A method for calculating the angular rate of active precession command of a hemispherical resonant gyroscope with standing waves

Abstract

A method for calculating the command angular rate of active precession of a hemispherical resonant gyroscope (HRG) standing waves belongs to the field of HRG control. The present invention solves the problem of deviation between the actual precession angular rate and the expected value due to the influence of temperature drift. Specifically, the method comprises the following steps: Step 1: Starting the HRG in full-angle mode, ensuring that the standing wave of the HRG shell is in a stable state and reaches the target amplitude of the standing wave, then using a command control word to perform active precession of the standing wave, so that the standing wave precesses under the action of an electric driving force; Step 2: Obtaining a relationship between the orthogonal control word after stabilization of the command angular rate of the standing wave active precession and the actual azimuth angle of the gyroscope; Step 3: Identifying the coefficients in the relationship between the orthogonal control word and the actual azimuth angle to obtain an identification result; Step 4: Using the identification result of Step 3, obtaining and outputting a calculation result of the command angular rate of the standing wave active precession. The method of the present invention can be applied to the field of HRG control.

Description

Technical Field

[0001] The invention belongs to the field of hemispherical resonant gyroscope control, and in particular relates to a method for calculating the angular rate of a hemispherical resonant gyroscope standing wave active precession instruction. Background Art

[0002] The active precession of a hemispherical resonant gyroscope (HRG) plays a crucial role in error compensation, and accurately obtaining the standing wave active precession command angular rate is crucial. Under ideal conditions, the HRG's standing wave active precession command angular rate and actual precession rate exhibit a fixed proportional relationship. However, in actual applications, the precession ratio is affected by temperature, exhibiting significant temperature sensitivity. This temperature dependency means that the same command angular rate will result in different actual precession rates under different temperature environments, resulting in deviations. Specifically, temperature changes can cause a deviation between the actual precession angular rate and the expected command angular rate, significantly affecting the stability of the active precession. Therefore, to ensure that the HRG can provide accurate measurement results under different temperature conditions, the precession ratio must be recalibrated and recalibrated in a temperature-dependent manner. However, the experimental process of repeatedly recalibrating and recalibrating the precession ratio is relatively cumbersome. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem that the actual precession angular rate deviates from the expected value due to the influence of temperature drift, and a method for calculating the standing wave active precession command angular rate of a hemispherical resonant gyroscope is proposed.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a method for calculating the angular rate of the standing wave active precession command of a hemispherical resonant gyroscope, the method specifically comprising the following steps:

[0005] Step 1: Start the hemispherical resonant gyro in full-angle mode, make the standing wave of the hemispherical resonant gyro shell stable and reach the target amplitude of the standing wave, and then use the command control word d v Active precession of standing waves is performed, where the standing waves precess under the action of electric driving force;

[0006] Step 2: Obtain the orthogonal control word d after the standing wave active precession command angular rate stabilizes q The relationship between the actual azimuth angle θ of the gyro;

[0007] Step 3: Orthogonal control word d q Identify the coefficients in the relationship between θ and θ to obtain the identification results;

[0008] Step 4: Use the identification result of step 3 to obtain the command angular rate solution result of the standing wave active precession, use the solved standing wave active precession command angular rate as output, and return to execute step 3.

[0009] The beneficial effects of the present invention are:

[0010] For different temperature environments, after the method of the present invention obtains the identification result using the least squares method, the command angular rate solution result of the standing wave active precession can be obtained based on the identification result, and then the dynamic changes of the parameters can be tracked. The standing wave active precession command angular rate calculated by the present invention can be used to correct the influence of temperature drift on the actual precession angular rate in real time without the need to recalibrate the precession ratio. Only the command angular rate calculated by the present invention can solve the problem of deviation between the actual precession angular rate and the expected value under different temperature environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 This is a flow chart of a method for calculating the angular rate of a hemispherical resonant gyroscope standing wave active precession command according to the present invention;

[0012] Figure 2 Schematic diagram of the motion trajectory of the oscillator in the free vibration state. DETAILED DESCRIPTION

[0013] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for calculating the angular rate of a standing wave active precession command of a hemispherical resonator gyroscope, the method specifically comprising the following steps:

[0014] Step 1: Start the hemispherical resonant gyro in full-angle mode, make the standing wave of the hemispherical resonant gyro shell stable and reach the target amplitude of the standing wave, and then use the command control word d v Active precession of standing waves is performed, where the standing waves precess under the action of electric driving force;

[0015] Step 2: Obtain the orthogonal control word d after the standing wave active precession command angular rate stabilizes q The relationship between the actual azimuth angle θ of the gyro;

[0016] Step 3: Orthogonal control word d q Identify the coefficients in the relationship between θ and θ to obtain the identification results;

[0017] Step 4: Use the identification result of step 3 to obtain the command angular rate solution result of the standing wave active precession, use the solved standing wave active precession command angular rate as output, and return to execute step 3.

