CN112630471B - Output compensation method of gyro accelerometer - Google Patents

Output compensation method of gyro accelerometer Download PDF

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CN112630471B
CN112630471B CN202011461327.0A CN202011461327A CN112630471B CN 112630471 B CN112630471 B CN 112630471B CN 202011461327 A CN202011461327 A CN 202011461327A CN 112630471 B CN112630471 B CN 112630471B
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gyro
accelerometer
acceleration
gyro accelerometer
shaft
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CN112630471A (en
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魏宗康
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CHINA AEROSPACE TIMES ELECTRONICS CO LTD
Beijign Institute of Aerospace Control Devices
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CHINA AEROSPACE TIMES ELECTRONICS CO LTD
Beijign Institute of Aerospace Control Devices
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P21/00—Testing or calibrating of apparatus or devices covered by the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
    • G01P15/14—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of gyroscopes
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
    • G01P15/18—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration in two or more dimensions

Abstract

The invention provides an output compensation method of a gyro accelerometer, which is based on time-varying input acceleration a x Lateral acceleration
Figure DDA0002832291110000011
Calculating the real acceleration output value of the gyro accelerometer by adopting an error compensation method according to the size of the non-vertical angle beta; the calculated output acceleration value of the gyro accelerometer not only comprises a relevant item of the acceleration of the input shaft, but also comprises an error item introduced under the action of the transverse acceleration.

