CN112327942B - Automatic leveling method for triaxial air-bearing satellite simulation platform - Google Patents
Automatic leveling method for triaxial air-bearing satellite simulation platform Download PDFInfo
- Publication number
- CN112327942B CN112327942B CN202011240519.9A CN202011240519A CN112327942B CN 112327942 B CN112327942 B CN 112327942B CN 202011240519 A CN202011240519 A CN 202011240519A CN 112327942 B CN112327942 B CN 112327942B
- Authority
- CN
- China
- Prior art keywords
- platform
- air
- moment
- mass
- formula
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000004088 simulation Methods 0.000 title claims abstract description 42
- 238000000034 method Methods 0.000 title claims abstract description 37
- 239000013598 vector Substances 0.000 claims abstract description 18
- 238000006073 displacement reaction Methods 0.000 claims abstract description 9
- 230000005484 gravity Effects 0.000 claims description 38
- 239000011159 matrix material Substances 0.000 claims description 12
- 230000007246 mechanism Effects 0.000 claims description 6
- 230000001131 transforming effect Effects 0.000 claims 1
- 238000012360 testing method Methods 0.000 abstract description 13
- 238000005188 flotation Methods 0.000 abstract description 6
- 230000004044 response Effects 0.000 description 7
- 238000013461 design Methods 0.000 description 5
- 238000002474 experimental method Methods 0.000 description 4
- 230000008569 process Effects 0.000 description 4
- 230000005486 microgravity Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 238000013016 damping Methods 0.000 description 2
- 238000005381 potential energy Methods 0.000 description 2
- 230000009471 action Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000002035 prolonged effect Effects 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D3/00—Control of position or direction
- G05D3/12—Control of position or direction using feedback
-
- 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
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
According to the automatic leveling method for the triaxial air-bearing satellite simulation platform, provided by the application, the motion vectors of the mass blocks in the direction of the three principal axes of inertia are controlled to realize zero angular velocity increment of the air-bearing platform so as to realize high-precision adjustment of the mass center of the platform under the condition that the rotational inertia of the triaxial air-bearing satellite simulation platform is uncertain, so that the accuracy of ground simulation and test data of the triaxial air-bearing satellite simulation platform is effectively improved. And adjusting a displacement vector of the mass block on the principal axis of inertia to coincide the mass block with the rotation center of the platform so as to adjust the angular velocity increment of the air flotation platform to be zero.
Description
Technical Field
The application relates to a novel automatic leveling method for a triaxial air-bearing satellite simulation platform, and belongs to the field of simulation nonlinear control.
Background
With the rapid development of aerospace industry, higher performance requirements are provided for experiments of simulating space microgravity and micro damping environment on the ground of a spacecraft. Because the spacecraft is extremely difficult to test and reconstruct in space, the ground simulation and test experiments of the spacecraft are particularly critical.
At present, an air floatation platform matched with a satellite full-physical simulation test is established in China, and microgravity and micro damping environment in the space are simulated through an air floatation mode. The three-axis air bearing table can realize three-degree-of-freedom rotation through the air bearing ball bearing, and is used for simulating three-axis attitude dynamics and controlling simulation. In order to strictly simulate the environment of micro friction and micro gravity during ground test, external disturbance moment needs to be overcome as much as possible, and the biggest obstacle is the influence of gravity on the air bearing table. In order to reduce the influence of gravity as much as possible, the distance between the center of mass of the air bearing table and the center of rotation needs to be adjusted to the minimum. The mass center of the air bearing table can be adjusted to observe the swinging motion, and the swinging period of the air bearing table is prolonged by moving the leveling mass block. The disadvantage of this method is that a lot of tests are required, and the rotation angle of the triaxial stage is limited, which is difficult in practical application. At the present stage, a manual leveling mode is usually adopted, but still a longer experimental period is required, and the adjustment error is larger.
In practical application, the newly added load or the replaced load on the air bearing table can have great influence on the mass center of the air bearing table. The leveling method for the triaxial air bearing platform at the present stage can be divided into two main types. First, self-leveling is performed assuming that the moment of inertia of the platform is known. For an air-floating platform with small moment of inertia, the main moment of inertia of the air-floating platform can be accurately measured, and the influence of the inertia product on the system is ignored. For an air floating platform with larger moment of inertia, the measurement of the moment of inertia is difficult, the product of the measured moment of inertia still has larger error, and the practicability of the air floating platform with larger moment of inertia is poor. And secondly, estimating the moment of inertia of the air floating platform by using a least square method. The method is more suitable for the air floating platform with larger moment of inertia, but the estimation error, especially for the inertia product, can greatly influence the accuracy of automatic leveling.
