CN108536164B - Attitude control method for flexible spacecraft non-angular velocity measurement - Google Patents

Attitude control method for flexible spacecraft non-angular velocity measurement Download PDF

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CN108536164B
CN108536164B CN201810255133.1A CN201810255133A CN108536164B CN 108536164 B CN108536164 B CN 108536164B CN 201810255133 A CN201810255133 A CN 201810255133A CN 108536164 B CN108536164 B CN 108536164B
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matrix
attitude
flexible
angular velocity
spacecraft
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CN108536164A (en
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张颖
丁清澍
吴爱国
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Shenzhen Graduate School Harbin Institute of Technology
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Shenzhen Graduate School Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • 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
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models

Abstract

The invention provides an attitude control method for measuring the angular velocity of a flexible spacecraft, which adopts a modified Rodrigues parameter to describe the attitude of the flexible spacecraft, establishes a kinematic equation based on the modified Rodrigues parameter, and establishes an attitude dynamics equation for the flexible spacecraft with a rigid central body and a flexible attachment by adopting a mixed coordinate method. Aiming at a posture control system model of the flexible spacecraft described by a modified Rodrigues parameter, a passive filter is introduced to replace angular velocity information, so that a posture control law without angular velocity measurement based on state feedback is designed. The method solves the problem that the flexible spacecraft can realize the stable control of the attitude of the spacecraft only by needing real-time measurement data of the angular velocity sensor in the flying process, and completes the high-robustness control of the flexible spacecraft. Simulation experiments prove that the attitude control method without angular velocity measurement has good robustness.