Description

Output compensation method of gyro accelerometer
Technical Field
The invention belongs to the technical field of high-precision apparent acceleration measurement, relates to accelerometer navigation calculation for an inertially stabilized platform, and particularly relates to an output compensation method for a gyro accelerometer.
Background
In a high-precision inertially stabilized platform, a quartz flexible accelerometer and a pendulum type integral gyro accelerometer are mainly adopted at present, the quartz flexible accelerometer and the pendulum type integral gyro accelerometer are both single-degree-of-freedom accelerometers, and each accelerometer is sensitive to the apparent acceleration in one direction.
A Pendulum Integral Gyro Accelerometer (PIGA) is a pendulum accelerometer using gyro moment for feedback, and its operation principle is shown in fig. 1 below. In the figure, OX 0 Y 0 Z 0 For a coordinate system fixedly connected to the outer frame, OX 0 Is an input shaft; oxyz is a Lei-Difference coordinate system, and an Oz axis is superposed with a rotor axis;
Figure BDA0002832291090000011
the angular velocities of the outer frame relative to the instrument base (the shell of the pendulum-type integral gyro accelerometer) and the inner frame relative to the outer frame are respectively; a is x Apparent acceleration input for the instrument along the outer frame axis; ml ofThe pendulum property of the instrument along the inner frame shaft; h is the angular momentum of the instrument rotor; m x The sum of various interference moments around the outer frame shaft; m is a group of D Is the motor torque. The figure also comprises: 1-angle sensor, 2-amplifier, 3-torque motor, 4-output device.
As can be seen from fig. 1, such a gyroscopic accelerometer is similar in structure to a two-degree-of-freedom gyroscope: the gyro rotor is provided with an inner frame and an outer frame. An angle sensor is arranged at one end of the inner frame shaft, and an output device and a torque motor are respectively arranged at the upper end and the lower end of the outer frame shaft. Along the rotor axis Oz there is an eccentric mass m, the centre of mass of which is at a distance l from the inner frame axis, thus forming a pendulum ml around the inner frame axis.
When the instrument is along the outer frame axis OX 0 Direction apparent acceleration a x While, an inertia moment mla proportional to the apparent acceleration is generated on the inner frame shaft x . Under the ideal condition, that is, under the condition of that there is no any interference moment along the inner and outer frame shafts, according to the gyro precession principle, the rotor can drive the inner and outer frames to wind OX together 0 The shaft precessing at a precessional angular velocity of
Figure BDA0002832291090000012
As a result of precession, a gyroscopic reaction moment is generated on the axis of the inner frame
Figure BDA0002832291090000013
Under steady state conditions, moment of inertia mla x Will be precisely torsioned by spinning top
Figure BDA0002832291090000014
Is balanced, therefore, has
Figure BDA0002832291090000015
Figure BDA0002832291090000021
Or
Figure BDA0002832291090000022
Under the zero initial condition, the ideal output value is obtained：
Figure BDA0002832291090000023
In order to ensure that H is vertical to the axis OX of the outer frame, the gyro accelerometer is additionally provided with a servo loop when suffering interference moment M x When the angle beta of the inner frame is not 0, the angle sensor outputs corresponding voltage signals, and the voltage signals are amplified and converted and then fed to the torque motor to generate a motor torque M Dx To counteract M x . It can be seen that the sensor of the servo loop is an inner frame angle sensor, and the measured value is β. Although the servo loop can keep the measured value β of the angle sensor at zero, it cannot be guaranteed that the rotor axis Oz and the outer frame axis OX are perpendicular to each other when there is a deviation in the mechanical zero position of the angle sensor, and for this reason, such non-perpendicular angle is collectively denoted by β. At this time, the output equation of the gyro accelerometer is:
Figure BDA0002832291090000024
in the formula 2, the first step is,
Figure BDA0002832291090000025
is Y 0 Axis and Z 0 Lateral acceleration of the shaft; OX 0 Y 0 Z 0 Is a coordinate system fixedly connected with the base of the gyro accelerometer.
The above equation 2 is a transcendental equation, and needs to be simplified to give some local qualitative analysis expressions. In engineering applications, the angular velocity is output according to a gyro accelerometer
Figure BDA0002832291090000026
The method of calculating acceleration is a simplified equation:
Figure BDA0002832291090000027
however, the simplified method can cause the measurement error of the gyro accelerometer, thereby influencing the use precision of the instrument and directly causing the point-falling error of the navigation and guidance of the missile.
In order to further construct a measurement error model of the gyro accelerometer and improve the use precision through error compensation, the invention provides a novel output compensation method of the gyro accelerometer so as to improve the visual acceleration precision measurement capability of the gyro accelerometer.
Disclosure of Invention
The technical problem of the invention is solved: the method is used for calculating the accurate acceleration output value of the gyro accelerometer and has high accuracy.
The technical scheme provided by the invention is as follows:
an output compensation method of a gyro accelerometer comprises the following steps:
step (1), measuring a coordinate system OX of the gyro accelerometer fixedly connected with the base 0 Y 0 Z 0 Input acceleration a of x And lateral acceleration
Figure BDA0002832291090000031
Wherein, a x And OX 0 The directions of the axes are consistent with each other,
Figure BDA0002832291090000032
and OY 0 The directions of the axes are consistent with each other,
Figure BDA0002832291090000033
and OZ 0 The axial directions are consistent;
Figure BDA0002832291090000034
and with
Figure BDA0002832291090000035
Is a constant value;
measuring a non-vertical angle beta of an outer frame shaft and a rotor shaft of the gyro accelerometer;
step (3) according to Y in step (1) 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA0002832291090000036
Determining the resultant acceleration
Figure BDA0002832291090000037
And OY 0 The included angle gamma of the shaft satisfies:
Figure BDA0002832291090000038
Figure BDA0002832291090000039
at this time, at Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA00028322910900000310
The differential equation of the gyro accelerometer in action is as follows:
Figure BDA00028322910900000311
in formula 6, m is the eccentric mass of the rotor, l is the eccentric distance of the rotor, H is the angular momentum of the instrument rotor, alpha is the rotation angle of the outer frame relative to the instrument base, referred to as the outer frame rotation angle for short,
Figure BDA00028322910900000312
the angular velocity of rotation of the outer frame;
step (4) when
Figure BDA00028322910900000313
Then, the angle is calculated according to the following two formulas
Figure BDA00028322910900000314
Figure BDA00028322910900000315
Figure BDA00028322910900000316
Step (5), setting the initial value of the outer frame angle alpha of the gyro accelerometer as alpha 0 For the angular velocity of the outer frame output by the gyro accelerometer
Figure BDA0002832291090000041
Compensating to output OX 0 Acceleration on axis a x ’：
Figure BDA0002832291090000042
In the formula (9), the first and second groups,
Figure BDA0002832291090000043
t is time.
