine component in equation (16) are obtained as follows:

[0064]

[0065] And let the parameter G be:

[0066]

[0067] Step 3.2, in the amplitude control loop with f ac If they are equal, then

[0068]

[0069] Will Substituting into equation (7) under steady-state conditions:

[0070]

[0071] Based on the identification parameter G, equation (22) is rearranged to transform it into equation (23):

[0072]

[0073] The control equation of equation (23) can be rewritten as follows:

[0074]

[0075] Let X2 = [p2 q2 b2] T , but

[0076]

[0077] The relationship between the damping distribution characteristic parameters and the parameters in X2 is obtained according to equation (23);

[0078] Step three, according to the data collected in step two, X1 = [p1 q1 b1] T and X2 = [p2 q2 b2] T are jointly identified, and then the damping distribution characteristic parameters and θ τ are obtained.

[0079] The other steps and parameters are the same as one of the first to fourth embodiments.

[0080] The sixth embodiment is different from the first to fifth embodiments in that the relationship between the damping distribution characteristic parameters and the parameters in X2 is as follows:

[0081] Damping parameter:

[0082]

[0083] Damping mismatch:

[0084]

[0085] Resonator damping axis angle:

[0086]

[0087] The other steps and parameters are the same as one of the first to fifth embodiments.

[0088] The seventh embodiment is different from the first to sixth embodiments in that the specific process of step three is as follows:

[0089] Step three one, initialize the forgetting factor λ∈(0,1), initialize the parameter vector estimate X1(0) =

[000] T , X2(0) = [0 0 0] T , initialize the covariance matrix P1(0) = λI, P2(0) = λI, where I is the unit matrix;

[0090] And initialize the iteration number j = 1;

[0091] Step three two, calculate the gain vector k1(j):

[0092] k1(j) = P1(j-1)·h T (j) / (λ+h(j)·P1(j-1)·h T (j)) (29)

[0093] Where h(j) is the jth row data of the data matrix H, h T (j) is the transpose of h(j);

[0094] Update parameter estimate X1(j), X1 = [p1(j) q1(j) b1(j)] T :

[0095] X1(j) = X1(j-1) + k1(j) · (d q (j) - h(j) · X1(j-1)) (30)

[0096] where d q (j) is the jth row data of data matrix D q ;

[0097] Step three three, update covariance matrix P1(j):

[0098] P1(j) = (P1(j-1) - k1(j) · h(j) · P1(j-1)) / λ (31)

[0099] Step three four, update parameter G(j):

[0100]

[0101] Step three five, calculate gain vector k2(j):

[0102] k2(j) = P2(j-1) · h T (j) / (λ + h(j) · P2(j-1) · h T (j)) (33)

[0103] Update parameter estimate X2(j), X2(j) = [p2(j) q2(j) b2(j)] T :

[0104] X2(j) = X2(j-1) + k2(j) · (G(j) · d a (j) - h(j) · X2(j-1)) (34)

[0105] where d a (j) is the jth row data of data matrix D a ;

[0106] Step three six, update covariance matrix P2(j):

[0107] P2(j) = (P2(j-1) - k2(j) · h(j) · P2(j-1)) / λ (35)

[0108] Step three seven, update damping parameter Damping mismatch and harmonic oscillator damping axis rotation angle θ τ [j]:

[0109]

[0110] Step 338, whether j=N is satisfied:

[0111] If j=N is satisfied, step 339 is executed.

[0112] If j=N is not satisfied, j=j+1 is set, and step 332 is returned to be executed.

[0113] Step 339, according to the calculated damping parameters of each sampling time Damping mismatch Harmonic oscillator damping axis rotation angle θ τ [j] to obtain the damping distribution characteristic parameter identification result.

[0114] The other steps and parameters are the same as one of the first to sixth embodiments.

[0115] Embodiment 8: Different from one of the first to seventh embodiments, in the damping distribution characteristic parameter, the identification result of the damping parameter is the mean value of the damping parameter .

[0116] The other steps and parameters are the same as one of the first to seventh embodiments.

[0117] Embodiment 9: Different from one of the first to eighth embodiments, in the damping distribution characteristic parameter, the identification result of the damping mismatch is the mean value of the damping mismatch .

