CN109540134B - Self-unlocking method and system for three-axis stabilized platform system framework - Google Patents

Self-unlocking method and system for three-axis stabilized platform system framework Download PDF

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CN109540134B
CN109540134B CN201811252608.8A CN201811252608A CN109540134B CN 109540134 B CN109540134 B CN 109540134B CN 201811252608 A CN201811252608 A CN 201811252608A CN 109540134 B CN109540134 B CN 109540134B
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platform
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shaft
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CN109540134A (en
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魏宗康
段宇鹏
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Beijing Aerospace Control Instrument Institute
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/18—Stabilised platforms, e.g. by gyroscope
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations

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  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Automation & Control Theory (AREA)
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Abstract

The invention discloses a self-unlocking method and a self-unlocking system for a three-axis stabilized platform system frame, which are used for outputting angular rates of 3 gyroscopes orthogonally arranged on a platform body
Figure DDA0001842038430000011
And 3 variables are used as input information of the decoupling link, and 3 shaft end torque motors which respectively act on the table body shaft, the inner ring shaft and the outer ring shaft are output after information fusion. The invention provides an unlocking method of a three-axis platform during frame locking and an unlocked frame angle for the first time, so that the stability of a platform body relative to an inertial space is realized. The invention provides the frame angle steady-state value at the singular point, ensures that the system is still stable and does not diverge, realizes the rapid decoupling and frame state switching of the three-axis platform when the frame is locked, can effectively isolate the angular motion of the carrier, and improves the full-attitude adaptability of the platform body relative to the inertial space stability.

Description

Self-unlocking method and system for three-axis stabilized platform system framework
Technical Field
The invention relates to a self-unlocking method and a self-unlocking system for a three-axis stabilized platform system frame, in particular to a servo loop multivariable decoupling method and a servo loop multivariable decoupling system for a three-axis platform system, which are mainly used for the fields of aviation and aerospace for realizing full-attitude high-precision navigation.
Background
Three-axis stabilized platforms have been widely used on attitude-constrained carriers, i.e., carriers that do not experience large attitude angles about two axes simultaneously in flight. But sometimes the carrier rocket and the missile-type missile need to be subjected to maneuvering orbital transfer flight; in particular tactical missiles, satellites and many military aircraft are required to operate at full attitude, high mobility. Under such conditions, the stage body is required to be stable.
Because the three-axis stabilized platform system has a frame locking phenomenon, namely an inner frame and an outer frame are in one plane, at the moment, the platform axis, the inner frame axis and the outer frame axis are in the same plane at the same time, so that the platform loses one degree of freedom. On the other hand, the gyroscope originally used to control the outer frame shaft cannot sense the rotation of the outer frame shaft, thereby losing control over the outer frame shaft.
The following examples illustrate the specific situation when "frame locking" occurs.
First, the coordinate system definition of the triaxial inertial platform system is shown in fig. 1, which depicts a schematic diagram of the relationship between the coordinate systems of the frames of the triaxial platform. In FIG. 1, let βzkThe relative angle of the inner frame relative to the table body, betaykIs the relative angle of the outer frame to the inner frame, betaxkIs the relative angle of the base (arrow body) relative to the outer frame.
At betazk＝0、βyk＝0、βxkWhen the table is 0, a platform structure including a stage body, an inner frame, an outer frame, and a base is shown in fig. 2. At the moment, the platform frame can isolate the foot motion of the base, and the platform body is stable relative to the inertial space. At the base OY1Angular velocity omega existing on the shafty1When the base drives the outer frame to rotate around the outer frame shaft, the rotation angle is betayk. When beta isykWhen the angle is 90 degrees, the outer frame shaft, the inner frame shaft and the platform body shaft are in one plane, and the three-axis platform is in frame locking, as shown in fig. 3. At this time, because the three-axis platform is at the OZ perpendicular to the plane1Angular motion cannot be isolated in the axial direction when ωz1When not equal to 0, the platform body omegaxpNot equal to 0, means that the platform body rotates relative to the inertial space and cannot isolate the angular motion of the carrier.
In order to eliminate the out-of-control of a stable loop when the angle of an inner frame is 90 degrees and avoid the locking of a frame system, the main solution of the three-axis stable platform system is to increase a stop nail on the inner frame so as to limit the movement range of the angle of the inner frame. For example, the inner frame angle can be operated within a range of ± 20 ° or ± 40 ° by adding the stop pin. The prior measure can only meet the requirement of large maneuvering motion of the carrier on the carrier with limited maneuvering posture.
Disclosure of Invention
The technical problem of the invention is solved: the method and the system overcome the defects of the prior art, realize the quick decoupling and frame state switching of the three-axis platform during the frame locking, effectively isolate the angular motion of a carrier and improve the full-attitude adaptability of a platform body relative to the inertial space stability.