The output compensation method of the gyro accelerometer provided by the invention has the following beneficial effects:
the invention comprehensively considers the influence of the time-varying input shaft acceleration and the transverse acceleration of the gyro accelerometer on the output, and provides a method for accurately calculating the theoretical acceleration value of the gyro accelerometer by using the accelerations of the base in three orthogonal directions and the non-vertical angle beta between the outer frame shaft and the rotor shaft as known quantities. Compared with the existing linear output calculation method only considering the action of the input acceleration, the acceleration compensated by the gyro accelerometer is more accurate and comprehensive and has wider applicability.
Drawings
FIG. 1 is a schematic diagram of a gyroscopic accelerometer;
FIG. 2 is a flow chart of a gyro accelerometer output calculation of the present invention;
FIG. 3 shows a base axis X of a gyroscopic accelerometer of example 1 0 、Y 0 The value of the overload experienced;
FIG. 4 is a raw acceleration calculation for a gyroscopic accelerometer of example 1;
FIG. 5 is an acceleration error caused by the gyro accelerometer in example 1 using the original calculation method;
FIG. 6 is a calculated value of an accelerometer of a gyroscopic accelerometer of example 1 compensated using the present invention;
fig. 7 shows the calculation error of the compensated acceleration of the gyro accelerometer in example 1.
Detailed Description
The features and advantages of the present invention will become more apparent and appreciated from the following detailed description of the invention.
The invention provides an output compensation method of a gyro accelerometer, as shown in figure 2, according to an input acceleration a x 、Y 0 Axis and Z 0 Transverse acceleration of shaft
Figure BDA0002832291090000051
And the size of the non-vertical angle beta, and calculating the real output of the gyro accelerometer by adopting different output models, wherein the method specifically comprises the following steps:
step (1), measuring a coordinate system OX of the gyro accelerometer fixedly connected with the base 0 Y 0 Z 0 Input acceleration a of x And lateral acceleration
Figure BDA0002832291090000052
Wherein, a x And OX 0 The directions of the axes are consistent with each other,
Figure BDA0002832291090000053
and OY 0 The directions of the axes are consistent with each other,
Figure BDA0002832291090000054
and OZ 0 The axial directions are consistent;
Figure BDA0002832291090000055
and
Figure BDA0002832291090000056
is a constant value;
measuring a non-vertical angle beta of an outer frame shaft and a rotor shaft of the gyro accelerometer;
step (3) according to Y in step (1) 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA0002832291090000057
Determining the resultant acceleration
Figure BDA0002832291090000058
And OY 0 The included angle gamma of the shaft satisfies:
Figure BDA0002832291090000059
Figure BDA00028322910900000510
at this time, at Y 0 Axis and Z 0 Transverse acceleration of shaft
Figure BDA00028322910900000511
The differential equation of the gyro accelerometer in action is as follows:
Figure BDA00028322910900000512
wherein m is the eccentric mass of the rotor, l is the eccentric distance of the rotor, H is the angular momentum of the rotor of the instrument, alpha is the rotation angle of the outer frame relative to the base of the instrument (namely the shell of the pendulum type integral gyro accelerometer), which is called the rotation angle of the outer frame for short,
Figure BDA00028322910900000513
the angular velocity of rotation of the outer frame;
step (4) when
Figure BDA00028322910900000514
Then, the angle is calculated according to the following two formulas
Figure BDA00028322910900000515
Figure BDA00028322910900000516
Figure BDA00028322910900000517
Step (5), setting the initial value of the outer frame angle alpha of the gyro accelerometer as alpha 0 For the angular velocity of the outer frame output by the gyro accelerometer
Figure BDA0002832291090000061
Compensating to output OX 0 Acceleration on axis a x ' the method is as follows:
Figure BDA0002832291090000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002832291090000063
t is time.
In the invention, in the step (1), the input acceleration a of the gyro accelerometer x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA0002832291090000064
Based on 3 orthogonally mounted quartz accelerometers with gyroscopic accelerometers mounted on the inertial platform bodyAnd (4) obtaining the amount.
In the invention, in the step (1), the gyro accelerometer can adopt an inclined installation mode relative to the thrust of the platform missile engine to ensure the input acceleration
Figure BDA0002832291090000065
In the invention, in the step (1), the input acceleration a of the gyro accelerometer x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA0002832291090000066
Acceleration with the amplitude less than or equal to 1g can be excited in the fixed orientation of the gravity field in a mode of inclining relative to the vector direction of the gravity acceleration.
In the invention, in the step (1), the input acceleration a of the gyro accelerometer x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure BDA0002832291090000067
Accelerations with amplitudes greater than 1g can be excited at large overloads including centrifuge, rocket sledge, live-action flight.
In the invention, in the step (1), a gyro rotor of the gyro accelerometer can be realized by adopting dynamic pressure air flotation, liquid floating support and other modes, a bias pendulum structure of the gyro accelerometer can be realized by an eccentric pendulum structure, a shifting shaft type pendulum structure and other modes, and a carrier measured by the gyro accelerometer can be an airplane, a ship, a motor vehicle, a missile and the like.
In the invention, in the step (2), the non-perpendicular angle beta of the outer frame shaft and the rotor shaft of the gyro accelerometer is measured by the optical sighting mechanism of the static base.
Examples
Example 1
Is provided with
Figure BDA0002832291090000071
β＝1000″，α 0 ＝π/4，
Figure BDA0002832291090000072
When the theoretical acceleration a x 、
Figure BDA0002832291090000073
In case of time-varying overload, as shown in FIG. 3, the two satisfy the relation
Figure BDA0002832291090000074
If according to the original calculation formula of the gyro accelerometer
Figure BDA0002832291090000075
Calculation was performed with the output acceleration as shown in fig. 4; compared with fig. 3, the difference value between the theoretical acceleration value and the error value is shown in fig. 5, and it can be seen that the error is an alternating variable, the amplitude of the error becomes larger with the increase of the acceleration, and the maximum acceleration error can reach 0.05 g. The result of the compensation method of the present invention is shown in FIG. 6, in which the ordinate represents the acceleration a output from the gyro accelerometer x ', units are g; the difference between the two is shown in FIG. 7, and the error of the maximum acceleration is 0.0015 g. Therefore, the output result of the gyro accelerometer compensated by the method is more accurate.
The invention has been described in detail with reference to specific embodiments and illustrative examples, but the description is not intended to be construed in a limiting sense. Those skilled in the art will appreciate that various equivalent substitutions, modifications or improvements may be made to the technical solution of the present invention and its embodiments without departing from the spirit and scope of the present invention, which fall within the scope of the present invention. The scope of the invention is defined by the appended claims.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (7)