[0018] The command angular rate refers to the desired angular rate of the standing wave under the action of the electric driving force.

[0019] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the electric driving force in step 1 is specifically:

[0020] Under the condition of phase delay, the x-channel control force and y-channel control force under the action of the electric driving force are:

[0021]

[0022] Among them, f x Indicates the x channel control force, f y Indicates the y channel control force, f a Represents the specific force acting on the semi-major axis of the elliptical orbit (the elliptical orbit is the motion trajectory of the oscillator in the free vibration state), is the phase delay, 2θ is the standing wave azimuth, ω0 is the eigenfrequency of the resonator, t represents time, f q represents the specific force acting on the semi-minor axis of the elliptical orbit, f v Active drive control force.

[0023] Other steps and parameters are the same as those in the first embodiment.

[0024] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the specific force acting on the semi-minor axis of the elliptical orbit satisfies:

[0025] f q =G c ·d q (2)

[0026] Among them, d q f q The corresponding orthogonal control word, G c For gain.

[0027] Other steps and parameters are the same as those in the first or second embodiment.

[0028] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the active drive control force satisfies:

[0029] f v =G c ·d v (3)

[0030] Among them, G c For gain.

[0031] The other steps and parameters are the same as those in the first to third embodiments.

[0032] Specific embodiment 5: This embodiment differs from specific embodiments 1 to 4 in that the specific process of step 2 is as follows:

[0033] Under the control force of formula (1), the secondary demodulation quantity Q satisfies:

[0034]

[0035] Among them, E and Q are both secondary demodulation quantities, represents the first derivative of Q, τ is the vibration time constant, Δω is the frequency decomposition, θ ω is the angle between the eigenfrequency axis and the x-axis of the elliptical orbit, a is the main standing wave amplitude, Δφ is the phase difference between the reference signal and the vibration signal, and the motion trajectory of the resonator in the free vibration state is as follows: Figure 2 As shown, f ac Represents the time phase with the reference signal u rc The control force is in phase and in the same direction as the semi-major axis of the elliptical orbit in spatial orientation; f as Represents the time phase with the reference signal u rc A control force that is orthogonal and in the same direction as the semi-major axis of the elliptical orbit in spatial orientation; f qc Represents the time phase with the reference signal u rc The control force is in phase and in the same direction as the semi-minor axis of the elliptical orbit in spatial orientation; f qs Represents the time phase with the reference signal u rc The control force is orthogonal and in the same direction as the semi-minor axis of the elliptical orbit in spatial orientation; q is the auxiliary standing wave amplitude;

[0036] Under closed-loop control:

[0037]

[0038] f qs =f q (6)

[0039] Combining equations (5) and (6), we can obtain:

[0040] f q =aω0Δωsin4(θ-θ ω ) (7)

[0041] Remove the gain G from both sides of formula (7) c have to:

[0042]

[0043] The orthogonal control word d q Arranged into the form of formula (9):

[0044] d q =d0+d1sin4θ+d2cos4θ (9)

[0045] Among them, d0 is the coefficient of the DC component, d1 is the coefficient of the sine component, and d2 is the coefficient of the cosine component.

[0046] The other steps and parameters are the same as those in the first to fourth embodiments.

[0047] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the specific process of step 3 is as follows:

[0048] Step 3: 1. Divide a full cycle into 18 intervals evenly, where the angle range corresponding to the nth interval is [-180+20n, -160+20n), n = 0, 1, ..., 17;

[0049] After adding flags to each interval, initialize the flag values ​​of each interval to 0;

[0050] Step 3.2: Calculate the actual azimuth angle θ of the hemispherical resonant gyroscope at time t t Then, judge θ t The interval to which it belongs;

[0051] If θ t The FLAG value corresponding to the nth interval is 0, then the orthogonal control amount at time t is sampled, and the sampled orthogonal control amount and azimuth angle θ are t As the nth group of sampling points Set the FLAG value corresponding to the nth interval to 1, and then execute step 33;

[0052] If θ t If the FLAG value corresponding to the nth interval is 1, then directly execute step 33;

[0053] Step 3: Determine whether the FLAG value corresponding to each interval is 1;

[0054] If not, set t=t+1 and return to step 32;

[0055] If satisfied, proceed to steps three and four;

[0056] Step 3 and 4: Use the 18 groups of sampling points to calculate the orthogonal control word d q Identify the coefficients in the relationship between θ and θ.