The above object of the present invention is achieved by the following technical solutions: a self-unlocking method of a three-axis inertially stabilized platform system frame is realized based on the three-axis inertially stabilized platform system, the stabilized platform system comprises a base, an outer frame, an inner frame and a platform body, and corresponding body coordinate systems are respectively a base body coordinate system X1Y1Z1Outer frame body coordinate system Xp2Yp2Zp2Inner frame body coordinate system Xp1Yp1Zp1And table body coordinate system XpYpZp(ii) a The origins of the four coordinate systems coincide, and: z of table body coordinate systempZ of axis and inner frame body coordinate systemp1Y of coordinate system of outer frame body with coincident axesp2Y of axis and inner frame body coordinate systemp1X of axis coincident, base body coordinate system1X of axis and outer frame body coordinate systemp2The axes are overlapped; wherein the base is fixedly connected with the carrier, and when the stabilized platform system rotates relatively internally under the driving of the carrier, the base rotates around the X of the coordinate system of the outer frame bodyp2The shaft rotates, the outer frame rotates around the Y of the coordinate system of the inner frame bodyp1Z of coordinate system of axis rotation and internal frame around table bodypRotating the shaft;
the self-unlocking method of the three-axis inertially stabilized platform system frame comprises the following steps:
(1) obtaining the angular velocity of the table body in X according to the output angular velocity of a gyroscope arranged on the table bodypAxis, YpAxis and ZpComponent of angular velocity on the shaft
Figure BDA0001842038410000021
(2) The angle of the inside relative rotation of triaxial inertially stabilized platform system is obtained in the measurement, include: x of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of coordinate system of inner frame wound stage bodypAngle of rotation beta of the shaftzk；
(3) Calculating the synthetic rotation angular speed of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula;
(4) obtaining an angular velocity determination equation of the three frames of the platform by adopting the decoupling calculation formula in the step (3);
(5) according to the angular velocity determination equation of the three frames of the platform, the three frame angles and the angular velocity measured by the gyroscope arranged on the platform body, the self-unlocking condition of the frame is judged as follows
1) At betaykNot equal to 90 DEG and betaykWhen the angle is not equal to-90 degrees, the inner frame and the outer frame of the platform are not in the same plane, and the platform body of the platform is stable relative to the inertia space without the need of self-unlocking of the frame;
2) at betaykAt 90 ° or βyk-90 °, and base angular velocity
Figure BDA0001842038410000031
In the process, the inner frame and the outer frame of the platform are arranged in one plane, and the platform body of the platform is stable relative to the inertia space without self-unlocking of the frame;
3) at betaykAt 90 ° or βykIs equal to-90 DEG when
Figure BDA0001842038410000032
When one of the two frames is non-zero, the platform inner frame and the platform outer frame are arranged in a plane, and the platform body of the platform can be stable relative to the inertia space only by unlocking the frames;
(6) when the platform body is stable relative to the inertia space only by self-unlocking of the frame, the inner frame is driven by the outer frame to rapidly rotate relative to the platform body, and self-unlocking of the frame is realized to ensure that the platform body is still stable relative to the inertia space.
And (3) calculating the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula, wherein the specific decoupling calculation formula is as follows:
Figure BDA0001842038410000033
Figure BDA0001842038410000034
Figure BDA0001842038410000035
wherein, ω iszIs a table body ZpThe resultant rotational angular velocity of the shaft; omegayIs an inner frame Yp1The resultant rotational angular velocity of the shaft; omegaxIs an outer frame Xp2The resultant rotational angular velocity of the shaft;
in the step (6), the inner frame is driven by the outer frame to rapidly rotate relative to the platform body, and the calculation process of the angle value for realizing the self-unlocking of the frame to ensure that the platform body is still stable relative to the inertia space is as follows:
(1) measuring to obtain betaxk、βykAnd betazkAre each betaxk0、βyk0And betazk0；
(2) The angular velocity of the platform base is set under the base body coordinate system
Figure BDA0001842038410000041
When in use
Figure BDA0001842038410000042
Figure BDA0001842038410000043
When one of the two is non-zero, the base surrounds the X of the coordinate system of the outer frame bodyp2Angular velocity of shaft rotation
Figure BDA0001842038410000044
Y of body coordinate system of outer frame around inner framep1Angular velocity of shaft rotation
Figure BDA0001842038410000045
Z of internal frame winding table body coordinate systempAngular velocity of shaft rotation
Figure BDA0001842038410000046
Are respectively expressed as
Figure BDA0001842038410000047
Figure BDA0001842038410000048
Figure BDA0001842038410000049
Wherein,
Figure BDA00018420384100000410
(3) determining X of the coordinate system of the base around the outer frame bodyp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of body coordinate system of inner frame winding table bodypAngle of rotation beta of the shaftzkThe steady state value of (1), namely the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertial space, is divided into the following four conditions:
(a)βyk<90 and betaykSin beta at 90 deg. or soyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure the platform system is stable, cos (. beta.) is providedxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA00018420384100000411
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0。
(b)βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA00018420384100000412
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°。
(c)βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000051
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0。
(d)βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000052
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
In the step (2), the relative rotation angle of the inner part of the triaxial inertially stabilized platform system is measured by the following method:
at X of the outer framep2An angle sensor is arranged on the shaft, and the X of the base around the external frame body coordinate system is obtained through measurementp2Angle of rotation beta of the shaftxk(ii) a Y of the inner framep1An angle sensor is arranged on the shaft, and the Y of the coordinate system of the outer frame around the inner frame body is obtained through measurementp1Angle of rotation beta of the shaftyk(ii) a On the table body ZpThe sensor arranged on the shaft measures the rotating angle beta of the inner frame around the Zp shaft of the body coordinate system of the table bodyzk。
In step (2), the angle of rotation betayk′、βxk、βyk、βzkThe value range of the angle is-180 degrees to +180 degrees.
