CN107065913B - Sliding mode variable structure attitude control method of flexible spacecraft - Google Patents
Sliding mode variable structure attitude control method of flexible spacecraft Download PDFInfo
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- CN107065913B CN107065913B CN201710326702.2A CN201710326702A CN107065913B CN 107065913 B CN107065913 B CN 107065913B CN 201710326702 A CN201710326702 A CN 201710326702A CN 107065913 B CN107065913 B CN 107065913B
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- 238000013016 damping Methods 0.000 claims description 5
- 239000000126 substance Substances 0.000 claims description 5
- 230000008878 coupling Effects 0.000 claims description 3
- 238000010168 coupling process Methods 0.000 claims description 3
- 238000005859 coupling reaction Methods 0.000 claims description 3
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 230000006872 improvement Effects 0.000 description 5
- 238000010586 diagram Methods 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 244000145845 chattering Species 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/244—Spacecraft control systems
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Abstract
The invention provides a sliding mode variable structure attitude control method of a flexible spacecraft with perturbation of rotational inertia. The invention has the beneficial effects that: the attitude control method designed by the invention enables the spacecraft system to have good stability, and when the inertia parameters of the spacecraft system are changed greatly, the attitude of the spacecraft can be stabilized quickly.
Description
Technical Field
The invention relates to a spacecraft, in particular to a sliding mode variable structure attitude control method of a flexible spacecraft.
Background
In the traditional attitude control method, perturbation is not considered to exist in the moment of inertia of the flexible spacecraft, and the traditional sliding mode variable structure control method can cause large buffeting.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a sliding mode variable structure attitude control method of a flexible spacecraft.
The invention provides a sliding mode variable structure attitude control method of a flexible spacecraft, which comprises the following steps of establishing a quaternion-based kinematic equation and a dynamics equation of the flexible spacecraft:
wherein, T (q)0,qv)＝(q0I3+[qv×]),
Wherein q is0,qvA scalar part and a vector part which are attitude quaternions respectively; ω is the attitude angle of the spacecraft; delta is a coupling matrix between the flexible portion of the flexible spacecraft and the rigid body main body; c and K are respectively a damping matrix and a rigidity matrix,
ωni1,2, N is the natural frequency, ζiI is 1, …, and N is damping coefficient; j. the design is a square0Is the nominal value of the moment of inertia, JmbThe moment of inertia of the rigid body part is obtained, the delta J is an uncertain coefficient of the moment of inertia, the spacecraft is provided with a flexible attachment, and the moment of inertia contains perturbation terms.
As a further improvement of the present invention, assuming a measurable flexural mode, the slip form is designed as follows:
s＝ω+Gqv
the designed sliding mode variable structure control law based on state feedback is as follows:
F(s)＝{sgn(s1),sgn(s2),sgn(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi.
wherein, W, D and G are positive definite diagonal matrixes.
As a further improvement of the invention, the switching function F(s) contained in the sliding mode variable structure control law based on state feedback is replaced by F1(s)：
F1(s)＝{f(s1),f(s2),f(s3)}T
As a further improvement of the present invention, in the case where the flexible mode is not measurable, the following mode observer is designed:
where the matrix P is a solution of the following Lyapunov equation:
the slip form is designed as follows:
s＝ω+Gqv
the designed sliding mode variable structure control law based on the observer is as follows:
F(s)＝{sgn(s1),sgn(s2),sgn(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi.
wherein, W, D and G are positive definite diagonal matrixes, and the matrix P is a solution of the following Lyapunov equation
As a further improvement of the invention, the switching function F(s) contained in the sliding mode variable structure control law based on the observer is replaced by F1(s)：
F1(s)＝{f(s1),f(s2),f(s3)}T
The invention has the beneficial effects that:
1. the attitude control method designed by the invention enables the spacecraft system to have good stability, and when the inertia parameters of the spacecraft system are changed greatly, the attitude of the spacecraft can be stabilized quickly;
2. the flexible accessory has better capability of inhibiting the vibration of the flexible mode, and the vibration of the flexible accessory can be effectively inhibited.
Drawings
Fig. 1 is a block diagram of a sliding mode attitude control system with measurable flexible modes.
Fig. 2 is a block diagram of a sliding mode attitude control system in which the flexural mode is not measurable.
Detailed Description
The present invention will be further described with reference to the following embodiments.