[0057] The other steps and parameters are the same as those in the first to fifth embodiments.

[0058] To ensure the accuracy of discrete least squares sinusoidal signal identification, the sampling points must be evenly distributed over one or more full cycles. Therefore, the present invention evenly divides a full cycle (360°) into 18 angular intervals and adds a flag to each interval to indicate whether the data has a corresponding sampling point.

[0059] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that the specific processes of steps three and four are as follows:

[0060] Each group of sampling points is organized into the following form:

[0061]

[0062] According to 18 groups of sampling points, we get formula (11):

[0063]

[0064] The intermediate variable matrix Φ and the least squares estimate R are defined as follows:

[0065]

[0066] in, represents the optimal estimate of d1, represents the optimal estimate of d2, represents the optimal estimate of d0; then the least squares estimate R is:

[0067] R=(Φ T Φ) -1 Φ T D q (14)

[0068] Among them, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix;

[0069] According to formula (14):

[0070]

[0071] In the known d v Under the conditions of , θ, and Δω, according to formula (15), we can get:

[0072]

[0073] The other steps and parameters are the same as those in the first to sixth embodiments.

[0074] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the specific process of step four is as follows:

[0075] Command angular rate of active precession of standing waves for:

[0076]

[0077] After phase delay compensation Then, by substituting equations (3) and (16) into equation (21), we can obtain:

[0078]

[0079] The other steps and parameters are the same as those in the first to seventh embodiments.

[0080] Example

[0081] To address the problem of deviation between the actual precession angular rate and the expected value due to temperature drift, the present invention proposes a method for calculating the standing wave active precession command angular rate. The standing wave active precession command angular rate calculated by the present invention can compensate for temperature drift, thereby preventing deviation between the actual precession angular rate and the expected value when the ambient temperature changes. The present method is further described below:

[0082] Step 1: Start the hemispherical resonant gyro in full-angle mode, make the standing wave of the hemispherical resonant gyro shell stable and reach the target amplitude of the standing wave, and then use the command control word d v Active precession of standing waves is performed, where the standing waves precess under the action of electric driving force;

[0083] Under the condition of phase delay, the x-channel control force and y-channel control force under the action of the electric driving force are:

[0084]

[0085] Among them, f x Indicates the x channel control force, f y Indicates the y channel control force, f a Represents the specific force acting on the semi-major axis of the elliptical orbit (the elliptical orbit is the motion trajectory of the oscillator in the free vibration state), is the phase delay, 2θ is the standing wave azimuth, ω0 is the eigenfrequency of the resonator, t represents time, f q represents the specific force acting on the semi-minor axis of the elliptical orbit, f v Active drive control force.

[0086] After phase delay compensation, the x-channel control force f x and the y-channel control force f y Simplified to:

[0087]

[0088] Under the control force shown in formula (1), the standing wave begins to precess actively without external angular velocity input.

[0089] The specific force acting on the semi-minor axis of the elliptical orbit satisfies:

[0090] fq =G c ·d q (2)

[0091] Among them, d q f q The corresponding orthogonal control word, G c For gain.

[0092] Active drive control force meets:

[0093] f v =G c ·d v (3)

[0094] Among them, G c For gain.

[0095] Step 2: Under the control force of formula (1), the secondary demodulation quantity Q satisfies:

[0096]

[0097] Among them, E and Q are both secondary demodulation quantities, represents the first derivative of Q, τ is the vibration time constant, Δω is the frequency decomposition, θ ω is the angle between the eigenfrequency axis and the x-axis of the elliptical orbit, a is the main standing wave amplitude, Δφ is the phase difference between the reference signal and the vibration signal, and the motion trajectory of the resonator in the free vibration state is as follows: Figure 2 As shown, f ac Represents the time phase with the reference signal u rc The control force is in phase and in the same direction as the semi-major axis of the elliptical orbit in spatial orientation; f as Represents the time phase with the reference signal u rc A control force that is orthogonal and in the same direction as the semi-major axis of the elliptical orbit in spatial orientation; f qc Represents the time phase with the reference signal u rc The control force is in phase and in the same direction as the semi-minor axis of the elliptical orbit in spatial orientation; f qs Represents the time phase with the reference signal u rc The control force is orthogonal and in the same direction as the semi-minor axis of the elliptical orbit in spatial orientation; q is the auxiliary standing wave amplitude;