1. An output compensation method of a gyro accelerometer is characterized by comprising the following steps:
step (1), measuringOutput gyro accelerometer is along coordinate system OX that links firmly with base 0 Y 0 Z 0 Input acceleration a of x And lateral acceleration
Figure FDA0003756250850000011
Wherein, a x And OX 0 The directions of the axes are consistent with each other,
Figure FDA0003756250850000012
and OY 0 The directions of the axes are consistent with each other,
Figure FDA0003756250850000013
and OZ 0 The axial directions are consistent;
Figure FDA0003756250850000014
and
Figure FDA0003756250850000015
is a constant value;
measuring a non-vertical angle beta of an outer frame shaft and a rotor shaft of the gyro accelerometer;
step (3) according to Y in step (1) 0 Axis and Z 0 Transverse acceleration of the shaft
Figure FDA0003756250850000016
To determine the resultant acceleration
Figure FDA0003756250850000017
And OY 0 The included angle gamma of the shaft satisfies:
Figure FDA0003756250850000018
Figure FDA0003756250850000019
at this time, at Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure FDA00037562508500000110
The differential equation of the gyro accelerometer in action is as follows:
Figure FDA00037562508500000111
in formula 6, m is the eccentric mass of the rotor, l is the eccentric distance of the rotor, H is the angular momentum of the rotor of the gyro accelerometer, alpha is the rotation angle of the outer frame relative to the base, referred to as the rotation angle of the outer frame for short,
Figure FDA00037562508500000112
the angular velocity of rotation of the outer frame;
step (4) when
Figure FDA00037562508500000113
Then, the angle is calculated according to the following two formulas
Figure FDA00037562508500000114
Figure FDA00037562508500000115
Figure FDA00037562508500000116
Step (5), setting an initial value of an outer frame rotation angle alpha of the gyro accelerometer as alpha 0 For the angular velocity of the outer frame output by the gyro accelerometer
Figure FDA0003756250850000021
Compensating to output OX 0 Acceleration on axis a x ’：
Figure FDA0003756250850000022
In the formula (9), the first and second groups,
Figure FDA0003756250850000023
t is time.
2. The method for compensating the output of the gyro accelerometer according to claim 1, wherein in the step (1), the gyro accelerometer is mounted on an inertial platform body, and the input acceleration a of the gyro accelerometer is x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure FDA0003756250850000024
Measured from 3 orthogonally mounted quartz accelerometers on the inertial platform stage.
3. The method for compensating the output of the gyro accelerometer according to claim 1, wherein in the step (1), the gyro accelerometer is installed in an inclined manner relative to the thrust of the platform missile engine so that the input acceleration is obtained
Figure FDA0003756250850000025
4. The output compensation method of the gyro-accelerometer according to claim 1, wherein in the step (1), the input acceleration a of the gyro-accelerometer is x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure FDA0003756250850000026
In a manner inclined with respect to the vector direction of gravitational accelerationAnd exciting the acceleration with the amplitude less than or equal to 1g in the fixed orientation of the gravity field.
5. The output compensation method of a gyro accelerometer according to claim 1, wherein in step (1), the input acceleration a of the gyro accelerometer is x And Y 0 Axis and Z 0 Transverse acceleration of the shaft
Figure FDA0003756250850000027
The acceleration with the amplitude larger than 1g is excited on the large overload including the centrifuge, the rocket sled and the live ammunition flying.
6. The output compensation method of the gyro accelerometer according to claim 1, wherein in the step (1), the gyro rotor of the gyro accelerometer is implemented by using a dynamic pressure air flotation or liquid floating support mode, and the yaw structure of the gyro accelerometer is implemented by using an eccentric pendulum structure or a tilt-shift pendulum structure.
7. The method for compensating the output of the gyro-accelerometer according to claim 1, wherein in the step (2), the non-perpendicular angle β of the outer frame axis and the rotor axis of the gyro-accelerometer is measured by a static base optical aiming mechanism.
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CN108710001A (en) * 2018-04-28 2018-10-26 北京航天控制仪器研究所 Two axis one gyroaccelerometers of one kind and method of servo-controlling
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