As shown in fig. 1 to 2, a method for controlling a sliding mode variable structure attitude of a flexible spacecraft includes:
1. a sliding mode control law based on state feedback is designed for the measurable condition of a flexible mode
F1(s)＝{f(s1),f(s2),f(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi.
Wherein, W, D and G are positive definite diagonal matrixes.
2. An observer-based sliding mode control law is designed for the condition that the flexible mode is not measurable
F1(s)＝{f(s1),f(s2),f(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi.
Wherein, W, D and G are positive definite diagonal matrixes. The matrix P is the solution of the following Lyapunov equation
Establishing a quaternion-based kinematic equation and a dynamics equation for the flexible spacecraft with perturbation of rotational inertia as follows:
wherein, J0Is the nominal value of the moment of inertia, and Δ J is the uncertainty coefficient of the moment of inertia. The spacecraft has a flexible attachment and the moment of inertia contains perturbation terms.
Consider the following two cases:
(1) and (3) designing a sliding mode variable structure control law based on state feedback for the flexible spacecrafts (1) - (2) under the assumption that the mode of the system is measurable.
Step 1 design slip form surface
Selecting the following sliding mode switching surface function:
s＝ω+Gqv
and, prove that the above-mentioned hyperplane can guarantee the slip form movement is stable, namely the whole movement process of the system, can be stable in limited time.
And (3) proving that: the chosen Lyapunov function is as follows:
step2 design control law
The control is designed to have the following form:
u＝-Ws-DF(s)+ueq (3)
wherein the content of the first and second substances,
the sliding mode variable structure control law can enable the state of the system to move to the sliding mode surface s-0 within a limited time from any initial point, namely s-omega + GqvAnd can be maintained on the slip manifold.
The equivalent control u is designed as followseqThe following Lyapunov function was chosen:
order toObtaining:
wherein the content of the first and second substances,
(2) when the flexible mode of the spacecraft cannot be measured, a sliding mode variable structure control law based on an observer is designed for the flexible spacecraft (1) - (2).
First, the following observed errors of the flexural mode are defined:
the following modal observer was selected:
where the matrix P is a solution of the following Lyapunov equation:
and designing a sliding mode variable structure control law based on the observer.
Step 1 design slip form surface
Selecting the following sliding mode switching surface function:
s＝ω+Gqv
and, prove that the above-mentioned hyperplane can guarantee the slip form movement is stable, namely the whole movement process of the system, can be stable in limited time.
And (3) proving that: the chosen Lyapunov function is as follows:
step2 design control law
The control is designed to have the following form:
u＝-Ws-DF(s)+ueq (7)
wherein the content of the first and second substances,
the sliding mode variable structure control law can enable the state of the system to move to the sliding mode surface s-0 within a limited time from any initial point, namely s-omega + GqvAnd can be maintained on the slip manifold.
The equivalent control u is designed as followseqThe following Lyapunov function was chosen:
order to
Wherein the content of the first and second substances,
the resulting control law was then demonstrated to ensure that the flexible spacecraft eventually tended to stabilize. Therefore, verification is required
Finally, the designed sliding mode variable structure control laws (3) - (6) based on state feedback and the sliding mode variable structure control laws (7) - (10) based on the observer are improved. The switching functions f(s) in the control laws (3) - (6) and the control laws (7) - (10) are very likely to cause chattering of the variable structure control itself. Meanwhile, when the flexible spacecraft carries out attitude maneuver, the control moment required at the initial moment is the largest. The requirement on the output torque of the actuating mechanism of the spacecraft can be increased, the modal displacement of the flexible attachment can be increased, and the buffeting of the flexible attachment can be increased. Therefore, the switching function f(s) is replaced by the following form:
F1(s)＝{f(s1),f(s2),f(s3)}T
in the following, we will illustrate the control effect of the sliding mode variable structure control law based on state feedback and the sliding mode variable structure control law based on observer by way of example.
Considering the nominal value J of the moment of inertia of a spacecraft with a flexible attachment0Comprises the following steps:
the moment of inertia uncertainty coefficient Δ J is:
rigid-flexible coupling matrix between flexible spacecraft and flexible accessories:
the vibration frequency of the flexible attachment is:
ωn＝[0.7681,1.1038,1.8733,2.5496]
the vibration damping of the flexible attachment is:
ξ＝[0.005607,0.00862,0.01283,0.02516]
the parameters of the sliding mode variable structure controller based on state feedback are as follows:
G＝diag{0.2 0.2 0.2}；W＝diag{200 200 200}；D＝diag{200 200 200}
parameters of the sliding mode variable structure controller based on the observer are as follows:
G＝diag{0.2 0.2 0.2}；W＝diag{200 200 200}；
D＝diag{200 200 200}；。
Q＝diag{50 50 50 50 50 50 50 50}；
the invention provides a sliding mode variable structure attitude control method of a flexible spacecraft, which is designed aiming at the problem of attitude control of the flexible spacecraft with perturbation of rotational inertia. The method aims to solve the problems of attitude control of the flexible spacecraft and vibration suppression of the flexible accessories. The invention adopts a quaternion method to express a kinematic equation of the attitude of the flexible spacecraft, establishes a complex spacecraft dynamical equation with a flexible accessory in a central rigid body and perturbation of rotational inertia, and provides a simplified flexible spacecraft attitude dynamical equation based on mixed coordinates. And then, a sliding mode variable structure attitude controller is designed by utilizing a Lyapunov direct method, improvement and optimization are carried out aiming at the problem of buffeting in sliding mode variable structure control, the original switch function term in the sliding mode control is replaced by a positive and negative cut function, and the flutter in a system is restrained. And finally, verifying the effectiveness of the designed control method by using a simulink module in MATLAB.
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 (4)
1. A sliding mode variable structure attitude control method of a flexible spacecraft is characterized by comprising the following steps: establishing a quaternion-based kinematic equation and a dynamic equation of the flexible spacecraft as follows:
wherein, T (q)0,qv)＝(q0I3+[qv×]),
Wherein q is0,qvA scalar part and a vector part which are attitude quaternions respectively; ω is the attitude angle of the spacecraft; delta is a coupling matrix between the flexible portion of the flexible spacecraft and the rigid body main body; c and K are respectively a damping matrix and a rigidity matrix,
ωni1,2, N is the natural frequency, ζiN is a damping coefficient; j. the design is a square0Is the nominal value of the moment of inertia, JmbThe spacecraft is provided with a flexible attachment, and the rotational inertia contains perturbation terms;
wherein the content of the first and second substances,
assuming a measurable mode of flexibility, the slip form is designed as follows:
s＝ω+Gqv
the designed sliding mode variable structure control law based on state feedback is as follows:
F(s)＝{sgn(s1),sgn(s2),sgn(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi,
wherein, W, D and G are positive definite diagonal matrixes.
2. The sliding mode variable structure attitude control method of the flexible spacecraft according to claim 1, characterized in that: replacing a switching function F(s) contained in a sliding mode variable structure control law based on state feedback with F1(s)：
3. The sliding mode variable structure attitude control method of the flexible spacecraft according to claim 1, characterized in that: in the case of an immeasurable flexible mode, the following mode observer is designed:
where the matrix P is a solution of the following Lyapunov equation:
the slip form is designed as follows:
s＝ω+Gqv
the designed sliding mode variable structure control law based on the observer is as follows:
F(s)＝{sgn(s1),sgn(s2),sgn(s3)}T
τ＝[τ1 τ2 τ3]T
τi＝-gisgn(si),
maxΨi(ω,q0,qv)≤gi,
wherein, W, D and G are positive definite diagonal matrixes.
4. The sliding mode variable structure attitude control method of the flexible spacecraft according to claim 3, characterized in that: replacing a switching function F(s) contained in a sliding mode variable structure control law based on an observer by F1(s)：
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| CN107943062A (en) * | 2017-09-13 | 2018-04-20 | 哈尔滨工业大学深圳研究生院 | Flexible Satellite Attitude sliding-mode control with external disturbance torque |
| CN107831775B (en) * | 2017-11-14 | 2021-06-08 | 哈尔滨工业大学深圳研究生院 | Attitude control method based on flexible spacecraft non-angular velocity measurement |
| CN109213184B (en) * | 2018-11-06 | 2021-06-08 | 哈尔滨工业大学（深圳） | Finite-time multi-mode sliding mode attitude control algorithm of flexible spacecraft |
| CN109507892A (en) * | 2019-01-22 | 2019-03-22 | 哈尔滨工业大学（深圳） | The adaptive sliding mode pose stabilization control method of flexible spacecraft |
| CN110083171A (en) * | 2019-04-30 | 2019-08-02 | 哈尔滨工业大学（深圳） | The method and system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft |
| CN111498147B (en) * | 2020-04-03 | 2021-09-21 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Finite time segmentation sliding mode attitude tracking control algorithm of flexible spacecraft |
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