[0098] Under closed-loop control: make Q=0, a>>q, which means a is much larger than q, E is much larger than Q, and there is but

[0099]

[0100] f qs =f q (6)

[0101] Combining equations (5) and (6), we can obtain:

[0102] f q =aω0Δωsin4(θ-θ ω ) (7)

[0103] Remove the gain G from both sides of formula (7) c have to:

[0104]

[0105] The orthogonal control word d q Arranged into the form of formula (9):

[0106] d q =d0+d1 sin4θ+d2 cos4θ (9)

[0107] Among them, d0 is the coefficient of the DC component, d1 is the coefficient of the sine component, and d2 is the coefficient of the cosine component.

[0108] Step 3: Orthogonal control word d q Identify the coefficients in the relationship between θ and θ, specifically:

[0109] To ensure the accuracy of discrete least squares sinusoidal signal identification, the sampling points must be evenly distributed over one or more full cycles. Therefore, the present invention evenly divides a full cycle (360°) into 18 angular intervals and adds a flag to each interval to indicate whether the data has a corresponding sampling point.

[0110] Step 3: 1. Divide a full cycle into 18 intervals evenly, where the angle range corresponding to the nth interval is [-180+20n, -160+20n), n = 0, 1, ..., 17;

[0111] After adding flags to each interval, initialize the flag values ​​of each interval to 0;

[0112] Step 3.2: Calculate the actual azimuth angle θ of the hemispherical resonant gyroscope at time t t Then, judge θ t The interval to which it belongs;

[0113] If θ t The FLAG value corresponding to the nth interval is 0, then the orthogonal control amount at time t is sampled, and the sampled orthogonal control amount and azimuth angle θ are t As the nth group of sampling points Set the FLAG value corresponding to the nth interval to 1, and then execute step 33;

[0114] If θt If the FLAG value corresponding to the nth interval is 1, then directly execute step 33;

[0115] Step 3: Determine whether the FLAG value corresponding to each interval is 1;

[0116] If not, set t=t+1 and return to step 32;

[0117] If satisfied, proceed to steps three and four;

[0118] Steps 3 and 4: Arrange each set of sampling points into the following format:

[0119]

[0120] According to 18 groups of sampling points, we get formula (11):

[0121]

[0122] The intermediate variable matrix Φ and the least squares estimate R are defined as follows:

[0123]

[0124]

[0125] in, represents the optimal estimate of d1, represents the optimal estimate of d2, represents the optimal estimate of d0;

[0126] The least squares estimate R is:

[0127] R=(Φ T Φ) -1 Φ T D q (14)

[0128] Among them, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix;

[0129] According to formula (14):

[0130]

[0131] In the known d v Under the conditions of , θ, and Δω, according to formula (15), we can get:

[0132]

[0133] Step 4: The actual azimuth rate of the hemispherical resonant gyroscope under the control force for:

[0134]

[0135] Among them, Ω z represents the external rotational speed, k1 represents the proportional coefficient related to the angular velocity of the spherical shell, represents the damping unevenness coefficient, θ τ represents the angle of the intrinsic damping axis of the spherical shell of the resonator;

[0136] At the external speed Ω z = 0, a>>q, E>>Q, Δφ=π / 2, formula (17) can be organized as follows:

[0137]

[0138] because

[0139]

[0140] Substituting formula (19) into formula (18) yields:

[0141]

[0142] From formula (20), the command angular rate of the active precession of the standing wave is for:

[0143]

[0144] After phase delay compensation Then, by substituting equations (3) and (16) into equation (21), we can obtain:

[0145]

[0146] The calculated standing wave active precession command angular rate is used as output and the process returns to step 3.

[0147] At some time in the future, the coefficients are re-identified, and then the command angular rate of the standing wave active precession is recalculated based on the identification results. Between obtaining two adjacent solution results, the output value of the standing wave active precession command angular rate always remains the previous solution result.

