CN114756041A - Maneuvering path design method for magnetic suspension universal maneuvering satellite platform - Google Patents
Maneuvering path design method for magnetic suspension universal maneuvering satellite platform Download PDFInfo
- Publication number
- CN114756041A CN114756041A CN202210415476.6A CN202210415476A CN114756041A CN 114756041 A CN114756041 A CN 114756041A CN 202210415476 A CN202210415476 A CN 202210415476A CN 114756041 A CN114756041 A CN 114756041A
- Authority
- CN
- China
- Prior art keywords
- maneuvering
- axis
- deflection
- load
- cabin
- 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.)
- Granted
Links
- 239000000725 suspension Substances 0.000 title claims abstract description 30
- 238000000034 method Methods 0.000 title claims abstract description 25
- 238000013016 damping Methods 0.000 claims abstract description 18
- 230000001133 acceleration Effects 0.000 claims description 9
- 239000002775 capsule Substances 0.000 claims description 3
- 230000005284 excitation Effects 0.000 claims description 3
- 238000005339 levitation Methods 0.000 claims description 3
- 239000004576 sand Substances 0.000 claims description 3
- 238000005094 computer simulation Methods 0.000 claims 1
- 238000004088 simulation Methods 0.000 description 9
- 238000010586 diagram Methods 0.000 description 5
- 238000006073 displacement reaction Methods 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 230000003287 optical effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
- G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
- G05D1/0833—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using limited authority control
Landscapes
- Engineering & Computer Science (AREA)
- Computer Security & Cryptography (AREA)
- Aviation & Aerospace Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
The invention relates to a maneuvering path design method for a magnetic suspension universal maneuvering satellite platform. The invention establishes a Lorentz force magnetic bearing deflection dynamic model of an on-orbit platform cabin-load cabin based on the rigidity damping characteristic of the Lorentz force magnetic bearing. On the basis, a maneuvering path design method for the magnetic suspension universal maneuvering satellite platform is designed based on a frequency characteristic analysis principle, and a maneuvering path is reasonably determined according to the magnetic bearing rigidity damping and the controller parameters, so that the vibration of a load cabin caused by maneuvering of the platform cabin is reduced as much as possible. The invention belongs to the technical field of novel satellite platform attitude control, and can be applied to an attitude maneuver control system of a magnetic suspension universal maneuvering satellite platform.
Description
Technical Field
The invention relates to a maneuvering path design method for a magnetic suspension universal maneuvering satellite platform, which is suitable for an attitude control system of the magnetic suspension universal maneuvering satellite platform.
Technical Field
The magnetic suspension universal mobile satellite platform is a novel satellite platform, because the satellite platform cabin and the load cabin are isolated by the magnetic suspension technology, the satellite platform cabin and the load cabin can not be contacted, and the vibration received by the satellite platform and the vibration generated by the satellite platform can not be transmitted to the load, thereby providing a very stable and ultra-static working environment for the load. The maneuvering control of the load is realized through the magnetic suspension technology, the attitude maneuvering of the whole satellite is avoided, the load cabin is directly driven and controlled through the Lorentz force magnetic bearing, and the high-precision high-dynamic pointing control can be realized.
When the magnetic suspension universal maneuvering satellite platform performs large-angle maneuvering, the platform cabin and the load cabin are connected by adopting the magnetic bearing, the rigidity of the platform cabin is limited, the problem of vibration of the load cabin can be caused, and the stability of the attitude of the satellite platform and the accurate pointing of the load cabin are not facilitated.
The method is based on dynamics simulation and combines the mechanical characteristics of the Lorentz force magnetic bearing to establish a Lorentz force magnetic bearing deflection dynamics model of an on-orbit platform cabin-load cabin; on the basis, a maneuvering path design method for the magnetic suspension universal maneuvering satellite platform is designed based on a frequency characteristic analysis principle, and a maneuvering path is reasonably determined according to the rigidity damping of the magnetic bearing and the parameters of the controller, so that the aim of reducing the vibration of a load cabin caused by maneuvering of the platform cabin is fulfilled as far as possible.