[0118] The other steps and parameters are the same as one of the first to eighth embodiments.

[0119] Embodiment 10: Different from one of the first to ninth embodiments, in the damping distribution characteristic parameter, the identification result of the harmonic oscillator damping axis rotation angle is the mean value of the harmonic oscillator damping axis rotation angle θ τ [j], j=1, 2, …, N.

[0120] The other steps and parameters are the same as one of the first to ninth embodiments.

[0121] Embodiment

[0122] The online identification method of the damping characteristic of the hemispherical harmonic oscillator using the active standing wave precession will be further described below in combination with the accompanying drawings:

[0123] The origin of the resonator mode excitation and detection coordinate system is defined as the center of the plate electrode, the x-axis of the resonator mode excitation and detection coordinate system coincides with the symmetry axis of the first electrode in the counterclockwise direction, the positive direction of the x-axis points from the origin to the first electrode, the y-axis is perpendicular to the x-axis, and the positive direction of the y-axis points from the origin to the third electrode in the counterclockwise direction. As shown in Figure 1 , the coordinate axes of the resonator mode excitation and detection coordinate system are the main coordinate axes x and y, the non-ideal resonator natural frequency axis x ω forms an angle θ ω with the x-axis of the resonator mode excitation and detection coordinate system τ , the non-ideal resonator natural damping axis x τ forms an angle θ ω with the x-axis of the resonator mode excitation and detection coordinate system τ , θ ω is called the resonator stiffness axis angle, and θ τ is called the resonator damping axis angle.

[0124] As shown in Figure 2 , the control loop in the control system of the hemispherical resonator gyroscope composed of the FPGA is shown. After starting, the output signal of the hemispherical resonator detection channel is demodulated by using the sine and cosine reference signals generated by the phase-locked loop circuit, specifically:

[0125] The electrical signal sensed by the detection electrode is:

[0126]

[0127] wherein a is the main standing wave amplitude, q is the quadrature wave amplitude, ω is the resonator vibration frequency, θ is the standing wave rotation angle, is the phase delay error.

[0128] The sine and cosine reference signals obtained by the phase-locked loop are:

[0129]

[0130] In the demodulation circuit, the reference signal is multiplied by the electrical signal of formula (1), and then the multiplication result is passed through a low-pass filter to extract the low-frequency signal of the gyroscope, thereby obtaining the demodulated low-frequency variables C x , C y , S x , S y :

[0131]

[0132] In the formula, LPF represents a low-pass filter.

[0133] The low-frequency variables in formula (3) are combined and calculated to obtain the typical parameters of the standing wave energy E and the quadrature error Q representing the working state of the hemispherical resonator gyroscope:

[0134]

[0135] The phase delay error and the standing wave angle θ can be calculated according to the parameters in formula (4) respectively

[0136]

[0137] The on-line identification method of the damping characteristics of the hemispherical resonator will be described in detail below according to the following steps.

[0138] Step one, the first-order derivative equations of the standing wave energy of the hemispherical resonator gyroscope and the first-order derivative of the quadrature error can be obtained by the Lynch average method as follows:

[0139]

[0140] Among them, E represents the standing wave energy, Q represents the quadrature error, represents the damping mismatch, represents the damping parameter, θ represents the standing wave angle, a is the main standing wave amplitude, q is the quadrature wave amplitude, ω is the resonator vibration frequency, f qs represents the quadrature control force, f ac represents the amplitude control force, θ τ represents the resonator damping axis angle, θ ω represents the resonator stiffness axis angle, and Δω is the frequency split.

[0141] Through the amplitude and quadrature control loop, the hemispherical resonator gyroscope is closed-loop controlled by using the rate integral control mode. In the stable state of the hemispherical resonator gyroscope, E=a 2 , Q=0, q=0. According to the form of the first-order derivative of the quadrature error, that is, considering the quadrature error of formula (8), the required quadrature control force of the resonator is obtained as:

[0142]

[0143] f qs =aωΔωsin4(θ-θ ω ) (9)

[0144] In formula (9), ωΔω is defined as formula (10), which represents the frequency difference between the main axis and the quadrature axis of the resonator, that is, the frequency split.

