CN107065913A - The sliding moding structure gesture stability algorithm of Spacecraft - Google Patents
The sliding moding structure gesture stability algorithm of Spacecraft Download PDFInfo
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- CN107065913A CN107065913A CN201710326702.2A CN201710326702A CN107065913A CN 107065913 A CN107065913 A CN 107065913A CN 201710326702 A CN201710326702 A CN 201710326702A CN 107065913 A CN107065913 A CN 107065913A
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- 239000011159 matrix material Substances 0.000 claims description 19
- 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
- 238000013016 damping Methods 0.000 claims description 3
- 230000003094 perturbing effect Effects 0.000 claims description 3
- 238000006748 scratching Methods 0.000 claims 1
- 230000002393 scratching effect Effects 0.000 claims 1
- 238000000034 method Methods 0.000 abstract description 6
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000009415 formwork Methods 0.000 description 10
- 238000010586 diagram Methods 0.000 description 2
- 230000006641 stabilisation Effects 0.000 description 2
- 238000011105 stabilization Methods 0.000 description 2
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000012795 verification 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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- Combustion & Propulsion (AREA)
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Abstract
There is the sliding moding structure gesture stability algorithm of the Spacecraft of perturbation the invention provides a kind of rotary inertia, the kinematical equation of Spacecraft is set up using Quaternion Method, the Complex Spacecraft kinetics equation that Rigid Base has perturbation with flexible appendage, rotary inertia is set up, the simplified Flexible Spacecraft kinetics equation based on hybrid coordinate is given.The beneficial effects of the invention are as follows：The gesture stability algorithm designed using the present invention makes Space Vehicle System have good stability, and when Space Vehicle System inertia parameter is varied widely, the posture of spacecraft can tend towards stability quickly.
Description
Technical field
The present invention relates to the sliding moding structure gesture stability algorithm of spacecraft, more particularly to a kind of Spacecraft.
Background technology
In traditional gesture stability algorithm, do not consider that the rotary inertia of Spacecraft has perturbation, and traditional cunning
Mould variable structure control algorithm can cause larger buffeting.
The content of the invention
In order to solve the problems of the prior art, the invention provides a kind of sliding moding structure posture control of Spacecraft
Algorithm processed.
The invention provides a kind of sliding moding structure gesture stability algorithm of Spacecraft, set up Spacecraft and be based on
The kinematical equation and kinetics equation of quaternary number are as follows：
Wherein, T (q0,qv)=(q0I3+[qv×]),
Wherein, q0,qvThe respectively scalar component and vector portion of attitude quaternion；ω is the attitude angle of spacecraft；δ is
Coupling matrix between the flex section and rigid body main body of Spacecraft；C, K are respectively damping matrix and stiffness matrix,
ωni, i=1,2 ..., N is natural frequency, ζi, i=1 ..., N is damped coefficient；J0It is rotary inertia nominal value,
JmbFor the rotary inertia of rigid body portion, △ J are rotary inertia uncertainty coefficient, and spacecraft carries flexible appendage, and rotates used
Amount contains perturbing term.
As a further improvement on the present invention, it is assumed that under the measurable situation of flexible mode, the sliding-mode surface of design is as follows：
S=w+Gqv
The sliding mode control law based on feedback of status of design is as follows：
F (s)={ sgn (s1),sgn(s2),sgn(s3)}T
τ=[τ1 τ2 τ3]T
τi=-gi(ω,q0,qv)sgn(si),
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix.
As a further improvement on the present invention, the switching function sliding mode control law based on feedback of status included
F (s) is substituted for following F1(s)：
F1(s)={ f (s1),f(s2),f(s3)}T
As a further improvement on the present invention, under the immesurable situation of flexible mode, following mode observation device is designed：
Wherein, matrix P is following Lyapunov non trivial solutions：
The sliding-mode surface of design is as follows：
S=w+Gqv
The sliding mode control law based on observer of design is as follows：
F (s)={ sgn (s1),sgn(s2),sgn(s3)}T
τ=[τ1 τ2 τ3]T
τi=-gi(ω,q0,qv)sgn(si),
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix, and matrix P is following Lyapunov non trivial solutions
As a further improvement on the present invention, the switching function F sliding mode control law based on observer included
(s) it is substituted for following F1(s)：
F1(s)={ f (s1),f(s2),f(s3)}T
The beneficial effects of the invention are as follows：
1st, the gesture stability algorithm designed using the present invention makes Space Vehicle System have good stability, when spacecraft system
When system inertia parameter is varied widely, the posture of spacecraft can tend towards stability quickly；
2nd, the ability for preferably suppressing flexible mode vibration is possessed, the vibration of flexible appendage can effectively be suppressed.
Brief description of the drawings
Fig. 1 is the block diagram of the measurable Sliding Mode Attitude control system of flexible mode.
Fig. 2 is the block diagram of the immesurable Sliding Mode Attitude control system of flexible mode.
Embodiment
With reference to embodiment, the invention will be further described.
As shown in Figure 1 to Figure 2, the sliding moding structure gesture stability algorithm of a kind of Spacecraft, including：
1st, the sliding formwork control ratio based on feedback of status is devised for the measurable situation of flexible mode
F1(s)={ f (s1),f(s2),f(s3)}T
τ=[τ1 τ2 τ3]T
τi=-gi(ω,q0,qv)sgn(si),
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix.
2nd, the sliding formwork control ratio based on observer is devised for the immeasurablel situation of flexible mode
F1(s)={ f (s1),f(s2),f(s3)}T
τ=[τ1 τ2 τ3]T
τi=-gi(ω,q0,qv)sgn(si),
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix.Matrix P is following Lyapunov non trivial solutions
The Spacecraft for containing perturbation to rotary inertia sets up kinematical equation and kinetics equation based on quaternary number
It is as follows：
Wherein, J0It is rotary inertia nominal value, △ J are rotary inertia uncertainty coefficient.It is characterized in that：Spacecraft is carried
Flexible appendage, and rotary inertia contains perturbing term.
Consider following two kinds of situations：
(1) mode for assuming system is measurable, and the sliding formwork based on feedback of status is designed for Spacecraft (1)-(2)
Variable-structure control is restrained.
Step 1 designs sliding-mode surface
Choose following sliding formwork switching surface function：
S=w+Gqv
And, it was demonstrated that above-mentioned hyperplane can ensure the whole motion process of sliding formwork motion stabilization, i.e. system, Ke Yi
It is stable in the limited time.
Prove：The Lyapunov functions of selection are as follows：
Step2 design control laws
Control of the design with following form：
U=-Ws-DF (s)+ueq (3)
Wherein,
The sliding mode control law can enable the state of system from arbitrary initial point, in finite time, motion
Onto sliding-mode surface s=0, i.e. s=w+Gqv, and can be maintained on sliding manifolds.
Equivalent control u is designed beloweq, select following Lyapunov functions：
OrderObtain：
Wherein,
(2) when spacecraft flexible mode can not be measured, the sliding formwork based on observer is designed for Spacecraft (1)-(2)
Variable-structure control is restrained.
First, the observation error for the flexible mode being defined as follows：
The following mode observation device of selection：
Wherein, matrix P is following Lyapunov non trivial solutions：
Next the sliding mode control law based on above-mentioned observer is designed.
Step 1 designs sliding-mode surface
Choose following sliding formwork switching surface function：
S=w+Gqv
And, it was demonstrated that above-mentioned hyperplane can ensure the whole motion process of sliding formwork motion stabilization, i.e. system, Ke Yi
It is stable in the limited time.
Prove：The Lyapunov functions of selection are as follows：
Step2 design control laws
Control of the design with following form：
U=-Ws-DF (s)+ueq (7)
Wherein,
The sliding mode control law can enable the state of system from arbitrary initial point, in finite time, motion
Onto sliding-mode surface s=0, i.e. s=w+Gqv, and can be maintained on sliding manifolds.
Equivalent control u is designed beloweq, select following Lyapunov functions：
Order
Wherein,
Then, it was demonstrated that obtained control law can ensure that Spacecraft finally tends towards stability.Accordingly, it would be desirable to verify
Finally, sliding mode control law (3)-(6) based on feedback of status to design and the sliding formwork based on observer
Variable-structure control rule (7)-(10) are improved.Control law (3)-(6) and switching function F (s) in control law (7)-(10) are non-
Chang Rongyi causes the flutter of variable-structure control in itself.Meanwhile, when Spacecraft carries out attitude maneuver, needed for initial time
Control moment is maximum.This can improve the requirement of the output torque to spacecraft executing agency itself, be scratched while can also increase
Property annex modal displacement, increase flexible appendage buffeting.Therefore, following form is substituted for switching function F (s)：
F1(s)={ f (s1),f(s2),f(s3)}T
We will illustrate the sliding mode control law based on feedback of status and the cunning based on observer by example below
The control effect of moding structure control rule.
Consider the nominal value J of the rotary inertia with flexible appendage spacecraft0For：
Rotary inertia uncertainty coefficient △ J are：
Rigid-flexible coupling matrix between Spacecraft and flexible appendage：
The vibration frequency of flexible appendage is：
ωn=[0.7681,1.1038,1.8733,2.5496]
The vibration damping of flexible appendage is：
ξ=[0.005607,0.00862,0.01283,0.02516]
Sliding Mode Controller parameter based on feedback of status is：
G=diag { 0.2 0.2 0.2 }；W=diag { 200 200 200 }；D=diag { 200 200 200 }
The parameter of Sliding Mode Controller based on observer is：
A kind of sliding moding structure gesture stability algorithm for Spacecraft that the present invention is provided, exists for rotary inertia and takes the photograph
Dynamic Flexible Spacecraft control problem, devises a kind of sliding moding structure gesture stability algorithm.The purpose of the invention algorithm
It is to solve Flexible Spacecraft control, suppresses the problem of flexible appendage has vibration.The invention is using Quaternion Method come table
Show the kinematical equation of Flexible Spacecraft, set up the complexity that Rigid Base has perturbation with flexible appendage, rotary inertia
Spacecraft dynamics equation, gives the simplified Flexible Spacecraft kinetics equation based on hybrid coordinate.Then utilize
Lyapunov direct methods, have devised sliding moding structure attitude controller, and for being buffeted present in Sliding mode variable structure control
Problem, is improved and optimizated, and original switch function in sliding formwork control is substituted with " the positive traditional method of indicating the pronunciation of a Chinese character " function, suppresses system
Flutter in system.Finally, the validity of the control algolithm designed with the simulink module verifications in MATLAB.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to assert
The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention,
On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention's
Protection domain.
Claims (5)
1. a kind of sliding moding structure gesture stability algorithm of Spacecraft, it is characterised in that：Set up Spacecraft and be based on four
The kinematical equation and kinetics equation of first number are as follows：
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Wherein, q0,qvThe respectively scalar component and vector portion of attitude quaternion；ω is the attitude angle of spacecraft；δ is flexibility
Coupling matrix between the flex section and rigid body main body of spacecraft；C, K are respectively damping matrix and stiffness matrix,
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The rotary inertia of rigid body portion, △ J are rotary inertia uncertainty coefficient, and spacecraft carries flexible appendage, and rotary inertia contains
There is perturbing term.
2. the sliding moding structure gesture stability algorithm of Spacecraft according to claim 1, it is characterised in that：Assuming that scratching
Under the property measurable situation of mode, the sliding-mode surface of design is as follows：
S=w+Gqv
The sliding mode control law based on feedback of status of design is as follows：
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<mover>
<mi>J</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>b</mi>
</mrow>
</msub>
<mi>s</mi>
<mo>,</mo>
</mrow>
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix.
3. the sliding moding structure gesture stability algorithm of Spacecraft according to claim 2, it is characterised in that：It will be based on
The switching function F (s) that the sliding mode control law of feedback of status is included is substituted for following F1(s)：
F1(s)={ f (s1),f(s2),f(s3)}T
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>arctan</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>xs</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mo>|</mo>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo><</mo>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3.</mn>
</mrow>
4. the sliding moding structure gesture stability algorithm of Spacecraft according to claim 1, it is characterised in that：Flexible mold
Under the immesurable situation of state, following mode observation device is designed：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mover>
<mi>&eta;</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mover>
<mi>&psi;</mi>
<mo>^</mo>
</mover>
<mo>&CenterDot;</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>K</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mover>
<mi>&eta;</mi>
<mo>^</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<mi>&psi;</mi>
<mo>^</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>&delta;</mi>
<mi>&omega;</mi>
<mo>+</mo>
<msup>
<mi>P</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>(</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>K</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>C</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mo>(</mo>
<mi>&delta;</mi>
<mi>&omega;</mi>
<mo>+</mo>
<msub>
<mi>G&delta;q</mi>
<mi>v</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>G</mi>
<mi>&delta;</mi>
<mo>&lsqb;</mo>
<mi>&omega;</mi>
<mo>&times;</mo>
<mo>&rsqb;</mo>
<msub>
<mi>q</mi>
<mi>v</mi>
</msub>
<mo>)</mo>
</mrow>
Wherein, matrix P is following Lyapunov non trivial solutions：
<mrow>
<mi>P</mi>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>K</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>K</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<msup>
<mi>P</mi>
<mi>T</mi>
</msup>
<mo>=</mo>
<mo>-</mo>
<mn>2</mn>
<mi>Q</mi>
</mrow>
The sliding-mode surface of design is as follows：
S=w+Gqv
The sliding mode control law based on observer of design is as follows：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>u</mi>
<mo>=</mo>
<mo>-</mo>
<mi>W</mi>
<mi>s</mi>
<mo>-</mo>
<mi>D</mi>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>&omega;</mi>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>J</mi>
<mrow>
<mi>m</mi>
<mi>b</mi>
<mn>0</mn>
</mrow>
</msub>
<mi>&omega;</mi>
<mo>+</mo>
<msup>
<mi>&delta;</mi>
<mi>T</mi>
</msup>
<mover>
<mi>&psi;</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msup>
<mi>&delta;</mi>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>C</mi>
<mover>
<mi>&psi;</mi>
<mo>^</mo>
</mover>
<mo>+</mo>
<mi>K</mi>
<mover>
<mi>&eta;</mi>
<mo>^</mo>
</mover>
<mo>-</mo>
<mi>C</mi>
<mi>&delta;</mi>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>J</mi>
<mrow>
<mi>m</mi>
<mi>b</mi>
<mn>0</mn>
</mrow>
</msub>
<mi>G</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>T</mi>
<mo>(</mo>
<mrow>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>q</mi>
<mi>v</mi>
</msub>
</mrow>
<mo>)</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>&tau;</mi>
<mo>,</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
F (s)={ sgn (s1),sgn(s2),sgn(s3)}T
<mrow>
<mi>sgn</mi>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo><</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
</mrow>
τ=[τ1 τ2 τ3]T
τi=-gi(ω,q0,qv)sgn(si),
<mrow>
<mi>&Psi;</mi>
<mo>=</mo>
<mo>-</mo>
<mi>&omega;</mi>
<mo>&times;</mo>
<mi>&Delta;</mi>
<mi>J</mi>
<mi>&omega;</mi>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>J</mi>
<mi>G</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mi>I</mi>
<mn>2</mn>
</mfrac>
<mi>T</mi>
<mo>(</mo>
<mrow>
<msub>
<mi>q</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>q</mi>
<mi>v</mi>
</msub>
</mrow>
<mo>)</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mover>
<mi>J</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>b</mi>
</mrow>
</msub>
<mi>s</mi>
<mo>,</mo>
</mrow>
gi(ω,q0,qv)≥maxΨi(ω,q0,qv).
Wherein, W, D, G are positive definite diagonal matrix, and matrix P is following Lyapunov non trivial solutions
<mrow>
<mi>P</mi>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>K</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>+</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>I</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>K</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>C</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<msup>
<mi>P</mi>
<mi>T</mi>
</msup>
<mo>=</mo>
<mo>-</mo>
<mn>2</mn>
<mi>Q</mi>
<mo>.</mo>
</mrow>
2
5. the sliding moding structure gesture stability algorithm of Spacecraft according to claim 4, it is characterised in that：It will be based on
The switching function F (s) that the sliding mode control law of observer is included is substituted for following F1(s)：
F1(s)={ f (s1),f(s2),f(s3)}T
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>arctan</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>xs</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mo>|</mo>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
</mrow>
<mo><</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>s</mi>
<mi>i</mi>
</msub>
<mo><</mo>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3.</mn>
</mrow>
3
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| CN107831775A (en) * | 2017-11-14 | 2018-03-23 | 哈尔滨工业大学深圳研究生院 | The attitude control method without angular velocity measurement based on Spacecraft |
| 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 |
| CN109213184A (en) * | 2018-11-06 | 2019-01-15 | 哈尔滨工业大学（深圳） | The multi-modal Sliding Mode Attitude control algolithm of the finite time 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 |
| CN111498147A (en) * | 2020-04-03 | 2020-08-07 | 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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| 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 |
| CN107831775A (en) * | 2017-11-14 | 2018-03-23 | 哈尔滨工业大学深圳研究生院 | The attitude control method without angular velocity measurement based on Spacecraft |
| 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 |
| CN109213184A (en) * | 2018-11-06 | 2019-01-15 | 哈尔滨工业大学（深圳） | The multi-modal Sliding Mode Attitude control algolithm of the finite time of flexible spacecraft |
| 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 |
| CN111498147A (en) * | 2020-04-03 | 2020-08-07 | 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 |
| 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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