Disclosure of Invention
The invention solves the technical problems that: a maneuvering path design method for a magnetic suspension universal maneuvering satellite platform is provided for the problem that the large-angle maneuvering of the magnetic suspension universal maneuvering satellite platform causes the vibration of a load cabin. The method reasonably determines the maneuvering path by analyzing the stiffness damping characteristic of the magnetic bearing and the parameters of the controller, thereby achieving the purpose of reducing the vibration of the load cabin caused by maneuvering of the platform cabin as much as possible.
The method specifically comprises the following steps:
(1) on-orbit platform cabin-load cabin Lorentz force magnetic bearing deflection dynamic model
The magnetic suspension universal mobile satellite platform consists of a platform cabin and a load cabin, wherein the load cabin mainly consists of a magnetic suspension pod and a payload (an optical tracking or directional energy weapon); the radial magnetic bearing controls the radial two-degree-of-freedom suspension of the magnetic suspension nacelle, the axial magnetic bearing controls the axial suspension of the magnetic suspension nacelle, the deflection magnetic bearing controls the two-degree-of-freedom deflection of the magnetic suspension nacelle, and the Lorentz force magnetic bearing is used as a research object because the spacecraft platform mainly relates to two rotational degrees of freedom when performing attitude maneuver; the spacecraft body system is OXYZ, the inertia system is OXYZ, and the corresponding coordinate axes at the initial moment are parallel.
When the magnetic levitation load compartment deflects around the x-axis and the y-axis, the control torque generated by the maneuvering process can be expressed as:
wherein T isαControlling the torque, T, for the x axisβControlling the moment for the y-axis, alpha being the deflection angle of the load compartment about the x-axis, beta being the deflection angle of the load compartment about the y-axis, JxIs the radial moment of inertia of the load compartment;
since the manoeuvre of the load compartment is controlled by the deflecting lorentz force magnetic bearing, the control moment generated by the deflecting lorentz force magnetic bearing can be expressed as:
wherein N represents the number of turns of the coil, B represents the intensity of the magnetic field, phi is the central angle corresponding to each group of coils of the Lorentz force magnetic bearing, and LrRadius of the stator skeleton of the Lorentz force magnetic bearing, IxFor controlling the current in the x-axis direction, IyFor controlling the current in the y-axis direction, equations (1) and (2) can be obtained simultaneously:
according to the formula (3), the Lorentz force magnetic bearing controls two degrees of freedom of the magnetic suspension load cabin to be mutually decoupled;
(2) determining stiffness damping characteristics of load capsule Lorentz force magnetic bearing deflection system
When only the load cabin deflects, aiming at the deflection freedom degree of the load cabin around the x axis, the load cabin adopts state feedback control, and the feedback control signal adopts:
wherein k is1And k2For the state feedback parameter, the dynamic equation of the freedom of deflection of the load compartment around the x-axis can be expressed as:
The system stiffness that yields the freedom to deflect around the x-axis is:
the system damping of the load compartment for the degree of freedom of deflection about the x-axis is:
the system damping ratio of the deflection freedom degree of the load cabin around the x axis can be obtained as follows:
the system undamped natural frequency of the freedom of deflection of the load compartment around the x-axis is as follows:
the system for obtaining the deflection freedom degree of the load cabin around the x axis has the damping natural frequency as follows:
due to the symmetrical characteristic of the parameters, the relevant parameters of the deflection freedom degree of the load cabin around the y axis are the same as the deflection freedom degree around the x axis;
(3) determining a maneuver path with minimum excitation amplitude
When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin following and simultaneously carry out deflection control, the coil current comprises two parts, namely deflection current IsAnd a motive current ImThus, the system of freedom for the yaw of the payload bay about the X-axis under the inertial system can be expressed as:
wherein theta is the deflection angle of the load cabin around the X axis under the inertial system,
equation (14) can be expressed as:
the following can be obtained:
designing a maneuvering angular acceleration instruction of a spacecraft platform cabin to be sine type:
wherein
The maneuvering angular acceleration of the platform cabin under the inertial system is represented, and when the command frequency is equal to the resonance frequency of the load cabin, the system resonates, namely:
The total maneuvering attitude angle is set to be omega, and the total maneuvering attitude angle is formed by (17):
the amplitude-frequency characteristic of the system is:
the maximum maneuvering angular speed of the spacecraft platform is
To avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible, and as can be seen from equation (20), when the satellite just resonates at the maximum maneuvering angular velocity, there are:
through simulation verification, in order to avoid resonance as much as possible, the maneuvering strategy can be given by:
wherein
2. To ensure the maneuvering speed, the system should be under-damped or critically damped, i.e.:
the following can be obtained:
to take into account both maneuvering speed and accuracy, λ should be as far away from 1 as possible,
should be as close to 1 as possible, and the simulation shows that lambda,
When the following conditions are met, the maneuvering speed and the precision can be simultaneously met:
then k is1And k2Can be determined by the following method:
the relevant parameters for the freedom of deflection of the load about the Y-axis are the same as the freedom of deflection about the X-axis.