For a triaxial air bearing platform, if the load on the platform is changed, the moment of inertia is greatly influenced. If the cold air thruster system is installed, the moment of inertia is affected by the change of the quality of the gas cylinder as the cold air is consumed. Therefore, if the automatic leveling accuracy of the triaxial air bearing platform is to be further improved, uncertainty of the moment of inertia of the platform needs to be considered.
In view of this, the present patent application is specifically filed.
Disclosure of Invention
The automatic leveling method for the triaxial air-bearing satellite simulation platform aims at solving the problems in the prior art, and aims at the triaxial air-bearing satellite simulation platform with the cold air thruster system, under the condition that the rotational inertia of the triaxial air-bearing satellite simulation platform has uncertainty, the motion vectors of the mass blocks in the direction of the three principal axes of inertia are controlled to realize zero increment of the angular speed of the air-bearing platform, so that the high-precision adjustment of the mass center of the platform is realized, and the accuracy of ground simulation and test data of the triaxial air-bearing satellite simulation platform is effectively improved.
In order to achieve the above design objective, the three-axis air-floating satellite simulation platform automatic leveling method is to adjust the displacement vector of the mass block on the principal axis of inertia so as to coincide the mass block with the rotation center of the platform, and then adjust the angular velocity increment of the air-floating platform to be zero.
Is provided withThe displacement distance of the mass blocks on the three principal axes of inertia is the following formula,
wherein m is m G is the mass of the mass block b Force vector, moment τ c The expression is as follows,
r is then i I=1, 2,3 is the position of the i-th slider with respect to the rotation center.
The moment tau required to be controlled by the automatic leveling method c The expression is also as follows:
s＝ω e +βq e
the moment τ obtained by the above formula c Under control, the triaxial air-bearing satellite simulation platform can rapidly and accurately finish automatic gravity center leveling.
Wherein, Φ=1+|ω+|ω|| 2 ，k 0 ＞0，μ＞0，σ 1 ＞0，σ 2 The parameter of the controller to be designed is more than 0, omega is the current angular velocity of the triaxial air bearing platform, omega e Is the difference between the actual angular velocity of the platform and the target angular velocity, q e Is the difference between the actual pose of the platform and the target pose.
In summary, the three-axis air-bearing satellite simulation platform automatic leveling method has the following advantages:
1. based on the application, automatic and accurate platform gravity center leveling control can be realized without artificial interference, the ground simulation and test period is obviously shortened, and a large amount of manpower and material resources are saved.
2. The gravity center automatic leveling method can cope with the automatic leveling of the gravity center under the condition of uncertain rotational inertia of the triaxial air-bearing simulation platform, and the accuracy of test data of related simulation experiments is obviously improved.
3. The method is designed based on Lyapunov stability theorem, and the robustness of the obtained control method is high.
4. The three-axis air floating platform can realize quick and automatic geological center leveling under the combined action of uncertain moment of inertia and external interference aiming at the condition of external interference, and has higher leveling efficiency.
Drawings
The following drawings are illustrative of specific embodiments of the application.
FIG. 1 is a schematic diagram of the principle and coordinates of the automatic square adjustment method of the three-axis air-bearing satellite simulation platform;
FIGS. 2-4 are graphs of the response of X, Y and Z-axis mass movement positions during self-leveling, respectively;
FIGS. 5-7 are graphs of response of X, Y and Z-axis angular velocity, respectively, during self-leveling;
FIG. 8 is a graph comparing kinetic energy response curves before and after auto leveling;
in fig. 8, the larger the kinetic energy is, the larger the deviation between the center of gravity position and the center of mass position is, the smaller the kinetic energy is, the smaller the deviation between the center of gravity position and the center of mass position is, namely, the smaller the disturbance caused by the unbalanced gravity moment to the triaxial air bearing platform is.
Detailed Description
Embodiments of the present application will be further described with reference to the accompanying drawings.
In embodiment 1, as shown in fig. 1, the three-axis air-bearing satellite simulation platform automatic leveling method provided by the application aims at adjusting motion vectors of mass blocks on three principal axes of inertia through linear driving mechanisms such as stepping motors. The automatic leveling means is to adjust the position of the mass block to coincide with the center of rotation of the platform as much as possible, and finally adjust the angular velocity increment of the floating platform to zero. And in the process of overlapping the adjusting mass block and the rotation center, other actuating mechanisms are not needed.
