CN102582849A - Space intersection control method of two-stage constant thrust - Google Patents

Abstract

The invention discloses a space intersection control method of two-stage constant thrust, which is used for solving the technical problem that the engine is opened and closed frequently during the intersection process when the prior intersection control method of constant thrust is achieved. The technical solution is that the minimum opening-closing time Tmin constraint of the engine is introduced to the intersection control problem of the two-stage constant thrust engine; and the optimal intersection thrust under quadratic optimization function index is designed by rolling forecast principle. Because of considering the minimum opening-closing time constraint of the engine, the problem that the engine is opened and closed frequently is solved and the design difficulty of the engine is reduced; and the optimal design method has good robustness for design model error, measurement error and intersection thrust error.

Description

Two-stage is thrust spatial intersection control method fixedly

Technical field

The present invention relates to a kind of spatial intersection control method, particularly relate to fixedly thrust spatial intersection control method of a kind of two-stage.

Background technology

Document " the fuel saving track of Finite Thrust intersection (Gu Dake, Duan Guangren, Zhang Maorui. aerospace journal, 2010,31 (1): 75-81) " control method that a kind of limited normal value thrust realizes intersection disclosed.This method is used the triangular transformation technology thrust constraint is converted into abandoned virtual controlling, controlling quantity is carried out parametric description and is expressed as piecewise constant function, and then optimal control problem is converted into nonlinear programming problem.This method has been considered the constraint of driving engine maximum thrust, and the engine thrust of optimization is got a plurality of differences and often is worth in the maximum thrust scope, and changes with the encounter conditions change, and calculated amount is big, needs the off-line optimizing.

Summary of the invention

In order to overcome the deficiency that existing normal value thrust realizes the frequent switching on and shutting down of driving engine in the intersection process of intersection control method; The present invention provides fixedly thrust spatial intersection control method of a kind of two-stage; This method is used the rolling forecast principle and has been set up the corresponding relation between optimization target function, intersection predicted state and the intersection Thrust Control amount; Relatively calculate through the target function value and can confirm engine optimum intersection thrust; Can solve under the minimum switching on and shutting down time set of the driving engine condition quadratic function and optimize fixedly thrust intersection controlling Design problem of index two-stage, can reduce motor switch machine number of times in the intersection process greatly, Project Realization is easy.

The technical solution adopted for the present invention to solve the technical problems is: a kind of two-stage is thrust spatial intersection control method fixedly, is characterized in may further comprise the steps:

Step 1: the discretization model of under relative coordinate system, setting up the Spacecraft Rendezvous motion:

X(k+1)＝F(X(k))+G(U(k))+Δ(k) (1)

State vector X and control vector U do

X＝[X ₁?X ₂?X ₃?X ₄?X ₅?X ₆] ^T，U＝[u _x?u _y?u _z] ^T

Wherein, X ₁=x, X ₂=y, X ₃=z,

And x, y and z are the relative position of pursuit spacecraft with respect to passive space vehicle;

With

Be the relative velocity of pursuit spacecraft with respect to passive space vehicle; u _x, u _yAnd u _zBe respectively the Acceleration Control amount of pursuit spacecraft at three axles of system of axes, controlling quantity amplitude discrete domain is A _U={ u _High,-u _Low, 0, u _Low, u _High, u wherein _High＞0 is the cooresponding peak acceleration controlling quantity of maximum thrust of driving engine, u _Low＞0 is the cooresponding little Acceleration Control amount of low thrust of driving engine, and u _High＞u _Low＞0; The disturbance acceleration that Δ (k) expression is caused by exciting force or other errors.The minimum work-hours of driving engine is spaced apart T _Min

Do not consider to disturb Δ (k) effect, initial time t ₀, establish discrete system be k constantly.According to formula (1), k is intersection state X (k) and consider that the invariability of controlling quantity calculates k+N intersection constantly state estimation value according to formula (2) recursion constantly:

$\hat{X}(k+1)=F\left(X\left(k\right)\right)+G\left(U\left(k\right)\right)$

$\hat{X}(k+2)=F\left(\hat{X}(k+1)\right)+G\left(U\left(k\right)\right)$ (2)

$\begin{array}{c}.\\ .\\ .\\ \hat{X}(k+N)=F\left(\hat{X}(k+N-1)\right)+G\left(U\left(k\right)\right)\end{array}$

Choose the discrete sampling time T _sIt is the minimum work-hours interval T of driving engine _Min1/N, N is a positive integer.

Step 2: according to formula (2) result, the double optimization index of calculating formula (3)

$J\left(k\right)={\mathrm{\α}}_1\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\hat{X}}_i^2(k+N)+{\mathrm{\α}}_2\underset{i=4}{\overset{6}{\mathrm{\Σ}}}{\hat{X}}_i^2(k+N)+\mathrm{\β}[u_x^2\left(k\right)+u_y^2\left(k\right)+u_z^2\left(k\right)]---\left(3\right)$

α in the formula ₁＞0, α ₂＞0, β＞0.