Description

Attitude control method for flexible spacecraft non-angular velocity measurement
Technical Field
The invention relates to the technical field of spacecraft control, in particular to an attitude control method for flexible spacecraft angular velocity-free measurement.
Background
The attitude controller designed by the traditional research needs measurement data of an angular velocity sensor, is expensive and prone to failure, influences the application of an actual spacecraft control system, and cannot guarantee excellent robustness.
Disclosure of Invention
Aiming at the defects or shortcomings in the prior art, the invention provides an attitude control method for measuring the angular velocity of a flexible spacecraft, wherein an attitude control law of asymptotically stable state feedback constructed based on a feedback linearization method is designed on the basis of a modified Rodrigues parameter system model under the condition that a flexible modal variable can be measured, and the use of an angular velocity sensor in an actual control system can be avoided.
In order to achieve the purpose, the invention adopts the technical scheme that:
an attitude control method for measuring the angular velocity of a flexible spacecraft comprises the following steps: s1, establishing a kinematic equation and a kinetic equation of the modified Rodrigues parameter system model; s2, selecting a filter; and S3, designing an attitude control law based on a passive method.
The invention has the beneficial effects that: the attitude controller of the flexible spacecraft, which is designed by adopting the method of the invention, can still ensure to stably control the attitude of the spacecraft under the condition of not using an angular velocity sensor, has good robustness, and when a spacecraft control system is in operation, the attitude of the spacecraft can quickly tend to be stable.
Drawings
FIG. 1 is a simulink model block diagram of an attitude control method for flexible spacecraft non-angular velocity measurement.
Detailed Description
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
The invention designs an attitude control law of asymptotically stable state feedback based on a feedback linearization method under the assumption that the modal variables eta and psi of the flexible spacecraft can be measured.
Step 1 establishes a kinematic equation and a kinetic equation
The posture of the flexible spacecraft is respectively described by adopting modified Rodrigues parameters, and a kinematic equation and a kinetic equation of a flexible spacecraft control system model based on the posture are respectively shown as follows:
the attitude of the flexible spacecraft is described by adopting a modified Rodrigues parameter, and the kinematic equation of the flexible spacecraft based on the attitude is as follows:
Figure BDA0001606637450000021
where ω is the attitude angular velocity of the spacecraft, and G (σ) is represented by the following equation:
Figure BDA0001606637450000022
and σ is modified RodriThe vector of the parameters of the gues,
Figure BDA0001606637450000023
its derivative, its antisymmetric matrix is:
Figure BDA0001606637450000024
kinetic equations for the modified Rodrigues parametric system model:
Figure BDA0001606637450000025
where S (ω) is the antisymmetric matrix of ω, i.e.
Figure BDA0001606637450000026
Jmb＝J-δTDelta is expressed as a matrix of the body inertia,
Figure BDA0001606637450000027
is the total velocity of the flexible attachment, ω represents the attitude angular velocity of the flexible spacecraft; u represents a control torque; delta is expressed as a coupling action matrix between rigid body dynamics and flexible dynamics; c, K are respectively expressed as a damping matrix and a rigidity matrix,
C＝diag{2ξiωni，i＝1，...，N}
Figure BDA0001606637450000028
in the invention, N elastic modes are considered, and the corresponding natural angular frequency is omeganiI is 1, 2, …, N, corresponding to a damping ratio of
Figure BDA0001606637450000029
i＝1，2，…，N。
Step2 selection filter
To replace the measurement of angular velocity, the following filter function is now chosen:
Figure BDA0001606637450000031
where z is a passive filter associated with the modified Rodrigues parameter, which is used instead of feedback of angular velocity. Cv(s) is a three-dimensional linear time invariant, strictly regular and strictly regular transition matrix.
And (3) proving that: consider CvAn arbitrary minimum realization of(s) is as follows:
Figure BDA0001606637450000032
according to the Kalman-Yakubovich-PopV theorem, the following positive matrix P exists1And Q1Satisfies the following relation:
P1A1+A1 TP1＝-Q1，P1B1＝C1 T
note: the above angular velocity-free measurement is achieved by using z ═ sCv(s) σ because of Cv(s) is strictly canonical, so sCv(s) is canonical and realizable from output z to input
Figure BDA0001606637450000033
Is passive.
Step3 design attitude control law based on passive method
The following state feedback control laws are designed:
Figure BDA0001606637450000034
wherein the content of the first and second substances,
Figure BDA0001606637450000035
under the action of a state feedback control law (8), the flexible spacecraft control system adopting the modified Rodrigues parameter to describe the attitude can realize attitude control without angular velocity measurement and keep the stable operation of the spacecraft attitude.
The system selects the following Lyapunov function V as:
Figure BDA0001606637450000036
wherein the positive definite symmetric matrix P satisfies the following lyapunov equation corresponding to the positive definite matrix Q:
Figure BDA0001606637450000037
in the formula, I is expressed as an identity matrix of a suitable dimension.
Finally, it is proved by theoretical derivation
Figure BDA0001606637450000041
According to the LaSalle invariant set principle, the method comprises the following steps: under the attitude control law based on state feedback, the closed-loop system can be ensured to be gradually stable.
The simulation experiment shown in fig. 1 is performed to verify the attitude control method for measuring the angular velocity of the flexible spacecraft of the invention, and the attitude control law based on state feedback provided by a modified Rodrigues parameter system model when the modal variables are measurable is verified.
Main body inertia matrix J of flexible spacecraftmbComprises the following steps:
Figure BDA0001606637450000042
the coupling action matrix delta of the rigid part and the flexible part of the spacecraft is as follows:
Figure BDA0001606637450000043
the natural angular frequencies of the three modal variables of the flexible spacecraft are:
Figure BDA0001606637450000044
the damping coefficient of the flexible attachment of the spacecraft is:
Figure BDA0001606637450000045
aiming at the state feedback control law simulation provided by the modified Rodrigues parameter system model, the attitude initial value described by the modified Rodrigues parameter is as follows:
σ(0)＝[0.2675 0.1110 0.4633]T，
the angular velocities of the initial pose are as follows:
ω(0)＝[0 0 0]T，
furthermore, the initial values of the flexible attachment trimodal variables are:
ηi＝0.001，ψi＝0.001，i＝1，2，3.
the attitude controller parameters based on state feedback are:
k＝75，A1＝-13I3×3，B1＝6I3×3，Q1＝2200I3×3，Q＝0.15I6×6
in summary, the invention designs an attitude control method based on state feedback without angular velocity measurement, aiming at the problem that the flexible spacecraft needs to use the measurement data of the angular velocity sensor in the traditional attitude control, but the flexible spacecraft is expensive and easy to fail, and the application of the actual spacecraft control system is influenced. The method aims to solve the problem that the flexible spacecraft needs real-time measurement data of an angular velocity sensor to realize stable control of the spacecraft attitude in the flying process, and high-robustness control of the flexible spacecraft is completed. The method adopts the modified Rodrigues parameter to describe the attitude of the flexible spacecraft, establishes a kinematic equation based on the modified Rodrigues parameter, and adopts a mixed coordinate method to establish an attitude kinetic equation for the flexible spacecraft with a flexible accessory on a central rigid body. For a posture control system model of the flexible spacecraft described by a modified Rodrigues parameter, feedback is realized by introducing a passive filter to replace angular velocity information, and further a posture control law without angular velocity measurement based on state feedback is designed. Finally, simulation experiments are carried out to verify that the designed attitude control algorithm of the flexible spacecraft has good robustness.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (3)