Specifically, the application is based on the angular velocity of the air flotation platform, and if the gravity interference moment is zero, the angular velocity of the air flotation platform is not changed any more; otherwise, an angular velocity increase occurs.
The main shaft of the body fixedly connected coordinate system of the air flotation platform is along the main rotational inertia direction, the origin of the coordinate system is positioned at the rotational center CR of the air flotation platform, and the vector r is the same as the rotational center CR of the air flotation platform off Representing the offset of the centroid from the center of rotation.
The kinematic and dynamic model of the triaxial air-bearing satellite simulation platform is shown as two coordinate systems in figure 1. Wherein X is i 、Y i And Z i Is an inertial coordinate system, x b 、y b And z b And the deviation angle of the body fixedly connected coordinate system relative to the inertial coordinate system is the relative posture of the triaxial air-bearing satellite simulation platform.
On the premise of determining the moment of inertia
And (3) leveling the mass center of the triaxial air-bearing satellite simulation platform along the principal axis of inertia, wherein the attitude kinematic equation of the platform is represented by the following quaternion:
wherein, is the rotation angular velocity of the air bearing table under the fixed coordinate system, then q= [ q ] 0 q 1 q 2 q 3 ] T Is a unit quaternion.
Under the influence of gravity, the kinematic equation of the triaxial air-bearing satellite simulation platform is represented by the following Euler equation:
wherein m is a For the total mass of the air bearing table, J represents the moment of inertia of the air bearing table, r off G represents the distance between the mass center of the air bearing table and the rotation center b Represents the vector of gravity under the body-fixedly-connected coordinate system, and tau c The moment generated for the self-leveling system.
In order to implement the leveling of the triaxial air-bearing satellite simulation platform, the gravity vector is converted into a body fixed-connection coordinate system,
then the first time period of the first time period,
g i ＝[0 0 -9.8] T m/s 2 (6)
in order to adjust the mass center of the platform by adjusting the mass slide block, so that the mass center of the platform and the rotation center are overlapped as much as possible to overcome the interference moment caused by gravity, namely, the posture of the platform is required to be adjusted to be in a posture that the Z axis is not overlapped with the gravity direction, and then leveling is carried out. If the Z axis coincides with the direction of gravity, leveling in the Z axis direction will not be possible.
Define the desired posing error as (q e0 ,q e ) The desired pose is (q d0 ,q d ) Wherein
q e ＝q d0 q-q 0 q d +q × q d (8)
The rotation matrix is given by:
the relative angular velocity can be expressed as follows:
ω e ＝ω-Cω d (10)
the attitude error kinematics and dynamics equation of the triaxial air-bearing satellite simulation platform are as follows:
the following sliding mode variables are defined:
s＝ω e +βq e (14)
wherein, beta > 0, the kinetic equation can be rewritten as:
then the first time period of the first time period,
the application does not pay attention to the constitution and the specific content of the delta (-), but further designs the control means of the automatic leveling method by searching the upper limit of the delta (-).
The application is controlled based on angular velocity information, and the purpose of the automatic leveling method is to adjust the position of a mass block through three linear driving mechanisms so as to enable the angular velocity increment of a platform to be zero.
Thus, the moment generated by the linear motion mechanism can be expressed as follows:
wherein m is m Is the mass of the mass block, r i I=1, 2,3 is the position of the i-th slider with respect to the rotation center, that is, the control amount to be designed.
The kinetic system equation shown in the following equation is cited here:
the closed loop system is globally stable, and the system state tracking error is bounded, i.e. |q e ||≤ε 1 ，||ω e ||≤ε 2 。
Wherein k is 0 ＞0，μ＞0，σ 1 ＞0，σ 2 And > 0 is the controller parameter to be designed.
The following Lyapunov function is selected:
because of the fact that,substituting the formulas (12) - (18) into formula (19) and deriving V,
further, the method comprises the steps of,
substituting the controller listed in the following formula into the following formula yields:
wherein,
substituting the following formula into the formula can result in:
order theThen, when s and q e When outside the following collection->
As can be seen from the following formula, at s and q e When bounded, omega e And is also bounded.
Based on the deduction process, the control moment tau of the application c Is generated by the displacement of the driving mass, and the moment direction generated by the mass is perpendicular to the motion direction and the gravity direction, which is realized by controlling the moving distance r of the mass.
