Hemispherical resonator gyroscope standing wave active precession instruction angular rate resolving method

Abstract

The invention discloses a hemispherical resonator gyroscope standing wave active precession instruction angular rate resolving method, and belongs to the field of hemispherical resonator gyroscope control. According to the method, the problem that deviation exists between the actual procession angular rate and the expected value due to the influence of temperature drift is solved. The method specifically comprises the steps that 1, the hemispherical resonator gyroscope is started in a full-angle mode, after a spherical shell standing wave of the hemispherical resonator gyroscope is in a stable state and reaches the target amplitude of the standing wave, standing wave active precession is conducted through an instruction control word, and the standing wave precession is conducted under the action of electric driving force; step 2, obtaining a relational expression between an orthogonal control word and an actual azimuth angle of the gyroscope after the angular rate of the standing wave active precession instruction is stable; 3, identifying coefficients in the relational expression of the orthogonal control word and the actual azimuth angle to obtain an identification result; and 4, obtaining an instruction angular rate resolving result of the active precession of the standing wave by using an identification result in the step 3, and outputting the instruction angular rate resolving result. The method can be applied to the field of hemispherical resonator gyroscope 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 the hemispherical resonant gyroscope plays an important role in the error compensation process, and it is crucial to accurately obtain the standing wave active precession command angular rate. Under ideal conditions, the standing wave active precession command angular rate of the hemispherical resonant gyroscope presents a fixed proportional relationship with the actual precession rate. However, in actual applications, the precession ratio is affected by temperature and shows obvious temperature sensitivity. This temperature correlation means that the same command angular rate will lead to different actual precession rates under different temperature environments, resulting in deviations. Specifically, temperature changes will cause a deviation between the actual precession angular rate and the expected command angular rate, which will significantly affect the stability of the active precession. Therefore, in order to ensure that the hemispherical resonant gyroscope can provide accurate measurement results under different temperature conditions, the precession ratio must be recalibrated and calibrated in a temperature-dependent manner, but the experimental process of repeated calibration and calibration of the precession ratio is relatively cumbersome. Summary of the invention

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

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

[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 according to the identification result, and then the dynamic change of the parameter can be tracked. The standing wave active precession command angular rate calculated by the present invention can 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 It 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 resonator in the free vibration state. DETAILED DESCRIPTION

[0013] Specific implementation method 1: Combination Figure 1 The present embodiment describes a method for calculating the angular rate of a standing wave active precession command of a hemispherical resonant gyroscope, and the method specifically comprises 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, and 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 is stabilized 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 result;

[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 velocity refers to the desired angular velocity of the standing wave under the action of the electric driving force.

[0019] Specific implementation method 2: This implementation method is different from the specific implementation method 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 represents the control force of the x channel, f y represents 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, and f q represents the specific force acting on the semi-minor axis of the elliptical orbit, f v Active drive control.

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

[0024] Specific implementation method three: This implementation method is different from specific implementation method 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] The other steps and parameters are the same as those in the first or second embodiment.

[0028] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 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 Specific Embodiments 1 to 3.

[0032] Specific implementation method 5: This implementation method is different from the specific implementation methods 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 get:

[0040] f q =aω0Δωsin4(θ-θ ω ) (7)

[0041] Remove the gain G from both sides of equation (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 Specific Embodiments 1 to 4.

[0047] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 3 is as follows:

[0048] Step 3: 1. Divide a whole 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 the flag FLAG to each interval, initialize the FLAG value 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, we can 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 the sampling time t is converted into the sampled orthogonal control amount and the azimuth angle θ t As the nth group of sampling points And 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 33: Determine whether the FLAG value corresponding to each interval is 1;

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

[0055] If satisfied, execute steps three and four;

[0056] Step 3 and 4: Use the 18 sets of sampling points to 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 Specific Implementation Methods 1 to 5.

[0058] In order to ensure the accuracy of discrete least squares identification of sinusoidal signals, the sampling points need to be evenly distributed in one or several full cycles. Therefore, the present invention evenly divides a full cycle (360°) into 18 angle intervals, and adds a flag FLAG to each interval to indicate whether this data has a corresponding sampling point.

[0059] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that the specific process of steps 3 and 4 is 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] Define the intermediate variable matrix Φ and the least squares estimate R 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), we have:

[0070]

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

[0072]

[0073] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

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

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

[0076]

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

[0078]

[0079] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0080] Example

[0081] In order to solve the problem that the actual precession angular rate deviates from the expected value due to the influence of 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 the temperature drift, so that when the ambient temperature changes, the actual precession angular rate will not deviate from the expected value. The method of the present invention is further described as follows:

[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, and 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 represents the control force of the x channel, f y represents 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, and f q represents the specific force acting on the semi-minor axis of the elliptical orbit, f v Active drive control.

