CN107703759A - A kind of moon detector in flexible landing optimal control system based on adaptive congestion control algorithm grid - Google Patents
A kind of moon detector in flexible landing optimal control system based on adaptive congestion control algorithm grid Download PDFInfo
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- CN107703759A CN107703759A CN201711117099.3A CN201711117099A CN107703759A CN 107703759 A CN107703759 A CN 107703759A CN 201711117099 A CN201711117099 A CN 201711117099A CN 107703759 A CN107703759 A CN 107703759A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The invention discloses a kind of moon detector in flexible landing optimal control system based on adaptive congestion control algorithm grid, the system is shown by velocity sensor, range finder, MCU, fuel consuming system, soft landing regime and formed.When lunar orbiter prepares soft landing, the distance between velocity sensor, the decrease speed of the current detector of range finder measurement and moonscape, and send measurement data to MCU, MCU is immediately performed adaptive congestion control algorithm grid method for optimally controlling, calculate send as an envoy to lunar orbiter safe landing and at least consume fuel fuel consumption rate control strategy, it is converted into operating instruction and sends fuel consuming system, and the current soft landing regime of real-time display to.The present invention can ensure the safe soft landing of lunar orbiter and farthest reduce the consumption of fuel.
Description
Technical field
The present invention relates to soft lunar landing control field, mainly a kind of moon talent scout based on adaptive congestion control algorithm grid
Survey device soft landing optimal control system.When lunar orbiter will land, the system can calculate optimal soft landing plan
Omit, to ensure detector safe landing and farthest reduce the consumption of fuel.
Background technology
Later 1950s so far, the U.S., the former Soviet Union/Russia, Japan, European Space Agency, the nations of China and India
Moon exploration successively has been carried out, the upsurge of a new round has been risen since the nineties.Wherein, moon detector in flexible landing is a kind of
Very important technological means.Soft landing is exactly to reduce vertical speed by certain means before landing, is allowed to one
Acceptable speed is landed, to protect aircraft and spacefarer.Due to there is no air on the moon, similar to vacuum, with landing
Umbrella is impossible, and bad control dynamics of air cushion, current technology be by lunar orbiter itself reaction force realize it is soft
Land.Now, lot of domestic and foreign experts and scholars expand further investigation to this.
The content of the invention
In order that lunar orbiter safe landing and the farthest consumption of reduction fuel, the invention provides one kind
Moon detector in flexible landing optimal control system based on adaptive congestion control algorithm grid, the system is by MCU as optimal control
Method processed realizes carrier.
The purpose of the present invention is achieved through the following technical solutions：A kind of moon based on adaptive congestion control algorithm grid
Ball detector soft landing optimal control system, optimal soft landing strategy can be calculated, to ensure detector safe landing simultaneously
And farthest reduce the consumption of fuel.It is characterized in that：By velocity sensor, range finder, MCU, fuel consumption system
System, soft landing regime display are formed.The running of the system includes：
Step A4：Lunar orbiter prepares opening speed sensor and range finder during soft landing, for surveying in real time
The decrease speed of the current detector of amount and the distance between with moonscape, and send measurement data to MCU；
Step A5：Adaptive congestion control algorithm grid method for optimally controlling inside MCU execution, calculates lunar orbiter of sening as an envoy to
Safe landing and the fuel consumption rate control strategy at least consuming fuel；
Step A6：Obtained fuel consumption rate control strategy is converted to fuel consuming system operating instruction by MCU, transmission
To fuel consuming system, and the current soft landing regime of real-time display.
Described MCU, including information acquisition module, initialization module, end time processing module, dominant vector parametrization
It is module, Non-Linear Programming (Nonlinear Programming, NLP) problem solver module, end condition judge module, adaptive
Mesh generation module, time scale modular converter, control instruction output module should be controlled.
The soft landing process of lunar orbiter can be described as：
Wherein t represents time, t0Represent soft landing process time started, tfRepresent soft landing course over time, and tfNo
It is fixed；Be referred to as state variable, represent the speed of lunar orbiter, acceleration,
The physical parameters such as the distance between quality and moonscape, x0It is its initial value,It is its first derivative；U (t) represents the moon
The fuel consumption rate of detector, ul、uuRespectively its lower limit and higher limit；It is according to the conservation of energy and mechanics
The differential equation group that principle is established；It is the constraint bar of the physical parameter foundation to moon detector in flexible landing finish time
Part.nx,ngIt is state variable and the quantity of constraint respectively.
Assuming that with Φ [x (tf)] representing the total flow of fuel, then the mathematical modeling for making fuel consumption minimum is represented by：
Wherein J [u (t)] represents control targe, is determined by fuel consumption rate u (t).It is one optimal in the question essence
Control problem.
Technical scheme is used by the present invention solves the problem：Adaptive congestion control algorithm grid is integrated with MCU most
Excellent control method, and a set of optimal control system is constructed based on this.The structure of the control system includes velocity pick-up
Device, range finder, MCU, fuel consuming system, soft landing regime are shown.Each part of the system is by moon talent scout
Survey the unified connection of data/address bus in device.