Then the control moment tau is required c The transformation is r, the reference formula is used for obtaining,
τ c ＝m m (-g b (t)×r) (27)
since the main diagonal elements of the cross-multiplied matrix are constant at zero, the matrixAnd (3) singularity. So that vector r cannot pass through the pair +.>And (5) obtaining the inverse.
The application gives a solution for r as follows:
the control output r of the auto-leveling method of the present application is thus given by the formula.
On the premise of uncertain moment of inertia
The posture kinematics of the triaxial air-bearing satellite simulation platform is consistent with that of the moment of inertia determination, and then the posture kinematics equation can be expressed by a quaternion as follows:
wherein, represents the rotation angular velocity of the air bearing table under the fixed coordinate system, and q= [ q ] 0 q 1 q 2 q 3 ] T Is a unit quaternion.
The kinematic equation under the influence of gravity can be expressed by the following euler equation:
wherein m is a For the total mass of the air bearing table, J (·) represents the moment of inertia, r, of the air bearing table with uncertainty off G represents the distance between the mass center of the air bearing table and the rotation center b Representing the vector of gravity under the body fixedly connected coordinate system, T d (. Cndot.) is an unknown external disturbance moment, τ c The moment generated for the self-leveling system.
In order to realize leveling of the platform, the gravity vector is required to be converted into a body fixed coordinate system:
wherein,
g i ＝[0 0 -9.8] T m/s 2 (34)
accordingly, a desired attitude error is defined as (q e0 ,q e ) The desired pose is (q d0 ,q d )，
q e ＝q d0 q-q 0 q d +q × q d (36)
The rotation matrix is given by:
the relative angular velocity can be expressed as follows:
ω e ＝ω-Cω d (38)
the attitude error kinematics and dynamics equations can be expressed as follows:
the following sliding mode variables are defined:
s＝ω e +βq e (42)
where β > 0, the kinetic equation can be rewritten as:
and is also provided with
Delta (·) can be seen as a system uncertainty term, which consists of two parts: 1. nonlinear terms of the system; 2. external interference terms. One of the difficulties with control system design is the existence of similar uncertainty items in the dynamics system. The application does not pay attention to the constitution and the specific content of delta (-), but further designs a control system by finding the upper limit of delta (-).
Under the premise of considering external interference and gravity interference, the following conclusion is drawn:
1) Presence of unknown positive constant c J > 0 and c f > 0 makes J (·) c +. J < infinity, andthis is true.
2) External disturbance moment T d (. Cndot.) satisfy T d (·)≤c g +c d ||ω|| 2 Wherein c g ≥0,c d And 0 is equal to or more than constant.
3)、ω d ,q d ,Are all bounded and have the following formulas:
wherein c ω And 0 is equal to or more than constant. Due toI C i=1, the above conclusion 3) is thus true.
4)、Wherein c 0 And 0 is equal to or more than constant.
For gravity disturbance forces in delta ()Moment term r off ×m a g b Before the platform is leveled, the platform is usually leveled manually, and r off Typically in minor amounts. Thus, r can be derived off ≤c r ，c r 0 is constant, further, m a And I g b The values are constant. At the same time, the following conclusion 5) can also prove to be true.
5)、||r off ×m a g b ||≤c g Wherein c g And 0 is equal to or more than constant.
From the above conclusion, it can be seen that the following formula is ensured to be established despite the fact that the delta (-) contains a nonlinear term, an uncertain term and a time-varying term
||Δ(·)||≤b 0 +b 1 ||ω||+b 2 ||ω|| 2 ≤bΦ (46)
Φ＝1+||ω||+||ω|| 2 (47)
Therefore, the application can be suitable for the condition of interference and uncertainty of rotational inertia to realize rapid and accurate automatic leveling of the platform.
The moments of the displacement of the adjusting mass along the three principal axes of inertia are expressed as follows:
wherein m is m Is the mass of the mass block, r i I=1, 2,3 is the position of the i-th slider with respect to the rotation center, that is, the control amount to be designed.
The control torque of the dynamic system as described by the formula is as follows:
under the control moment, the platform leveling closed-loop system is globally stable, and the system state tracking error is bounded, namely ||q e ||≤ε 1 ，||ω e ||≤ε 2 . Wherein k is 0 ＞0，μ＞0，σ 1 ＞0，σ 2 And > 0 is the controller parameter to be designed.
The following Lyapunov function is selected:
due toSubstituting the formula and deriving V can result in:
further, the method comprises the steps of,
substituting the controller described by the formula into the formula:
wherein,
substituting the formula into:
order theThen when s and q e When outside the following collection->
According to the formula, the values in s and q e When bounded, omega e And is also bounded.