The sensor adopts a photoelectric encoder or a sine-cosine rotary encoder.
And (4) calculating the synthetic rotation angular speed of the table body, the inner frame and the outer frame in the step (3) by adopting a digital computer.
And the base of the triaxial inertially stabilized platform system is fixedly connected with the carrier.
The output torque of the torque motor arranged on the outer frame is more than 1 N.m.
The gyroscopes installed on the platform body are two-degree-of-freedom gyroscopes, the number of which needs to be at least two, and the two gyroscopes are installed in an orthogonal mode.
The gyroscopes installed on the platform body are single-degree-of-freedom gyroscopes, the number of the gyroscopes needs to be at least three, and every two gyroscopes are installed in an orthogonal mode.
A three-axis inertially stabilized platform system frame self-unlocking system comprising: the device comprises a determining module, a measuring module, an angular velocity calculating module, an equation determining module, a judging module and a self-unlocking module;
the determining module obtains the angular velocity of the table body in X according to the angular velocity output by the gyroscope arranged on the table bodypAxis, YpAxis and ZpComponent of angular velocity on the shaft
Figure BDA0001842038410000053
The measuring module measures and obtains the inside relative pivoted angle of triaxial inertially stabilized platform system, includes: x of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of coordinate system of inner frame wound stage bodypAngle of rotation beta of the shaftzk；
The angular velocity calculation module calculates the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula;
the equation determining module obtains an angular velocity determining equation of the three frames of the platform by adopting a decoupling calculation formula;
the judgment module judges the frame self-unlocking condition according to the angular velocity determination equation of the three frames of the platform, the three frame angles and the angular velocity measured by the gyroscope arranged on the platform body, and the judgment module comprises the following steps
1) At betaykNot equal to 90 DEG and betaykWhen the angle is not equal to-90 degrees, the inner frame and the outer frame of the platform are not in the same plane, and the platform body of the platform is stable relative to the inertia space without the need of self-unlocking of the frame;
2) at betaykAt 90 ° or βyk-90 °, and base angular velocity
Figure BDA0001842038410000061
In the process, the inner frame and the outer frame of the platform are arranged in one plane, and the platform body of the platform is stable relative to the inertia space without self-unlocking of the frame;
3) at betaykAt 90 ° or βykIs equal to-90 DEG when
Figure BDA0001842038410000062
One of them is non-zero, the platform inner frame and the platform outer frame are oneIn the plane, the platform body of the platform can be stable relative to the inertial space only by unlocking the frame;
when the platform body is stable relative to the inertial space only by self-unlocking the frame, the self-unlocking module drives the inner frame to rotate rapidly relative to the platform body through the outer frame, so that the self-unlocking of the frame is realized to ensure that the platform body is still stable relative to the inertial space.
Compared with the prior art, the invention has the following advantages:
(1) the self-unlocking method of the three-axis inertial platform system frame completely covers the condition that 3 attitude angles are in any quadrant, and overcomes the defect that the prior art has an inner frame angle betaykThe "frame lock" problem when ± 90 °;
(2) the invention provides a self-unlocking method of a three-axis inertial platform system frame, although sec beta exists in a calculation linkykBut gives the steady state value of the frame angle at this singular point, ensuring that the system is still stable and does not diverge.
(3) The invention realizes the rapid decoupling and frame state switching of the triaxial platform during the frame locking, can effectively isolate the angular motion of the carrier, and improves the full-attitude adaptability of the platform body relative to the inertial space stability.
Drawings
FIG. 1 is a schematic diagram of the relationship between coordinates of four bodies in a three-axis inertially stabilized platform system;
FIG. 2 is a schematic view of a three-axis platform structure when the angles of the three frames are zero;
FIG. 3 is a schematic view of a three-axis platform structure when the frame is locked;
FIG. 4 is a schematic structural diagram of a three-axis inertially-stabilized platform according to the self-unlocking scheme of the present invention before unlocking;
FIG. 5 is a schematic structural diagram of the three-axis inertially-stabilized platform after being unlocked according to the self-unlocking scheme of the present invention;
FIG. 6 shows simulation results of three frame angles for implementing self-unlocking according to the present invention;
FIG. 7 is a table OY for realizing self-unlocking according to the present inventionpAnd OXpShaft angular velocity simulation knotFruit;
FIG. 8 is a flow chart of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The invention discloses a self-unlocking method of a three-axis stabilized platform system frame, which is used for outputting angular rates of 3 gyroscopes orthogonally arranged on a platform body
Figure BDA0001842038410000071
And 3 variables are used as input information of the decoupling link, and 3 shaft end torque motors which respectively act on the table body shaft, the inner ring shaft and the outer ring shaft are output after information fusion. The invention provides an unlocking method of a three-axis platform during frame locking and an unlocked frame angle for the first time, so that the stability of a platform body relative to an inertial space is realized. The invention provides the frame angle steady-state value at the singular point, ensures that the system is still stable and does not diverge, realizes the rapid decoupling and frame state switching of the three-axis platform when the frame is locked, can effectively isolate the angular motion of the carrier, and improves the full-attitude adaptability of the platform body relative to the inertial space stability.