Step three: According to equation (3) there must be optimal control

and

satisfies the following formula

$\underset{u_x=u_x^{*},u_y=u_y^{*},u_z=u_z^{*}}{J\left(k\right)}\≤\underset{\left|u_x\right|\∈A_U,\left|u_y\right|\∈A_U,\left|u_z\right|\∈A_U}{J\left(k\right)}---\left(4\right)$

Ie

and

is the time to k + N k optimal amount of control.

Step 4: with optimal control amount

and

as the real system controlling quantity; Calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating the Thrust Control engine operation.

Step 5: at (t _Min+ t ₀) constantly repeat above-mentioned optimal control amount computation process, obtain (T _Min+ t ₀) time be carved into (2T _Min+ t ₀) constantly engine optimum thrust magnitude.Every like this at a distance from T _MinEngine optimum thrust of Time Calculation arrives the mooring point until the spacecraft motion.

The invention has the beneficial effects as follows: since to two-stage fixedly trust engine intersection control problem through introducing driving engine minimum switching on and shutting down time T _MinOptimal Rendezvous thrust under the rolling forecast principle design double optimization function index is adopted in constraint; At every separated T _MinTime only needs to calculate the relatively size of 125 kinds of different target function values, makes things convenient for the engineering real-time implementation; Owing to considered the minimum switching on and shutting down work-hours constraint of driving engine, avoided the frequent switching on and shutting down problem of driving engine and reduced the engine design difficulty; This Optimization Design is good to the robustness of design mock-up error, measured error and intersection thrust error.

Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.

Description of drawings

Fig. 1 is the fixedly diagram of circuit of thrust spatial intersection control method of two-stage of the present invention;

Fig. 2 is two related spacecraft space relative coordinate system figure of the inventive method;

Fig. 3 embodiment of the invention x direction of principal axis acceleration/accel instruction curve;

Fig. 4 embodiment of the invention y direction of principal axis acceleration/accel instruction curve;

Fig. 5 embodiment of the invention z direction of principal axis acceleration/accel instruction curve;

Each relative distance change curve of Fig. 6 embodiment of the invention pursuit spacecraft and passive space vehicle;

Each relative velocity change curve of Fig. 7 embodiment of the invention pursuit spacecraft and passive space vehicle.

The specific embodiment

The two-stage of motor switch machine The limited time of the present invention fixedly thrust spatial intersection control method process is:

1) discretization model of Spacecraft Rendezvous motion under relative coordinate system is suc as formula (1)

X(k+1)＝F(X(k))+G(U(k))+Δ(k) (5)

State vector X and control vector U do

X＝[X ₁?X ₂?X ₃?X ₄?X ₅?X ₆] ^T，U＝[u _x?u _y?u _z] ^T

Wherein, X ₁=x, X ₂=y, X ₃=z,

And x, y and z are the relative position of pursuit spacecraft with respect to passive space vehicle;

With Be the relative velocity of pursuit spacecraft with respect to passive space vehicle; u _x, u _yAnd u _zBe respectively the Acceleration Control amount of pursuit spacecraft at three axles of system of axes, controlling quantity amplitude discrete domain is A _U={ u _High,-u _Low, 0, u _Low, u _High, u wherein _High＞0 is the cooresponding peak acceleration controlling quantity of maximum thrust (coarse regulation thrust) of driving engine, u _Low＞0 is the cooresponding little Acceleration Control amount of low thrust (accurate adjustment joint thrust) of driving engine, and u _High＞u _Low＞0; The disturbance acceleration that Δ (k) expression is caused by exciting force or other errors.If the minimum work-hours of driving engine is spaced apart T _Min, i.e. the minimum time length of driving engine opening and closing is T _Min

Do not consider to disturb Δ (k) effect, initial time t ₀, establish discrete system be k constantly.According to formula (1), k is intersection state X (k) and consider that the invariability of controlling quantity calculates k+N intersection constantly state estimation value according to formula (2) recursion constantly:

$\hat{X}(k+1)=F\left(X\left(k\right)\right)+G\left(U\left(k\right)\right)$

$\hat{X}(k+2)=F\left(\hat{X}(k+1)\right)+G\left(U\left(k\right)\right)$ (6)

$\begin{array}{c}.\\ .\\ .\\ \hat{X}(k+N)=F\left(\hat{X}(k+N-1)\right)+G\left(U\left(k\right)\right)\end{array}$

Choose the discrete sampling time T _sIt is the minimum work-hours interval T of driving engine _Min1/N, N is a positive integer.