Compared with the prior art, the scheme of the invention has the main advantages that: the rigidity and damping characteristics of a magnetic bearing are not considered when the conventional magnetic suspension universal satellite platform is maneuvering, vibration of a load cabin is easily caused in the maneuvering process, and the application of an effective load is not facilitated. According to the invention, by designing the maneuvering path for the magnetic suspension universal maneuvering satellite platform, the maneuvering angular velocity path can be reasonably determined according to the maximum maneuvering capacity of the spacecraft platform cabin under the condition of determining the parameters of the controller, so that the maneuvering rapidity and stability of the loading cabin are ensured.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a magnetic levitation universal satellite platform structure and coordinate system;
FIG. 3 is a simulation diagram of x-axis angular displacement of a load compartment in a conventional maneuvering method;
FIG. 4 is a simulation diagram of the x-axis angular displacement of the lower load compartment of the system according to the embodiment of the present invention;
detailed description of the preferred embodiments
The implementation object of the invention is a magnetic suspension universal mobile satellite platform, the specific implementation scheme is shown in figure 1, and the specific implementation steps are as follows:
when the magnetic suspension load compartment deflects around the x-axis and the y-axis, the control torque generated by the maneuvering process can be expressed as:
wherein T isαControlling the torque, T, for the x axisβControlling the moment for the y-axis, alpha being the deflection angle of the load compartment about the x-axis, beta being the deflection angle of the load compartment about the y-axis, JxIs the radial moment of inertia of the load compartment;
since the manoeuvre of the load compartment is controlled by the deflecting lorentz force magnetic bearing, the control moment generated by the deflecting lorentz force magnetic bearing can be expressed as:
wherein N represents the number of turns of the coil, B represents the intensity of the magnetic field, phi is the central angle corresponding to each group of coils of the Lorentz force magnetic bearing, and LrRadius of the stator skeleton of the Lorentz force magnetic bearing, IxFor controlling the current in the x-axis direction, IyFor controlling the current in the y-axis direction, equations (1) and (2) can be obtained simultaneously:
According to the formula (3), two degrees of freedom of the magnetic suspension load cabin controlled by the Lorentz force magnetic bearing are mutually decoupled;
(2) determining stiffness damping characteristics of load capsule Lorentz force magnetic bearing deflection system
When only the load cabin deflects, aiming at the degree of freedom of the load cabin deflecting around the x axis, the load cabin adopts state feedback control, and the feedback control signal adopts:
wherein k is1And k2For the state feedback parameter, the dynamic equation of the freedom of the load cabin deflection around the x axis can be expressed as follows:
the system stiffness that can be obtained for the freedom of deflection about the x-axis is:
the system damping of the load compartment for the degree of freedom of deflection about the x-axis is:
the system damping ratio of the deflection freedom of the load compartment around the x-axis can be obtained as follows:
the system undamped natural frequency of the freedom of deflection of the load compartment around the x-axis is as follows:
the system for obtaining the deflection freedom degree of the load cabin around the x axis has the damping natural frequency as follows:
due to the symmetrical characteristic of the parameters, the relevant parameters of the deflection freedom degree of the load cabin around the y axis are the same as the deflection freedom degree around the x axis;
(3) determining a maneuver path having a minimum excitation amplitude
When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin following and simultaneously carry out deflection control, the coil current comprises two parts, namely deflection current I sAnd a maneuvering current ImThus, the system of freedom of yaw of the payload bay about the X-axis under the inertial system can be expressed as:
wherein theta is the deflection angle of the load compartment around the X axis under the inertial system,
equation (14) can be expressed as:
the following can be obtained:
designing a maneuvering angular acceleration instruction of a spacecraft platform cabin to be sine type:
wherein
The maneuvering angular acceleration of the platform cabin under the inertial system is represented, and when the command frequency is equal to the resonance frequency of the load cabin, the system resonates, namely:
the total maneuvering attitude angle is set to be omega, and the total maneuvering attitude angle is formed by the following components (17):
the amplitude-frequency characteristic of the system is:
the maximum maneuvering angular speed of the spacecraft platform is
To avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible, and as can be seen from equation (20), when the satellite just resonates at the maximum maneuvering angular velocity, there are:
through simulation verification, in order to avoid resonance as much as possible, the maneuvering strategy can be given by:
wherein
2. To ensure the maneuvering speed, the system should be under-damped or critically damped, i.e.:
the following can be obtained:
to take into account both maneuvering speed and accuracy, λ should be as far away from 1 as possible,
should be as close to 1 as possible, and the simulation shows that lambda,
When the following conditions are met, the maneuvering speed and the precision can be simultaneously met:
then k is1And k 2Can be determined by the following method:
the relevant parameters for the freedom of deflection of the load about the Y-axis are the same as the freedom of deflection about the X-axis.
Under the system, a simulation diagram of the x-axis angular displacement of the load cabin without the maneuvering path design method is shown in fig. 3, and a simulation diagram of the x-axis angular displacement of the load cabin adopting the maneuvering path design method is shown in fig. 4, so that the maneuvering path design method has better attitude stability and maneuvering speed.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (2)
1. A maneuvering path design method for a magnetic suspension universal maneuvering satellite platform is characterized by comprising the following steps: based on dynamic simulation and combined with the mechanical characteristics of the Lorentz force magnetic bearing, a Lorentz force magnetic bearing deflection dynamic model of the on-orbit platform cabin-load cabin is established; on the basis, a maneuvering path design method for a magnetic suspension universal maneuvering satellite platform is designed based on a frequency characteristic analysis principle, and a maneuvering path is reasonably determined according to the rigidity damping of a magnetic bearing and controller parameters, so that the vibration of a load cabin caused by maneuvering of the platform cabin is reduced as much as possible, and the method specifically comprises the following steps:
(1) On-orbit platform cabin-load cabin Lorentz force magnetic bearing deflection dynamic model
When the magnetic levitation load compartment deflects around the x-axis and the y-axis, the control torque generated by the maneuvering process can be expressed as:
wherein T isαControlling the torque, T, for the x axisβControlling the moment for the y-axis, alpha being the deflection angle of the load compartment about the x-axis, beta being the deflection angle of the load compartment about the y-axis, JxIs the radial moment of inertia of the load compartment;
since the manoeuvre of the load compartment is controlled by the deflecting lorentz force magnetic bearing, the control moment generated by the deflecting lorentz force magnetic bearing can be expressed as:
wherein N represents the number of turns of the coil, B represents the intensity of the magnetic field, phi is the central angle corresponding to each group of coils of the Lorentz force magnetic bearing, and LrRadius of the stator skeleton of the Lorentz force magnetic bearing, IxIn the x-axis directionControl current, IyFor controlling the current in the y-axis direction, equations (1) and (2) can be obtained simultaneously:
according to the formula (3), the Lorentz force magnetic bearing controls two degrees of freedom of the magnetic suspension load cabin to be mutually decoupled;