1. The attitude control method for measuring the angular velocity of the flexible spacecraft is characterized by comprising the following steps: the method comprises the following steps: s1, establishing a kinematic equation and a kinetic equation;
the attitude of the flexible spacecraft is described by adopting a modified Rodrigues parameter, and a kinematic equation of a mathematical model of the flexible spacecraft system based on the attitude is as follows:
Figure FDA0003173026170000011
wherein the content of the first and second substances,
Figure FDA0003173026170000012
in addition, omega represents the attitude angular velocity of the flexible spacecraft, sigma is a modified Rodrigues parameter vector,
Figure FDA0003173026170000013
its derivative, its antisymmetric matrix is:
Figure FDA0003173026170000014
the attitude dynamics equation established for the spacecraft with the flexible attachment on the central rigid body by adopting the mixed coordinate method is as follows:
Figure FDA0003173026170000015
wherein S (ω) is the antisymmetric matrix of angular velocity ω, i.e.
Figure FDA0003173026170000016
Jmb＝J-δTDelta is expressed as a matrix of the body inertia,
Figure FDA0003173026170000017
is the total velocity of the flexible attachment; u is a control moment; delta is expressed as a coupling action matrix between rigid body dynamics and flexible dynamics; C. k is respectively expressed as a damping matrix and a rigidity matrix;
s2, selecting a filter, and designing the following filter:
Figure FDA0003173026170000021
wherein z is a passive filter associated with the modified Rodrigues parameter, which is used to replace the feedback of angular velocity; cv(s) is a three-dimensional linear time-invariant, strictly true and strictly regular transfer matrix;
s3, designing a control law based on a passive method:
Figure FDA0003173026170000022
Figure FDA0003173026170000023
wherein η represents the flexible modal displacement of the flexible attachment, k is the gain coefficient, and the positive definite symmetric matrix P satisfies the following lyapunov matrix equation corresponding to the positive definite matrix Q:
Figure FDA0003173026170000024
2. the attitude control method according to claim 1, characterized in that: the attitude control method considers N elastic modes, and the corresponding natural angular frequency is omeganiI is 1, 2, …, N, corresponding to a damping ratio of ζi1, 2, N, then
Figure FDA0003173026170000025
3. The attitude control method according to claim 1, characterized in that: cvAn arbitrary minimum realization of(s) is as follows:
Figure FDA0003173026170000026
wherein A is1、B1、C1A system matrix, an input matrix and an output matrix respectively representing a z-state space of the filter, a positive definite matrix P being present1And Q1Satisfies the following relation:
P1A1+A1 TP1＝-Q1，P1B1＝C1 T。
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CN110134137B (en) * 2019-06-18 2021-11-23 哈尔滨工业大学（深圳） Spacecraft attitude tracking control method based on extended state observer
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