As described above, the automatic leveling method for the triaxial air-bearing satellite simulation platform realizes zero increment of the angular velocity of the platform by driving the displacement of the mass block along three principal axes of inertia. The direction of the moment is controlled perpendicular to the direction of movement and the direction of gravity, in practice by controlling the displacement distance r of the mass.
In order to obtain the actual control quantity, the control moment tau is required to be controlled c Transformed into r.
From the formula
τ c ＝m m (-g b (t)×r) (58)
Since the main diagonal elements of the cross-multiplied matrix are constant at zero, the matrixAnd (3) singularity.
The solution given for r is as follows:
the output r of the automatic leveling method for the triaxial air-bearing satellite simulation platform is given by the above method.
As shown in fig. 2 to 8, the applicant has verified on a triaxial air-bearing simulation platform of the following structure. The platform is provided with three linear motion mechanisms and three mass blocks, the mass blocks are driven by a stepping motor, and the fastest motion speed can reach 100mm/s. The platform can freely rotate 360 degrees around the Z axis, and the rotation angles of other two axes are +/-30 degrees. The platform is provided with a triaxial high-precision fiber optic gyroscope for accurately measuring angular velocity information, and is provided with a biaxial inclinometer for accurately measuring X-axis and Y-axis attitude information, wherein Z-axis attitude information is obtained by integrating angular velocity measured by the gyroscope.
Because the leveling capability is limited by the mass and mass travel, the platform needs to be manually leveled before auto-leveling, and the platform can enter an auto-leveling process when adjusted to a more stable state.
The test parameters are shown in the following table: triaxial platform automatic leveling test parameter
As shown in fig. 2 to 4, the response curves of the moving positions of the mass in the experiment can be seen that the moving distance of the mass in the experiment is short. This illustrates that the true centroid deviation is well within the capabilities of the self-leveling system.
As shown in fig. 5 to 7, the response curves of the angular velocity in the test can be seen that the angular velocity is finally stabilized at zero point, and the system also completes the self-leveling process within 20s, so that the method is proved to be effective from the test point of view. The effectiveness of the leveling algorithm is further demonstrated by the following method. After the automatic leveling is completed, an arbitrary angular velocity is applied to the three-axis air bearing platform, so that the total energy of the three-axis platform can be expressed as the sum of kinetic energy and potential energy
E sum ＝E d +E s (60)
Wherein E is d ＝0.5ω T J omega is kinetic energy, E s Is potential energy. If the system is balanced, there is E s Approximately 0, then the rotational kinetic energy of the system is conserved at this time, E d (t)＝E d (0). Therefore, the rotation kinetic energy change curve of the system can embody the performance of the automatic leveling algorithm.
As shown in figure 8 of the drawings,in order to apply the kinetic energy response curve after angular velocity excitation to the triaxial air bearing platform after self-leveling, < +.>Is a triaxial bench kinetic energy response curve before leveling. From the figure, the dynamic fluctuation can be greatly reduced by automatically leveling the triaxial air bearing platform, namely the influence of gravity on the angular speed of the triaxial air bearing platform is reduced. If the influence of gravity on the angular velocity can be ignored, the influence of gravity on the angular momentum of the triaxial air bearing table is very little, and the influence of gravity on the platform can be ignored when the gesture maneuver simulation is performed. />
In summary, the embodiments presented in connection with the figures are only preferred. It will be obvious to those skilled in the art that other alternative structures which are in accordance with the design concept of the present application can be directly deduced and are also within the scope of the present application.