The invention is realized based on a three-axis inertial stabilization platform system, the stabilization platform system comprises a base, an outer frame, an inner frame and a platform body, and the corresponding body coordinate systems are respectively a base body coordinate system X1Y1Z1Outer frame body coordinate system Xp2Yp2Zp2Inner frame body coordinate system Xp1Yp1Zp1And table body coordinate system XpYpZp(ii) a The origins of the four coordinate systems coincide, and: z of table body coordinate systempZ of axis and inner frame body coordinate systemp1Y of body coordinate system of axis coincidence and outer framep2Y of axis and inner frame body coordinate systemp1X of axis coincident, base body coordinate system1X of axis and outer frame body coordinate systemp2The axes are overlapped; wherein the base is fixedly connected with the carrier, and the inner part of the stable platform system is generated under the driving of the carrierWhen rotating, the base winds X of the coordinate system of the outer frame bodyp2The shaft rotates, the outer frame rotates around the Y of the coordinate system of the inner frame bodyp1Z of coordinate system of axis rotation and internal frame around table bodypRotating the shaft;
and calculating the synthetic rotation angular velocity of the table body, the inner frame and the outer frame, wherein the specific calculation formula is as follows:
Figure BDA0001842038410000081
Figure BDA0001842038410000082
Figure BDA0001842038410000083
wherein, ω iszIs a table body ZpThe resultant rotational angular velocity of the shaft; omegayIs an inner frame Yp1The resultant rotational angular velocity of the shaft; omegaxIs an outer frame Xp2The resultant rotational angular velocity of the shaft.
By adopting the decoupling calculation formula, a platform body coordinate system X can be obtainedpYpZpAngular velocities in three directions of
Figure BDA0001842038410000084
Figure BDA0001842038410000085
Figure BDA0001842038410000086
Inner frame body coordinate system Xp1Yp1Zp1Angular velocities in three directions of
Figure BDA0001842038410000087
Figure BDA0001842038410000088
Figure BDA0001842038410000089
Coordinate system X of outer frame bodyp2Yp2Zp2Angular velocities in three directions of
Figure BDA0001842038410000091
Figure BDA0001842038410000092
Figure BDA0001842038410000093
Angular velocities of three frames of
Figure BDA0001842038410000094
Figure BDA0001842038410000095
Figure BDA0001842038410000096
Is provided with
Figure BDA0001842038410000097
Then there is
Figure BDA0001842038410000098
Figure BDA0001842038410000099
Figure BDA00018420384100000910
Stability is judged by Lyapunov's law. Equation of
Figure BDA00018420384100000911
From sin (. beta.)xk+ α) ═ 0, with two solutions βxkα and βxk＝π-α。
The differential equation after linearizing the above equation is
Figure BDA00018420384100000912
In the stability analysis, four cases are required:
a.βyk<90 and betayk→ 90 deg. sin βyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA00018420384100000913
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0。
b.βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000101
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°。
c.βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000102
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0。
d.βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000103
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
For the purpose of image illustration, the self-unlocking method of the triaxial inertial platform system framework provided by the invention is schematically shown in fig. 4 and 5. FIG. 4 is a graph of ω as compared to FIG. 3z1Not equal to 0, the outer frame drives the inner frame to wind the base OX together1And a table body OZpRotate quickly to the position of figure 5. At this time, the base drives the outer frame to wind the OZ together1The platform body keeps stable relative to the inertia space in the rotating process.
The preferred embodiment is:
in this embodiment, the simulation calculation is performed by using the calculation formula of the present invention, where the setting conditions are as follows: coordinate system X of base surrounding outer framep2Angle of rotation beta of the shaft xk0; coordinate system Y of outer frame around inner framep1Angle of rotation beta of the shaftykApproaching 90 ° at a speed of 1 °/s; coordinate system Z of internal frame winding table bodypAngle of rotation beta of the shaft zk0; i.e. the three axes of rotation are approximately in one plane. At this time, when βykAngular velocity of base at 90 DEG
Figure BDA0001842038410000104
When sin α is 1 and cos α is 0, α is therefore 90 °; from cos (. beta.) ofxk+ α) ═ 1, finding βxk180 ° - α -90 °, as shown in fig. 6, βxkQuickly stabilized at +90 deg. and betazkAlso follows rapidly to +90, betaykGradually decrease at a rate of-1 °/s; platform body OYpAnd OXpThe simulation result of the angular velocity of the shaft is shown in fig. 7, and it can be seen that the value of the angular velocity of the stage during the self-unlocking process is very small (10)-10～10-9In the order of degrees/s) can be neglected to be zero. The ordinate of the upper diagram in FIG. 6 is Bzk denotes βzkIn the ordinate of the diagram, Byk represents betaykThe ordinate of the lower graph is Bxk representing betaxkTime represents Time and 0 point represents Time. In FIG. 7, wxp denotes
Figure BDA0001842038410000111
wyp denotes
Figure BDA0001842038410000112
wzp denotes
Figure BDA0001842038410000113
Time denotes Time.