[0145]

[0146] Among them, ω x is the vibration frequency on the main coordinate axis x, and ω y is the vibration frequency on the main coordinate axis y.​​​​​

[0147] Step two, on the basis of amplitude and quadrature control, a certain active driving force f is introduced v Drive the standing wave precession, use the spindle amplitude control amount d a , quadrature control amount d q And the additional driving control amount d v Superimposed on the driving electrode of the hemispherical resonator gyroscope, drive the hemispherical resonator gyroscope to vibrate;

[0148] The control loop controls the force and the additional active driving force through the excitation electrode to act on the resonator, and the gain of the hemispherical resonator gyroscope driving signal to the resonator electrostatic excitation force is G c , the spindle amplitude control amount d a , the quadrature control amount d q And the additional driving control amount d v The relationship with the control amount is:

[0149]

[0150] Where, f a is the spindle amplitude control force, f q is the quadrature control force, and f v is the active driving force;

[0151] According to the coordinate system shown in Figure 1 The spindle control force f a , the quadrature control force f q , the active driving force f v Output by the control loop is decomposed into the hemispherical resonator gyroscope base coordinate system XOY, that is, transformed into the force on the hemispherical resonator in two coordinate axes according to formula (12):

[0152]

[0153] Where, the phase delay error Is generated in the circuit signal processing, which can be regarded as a constant.

[0154] At each data sampling time in the vibration process of the hemispherical resonator gyroscope, the combined signal S, the combined signal R, the spindle amplitude control amount and the quadrature control amount are collected, and the standing wave rotation angle at each sampling time is calculated according to S and R;

[0155] Because the spatial position of the resonator standing wave changes with time, in order to ensure that the data collection covers as much standing wave rotation angle information as possible, the following method is used to determine the sampling time and position:

[0156] Let the sampling start time be t0, the standing wave angle at t0 be denoted as θ(0), and the rotational speed at t0 be denoted as ω(0). The expected standing wave angle to be collected at the next sampling time is θ(1) = θ(0) + Δθ, where Δθ is a preset angle increment. Then, the next sampling time t1 = t0 + Δθ / ω(0), and so on. That is, the sampling time of the next sample point is dynamically determined by using the sampling time and rotational speed of the previous sample point. The above sampling process can be specifically expressed as:

[0157] Step 2.1: Initialize sampling time i = 0;

[0158] Step 22: The i-th sampling time t i The standing wave rotation angle is denoted as θ(i), and t i Let the rotational speed at time t be denoted as ω(i). Then, at the (i+1)th sampling time t i+1 The desired standing wave rotation angle is θ(i+1) = θ(i) + Δθ, where Δθ is the preset angle increment. Therefore, at the (i+1)th sampling time t... i+1 =t i +Δθ / ω(i);

[0159] Steps two and three: at the (i+1)th sampling time t i+1 For S(i+1), R(i+1), and the spindle amplitude control quantity d a (i+1) and quadrature control quantity d q (i+1) is used for data collection;

[0160] Calculate the standing wave rotation angle θ(i+1) at the (i+1)th sampling time based on S(i+1) and R(i+1);

[0161] Step 2.4: Determine if i < N-1:

[0162] If the condition is not met, then let i = i + 1 and return to step two.

[0163] If satisfied, proceed to step two five;

[0164] Step 25: Store the data collected at each sampling time in the FPGA in the form of an array matrix as shown in Equation (13);

[0165] Because of the need to solve the sinusoidal equation in subsequent steps, the standing wave rotation angle θ is processed, and sin4θ(i) and cos4θ(i) are obtained and then stored.

[0166] The obtained data points are written in matrix form as follows:

[0167]

[0168] Among them, D aD is an array matrix composed of the main axis amplitude control quantity data of each sampling moment, D q H is a coefficient array matrix related to the standing wave corner data of each sampling moment. The array matrix D q and H will be used for the subsequent least square method solution of the damping distribution characteristics.

[0169] The data acquisition algorithm is shown in Table 1:

[0170] Table 1 Data dynamic sampling algorithm

[0171]

[0172] Step three, according to the data collected in step two, the damping distribution characteristics of the hemispherical resonator gyroscope are identified.