Claims (1)
1. An automatic leveling method for a triaxial air-bearing satellite simulation platform is characterized by comprising the following steps of: adjusting a mass block displacement vector on an inertia main shaft, and overlapping the mass block with the rotation center of the platform to adjust the angular velocity increment of the air-bearing platform to be zero;
on the premise of determining the moment of inertia
And (3) leveling the mass center of the triaxial air-bearing satellite simulation platform along the principal axis of inertia, wherein the attitude kinematic equation of the platform is represented by the following quaternion:
wherein, is the rotation angular velocity of the air bearing table under the fixed coordinate system, then q= [ q ] 0 q 1 q 2 q 3 ] T The unit quaternion;
under the influence of gravity, the kinematic equation of the triaxial air-bearing satellite simulation platform is represented by the following Euler equation:
wherein m is a For the total mass of the air bearing table, J represents the moment of inertia of the air bearing table, r off G represents the distance between the mass center of the air bearing table and the rotation center b Represents the vector of gravity under the body-fixedly-connected coordinate system, and tau c Moment generated for the automatic leveling system;
in order to implement the leveling of the triaxial air-bearing satellite simulation platform, the gravity vector is converted into a body fixed-connection coordinate system,
then the first time period of the first time period,
g i ＝[0 0 -9.8] T m/s 2 (6)
in order to adjust the mass center of the platform by adjusting the mass slide block so that the mass center of the platform and the rotation center are overlapped as much as possible to overcome the interference moment caused by gravity, namely, the posture of the platform is required to be adjusted to be in a posture that the Z axis is not overlapped with the gravity direction, and then leveling is carried out; if the Z axis coincides with the gravity direction, the leveling in the Z axis direction cannot be performed;
define the desired posing error as (q e0 ,q e ) The desired pose is (q d0 ,q d ) Wherein
q e ＝q d0 q-q 0 q d +q × q d (8)
The rotation matrix is given by:
the relative angular velocity can be expressed as follows:
ω e ＝ω-Cω d (10)
the attitude error kinematics and dynamics equation of the triaxial air-bearing satellite simulation platform are as follows:
the following sliding mode variables are defined:
s＝ω e +βq e (14)
wherein, beta > 0, the kinetic equation can be rewritten as:
then the first time period of the first time period,
thus, the moment generated by the linear motion mechanism can be expressed as follows:
wherein m is m Is the mass of the mass block, r i I=1, 2,3 is the position of the i-th slider with respect to the rotation center, that is, the control amount to be designed;
the kinetic system equation shown in the following equation is cited here:
the closed loop system is globally stable, and the system state tracking error is bounded, i.e. |q e ||≤ε 1 ，||ω e ||≤ε 2 ；
Wherein k is 0 ＞0，μ＞0，σ 1 ＞0，σ 2 > 0 is the controller parameter to be designed;
the following Lyapunov function is selected:
because of the fact that,substituting the formulas (12) - (18) into formula (19) and deriving V,
further, the method comprises the steps of,
substituting the controller listed in the following formula into the following formula yields:
wherein,
substituting the following formula into the formula can result in:
order theThen, when s and q e When outside the following collection->
As can be seen from the following formula, at s and q e When bounded, omega e Is also bounded;
then the control moment tau is required c TransformationFor r, the reference formula gives,
τ c ＝m m (-g b (t)×r) (27)
since the main diagonal elements of the cross-multiplied matrix are constant at zero, the matrixSingular; so that vector r cannot pass through the pair +.>Obtaining by inversion;
wherein, solution of r:
so far, the control output r of the automatic leveling method is correspondingly given by a formula;
on the premise of uncertain moment of inertia
The posture kinematics of the triaxial air-bearing satellite simulation platform is consistent with that of the moment of inertia determination, and then the posture kinematics equation can be expressed by a quaternion as follows:
wherein, represents the rotation angular velocity of the air bearing table under the fixed coordinate system, and q= [ q ] 0 q 1 q 2 q 3 ] T The unit quaternion;
the kinematic equation under the influence of gravity can be expressed by the following euler equation:
wherein m is a For the total mass of the air bearing table, J (·) represents the moment of inertia, r, of the air bearing table with uncertainty off G represents the distance between the mass center of the air bearing table and the rotation center b Representing the vector of gravity under the body fixedly connected coordinate system, T d (. Cndot.) is an unknown external disturbance moment, τ c Moment generated for the automatic leveling system;