[0148] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for calculating the angular rate of active precession command of a hemispherical resonant gyroscope standing wave, characterized in that: The method specifically comprises the following steps: Step 1: Start the hemispherical resonant gyro in full-angle mode, make the standing wave of the hemispherical resonant gyro shell stable and reach the target amplitude of the standing wave, and then use the command control word Active precession of standing waves is performed, where the standing waves precess under the action of electric driving force; Step 2: Obtain the orthogonal control word after the standing wave active precession command angular rate is stabilized The actual azimuth angle of the gyro The relationship between Step 3: Orthogonal control words and Identify the coefficients in the relationship and obtain the identification results; The specific process of step three is: Step 3: Divide a whole cycle into 18 intervals evenly, among which the first The angle range corresponding to the interval is , ; After adding flags to each interval, initialize the flag values ​​of each interval to 0; Step 3.2: Calculate the actual azimuth angle of the hemispherical resonant gyroscope at time t Then judge The interval to which it belongs; like Belong to The FLAG value corresponding to the interval is 0, then the orthogonal control amount at time t is sampled, and the sampled orthogonal control amount and azimuth angle are As the first Group sampling points , and set the The FLAG value corresponding to each interval is 1, and then step 33 is executed; like Belong to If the FLAG value corresponding to the interval is 1, then directly execute step 33; Step 3: Determine whether the FLAG value corresponding to each interval is 1; If not, set t = t + 1 and return to step 32; If satisfied, proceed to steps three and four; Step 3 and 4: Use the 18 groups of sampling points to orthogonal control words and Identify the coefficients in the relationship; The specific process of steps three and four is as follows: Each group of sampling points is organized into the following form: (10) According to 18 groups of sampling points, formula (11) is obtained: (11) Define the intermediate variable matrix And the least squares estimate R is as follows: (12) (13) in, express The best estimate of express The best estimate of express The best estimate of ; The least squares estimate R is: (14) Among them, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix; According to formula (14): (15) Where a is the main standing wave amplitude, is the eigenfrequency of the oscillator, For frequency decomposition, For gain, is the angle between the eigenfrequency axis and the x-axis of the elliptical orbit; According to formula (15), we can get: (16) Step 4: Utilize the identification result of step 3 to obtain the command angular rate solution of the standing wave active precession, use the solved command angular rate of the standing wave active precession as output, and return to execute step 3; The specific process of step 4 is as follows: Command angular rate of active precession of standing waves for: (21) After phase delay compensation , then we can substitute equation (3) and equation (16) into equation (21) and get: (22)。 2. A method for calculating the angular rate of a standing wave active precession command of a hemispherical resonator gyroscope according to claim 1, characterized in that: The electric driving force in step 1 is specifically: Under the condition of phase delay, the x-channel control force and y-channel control force under the action of the electric driving force are: (1) in, Indicates the x channel control power, Indicates the y channel control force, represents the specific force acting on the semi-major axis of the elliptical orbit, is the phase delay, is the standing wave azimuth, is the eigenfrequency of the oscillator, Indicates time, represents the specific force acting on the semi-minor axis of the elliptical orbit, Active drive control force.

3. A method for calculating the angular rate of the standing wave active precession command of a hemispherical resonator gyroscope according to claim 2, characterized in that: The specific force acting on the semi-minor axis of the elliptical orbit satisfies: (2) in, for The corresponding orthogonal control word, For gain.

4. A method for calculating the angular rate of active precession command of a hemispherical resonator gyroscope standing wave according to claim 3, characterized in that: The active drive control force satisfies: (3) in, For gain.

5. A method for calculating the angular rate of active precession command of a hemispherical resonator gyroscope standing wave according to claim 4, characterized in that: The specific process of step 2 is as follows: The secondary demodulation quantity Q satisfies: (4) Among them, E and Q are both secondary demodulation quantities, represents the first-order derivative of Q, is the vibration time constant, For frequency decomposition, is the angle between the eigenfrequency axis and the x-axis of the elliptical orbit, a is the main standing wave amplitude, is the phase difference between the reference signal and the vibration signal, Represents the time phase with the reference signal A control force that is in phase and in the same direction as the semi-major axis of the elliptical orbit; Represents the time phase with the reference signal A control force that is orthogonal and in the same direction as the semi-major axis of the elliptical orbit; Represents the time phase with the reference signal Control forces that are in phase and in the same direction as the semi-minor axis of the elliptical orbit; Represents the time phase with the reference signal The control force is orthogonal and in the same direction as the semi-minor axis of the elliptical orbit in spatial orientation; q is the auxiliary standing wave amplitude; Under closed-loop control: (5) (6) Combining equations (5) and (6), we can obtain: (7) Eliminate the gain on both sides of formula (7) have to: (8) Orthogonal Control Word Arranged into the form of formula (9): (9) in, is the coefficient of the DC component, are the coefficients of the sine components, is the coefficient of the cosine component.

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