The above embodiments can verify that the self-unlocking method of the present invention is correct, and fig. 8 is a flowchart for implementing the present invention.
The invention discloses a self-unlocking system of a three-axis inertially stabilized platform system frame, which comprises: the device comprises a determining module, a measuring module, an angular velocity calculating module, an equation determining module, a judging module and a self-unlocking module;
the determining module obtains the angular velocity of the table body in X according to the angular velocity output by the gyroscope arranged on the table bodypAxis, YpAxis and ZpComponent of angular velocity on the shaft
Figure BDA0001842038410000114
The measuring module measures and obtains the inside relative pivoted angle of triaxial inertially stabilized platform system, includes: x of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of coordinate system of inner frame wound stage bodypAngle of rotation beta of the shaftzk；
The angular velocity calculation module calculates the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula;
the equation determining module obtains an angular velocity determining equation of the three frames of the platform by adopting a decoupling calculation formula;
the judgment module judges the frame self-unlocking condition according to the angular velocity determination equation of the three frames of the platform, the three frame angles and the angular velocity measured by the gyroscope arranged on the platform body, and the judgment module comprises the following steps
1) At betaykNot equal to 90 DEG and betaykWhen the angle is not equal to-90 degrees, the inner frame and the outer frame of the platform are not in the same plane, and the platform body of the platform is stable relative to the inertia space without the need of self-unlocking of the frame;
2) at betaykAt 90 ° or βyk-90 °, and base angular velocity
Figure BDA0001842038410000115
In the process, the inner frame and the outer frame of the platform are arranged in one plane, and the platform body of the platform is stable relative to the inertia space without self-unlocking of the frame;
3) at betaykAt 90 ° or βykIs equal to-90 DEG when
Figure BDA0001842038410000116
When one of the two frames is non-zero, the platform inner frame and the platform outer frame are arranged in a plane, and the platform body of the platform can be stable relative to the inertia space only by unlocking the frames;
when the platform body is stable relative to the inertial space only by self-unlocking the frame, the self-unlocking module drives the inner frame to rotate rapidly relative to the platform body through the outer frame, so that the self-unlocking of the frame is realized to ensure that the platform body is still stable relative to the inertial space.
The angular velocity calculation module calculates the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula, wherein the specific decoupling calculation formula is as follows:
Figure BDA0001842038410000121
Figure BDA0001842038410000122
Figure BDA0001842038410000123
wherein, ω iszIs a table body ZpThe resultant rotational angular velocity of the shaft; omegayIs an inner frame Yp1The resultant rotational angular velocity of the shaft; omegaxIs an outer frame Xp2The resultant rotational angular velocity of the shaft;
in the self-unlocking module, the inner frame is driven by the outer frame to rotate relative to the platform body quickly, and the calculation process of the angle value of the frame self-unlocking to ensure that the platform body is still stable relative to the inertia space is as follows:
(1) measuring to obtain betaxk、βykAnd betazkAre each betaxk0、βyk0And betazk0；
(2) The angular velocity of the platform base is set under the base body coordinate system
Figure BDA0001842038410000124
When in use
Figure BDA0001842038410000125
Figure BDA0001842038410000126
When one of the two is non-zero, the base surrounds the X of the coordinate system of the outer frame bodyp2Angular velocity of shaft rotation
Figure BDA0001842038410000127
Y of body coordinate system of outer frame around inner framep1Angular velocity of shaft rotation
Figure BDA0001842038410000128
Z of internal frame winding table body coordinate systempAngular velocity of shaft rotation
Figure BDA0001842038410000129
Are respectively expressed as
Figure BDA00018420384100001210
Figure BDA00018420384100001211
Figure BDA00018420384100001212
Wherein,
Figure BDA00018420384100001213
(3) determining X of the coordinate system of the base around the outer frame bodyp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of body coordinate system of inner frame winding table bodypAngle of rotation beta of the shaftzkThe steady state value of (1), namely the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertial space, is divided into the following four conditions:
(a)βyk<90 and betaykSin beta at 90 deg. or soyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure the platform system is stable, cos (. beta.) is providedxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000131
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0。
(b)βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000132
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°。
(c)βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000133
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0。
(d)βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure BDA0001842038410000134
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
The measuring module measures the relative rotation angle of the inner part of the triaxial inertially stabilized platform system by the following method:
at X of the outer framep2An angle sensor is arranged on the shaft, and the X of the base around the external frame body coordinate system is obtained through measurementp2Angle of rotation beta of the shaftxk(ii) a Y of the inner framep1An angle sensor is arranged on the shaft, and the Y of the coordinate system of the outer frame around the inner frame body is obtained through measurementp1Angle of rotation beta of the shaftyk(ii) a On the table body ZpThe sensor arranged on the shaft measures the rotating angle beta of the inner frame around the Zp shaft of the body coordinate system of the table bodyzk。
In the measuring module, the angle of rotation betayk′、βxk、βyk、βzkThe value range of the angle is-180 degrees to +180 degrees.
The sensor adopts a photoelectric encoder or a sine-cosine rotary encoder.
The angular velocity calculating module calculates the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a digital computer.
And the base of the triaxial inertially stabilized platform system is fixedly connected with the carrier.
The output torque of the torque motor arranged on the outer frame is more than 1 N.m.
The gyroscopes installed on the platform body are two-degree-of-freedom gyroscopes, the number of which needs to be at least two, and the two gyroscopes are installed in an orthogonal mode.
The gyroscopes installed on the platform body are single-degree-of-freedom gyroscopes, the number of the gyroscopes needs to be at least three, and every two gyroscopes are installed in an orthogonal mode.
The self-unlocking method and the self-unlocking system for the three-axis inertial platform system frame completely cover the condition that 3 attitude angles are in any quadrant, and overcome the defect that the prior art has an inner frame angle betaykThe "frame lock" problem when ± 90 °; and the invention is characterized in that although sec beta exists in the calculation linkykBut the frame angle steady state value at the singular point is given, so that the system is still stable and is ensured not to be diverged.
The above description is only one embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (9)

1. A self-unlocking method of a three-axis inertially stabilized platform system frame is characterized by comprising the following steps: based on the realization of a three-axis inertia stabilized platform system, the stabilized platform system comprises a base, an outer frame, an inner frame and a platform body, and the corresponding body coordinate systems are respectively a base body coordinate system X1Y1Z1Outer frame body coordinate system Xp2Yp2Zp2Inner frame body coordinate system Xp1Yp1Zp1And table body coordinate system XpYpZp(ii) a The origins of the four coordinate systems coincide, and: z of table body coordinate systempZ of axis and inner frame body coordinate systemp1Y of coordinate system of outer frame body with coincident axesp2Y of axis and inner frame body coordinate systemp1X of axis coincident, base body coordinate system1X of axis and outer frame body coordinate systemp2The axes are overlapped; wherein the base is fixedly connected with the carrier, and when the stabilized platform system rotates relatively internally under the driving of the carrier, the base rotates around the X of the coordinate system of the outer frame bodyp2The shaft rotates, the outer frame rotates around the Y of the coordinate system of the inner frame bodyp1Z of coordinate system of axis rotation and internal frame around table bodypRotating the shaft;
the self-unlocking method of the three-axis inertially stabilized platform system frame comprises the following steps:
(1) obtaining the angular velocity of the table body in X according to the output angular velocity of a gyroscope arranged on the table bodypAxis, YpAxis and ZpComponent of angular velocity on the shaft
Figure FDA0002592906910000011
(2) The angle of the inside relative rotation of triaxial inertially stabilized platform system is obtained in the measurement, include: x of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of coordinate system of inner frame wound stage bodypAngle of rotation beta of the shaftzk；
(3) Calculating the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula, wherein the specific decoupling calculation formula is as follows:
Figure FDA0002592906910000012
Figure FDA0002592906910000013
Figure FDA0002592906910000014
wherein, ω iszIs a table body ZpThe resultant rotational angular velocity of the shaft; omegayIs an inner frame Yp1The resultant rotational angular velocity of the shaft; omegaxIs an outer frame Xp2Shaft assemblyRotational angular velocity;
(4) obtaining an angular velocity determination equation of the three frames of the platform by adopting the decoupling calculation formula in the step (3);
by adopting a decoupling calculation formula, a platform body coordinate system X can be obtainedpYpZpAngular velocities in three directions of
Figure FDA0002592906910000021
Figure FDA0002592906910000022
Figure FDA0002592906910000023
Inner frame body coordinate system Xp1Yp1Zp1Angular velocities in three directions of
Figure FDA0002592906910000024
Figure FDA0002592906910000025
Figure FDA0002592906910000026
Coordinate system X of outer frame bodyp2Yp2Zp2Angular velocities in three directions of
Figure FDA0002592906910000027
Figure FDA0002592906910000028
Figure FDA0002592906910000029
Angular velocities of three frames of
Figure FDA00025929069100000210
Figure FDA00025929069100000211
Figure FDA00025929069100000212
(5) According to the angular velocity determination equation of the three frames of the platform, the three frame angles and the angular velocity measured by the gyroscope arranged on the platform body, the self-unlocking condition of the frame is judged as follows
1) At betaykNot equal to 90 DEG and betaykWhen the angle is not equal to-90 degrees, the inner frame and the outer frame of the platform are not in the same plane, and the platform body of the platform is stable relative to the inertia space without the need of self-unlocking of the frame;
2) at betaykAt 90 ° or βyk-90 °, and base angular velocity
Figure FDA0002592906910000031
In the process, the inner frame and the outer frame of the platform are arranged in one plane, and the platform body of the platform is stable relative to the inertia space without self-unlocking of the frame;
3) at betaykAt 90 ° or βykIs equal to-90 DEG when
Figure FDA0002592906910000032
When one of the two frames is non-zero, the platform inner frame and the platform outer frame are arranged in a plane, and the platform body of the platform can be stable relative to the inertia space only by unlocking the frames;
(6) when the platform body is stable relative to the inertia space only by self-unlocking of the frame, the inner frame is driven by the outer frame to rapidly rotate relative to the platform body, so that self-unlocking of the frame is realized to ensure that the platform body is still stable relative to the inertia space;