[0173] The specific process of step three is:

[0174] Step three one, on the basis of closed loop control, a certain external driving control force f v driving standing wave precession, obtaining the orthogonal control force applied to the resonator at this time and the main axis control force are respectively:

[0175]

[0176] Wherein, is the phase delay error, f a is the main axis amplitude control force, f q is the orthogonal control force;

[0177] In the orthogonal control loop f qs is equal, then the actual orthogonal control force output by the orthogonal control loop is:

[0178]

[0179] Convert equation (15) to equation (16) of the orthogonal control quantity:

[0180]

[0181] Wherein, G c is the gain from the hemispherical resonator gyroscope driving signal to the resonator electrostatic excitation force;

[0182] The equation is equivalent to the superposition of a direct current component and a sine component in form, then the orthogonal control quantity equation of equation (16) is rewritten as:

[0183] d q=b1+p1sin4θ+q1cos4θ (17)

[0184] Where b1, p1, and q1 are all coefficients of the orthogonal control equation;

[0185] Let X1 = [p1 q1 b1] T Applying the least squares formula, D q =HX1, then

[0186] X1=(H T H) -1 H T D q (18)

[0187] Returning to the original control equation, the coefficients of the sinusoidal component in equation (16) are obtained as follows:

[0188]

[0189] Since the frequency split Δω depends only on the manufacturing process of the resonator and remains essentially unchanged in a hemispherical resonator gyroscope system, it can be measured and eliminated at the factory. Let parameter G be:

[0190]

[0191] Step 3.2, in the amplitude control loop with f ac If they are equal, then

[0192]

[0193] Will Substituting into equation (7) under steady-state conditions:

[0194]

[0195] Based on the identification parameter G, equation (22) is rearranged to transform it into equation (23), thus obtaining the control quantity representation for spindle control:

[0196]

[0197] The equation is also a superposition of a DC component and a sinusoidal component, so the control equation of equation (23) can be rewritten as:

[0198]

[0199] Let X2 = [p2 q2 b2] T Applying the least squares formula, we get but

[0200]

[0201] The relationship between the damping distribution characteristic parameters and the parameters in X2 is obtained according to formula (23) as follows:

[0202] Damping parameters:

[0203]

[0204] Damping mismatch:

[0205]

[0206] Resonator damping axis angle:

[0207]

[0208] Step three, according to the data collected in step two, X1 = [p1 q1 b1] T and X2 = [p2 q2 b2] T are jointly identified, and then the damping distribution characteristic parameters and θ τ are obtained.

[0209] Step three one, initialize the forgetting factor λ ∈ (0, 1), initialize the parameter vector estimate X1 (0) =

[000] T , X2 (0) =

[000] T , initialize the covariance matrix P1 (0) = λI, P2 (0) = λI, where I is the unit matrix;

[0210] and initialize the iteration number j = 1;

[0211] Step three two, calculate the gain vector k1 (j):

[0212] k1 (j) = P1 (j-1) · h T (j) / (λ+h(j)·P1(j-1)·h T (j)) (29)

[0213] where h(j) is the jth row data of the data matrix H, h T (j) is the transpose of h(j);

[0214] Update the parameter estimate X1 (j), X1 = [p1 (j) q1 (j) b1 (j)] T :

[0215] X1 (j) = X1 (j-1) + k1 (j) · (d q (j)-h(j)·X1(j-1)) (30)

[0216] where d q (j) is the jth row data of the data matrix D q (j) is the jth row data of the data matrix D

[0217] Step three- three, updating the covariance matrix P1(j):

[0218] P1(j) = (P1(j-1) - k1(j) - h(j) - P1(j-1)) / λ (31)

[0219] Step three- four, updating the parameter G(j):

[0220]

[0221] Step three- five, calculating the gain vector k2(j):

[0222] k2(j) = P2(j-1) - h T (j) / (λ + h(j) - P2(j-1) - h T (j)) (33)

[0223] Updating the parameter estimate X2(j), X2(j) = [p2(j) q2(j) b2(j)] T :

[0224] X2(j) = X2(j-1) + k2(j) - (G(j) - d a (j) - h(j) - X2(j-1)) (34)

[0225] where d a (j) is the jth row data of the data matrix D a (j) is the jth row data of the data matrix D

[0226] Step three- six, updating the covariance matrix P2(j):

[0227] P2(j) = (P2(j-1) - k2(j) - h(j) - P2(j-1)) / λ (35)

[0228] Step three- seven, updating the damping parameter damping mismatch and the harmonic oscillator damping axis rotation angle θ τ [j]:

[0229]

[0230] Step three- eight, whether j = N is satisfied:

[0231] If j = N is satisfied, step three- nine is executed.