2) according to formula (2) result, the double optimization index of calculating formula (3)

$J\left(k\right)={\mathrm{\α}}_1\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\hat{X}}_i^2(k+N)+{\mathrm{\α}}_2\underset{i=4}{\overset{6}{\mathrm{\Σ}}}{\hat{X}}_i^2(k+N)+\mathrm{\β}[u_x^2\left(k\right)+u_y^2\left(k\right)+u_z^2\left(k\right)]---\left(7\right)$

α in the formula ₁＞0, α ₂＞0, β＞0.

3) According to equation (3) there must be optimal control

and

satisfies the following formula

$\underset{u_x=u_x^{*},u_y=u_y^{*},u_z=u_z^{*}}{J\left(k\right)}\≤\underset{\left|u_x\right|\∈A_U,\left|u_y\right|\∈A_U,\left|u_z\right|\∈A_U}{J\left(k\right)}---\left(8\right)$

Ie

and

is the time to k + N k optimal amount of control.

4) optimal control amount

and

can be calculated the corresponding thrust of pursuit spacecraft driving engine as the real system controlling quantity, and according to calculating the Thrust Control engine operation.

5) at (T _Min+ t ₀) constantly repeat above-mentioned optimal control amount computation process, can obtain (T _Min+ t ₀) time be carved into (2T _Min+ t ₀) constantly engine optimum thrust magnitude.Every like this at a distance from T _MinEngine optimum thrust of Time Calculation arrives the mooring point until the spacecraft motion.

Select pursuit spacecraft that the passive space vehicle on the circular orbit is carried out near the motor-driven verification condition that is controlled to be.

The model of Spacecraft Rendezvous motion under relative coordinate system chosen classical CW model:

$\stackrel{\·\·}{x}-2n\stackrel{\·}{y}-3n^{2}x=u_x$

$\stackrel{\·\·}{y}+2n\stackrel{\·}{x}=u_y$

$\stackrel{\·\·}{z}+n^{2}z=u_z$

Wherein

μ is the terrestrial gravitation constant, μ=3.98 * 10 ¹⁴m ³/ s ², r is the orbit radius of passive space vehicle.

Get r=6.48 * 10 ⁶M, then n=0.0012m/s.The state-space expression of following formula does

$\stackrel{\·}{X}\left(t\right)=\mathrm{AX}\left(t\right)+\mathrm{BU}\left(t\right)$

Wherein $A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ {3\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}}^2& 0& 0& 0& 2\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}& 0\\ 0& 0& 0& -2\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}& 0& 0\\ 0& 0& -{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}}^2& 0& 0& 0\end{array}\right],$ $B=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

Adopt first order difference to be similar to state X, get the discrete sampling time T the derivative of time _s=0.01s, the minimum work-hours T of driving engine _Min=3s, then:

$\frac{\mathrm{dX}}{\mathrm{dt}}\stackrel{\&CenterDot;}{=}\frac{X(k+1)-X\left(k\right)}{T_s}$

Discretization model does

$\hat{X}(k+1)=\tilde{A}X\left(k\right)+\tilde{B}U\left(k\right)$

$\hat{X}(k+1+1|k)=\tilde{A}\hat{X}(k+1|k)+\tilde{B}U\left(k\right)$

$\begin{array}{c}={\tilde{A}}^{2}X\left(k\right)+(\tilde{A}\tilde{B}+\tilde{B})U\left(k\right)\\ .\\ .\\ .\end{array}$

$\hat{X}(k+N|k)=\tilde{A}X(k+N-1|k)+\tilde{B}U\left(k\right)$

$={\tilde{A}}^{N}X\left(k\right)+({\tilde{A}}^{N-1}\tilde{B}+...+\tilde{B})U\left(k\right)$

In the formula

N=T _Min/ T _s, N=300 in this example.

The controlling quantity amplitude is A _U={ u _High,-u _Low, 0, u _Low, u _HighSetting pursuit spacecraft intersection coarse adjustment controlling quantity u _Max=0.3m/s ², intersection accurate adjustment controlling quantity u _1ow=0.01m/s ², intersection mooring point parameter ρ _d=10m.

Target function $J\left(k\right)={\mathrm{\&alpha;}}_1\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_i^2(k+N_{\mathrm{Step}}|k)+{\mathrm{\&alpha;}}_2\underset{i=4}{\overset{6}{\mathrm{\&Sigma;}}}{X}_i^2(k+N_{\mathrm{Step}}|k)+\mathrm{\&beta;}[u_x^2\left(k\right)+u_y^2\left(k\right)+u_z^2\left(k\right)]$

Middle parameter alpha ₁=0.003, α ₂=1, β=25.