[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 any 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 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 get:

[0102] f q =aω0Δωsin4(θ-θ ω ) (7)

[0103] Remove the gain G from both sides of equation (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 The coefficients in the relationship between θ and θ are identified as follows:

[0109] In order to ensure the accuracy of discrete least squares identification of sinusoidal signals, the sampling points need to be evenly distributed in one or several full cycles. Therefore, the present invention evenly divides a full cycle (360°) into 18 angle intervals, and adds a flag FLAG to each interval to indicate whether this data has a corresponding sampling point.

[0110] Step 3: 1. Divide a whole 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 the flag FLAG to each interval, initialize the FLAG value 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, we can 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 the sampling time t is converted into the sampled orthogonal control amount and the azimuth angle θ t As the nth group of sampling points And 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 33: Determine whether the FLAG value corresponding to each interval is 1;

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

[0117] If satisfied, execute steps three and four;

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

[0119]

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

[0121]

[0122] Define the intermediate variable matrix Φ and the least squares estimate R 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), we have:

[0130]

[0131] In the known v Under the conditions of , θ, 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 rotation speed, k1 represents the proportionality 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 external speed Ω z Under the conditions of 0, a>>q, E>>Q, Δφ=π / 2, equation (17) can be rearranged as follows:

[0137]

[0138] because

[0139]

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

[0141]

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

[0143]

[0144] After phase delay compensation Then, by substituting equation (3) and equation (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 three.

[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 calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still 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 d v Active precession of standing waves is performed, and the standing waves precess under the action of electric driving force; Step 2: Obtain the orthogonal control word d after the standing wave active precession command angular rate is stabilized q The relationship between the actual azimuth angle θ of the gyro; Step 3: Orthogonal control word d q Identify the coefficients in the relationship between θ and θ to obtain the identification result; 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.

2. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave 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: Among them, f x represents the control force of the x channel, f y represents the y channel control force, f a represents the specific force acting on the semi-major axis of the elliptical orbit, is the phase delay, 2θ is the standing wave azimuth, ω0 is the eigenfrequency of the resonator, t represents time, and f q represents the specific force acting on the semi-minor axis of the elliptical orbit, f v Active drive control.

3. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 2, characterized in that: The specific force acting on the semi-minor axis of the elliptical orbit satisfies: f q =G c ·d q (2) Among them, d q f q The corresponding orthogonal control word, G c For gain.

4. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 3, characterized in that: The active drive control force satisfies: f v =G c ·d v (3) Among them, G c For gain.

5. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 4, characterized in that: The specific process of step 2 is as follows: The secondary demodulation quantity Q satisfies: 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 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; Under closed-loop control: f qs =f q (6) Combining equations (5) and (6), we get: f q =aω0Δωsin4(θ-θ ω ) (7) Remove the gain G from both sides of equation (7) c have to: The orthogonal control word d q Arranged into the form of formula (9): d q =d0+d1sin4θ+d2cos4θ (9) 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.

6. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 5, characterized in that: The specific process of step three is: Step 3:

1. Divide a whole cycle into 18 intervals evenly, where the angle range corresponding to the nth interval is [-180+20n, -160+20n), n = 0, 1, ..., 17; After adding the flag FLAG to each interval, initialize the FLAG value of each interval to 0; Step 3.2: Calculate the actual azimuth angle θ of the hemispherical resonant gyroscope at time t t Then, we can judge θ t The interval to which it belongs; If θ t The FLAG value corresponding to the nth interval is 0, then the orthogonal control amount at the sampling time t is converted into the sampled orthogonal control amount and the azimuth angle θ t As the nth group of sampling points And set the FLAG value corresponding to the nth interval to 1, and then execute step 33; If θ t If the FLAG value corresponding to the nth interval is 1, directly execute step 33; Step 33: Determine whether the FLAG value corresponding to each interval is 1; If not satisfied, set t=t+1 and return to step 32; If satisfied, execute steps three and four; Step 3 and 4: Use the 18 sets of sampling points to orthogonal control word d q Identify the coefficients in the relationship between θ and θ.

7. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 6, characterized in that: The specific process of steps three and four is as follows: Each group of sampling points is organized into the following form: According to 18 groups of sampling points, we get formula (11): Define the intermediate variable matrix Φ and the least squares estimate R as follows: in, represents the optimal estimate of d1, represents the optimal estimate of d2, represents the optimal estimate of d0; The least squares estimate R is: R=(Φ T F) -1 F T D q (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), we have: According to formula (15), we can get:

8. A method for calculating the angular rate of active precession command of a hemispherical resonant gyro standing wave according to claim 7, characterized in that: The specific process of step 4 is as follows: Command angular rate of active precession of standing wave for: After phase delay compensation Then, by substituting equation (3) and equation (16) into equation (21), we can obtain:

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