CN102582849B - 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.The method application triangular transformation technology is converted into abandoned virtual controlling by the thrust constraint, controlling quantity is carried out to parametric description and is expressed as piecewise constant function, and then optimal control problem is converted into to 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 and change with encounter conditions, and calculated amount is large, needs off-line optimization.

Summary of the invention

In order to overcome existing normal value thrust, realize the deficiency of intersection control method frequent switching on and shutting down of driving engine in the intersection process, the invention provides fixedly thrust spatial intersection control method of a kind of two-stage, the method application rolling forecast principle has been set up the optimization target function, corresponding relation between intersection predicted state and intersection thrust controlling quantity, by the target function value, relatively calculate and can determine engine optimum intersection thrust, can solve the lower quadratic function that imposes a condition of minimum switching on and shutting down time of driving engine and optimize fixedly thrust intersection control design problem of index two-stage, can greatly reduce motor switch machine number of times in the intersection process, 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 comprising the following steps:

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

X(k+1)＝F(X(k))+G(U(k))+Δ(k) (1)

State vector X and control vector U are

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

For 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 peak acceleration controlling quantity corresponding to maximum thrust of driving engine, u _low>0 is the little Acceleration Control amount corresponding to low thrust of driving engine, and u _High>u _low>0; Δ (k) means the disturbance acceleration 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 to k constantly.According to formula (1), k is intersection state X (k) 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 formula ₁>0, α ₂>0, β>0.

Step 3: certainly exist optimal control according to formula (3)

With

Meet following formula

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

Namely

With

During for k, be carved into the optimal control amount of k+N.

Step 4: by the optimal control amount

With

As the real system controlling quantity, calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating the work of thrust control engine.

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.Like this every T _minEngine optimum thrust of Time Calculation, until the spacecraft motion arrives mooring point.

The invention has the beneficial effects as follows: due to two-stage fixedly trust engine intersection control problem by introducing the minimum switching on and shutting down time T of driving engine _minConstraint, adopt Optimal Rendezvous thrust under rolling forecast principle design double optimization function index; Every T _minTime, only need to calculate the relatively size of 125 kinds of different target function values, facilitates the engineering real-time implementation; Owing to having 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 drawings and Examples, the present invention is elaborated.

The accompanying drawing explanation

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 present invention x direction of principal axis acceleration/accel instruction curve;

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

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

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

Each axle relative velocity change curve of Fig. 7 embodiment of the present 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 are

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 For 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 peak acceleration controlling quantity corresponding to maximum thrust (coarse regulation thrust) of driving engine, u _low>0 is the little Acceleration Control amount corresponding to low thrust (accurate adjustment joint thrust) of driving engine, and u _High>u _low>0; Δ (k) means the disturbance acceleration 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 to k constantly.According to formula (1), k is intersection state X (k) 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 formula ₁>0, α ₂>0, β>0.

3) according to formula (3), certainly exist optimal control

With

Meet following formula

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

Namely

With

During for k, be carved into the optimal control amount of k+N.

4) by the optimal control amount

With As the real system controlling quantity, can calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating the work of thrust control engine.

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.Like this every T _minEngine optimum thrust of Time Calculation, until the spacecraft motion arrives mooring point.

Select pursuit spacecraft to the passive space vehicle on circular orbit 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 Gravitational coefficient of the Earth, μ=3.98 * 10 ¹⁴m ³/ s ², r is the orbit radius of passive space vehicle.

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

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

Wherein $A=\left[\begin{array}{cccccc}0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\\ {3\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000144469890000032.png"\; state="\{\{state\}\}">n</figure-callout>}}^2& 0& 0& 0& 2\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}& 0\\ 0& 0& 0& -2\mathrm{<figure-callout\; id="0"\; label="n"\; filenames="HDA0000144469890000021.png,HDA0000144469890000022.png"\; state="\{\{state\}\}">n</figure-callout>}& 0& 0\\ 0& 0& -{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000144469890000032.png"\; state="\{\{state\}\}">n</figure-callout>}}^2& 0& 0& 0\end{array}\right],$ $B=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\\ 1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

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

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

Discretization model is

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

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

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

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

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

In 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 _minAfter=3s, be t ₁=3s, have 5 kinds of selections on each axle of controlling quantity, three axle controlling quantity combinations have 125 kinds, therefore estimate t ₁State of the system has 125 kinds of possibility situations constantly.These 125 kinds of estimated state amounts and corresponding control inputs substitution target function are calculated, by relatively choosing the controlling quantity combination that makes the target function minimum.T ₀Constantly by comparing u _x=-0.3m/s ², u _y=0.3m/s ², u _z=0.01m/s ², can make the target function minimum, so t ₀Constantly select u _x=-0.3m/s ², u _y=0.3m/s ², u _z=0.01m/s ²As the real system controlling quantity, calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating thrust control engine work T _minTime.Every T _min=3s calculates an engine optimum thrust, until the spacecraft motion arrives mooring point.

The mooring point state calculated according to the present invention is

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

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

Claims (1)

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

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

X(k+1)＝F(X(k))+G(U(k))+Δ(k) (1)

State vector X and control vector U are

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

For 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 relative coordinate system, controlling quantity amplitude discrete domain is A _U={ u _High,-u _low, 0, u _low, u _High, u wherein _High>0 is the peak acceleration controlling quantity corresponding to maximum thrust of driving engine, u _low>0 is the little Acceleration Control amount corresponding to low thrust of driving engine, and u _High>u _low>0; Δ (k) means the disturbance acceleration 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 discretization model be to k constantly; According to formula (1), k is intersection state X (k) consider that the invariability of controlling quantity calculates k+N intersection constantly state estimation value according to formula (2) recursion constantly:

$\begin{array}{c}\hat{X}(k+1)=F\left(X\left(k\right)\right)+G\left(U\left(k\right)\right)\\ \hat{X}(k+2)=F\left(\hat{X}(k+1)\right)+G\left(U\left(k\right)\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \hat{X}(k+N)=F\left(\hat{X}(k+N-1)\right)+G\left(U\left(k\right)\right)\end{array}---\left(2\right)$

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 formula ₁>0, α ₂>0, β>0;

Step 3: certainly exist optimal control according to formula (3)

With

Meet following formula

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

Namely With

During for k, be carved into the optimal control amount of k+N;

Step 4: by the optimal control amount

With

As the real system controlling quantity, calculate the corresponding thrust of pursuit spacecraft driving engine, and according to calculating the work of thrust control engine;

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; Like this every T _minEngine optimum thrust of Time Calculation, until the spacecraft motion arrives mooring point.

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