(2) determining stiffness damping characteristics of load capsule Lorentz force magnetic bearing deflection system
When only the load cabin deflects, aiming at the deflection freedom degree of the load cabin around the x axis, the load cabin adopts state feedback control, and the feedback control signal adopts:
Wherein k is1And k2For the state feedback parameter, the dynamic equation of the freedom of deflection of the load compartment around the x-axis can be expressed as:
the system stiffness that can be obtained for the freedom of deflection about the x-axis is:
the system damping of the load compartment for the degree of freedom of deflection about the x-axis is:
the system damping ratio of the deflection freedom of the load compartment around the x-axis can be obtained as follows:
the system undamped natural frequency of the freedom of deflection of the load compartment around the x-axis is as follows:
the system for obtaining the deflection freedom degree of the load cabin around the x axis has the damping natural frequency as follows:
due to the symmetrical characteristic of the parameters, the relevant parameters of the deflection freedom degree of the load cabin around the y axis are the same as the deflection freedom degree around the x axis;
(3) determining a maneuver path with minimum excitation amplitude
When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin following and simultaneously carry out deflection control, the coil current comprises two parts, namely deflection current IsAnd a motive current ImThus, the system of freedom for the yaw of the payload bay about the X-axis under the inertial system can be expressed as:
wherein theta is the deflection angle of the load cabin around the X axis under the inertial system,
equation (11) can be expressed as:
the following can be obtained:
designing a maneuvering angular acceleration path of a spacecraft platform cabin to be sinusoidal:
wherein
Representing the maneuvering angular acceleration under the inertial system of the platform cabin, and when the command frequency is equal to the resonance frequency of the load cabin, the system resonates, namely:
The total maneuvering attitude angle is set to be omega, and the total maneuvering attitude angle is formed by (14):
the amplitude-frequency characteristic of the system is:
the maximum maneuvering angular speed of the spacecraft platform is
To avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible, and the maneuvering strategy can be given by:
wherein
The relevant parameters for the freedom of deflection of the load about the Y-axis are the same as the freedom of deflection about the X-axis.
2. For the feedback parameter k in claim 11And k2The determination can be made by the following method:
to ensure the maneuvering speed, the system + system should be under-damped or critically damped, i.e.:
the following can be obtained:
to take into account both maneuvering speed and accuracy, λ should be as far away from 1 as possible,
should be as close to 1 as possible, then k1And k2Can be determined by the following method:
namely:
the relevant parameters for the freedom of deflection of the load about the Y-axis are the same as the freedom of deflection about the X-axis.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210415476.6A CN114756041B (en) | 2022-04-18 | 2022-04-18 | Maneuvering path design method for magnetic suspension universal maneuvering satellite platform |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210415476.6A CN114756041B (en) | 2022-04-18 | 2022-04-18 | Maneuvering path design method for magnetic suspension universal maneuvering satellite platform |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114756041A true CN114756041A (en) | 2022-07-15 |
| CN114756041B CN114756041B (en) | 2024-09-20 |
Family
ID=82331271
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210415476.6A Active CN114756041B (en) | 2022-04-18 | 2022-04-18 | Maneuvering path design method for magnetic suspension universal maneuvering satellite platform |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114756041B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117585195A (en) * | 2024-01-19 | 2024-02-23 | 中国人民解放军战略支援部队航天工程大学 | Fusion attitude measurement and control method and system of magnetic levitation satellite platform |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102303709A (en) * | 2011-08-31 | 2012-01-04 | 北京航空航天大学 | Large-torque magnetic suspension flywheel |