in order to realize leveling of the platform, the gravity vector is required to be converted into a body fixed coordinate system:
wherein,
g i ＝[0 0 -9.8] T m/s 2 (34)
accordingly, a desired attitude error is defined as (q e0 ,q e ) The desired pose is (q d0 ,q d )，
q e ＝q d0 q-q 0 q d +q × q d (36)
The rotation matrix is given by:
the relative angular velocity can be expressed as follows:
ω e ＝ω-Cω d (38)
the attitude error kinematics and dynamics equations can be expressed as follows:
the following sliding mode variables are defined:
s＝ω e +βq e (42)
where β > 0, the kinetic equation can be rewritten as:
and is also provided with
Under the premise of considering external interference and gravity interference, the following conclusion is drawn:
1) Presence of unknown positive constant c J > 0 and c f > 0 makes J (·) c +. J < infinity, andestablishment;
2) External disturbance moment T d (. Cndot.) satisfy T d (·)≤c g +c d ||ω|| 2 Wherein c g ≥0,c d 0 is not less than constant;
3)、ω d ,q d ,are all bounded and have the following formulas:
wherein c ω 0 is not less than constant; due toI C i=1, the conclusion 3) above is thus true;
4)、wherein c 0 0 is not less than constant;
for gravity disturbance moment term r in delta (·) off ×m a g b Before the platform is leveled, the platform is usually leveled manually, and r off Typically in minor amounts; thus, r can be derived off ≤c r ，c r 0 is constant, further, m a And I g b The I is constant; at the same time, the following conclusion 5) can also prove to be true;
5)、||r off ×m a g b ||≤c g wherein c g 0 is not less than constant;
from the above conclusion, it can be seen that the following formula is ensured to be established despite the fact that the delta (-) contains a nonlinear term, an uncertain term and a time-varying term
||Δ(·)||≤b 0 +b 1 ||ω||+b 2 ||ω|| 2 ≤bΦ (46)
Φ＝1+||ω||+||ω|| 2 (47)
The moments of the displacement of the adjusting mass along the three principal axes of inertia are expressed as follows:
wherein m is m Is the mass of the mass block, r i I=1, 2,3 is the position of the i-th slider with respect to the rotation center, that is, the control amount to be designed;
the control torque of the dynamic system as described by the formula is as follows:
under the control moment, the platform leveling closed-loop system is globally stable, and the system state tracking error is bounded, namely ||q e ||≤ε 1 ，||ω e ||≤ε 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein k is 0 ＞0，μ＞0，σ 1 ＞0，σ 2 > 0 is the controller parameter to be designed;
the following Lyapunov function is selected:
due toSubstituting the formula and deriving V can result in:
further, the method comprises the steps of,
substituting the controller described by the formula into the formula:
wherein,
substituting the formula into:
order theThen when s and q e When outside the following collection->
According to the formula, the values in s and q e When bounded, omega e Is also bounded;
in order to obtain the actual control quantity, the control moment tau is required to be controlled c Transforming into r;
from the formula
τ c ＝m m (-g b (t)×r) (58)
Since the main diagonal elements of the cross-multiplied matrix are constant at zero, the matrixSingular;
the solution given for r is as follows:
the output r of the automatic leveling method of the triaxial air-bearing satellite simulation platform is given by the above formula.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011240519.9A CN112327942B (en) | 2020-11-09 | 2020-11-09 | Automatic leveling method for triaxial air-bearing satellite simulation platform |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011240519.9A CN112327942B (en) | 2020-11-09 | 2020-11-09 | Automatic leveling method for triaxial air-bearing satellite simulation platform |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112327942A CN112327942A (en) | 2021-02-05 |
| CN112327942B true CN112327942B (en) | 2023-10-17 |
Family
ID=74317025
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011240519.9A Active CN112327942B (en) | 2020-11-09 | 2020-11-09 | Automatic leveling method for triaxial air-bearing satellite simulation platform |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112327942B (en) |
Families Citing this family (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113608244B (en) * | 2021-07-27 | 2023-12-29 | 中国科学院微小卫星创新研究院 | Space gravitational wave detection satellite constellation ground demonstration verification system |
| CN114323519B (en) * | 2021-12-22 | 2023-10-13 | 上海卫星装备研究所 | Method and system for simulating quality characteristics of single satellite simulator for microsatellite structure test |
| CN115290254B (en) * | 2022-10-09 | 2023-02-03 | 中国西安卫星测控中心 | On-orbit identification method for rotational inertia of combined spacecraft |
| CN115793498A (en) * | 2023-02-06 | 2023-03-14 | 湖南揽月机电科技有限公司 | Leveling device of three-degree-of-freedom semi-physical simulation system and working method thereof |
| CN115793499B (en) * | 2023-02-06 | 2023-06-20 | 湖南揽月机电科技有限公司 | Three-degree-of-freedom semi-physical simulation system and working method thereof |