[0232] If j = N is not satisfied, j = j + 1 is set, and step three- two is returned to be executed.

[0233] Step three 39, calculating damping parameter The mean value of the damping mismatch is calculated, and the calculated mean value is taken as the damping parameter identified at the current moment. The mean value of the damping mismatch is calculated, and the calculated mean value is taken as the damping parameter identified at the current moment. τ The mean value of the damping mismatch is calculated, and the calculated mean value is taken as the damping parameter identified at the current moment.

[0234] The identification method of the embodiment can solve the problem of large amount of calculation of the traditional least square method, and the identification process is shown in Table 2.

[0235] Table 2

[0236]

[0237]

[0238] The method can identify the damping characteristic parameters online, and solve the problem that the traditional method can only identify before starting to work, and cannot monitor the damping characteristic parameters during the working process. It should be noted that the method does not need to identify the damping characteristic parameters in real time, and in actual application, the damping characteristic parameters can be identified once every fixed time, and when identification is needed, N groups of data can be collected in advance.

[0239] The above examples of the present application are only used to illustrate the calculation model and calculation process of the present application, and are not limited to the embodiments of the present application. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description, and it is impossible to enumerate all the embodiments here, and any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession, characterized in that, The method specifically includes the following steps: Step 1: Establish the equations for the first derivative of the standing wave energy and the first derivative of the orthogonal error of the hemispherical resonant gyroscope. Use the rate integral control mode to perform closed-loop control on the hemispherical resonant gyroscope to obtain the orthogonal control force required by the harmonic oscillator under the stable state of the hemispherical resonant gyroscope. Step 2: Introduce active driving force Drive the precession of the standing wave and control the amount of the main shaft amplitude. Orthogonal control quantity and external drive control quantity The driving electrodes acting in superposition on the hemispherical resonant gyroscope drive the hemispherical resonant gyroscope to vibrate; At each data sampling moment during the vibration process of the hemispherical resonant gyroscope, the combined signal S, the combined signal R, the principal axis amplitude control quantity and the orthogonal control quantity are collected, and the standing wave angle at each sampling moment is calculated based on S and R. Step 3: Identify the damping distribution characteristics of the hemispherical resonant gyroscope based on the orthogonal control force required by the harmonic oscillator in Step 1 and the data collected in Step 2. The specific process of step three is as follows: Step 31: Applying orthogonal control force to the harmonic oscillator and spindle control force They are respectively: (14) in, For phase delay error, Main spindle amplitude control force, Orthogonal control force; Indicates orthogonal control force. In orthogonal control loops Orthogonal control force If they are equal, then the actual orthogonal control force output by the orthogonal control loop is: (15) Transform equation (15) into the orthogonal control equation of equation (16): (16) in, The gain of the driving signal from the hemispherical resonant gyroscope to the electrostatic excitation force of the resonator; The amplitude of the main standing wave; The frequency of the harmonic oscillator. Frequency splitting; Indicates the standing wave angle; Indicates the rigid axis angle of the harmonic oscillator; The orthogonal control equation of equation (16) can then be rewritten as: (17) in, , and All of these are coefficients of the orthogonal control equations; make , ,but (18) in, It is an array matrix composed of orthogonal control quantity data at each sampling time. It is a coefficient array matrix related to the standing wave rotation data at each sampling time; The coefficients of the sine component in equation (16) are obtained as follows: (19) And let the parameters for: (20) Step 3.2, in the amplitude control loop With amplitude control force If they are equal, then (21) Will Substituting into equation (7) under steady-state conditions: (22) Based on identification parameters Rearranging terms in equation (22), we can transform equation (22) into equation (23): (23) in, Indicates the damping axis angle of the harmonic oscillator. This indicates a damping mismatch. Indicates the damping parameter; The control equation of equation (23) can be rewritten as follows: (24) make , ,but (25) in, It is an array matrix composed of the main shaft amplitude control data at each sampling time; According to equation (23), the damping distribution characteristic parameters are obtained and The relationship between parameters; Step 3: Based on the data collected in Step 2, and Joint identification is performed to obtain damping distribution characteristic parameters. , and .

2. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 1, characterized in that, The equations for the first derivative of the standing wave energy and the first derivative of the orthogonal error of the hemispherical resonant gyroscope are as follows: (7) (8) in, Represents the energy of the standing wave. Indicates orthogonal error The amplitude is that of an orthogonal wave.

3. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 2, characterized in that, The rate integral control mode is used to perform closed-loop control on the hemispherical resonant gyroscope to obtain the orthogonal control force required by the resonator in the stable state of the hemispherical resonant gyroscope; specifically: A closed-loop control of the hemispherical resonant gyroscope is achieved using a rate integral control mode through amplitude and quadrature control loops. Under stable conditions, the hemispherical resonant gyroscope exhibits the following characteristics: , , , , According to the first derivative of orthogonal error From the form, the required orthogonal control force of the harmonic oscillator is obtained as: (9) In equation (9), The definition is given by equation (10); (10) in, The vibration frequency on the principal coordinate axis x, The vibration frequency on the main coordinate axis y.

4. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 3, characterized in that, At each data sampling moment during the vibration process of the hemispherical resonant gyroscope, the combined signal S, the combined signal R, the principal axis amplitude control quantity, and the orthogonal control quantity are collected, and the standing wave angle at each sampling moment is calculated based on S and R; the specific process is as follows: Step 2.1 Initialize sampling time ; Step 22, the first Each sampling time The standing wave angle is denoted as ,Will The rotational speed at time is denoted as Then the first Each sampling time The desired standing wave angle to be acquired is , If the preset angle increment is used, then the first... Each sampling time ; Steps two and three, in the... Each sampling time right , Spindle amplitude control quantity and orthogonal control quantity Collect data; according to and Calculate the first Standing wave angle at each sampling time ; Step 24: Determine if the conditions are met. : If not satisfied, then let Return to step two; If satisfied, proceed to step two five; Step 25: Store the data collected at each sampling time in the FPGA in the form of an array matrix as shown in Equation (13); (13)。 5. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 4, characterized in that, The damping distribution characteristic parameters and The relationship between the parameters is as follows: Damping parameters: (26) Damping mismatch: (27) Harmonic oscillator damping axis angle: (28)。 6. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 5, characterized in that, The specific process of step 33 is as follows: Step 331: Initialize the forgetting factor Initialize parameter vector estimates , Initialize the covariance matrix , ,in, It is the identity matrix; And initialize the number of iterations. ; Step 332: Calculate the gain vector : (29) in, For data matrix The row data, for transpose; Update parameter estimates , : (30) in, For data matrix The Row data; Step 3.3.3 Update the covariance matrix : (31) Step 334: Update parameters : (32) Step 335: Calculate the gain vector : (33) Update parameter estimates , : (34) in, For data matrix The Row data; Step 336: Update the covariance matrix : (35) Step 337: Update damping parameters Damping mismatch Harmonic oscillator damping axis rotation angle : (36) (37) (38) Step 338, Is it satisfied? : If satisfied Then proceed to step three-three-nine; If not satisfied Then let Return to step 332; Step 339: Based on the calculated damping parameters at each sampling time... Damping mismatch Harmonic oscillator damping axis rotation angle The damping distribution characteristic parameters were identified.

7. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 6, characterized in that, Among the damping distributed characteristic parameters, the identification result of the damping parameter is: damping parameter , The mean.

8. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 6, characterized in that, Among the damping distribution characteristic parameters, the identification result of damping mismatch is: damping mismatch. , The mean.

9. The method for online identification of the damping characteristics of a hemispherical harmonic oscillator using active standing wave precession as described in claim 6, characterized in that, Among the damping distribution characteristic parameters, the identification result of the resonator damping axis rotation angle is: resonator damping axis rotation angle , The mean.

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