the calculation process of the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertia space is as follows:
(1) measured to obtain betaxk、βykAnd betazkAre each betaxk0、βyk0And betazk0；
(2) The angular velocity of the platform base arranged under the base body coordinate system is
Figure FDA0002592906910000033
When in use
Figure FDA0002592906910000034
Figure FDA0002592906910000035
When one of the two is non-zero, the base surrounds the X of the coordinate system of the outer frame bodyp2Angular velocity of shaft rotation
Figure FDA0002592906910000036
Y of body coordinate system of outer frame around inner framep1Angular velocity of shaft rotation
Figure FDA0002592906910000037
Z of internal frame winding table body coordinate systempAngular velocity of shaft rotation
Figure FDA0002592906910000038
Are respectively expressed as
Figure FDA0002592906910000039
Figure FDA00025929069100000310
Figure FDA00025929069100000311
Wherein,
Figure FDA00025929069100000312
(3) determining X of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of body coordinate system of inner frame winding table bodypAngle of rotation beta of the shaftzkThe steady state value of (1), namely the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertial space, is divided into the following four conditions:
(a)βyk<90 and betaykSin beta at 90 deg. or soyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure the platform system is stable, cos (. beta.) is providedxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000041
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0；
(b)βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000042
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°；
(c)βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000043
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0；
(d)βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000044
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
2. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: in the step (6), the inner frame is driven by the outer frame to rapidly rotate relative to the platform body, and the calculation process of the angle value for realizing the self-unlocking of the frame to ensure that the platform body is still stable relative to the inertia space is as follows:
(1) measured to obtain betaxk、βykAnd betazkAre each betaxk0、βyk0And betazk0；
(2) Is arranged atThe angular velocity of the platform base under the base body coordinate system is
Figure FDA0002592906910000045
When in use
Figure FDA0002592906910000046
Figure FDA0002592906910000047
When one of the two is non-zero, the base surrounds the X of the coordinate system of the outer frame bodyp2Angular velocity of shaft rotation
Figure FDA0002592906910000048
Y of body coordinate system of outer frame around inner framep1Angular velocity of shaft rotation
Figure FDA0002592906910000049
Z of internal frame winding table body coordinate systempAngular velocity of shaft rotation
Figure FDA00025929069100000410
Are respectively expressed as
Figure FDA0002592906910000051
Figure FDA0002592906910000052
Figure FDA0002592906910000053
Wherein,
Figure FDA0002592906910000054
(3) determining X of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkOuter frame and inner frameY of frame body coordinate systemp1Angle of rotation beta of the shaftykZ of body coordinate system of inner frame winding table bodypAngle of rotation beta of the shaftzkThe steady state value of (1), namely the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertial space, is divided into the following four conditions:
(a)βyk<90 and betaykSin beta at 90 deg. or soyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure the platform system is stable, cos (. beta.) is providedxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000055
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0；
(b)βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000056
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°；
(c)βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, the process of the present invention,due to the fact that
Figure FDA0002592906910000057
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0；
(d)βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000058
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
3. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: in the step (2), the relative rotation angle of the inner part of the triaxial inertially stabilized platform system is measured by the following method:
at X of the outer framep2An angle sensor is arranged on the shaft, and the X of the base around the external frame body coordinate system is obtained through measurementp2Angle of rotation beta of the shaftxk(ii) a Y of the inner framep1An angle sensor is arranged on the shaft, and the Y of the coordinate system of the outer frame around the inner frame body is obtained through measurementp1Angle of rotation beta of the shaftyk(ii) a On the table body ZpThe sensor arranged on the shaft measures the rotating angle beta of the inner frame around the Zp shaft of the body coordinate system of the table bodyzk。
4. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: in step (2), the angle of rotation betayk′、βxk、βyk、βzkThe value range of the angle is-180 degrees to +180 degrees.
5. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: the sensor adopts a photoelectric encoder or a sine-cosine rotary encoder.
6. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: and (4) calculating the synthetic rotation angular speed of the table body, the inner frame and the outer frame in the step (3) by adopting a digital computer.
7. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: and the base of the triaxial inertially stabilized platform system is fixedly connected with the carrier.
8. The self-unlocking method of the triaxial inertially stabilized platform system frame according to claim 1, wherein: the output torque of the torque motor arranged on the outer frame is more than 1 N.m.