| CN116923738B (en) * | 2023-08-18 | 2024-04-05 | 哈尔滨工业大学 | Digital intelligent adjusting device and method for quality characteristics of satellite attitude control full-physical simulation platform |
| CN118502269B (en) * | 2024-07-16 | 2024-11-05 | 湖南揽月机电科技有限公司 | Target tracking control method for air flotation platform |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103868648A (en) * | 2014-04-01 | 2014-06-18 | 哈尔滨工业大学 | Barycenter measuring method for three-axis air floatation simulation experiment platform |
| CN103869833A (en) * | 2014-04-01 | 2014-06-18 | 哈尔滨工业大学 | Method for adjusting mass center of three-axis air bearing table based on non-orthogonal structure |
| CN104806861A (en) * | 2015-04-24 | 2015-07-29 | 哈尔滨工业大学 | Leveling method for multi-shaft support air-floating platform based on capacitive sensors |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103292127B (en) * | 2013-05-20 | 2014-12-10 | 哈尔滨工业大学 | Measurement control system of multi-shaft support air floatation platform |
-
2020
- 2020-11-09 CN CN202011240519.9A patent/CN112327942B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103868648A (en) * | 2014-04-01 | 2014-06-18 | 哈尔滨工业大学 | Barycenter measuring method for three-axis air floatation simulation experiment platform |
| CN103869833A (en) * | 2014-04-01 | 2014-06-18 | 哈尔滨工业大学 | Method for adjusting mass center of three-axis air bearing table based on non-orthogonal structure |
| CN104806861A (en) * | 2015-04-24 | 2015-07-29 | 哈尔滨工业大学 | Leveling method for multi-shaft support air-floating platform based on capacitive sensors |
Non-Patent Citations (4)
| Title |
|---|
| 三轴气浮台重力梯度引起的不平衡力矩分析;李延斌等;《机床与液压》;20170115(第01期);第146-147页 * |
| 三轴气浮平台自动调平衡方法;向东等;《大连海事大学学报》;20080815(第03期);第27-30页 * |
| 多体卫星物理仿真动态调平衡干扰力矩分析;陈欢龙 等;《计算机仿真》;20101015;第66-70页 * |
| 大型三轴气浮台转动惯量和干扰力矩高精度联合辨识技术;洪振强等;《航天器环境工程》;20170215(第01期);第32-38页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112327942A (en) | 2021-02-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112327942B (en) | Automatic leveling method for triaxial air-bearing satellite simulation platform | |
| CN111099045B (en) | Full physical simulation method for double super satellite dynamics and control air floatation platform | |
| Fang et al. | Attitude sensing and dynamic decoupling based on active magnetic bearing of MSDGCMG | |
| Kim et al. | Automatic mass balancing of air-bearing-based three-axis rotational spacecraft simulator | |
| CN104570742B (en) | Feedforward PID (proportion, integration and differentiation) control based rapid high-precision relative pointing control method of noncoplanar rendezvous orbit | |
| Chen et al. | Spacecraft angular rates and angular acceleration estimation using single-gimbal magnetically suspended control moment gyros | |
| Hamel et al. | Visual servo trajectory tracking for a four rotor VTOL aerial vehicle | |
| CN108803639A (en) | A kind of quadrotor flight control method based on Backstepping | |
| CN107505846B (en) | A kind of anti-interference attitude harmony verification device of Space Manipulator System and control method | |
| CN110162855B (en) | Dynamic precision analysis and error distribution method for satellite rotation load of remote sensing satellite | |
| CN109212976B (en) | Input-limited small celestial body soft landing robust trajectory tracking control method | |
| Zhou et al. | A high precision compound control scheme based on non-singular terminal sliding mode and extended state observer for an aerial inertially stabilized platform | |
| CN103868648A (en) | Barycenter measuring method for three-axis air floatation simulation experiment platform | |
| CN110823448B (en) | Method for measuring axial mass center of rotor assembly of gyroscope with two degrees of freedom | |
| Wu et al. | Sliding-mode control for staring-mode spacecraft using a disturbance observer | |
| CN110068336A (en) | A kind of angular movement measurement method based on magnetic suspension control sensitivity gyro parallel configuration | |
| Keim et al. | Spacecraft inertia estimation via constrained least squares | |
| CN111947684B (en) | Inertial platform swinging dynamic precision testing method based on gravity vector measurement | |
| Guo et al. | Integrated vibration isolation and attitude control for spacecraft with uncertain or unknown payload inertia parameters | |
| Liu et al. | Automatic mass balancing of a spacecraft simulator based on non-orthogonal structure | |
| Li et al. | A Nonlinear Trajectory Tracking Control Strategy for Quadrotor With Suspended Payload Based on Force Sensor | |
| CN112987592A (en) | Dynamic leveling system and dynamic leveling method in control process of three-axis air bearing table | |
| CN111546344A (en) | Mechanical arm control method for alignment | |
| Bryła et al. | Compact and lightweight 3D printed platform for testing attitude determination and control system of small satellites | |
| CN116520719A (en) | Method and system suitable for full physical simulation of attitude dynamics of flexible spacecraft |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |