CN101872164A - Method of reducing astrodynamics system state sensitivity - Google Patents
Method of reducing astrodynamics system state sensitivity Download PDFInfo
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- CN101872164A CN101872164A CN 201010200353 CN201010200353A CN101872164A CN 101872164 A CN101872164 A CN 101872164A CN 201010200353 CN201010200353 CN 201010200353 CN 201010200353 A CN201010200353 A CN 201010200353A CN 101872164 A CN101872164 A CN 101872164A
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- 238000000034 method Methods 0.000 title claims abstract description 19
- 239000011159 matrix material Substances 0.000 claims description 18
- 230000001629 suppression Effects 0.000 description 2
- 230000002411 adverse Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
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Abstract
The invention provides a method of reducing astrodynamics system state sensitivity, which belongs to the dynamics and control technology field. The invention quantizes the influence of turbulence on system state by introducing the sensitivity index J2 of the state and then obtains the optimal solution of the system by obtaining the minimum value of an optimal performance index J equals to J1 plus cO.J2 considering the system state sensitivity. Compared with the traditional optimal control method based on maximum value principle, the optimal control method considering the system state sensitivity has the following advantages; (1) the previous optimal performance index J1 is almost not influenced and (2) on condition that the previous optimal performance index is ensured, the influence of the turbulence on the system state can be reduced effectively.
Description
Technical field:
The present invention relates to a kind of method that reduces the unwise sensitivity of Space Vehicle System, belong to astrodynamics and control technology field.
Background technology:
Traditional method for optimally controlling based on maximal principle can only the guaranteed performance index optimization, disturbance suppression is to the influence of system state simultaneously under the precondition that guarantees specific performance index optimum and there is not ability, and this influence many times all can bring adverse influence to system.For example, reenter in the process of the earth at spacecraft, the state error constantly that leaves the right or normal track all can cause very big influence to reentering process, cause bigger landing error with the uncertainty that reenters aerodynamic parameter in the process.Therefore, a kind of new method for optimally controlling of development, to reduce state under the prerequisite of guaranteed performance index optimum be a very urgent task to the susceptibility of disturbance.
Summary of the invention
Goal of the invention:
Technical matters to be solved of the present invention is not have influence this shortcoming of ability disturbance suppression to system state in order to overcome traditional method for optimally controlling based on maximal principle, a kind of method that reduces astrodynamics system state sensitivity is provided, and this method reenters control and martian atmosphere at the spacecraft earth and enters various fields such as guiding control extremely important using value is all arranged.
Technical scheme:
The present invention adopts following technical scheme for achieving the above object:
A kind of method that reduces astrodynamics system state sensitivity comprises the steps:
The A step, set up the system dynamics equation:
Wherein, x is that dimension is the state variable of n, and u is a control variable, and t is a time variable, and n is a natural number;
The B step is established any t ∈ [t
0, t
f], t wherein
0Be initial time, t
fBe the terminal point moment, system state is designated as x (t)=X (t|t
0, x
0), x
0Be initial time t
0State; The optimal performance index of taking into account system state sensitivity is defined as follows:
J=J
1+c
0·J
2; (2)
Wherein, J
1Be optimal performance index, J
2It is the system state sensitivity indexes; c
0Be penalty factor, be used to regulate the shared weight of sensitivity index;
The C step, the state x of definition any time t is to initial time t
0State x
0Susceptibility matrix S (t|t
0) as follows:
Easily verify susceptibility matrix S (t|t
0) have a following characteristic:
S(t
0|t
0)=I; (5)
S(t
2|t
1)=S(t
2|t
0)·S(t
1|t
0)
-1; (6)
Wherein, I is a unit matrix, ()
-1Be inversion operation;
The D step is found the solution the described system state susceptibility of formula (3) matrix S according to formula (4), (5), (6);
The E step is according to system state susceptibility matrix S define system state sensitivity index J
2As follows:
J
2=∑g(S
i,j(t
f,t)) (7)
Wherein g is to be the function of independent variable with the susceptibility matrix, i, and j is natural number;
The F step, convolution (1), formula (4) adopt optimized Algorithm to ask for the optimal performance index J of the defined taking into account system state sensitivity of formula (2).
Beneficial effect:
The present invention compares with traditional method for optimally controlling based on maximal principle, and following advantage is arranged:
(1) original optimal performance index J
1Influenced hardly.
(2) guaranteeing to effectively reduce the influence of disturbance under the optimized prerequisite of original performance index to system state.
Description of drawings:
Fig. 1 is a process flow diagram of the present invention.
Specific embodiments:
The present invention is described in further detail below in conjunction with accompanying drawing:
As shown in Figure 1, step of the present invention is as follows:
(1) set up the system dynamics equation:
Wherein, x is that dimension is the state variable of n, and u is a control variable, and t is a time variable, and n is a natural number;
(2) establish any t ∈ [t
0, t
f], t wherein
0Be initial time, t
fBe the terminal point moment, system state is designated as x (t)=X (t|t
0, x
0), x
0Be initial time t
0State; The state x of definition any time t is to initial time t
0State x
0Susceptibility matrix S (t|t
0) as follows:
Easily verify susceptibility matrix S (t|t
0) have a following characteristic:
S(t
0|t
0)=I; (4)
S(t
2|t
1)=S(t
2|t
0)·S(t
1|t
0)
-1; (5)
Wherein, I is a unit matrix, ()
-1Be inversion operation;
(3) find the solution the described system state susceptibility of formula (2) matrix S according to formula (3), (4), (5);
(4) according to system state susceptibility matrix S define system state sensitivity index J
2As follows:
J
2=∑g
2(S
i,j(t
f,t)) (6)
G wherein
2Be to be the function of independent variable with the susceptibility matrix, i, j is natural number;
(5) according to concrete engineering background definition optimal performance index J
1, the shortest such as the time, burnup is the most excellent.
J
1=g
1(x,u,t) (7)
G wherein
1Be with state, control and time are the function of independent variable;
(6) optimal performance index of taking into account system state sensitivity is defined as follows:
J=J
1+c
0·J
2; (8)
Wherein, J
1Be optimal performance index, J
2It is the system state sensitivity indexes; c
0Be penalty factor, be used to regulate the shared weight of sensitivity index;
(7) convolution (1), formula (3) adopt and join the optimal performance index J that an optimized Algorithm is asked for the defined taking into account system state sensitivity of formula (8).That is, formula (1)-(8) described optimal control problem is transferred to nonlinear programming problem, find the solution a kind of method that reduces astrodynamics system state sensitivity by seqential quadratic programming by means of point collocation.
Claims (1)
1. method that reduces astrodynamics system state sensitivity is characterized in that: comprises the steps,
The A step, set up the system dynamics equation:
Wherein, x is that dimension is the state variable of n, and u is a control variable, and t is a time variable, and n is a natural number;
The B step is established any t ∈ [t
0, t
f], t wherein
0Be initial time, t
fBe the terminal point moment, system state is designated as x (t)=X (t|t
0, x
0), x
0Be initial time t
0State; The optimal performance index of taking into account system state sensitivity is defined as follows:
J=J
1+c
0·J
2; (2)
Wherein, J
1Be optimal performance index, J
2It is the system state sensitivity indexes; c
0Be penalty factor, be used to regulate the shared weight of sensitivity index;
The C step, the state x of definition any time t is to initial time t
0State x
0Susceptibility matrix S (t|t
0) as follows:
Easily verify susceptibility matrix S (t|t
0) have a following characteristic:
S(t
0|t
0)=I; (5)
S(t
2|t
1)=S(t
2|t
0)·S(t
1|t
0)
-1; (6)
Wherein, I is a unit matrix, ()
-1Be inversion operation;
The D step is found the solution the described system state susceptibility of formula (3) matrix S according to formula (4), (5), (6);
The E step is according to system state susceptibility matrix S define system state sensitivity index J
2As follows:
J
2=∑g(S
i,j(t
f,t)) (7)
Wherein g is to be the function of independent variable with the susceptibility matrix, i, and j is natural number;
The F step, convolution (1), formula (4) adopt optimized Algorithm to ask for the optimal performance index J of the defined taking into account system state sensitivity of formula (2).
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CN2010102003538A CN101872164B (en) | 2010-06-13 | 2010-06-13 | Method of reducing astrodynamics system state sensitivity |
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CN2010102003538A CN101872164B (en) | 2010-06-13 | 2010-06-13 | Method of reducing astrodynamics system state sensitivity |
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CN101872164A true CN101872164A (en) | 2010-10-27 |
CN101872164B CN101872164B (en) | 2012-07-18 |
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ID=42997085
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Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN102890743A (en) * | 2011-07-19 | 2013-01-23 | 北京理工大学 | Method for analyzing uncertainty of drop point of planetary atmosphere entering into lander |
Citations (6)
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JPS6170605A (en) * | 1984-09-14 | 1986-04-11 | Hitachi Ltd | Digital control system |
US4983898A (en) * | 1989-02-23 | 1991-01-08 | Kabushiki Kaisha Toshiba | Method and system for changing control parameters in accordance with state of process in process control |
CN1995915A (en) * | 2006-12-27 | 2007-07-11 | 北京航空航天大学 | Deep space probe UPF celestial self-navigation method based on starlight angle |
CN101078936A (en) * | 2007-06-08 | 2007-11-28 | 北京航空航天大学 | High precision combined posture-determining method based on optimally genetic REQUEST and GUPF |
JP2009020580A (en) * | 2007-07-10 | 2009-01-29 | Nec Corp | Driving control device |
EP2270679A1 (en) * | 2009-07-01 | 2011-01-05 | Centre National D'etudes Spatiales | Method for optimal control of a system which can be modelled by Hamilton-Jacobi-Bellman equations |
-
2010
- 2010-06-13 CN CN2010102003538A patent/CN101872164B/en not_active Expired - Fee Related
Patent Citations (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS6170605A (en) * | 1984-09-14 | 1986-04-11 | Hitachi Ltd | Digital control system |
US4983898A (en) * | 1989-02-23 | 1991-01-08 | Kabushiki Kaisha Toshiba | Method and system for changing control parameters in accordance with state of process in process control |
CN1995915A (en) * | 2006-12-27 | 2007-07-11 | 北京航空航天大学 | Deep space probe UPF celestial self-navigation method based on starlight angle |
CN101078936A (en) * | 2007-06-08 | 2007-11-28 | 北京航空航天大学 | High precision combined posture-determining method based on optimally genetic REQUEST and GUPF |
JP2009020580A (en) * | 2007-07-10 | 2009-01-29 | Nec Corp | Driving control device |
EP2270679A1 (en) * | 2009-07-01 | 2011-01-05 | Centre National D'etudes Spatiales | Method for optimal control of a system which can be modelled by Hamilton-Jacobi-Bellman equations |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN102890743A (en) * | 2011-07-19 | 2013-01-23 | 北京理工大学 | Method for analyzing uncertainty of drop point of planetary atmosphere entering into lander |
CN102890743B (en) * | 2011-07-19 | 2015-08-05 | 北京理工大学 | Planetary scale enters lander drop point analysis on Uncertainty method |
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CN101872164B (en) | 2012-07-18 |
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