9. A self-unlocking system for a three-axis inertially stabilized platform system frame, comprising: the device comprises a determining module, a measuring module, an angular velocity calculating module, an equation determining module, a judging module and a self-unlocking module;
the determining module obtains the angular velocity of the table body in X according to the angular velocity output by the gyroscope arranged on the table bodypAxis, YpAxis and ZpComponent of angular velocity on the shaft
Figure FDA0002592906910000061
The measuring module measures and obtains the inside relative pivoted angle of triaxial inertially stabilized platform system, includes: x of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykInner frame winding table bodyZ of the body coordinate systempAngle of rotation beta of the shaftzk；
The angular velocity calculation module calculates the synthetic rotation angular velocity of the table body, the inner frame and the outer frame by adopting a decoupling calculation formula, wherein the specific decoupling calculation formula is as follows:
Figure FDA0002592906910000071
Figure FDA0002592906910000072
Figure FDA0002592906910000073
wherein, ω iszIs a table body ZpThe resultant rotational angular velocity of the shaft; omegayIs an inner frame Yp1The resultant rotational angular velocity of the shaft; omegaxIs an outer frame Xp2The resultant rotational angular velocity of the shaft;
the equation determining module obtains an angular velocity determining equation of three frames of the platform by adopting a decoupling calculation formula, and specifically comprises the following steps:
by adopting a decoupling calculation formula, a platform body coordinate system X can be obtainedpYpZpAngular velocities in three directions of
Figure FDA0002592906910000074
Figure FDA0002592906910000075
Figure FDA0002592906910000076
Inner frame body coordinate system Xp1Yp1Zp1Angular velocities in three directions of
Figure FDA0002592906910000077
Figure FDA0002592906910000078
Figure FDA0002592906910000079
Coordinate system X of outer frame bodyp2Yp2Zp2Angular velocities in three directions of
Figure FDA00025929069100000710
Figure FDA0002592906910000081
Figure FDA0002592906910000082
Angular velocities of three frames of
Figure FDA0002592906910000083
Figure FDA0002592906910000084
Figure FDA0002592906910000085
The judgment module judges the frame self-unlocking condition according to the angular velocity determination equation of the three frames of the platform, the three frame angles and the angular velocity measured by the gyroscope arranged on the platform body, and the judgment module comprises the following steps
1) At betaykNot equal to 90 DEG and betaykWhen not equal to-90 deg., it is flatThe inner frame and the outer frame of the platform are not in the same plane, so that the relative inertia space of the platform body is stable without self-unlocking of the frame;
2) at betaykAt 90 ° or βyk-90 °, and base angular velocity ωy1＝ωz1When the platform is 0, the inner frame and the outer frame of the platform are erected in one plane, and the platform body of the platform is stable relative to an inertia space without self-unlocking of the frame;
3) at betaykAt 90 ° or βykWhen ω is equal to-90 °, oy1、ωz1When one of the two frames is non-zero, the platform inner frame and the platform outer frame are arranged in a plane, and the platform body of the platform can be stable relative to the inertia space only by unlocking the frames;
when the platform body is stable relative to the inertia space only by the self-unlocking of the frame, the self-unlocking module drives the inner frame to rapidly rotate relative to the platform body by the outer frame, so that the self-unlocking of the frame is realized to ensure that the platform body is still stable relative to the inertia space;
the calculation process of the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertia space is as follows:
measured to obtain betaxk、βykAnd betazkAre each betaxk0、βyk0And betazk0；
The angular velocity of the platform base arranged under the base body coordinate system is
Figure FDA0002592906910000086
When in use
Figure FDA0002592906910000087
When one of the two is non-zero, the base surrounds the X of the coordinate system of the outer frame bodyp2Angular velocity of shaft rotation
Figure FDA0002592906910000088
Y of body coordinate system of outer frame around inner framep1Angular velocity of shaft rotation
Figure FDA0002592906910000089
Z of internal frame winding table body coordinate systempAngular velocity of shaft rotation
Figure FDA00025929069100000810
Are respectively expressed as
Figure FDA0002592906910000091
Figure FDA0002592906910000092
Figure FDA0002592906910000093
Wherein,
Figure FDA0002592906910000094
determining X of base around outer frame body coordinate systemp2Angle of rotation beta of the shaftxkY of coordinate system of outer frame around inner frame bodyp1Angle of rotation beta of the shaftykZ of body coordinate system of inner frame winding table bodypAngle of rotation beta of the shaftzkThe steady state value of (1), namely the angle value for realizing the self-unlocking of the frame to ensure the platform body to be still stable relative to the inertial space, is divided into the following four conditions:
(a)βyk<90 and betaykSin beta at 90 deg. or soyk＝1，tanβyk>0；βxkIs initially betaxk0To ensure the platform system is stable, cos (. beta.) is providedxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000095
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0+180°-α-βxk0；
(b)βyk>90 and betayk→ 90 deg. sin βyk＝1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000096
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0+Δβxk＝βzk0-α-90°；
(c)βyk<-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk>0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) ═ 1, i.e. βxk180 ° - α, wherein βxkHas a variation of Δ βxk＝180°-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000097
So betaykThe value of (b) will decrease; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0-180°+α+βxk0；
(d)βyk>-90 ° and βyk→ 90 deg. sin betayk＝-1，tanβyk<0；βxkIs initially betaxk0To ensure system stability, cos (. beta.) is presentxk+ α) being 1, i.e. βxkα, wherein βxkHas a variation of Δ βxk＝-α-βxk0(ii) a At this time, since
Figure FDA0002592906910000098
So betaykThe value of (b) will increase; beta is azkHas a steady state value of betazk＝βzk0-Δβxk＝βzk0+α+βxk0。
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