The intersection initial condition

X ₀＝[1000m -1000m?1000m -2m/s?2m/s -5m/s] ^T

Initial time t ₀=0s, according to the discretization model estimating system in the minimum switching on and shutting down time T of driving engine _MinBehind=the 3s t ₁=3s, controlling quantity has 5 kinds of selections on each, and the combination of three axle control amounts has 125 kinds, therefore estimates t ₁State of the system has 125 kinds of possibility situation constantly.These 125 kinds of estimated state amounts and control corresponding input substitution target function are calculated, through relatively choosing the controlling quantity combination that makes target function minimum.t ₀Constantly through comparing u _x=-0.3m/s ², u _y=0.3m/s ², u _z=0.01m/s ², can make target function minimum, so t ₀Constantly select u _x=-0.3m/s ², u _y=0.3m/s ², u _z=0.01m/s ²Calculate the corresponding thrust of pursuit spacecraft driving engine as the real system controlling quantity, and according to calculating Thrust Control engine operation T _MinTime.Every at a distance from T _Min=3s calculates an engine optimum thrust, arrives the mooring point until the spacecraft motion.

The mooring point state that calculates according to the present invention does

$X_{t_f}={\left[\begin{array}{cccccc}2.01m& 4.89m& 8.90m& -0.029m/s& -0.046m/s& 0.0033m/s\end{array}\right]}^T$

The total velocity increment that calculates is Δ V=7.88m/s.

Claims (1)

1. the fixing thrust spatial intersection control method of a two-stage is characterized in that may further comprise the steps:

Step 1: the discretization model of under relative coordinate system, setting up the Spacecraft Rendezvous motion:

X(k+1)＝F(X(k))+G(U(k))+Δ(k) (1)

State vector X and control vector U do

X＝[X ₁?X ₂?X ₃?X ₄?X ₅?X ₆] ^T，U＝[u _x?u _y?u _z] ^T

Wherein, X ₁=x, X ₂=y, X ₃=z,

And x, y and z are the relative position of pursuit spacecraft with respect to passive space vehicle;

With

Be the relative velocity of pursuit spacecraft with respect to passive space vehicle; u _x, u _yAnd u _zBe respectively the Acceleration Control amount of pursuit spacecraft at three axles of system of axes, controlling quantity amplitude discrete domain is A _U={ u _High,-u _Low, 0, u _Low, u _High, u wherein _High＞0 is the cooresponding peak acceleration controlling quantity of maximum thrust of driving engine, u _Low＞0 is the cooresponding little Acceleration Control amount of low thrust of driving engine, and u _High＞u _Low＞0; The disturbance acceleration that Δ (k) expression is caused by exciting force or other errors; The minimum work-hours of driving engine is spaced apart T _Min

Do not consider to disturb Δ (k) effect, initial time t ₀, establish discrete system be k constantly; According to formula (1), k is intersection state X (k) and consider that the invariability of controlling quantity calculates k+N intersection constantly state estimation value according to formula (2) recursion constantly:

$\hat{X}(k+1)=F\left(X\left(k\right)\right)+G\left(U\left(k\right)\right)$

$\hat{X}(k+2)=F\left(\hat{X}(k+1)\right)+G\left(U\left(k\right)\right)$ (2)

$\begin{array}{c}.\\ .\\ .\\ \hat{X}(k+N)=F\left(\hat{X}(k+N-1)\right)+G\left(U\left(k\right)\right)\end{array}$

Choose the discrete sampling time T _sIt is the minimum work-hours interval T of driving engine _Min1/N, N is a positive integer;

Step 2: according to formula (2) result, the double optimization index of calculating formula (3)

$J\left(k\right)={\mathrm{\&alpha;}}_1\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\hat{X}}_i^2(k+N)+{\mathrm{\&alpha;}}_2\underset{i=4}{\overset{6}{\mathrm{\&Sigma;}}}{\hat{X}}_i^2(k+N)+\mathrm{\&beta;}[u_x^2\left(k\right)+u_y^2\left(k\right)+u_z^2\left(k\right)]---\left(3\right)$

α in the formula ₁＞0, α ₂＞0, β＞0;

Step three: According to equation (3) there must be optimal control

and

satisfies the following formula

$\underset{u_x=u_x^{*},u_y=u_y^{*},u_z=u_z^{*}}{J\left(k\right)}\&le;\underset{\left|u_x\right|\&Element;A_U,\left|u_y\right|\&Element;A_U,\left|u_z\right|\&Element;A_U}{J\left(k\right)}---\left(4\right)$

Ie

and

is k to k + N times the optimal amount of control;

Step 4: with optimal control amount

and

as the real system controlling quantity; Calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating the Thrust Control engine operation;

Step 5: at (T _Min+ t ₀) constantly repeat above-mentioned optimal control amount computation process, obtain (T _Min+ t ₀) time be carved into (2T _Min+ t ₀) constantly engine optimum thrust magnitude; Every like this at a distance from T _MinEngine optimum thrust of Time Calculation arrives the mooring point until the spacecraft motion.

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