| CN104201935A (en) * | 2014-08-06 | 2014-12-10 | 北京航空航天大学 | Four-degrees-of-freedom magnetic suspension flywheel |
| CN111832127A (en) * | 2020-06-22 | 2020-10-27 | 北京控制工程研究所 | Lorentz force radial magnetic bearing design method |
| WO2022041298A1 (en) * | 2020-08-24 | 2022-03-03 | 北京航空航天大学宁波创新研究院 | Magnetic suspension rotor system, and extremely-small vibration control method and control apparatus therefor |
-
2022
- 2022-04-18 CN CN202210415476.6A patent/CN114756041B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102303709A (en) * | 2011-08-31 | 2012-01-04 | 北京航空航天大学 | Large-torque magnetic suspension flywheel |
| CN104201935A (en) * | 2014-08-06 | 2014-12-10 | 北京航空航天大学 | Four-degrees-of-freedom magnetic suspension flywheel |
| CN111832127A (en) * | 2020-06-22 | 2020-10-27 | 北京控制工程研究所 | Lorentz force radial magnetic bearing design method |
| WO2022041298A1 (en) * | 2020-08-24 | 2022-03-03 | 北京航空航天大学宁波创新研究院 | Magnetic suspension rotor system, and extremely-small vibration control method and control apparatus therefor |
Non-Patent Citations (3)
| Title |
|---|
| YUAN REN: "《Attitude-Rate Measurement and Control Integration Using Magnetically Suspended Control and Sensitive Gyroscopes》", 《IEEE》, 30 June 2018 (2018-06-30), pages 1 - 12 * |
| 刘强;赵勇;曹建树;任元: "新型微框架磁悬浮飞轮用洛伦兹力磁轴承", 宇航学报, vol. 38, no. 5, 30 May 2017 (2017-05-30) * |
| 王俊: "扰动隔离载荷与卫星平台一体化控制方法研究", 《哈尔滨工业大学硕士论文》, 1 June 2016 (2016-06-01) * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117585195A (en) * | 2024-01-19 | 2024-02-23 | 中国人民解放军战略支援部队航天工程大学 | Fusion attitude measurement and control method and system of magnetic levitation satellite platform |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114756041B (en) | 2024-09-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Kim et al. | Automatic mass balancing of air-bearing-based three-axis rotational spacecraft simulator | |
| CN109388906B (en) | Modeling method of flexible spacecraft dynamics model based on magnetic suspension bearing | |
| CN108897239B (en) | Spacecraft two-stage attitude control simulation system | |
| US20080228332A1 (en) | Active control of soft hybrid isolation systems | |
| Zhang et al. | Vibration control for rapid attitude stabilization of spacecraft | |
| US6463365B1 (en) | System and method for controlling the attitude of a space craft | |
| Fang et al. | Adaptive backstepping control of an indoor micro-quadrotor | |
| CN109085753A (en) | A kind of magnetic suspension control sensitivity gyro group pseudoinverse manipulation rule based on self-adaptation nonlinear weighting matrix | |
| Chen et al. | Spacecraft vibration control based on extended modal decoupling of Vernier-gimballing magnetically suspension flywheels | |
| CN114756041A (en) | Maneuvering path design method for magnetic suspension universal maneuvering satellite platform | |
| US11548626B2 (en) | Tuned mass damper for aircraft | |
| Saif | Feedback linearization control of quadrotor with tiltable rotors under wind gusts | |
| CN114322971B (en) | Magnetic suspension rotor same-frequency vibration force suppression method based on biquad generalized integrator | |
| Brown et al. | Energetics of control moment gyroscopes as joint actuators | |
| CN114527648B (en) | Rapid maneuvering control method for complex pico-nano satellite | |
| JPH09240599A (en) | Rocket control method by adjustment of thrust of engine | |
| CN114756039A (en) | Multi-body coupling attitude control method and system based on zero force control | |
| CN111306995B (en) | Method for designing combined controller for suppressing projectile flutter | |
| Guo et al. | Integrated power, attitude, and vibration control of gyroelastic body | |
| RU2474517C2 (en) | Method of killing elastic vibrations of clustered rocket body | |
| CN114527653B (en) | Double-cabin continuous maneuvering path planning optimization method based on double super platforms | |
| JPH11129997A (en) | Attitude control device of artificial satellite | |
| CN113568424B (en) | Space robot pose integrated control method for active rope winding | |
| Chen et al. | Analysis of parameter perturbation characteristics of gyrowheel | |
| CN118462602A (en) | Micro-vibration pump row control method based on two-stage magnetic suspension super-platform |
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 |