The running of the system is as follows：
Step C1：Lunar orbiter prepares opening speed sensor and range finder during soft landing, for surveying in real time
The decrease speed of the current detector of amount and the distance between with moonscape, and send measurement data to MCU；
Step C2：Adaptive congestion control algorithm grid method for optimally controlling inside MCU execution, calculates lunar orbiter of sening as an envoy to
Safe landing and the fuel consumption rate control strategy at least consuming fuel；
Step C3：Obtained fuel consumption rate control strategy is converted to fuel consuming system operating instruction by MCU, transmission
To fuel consuming system, and the current soft landing regime of real-time display.
The MCU for being integrated with adaptive congestion control algorithm grid method for optimally controlling is the core of the present invention, and it is internal including letter
Cease acquisition module, initialization module, end time processing module, dominant vector parameterized module, Non-Linear Programming
(Nonlinear Programming, NLP) problem solver module, end condition judge module, Self Adaptive Control mesh generation mould
Block, time scale modular converter, control instruction output module.
Information acquisition module includes the distance between the collection of current decrease speed and moonscape and gathers two submodules.
End time processing module introduces new time variable υ so that
T=(tf-t0)υ+t0 (3)
So as to by end time tfUnfixed mathematical modeling (2) is converted to the mathematical modeling for controlling time domain to be [0,1], such as
Shown in lower：
Wherein,
Dominant vector parameterized module realizes fuel consumption rate control using piece-wise constant strategy, specific as follows：
Assuming that entirely time domain [0,1] is controlled to be divided into [υ between p (p ＞ 0) individual control work zonek-1,υk) (k=1,2 ...,
P), and
0 ＜ υ1＜ ... ＜ υp-1＜ υp=1 (6)
So,It is represented by：
Wherein,For constant, represent[the υ between control work zonek-1,υk) in parameter value, χk(υ) is that unit switchs letter
Number, it is defined as follows：
So as to which fuel consumption rate control parameter can be by vectorRepresent.
NLP problem solver modules include SQP (Sequential Quadratic Programming, SQP)
Solve, simultaneous differential equations solves two submodules.Simultaneous differential equations includes equation group (9)
With equation group (10)
Wherein,
Simultaneous differential equations (9), (10) are solved using Runge-Kutta algorithm, mathematical modeling (4) can be obtained
Target function valueAnd object function is to the First-order Gradient information of control parameter vector：
It is also possible to obtain constraint function value G [x (1)] in mathematical modeling (4) and constraint function to control parameter to
The First-order Gradient information of amount：
Self Adaptive Control mesh generation module provides a kind of strategy of adaptive division control grid, specific as follows：
Dominant vector is parameterized first with fast wavelet transform (Fast Wavelet Transformation, FWT)
What resume module was crossedIt is transformed into wavelet field, you can obtain
Wherein,For wavelet coefficient column vector,For wavelet function column vector, ΛlIt is one (j, k) to set, is claimed
Index and gather for small echo.
Assuming that obtain optimal solution by the l times iterationIf wavelet coefficient therein meets
|d*l| ＜ εe (16)
Wherein, εe＞ 0 is given threshold value, then the wavelet coefficient can be ignored.The wavelet function being eliminatedIndex
With setTo represent.
Define wavelet function ψj,k-1、ψj,k+1For wavelet function ψj,kHorizontally adjacent function, ψj+1,2k、ψj+1,2k+1Hung down for it
Straight adjacent function.If the wavelet coefficient of at least one adjacent function of a certain wavelet function is zero, it is small that it is referred to as border
Wave function.All border wavelet coefficients byRepresent.
Select the border wavelet function of minimal numberMake its coefficientMeet
Wherein, εi∈ (0,1] represent given selection percentage.So, wavelet functionVertical neighborhood function can quilt
The potential wavelet function being considered as in next iteration, the set of its indexRepresent.
The small echo indexed set for finally giving next iteration is combined into：
Currently the set of small echo index it will potentially gather with next iteration and merge, while the small echo rope that removing is eliminated
Draw.So, with set Λl+1Corresponding time grid is exactly resulting more suitably control grid Δl+1, will be next time
It is employed in iteration.
Time scale modular converter is that current mathematical modeling (4) is transformed into a new time scale, in order to right
The control grid that Self Adaptive Control mesh generation module obtains optimizes, specific as follows：
Select border small echoThe part of middle minimal numberSo that
Wherein, εs∈ (0,1] it is given selection percentage.So, wavelet functionVertical neighborhood function can be considered as
It is important.Time domain corresponding to important vertical neighborhood function is as needed between the important control work zone that optimizes.
Assuming that after the adjustment of Self Adaptive Control mesh generation module, whole control time domain is present between P control work zone
[υk-1,υk) (k=1,2 ..., P), the length θ between each control work zonekRepresent, and its initial value is
For between insignificant control work zone therein, its length is definite value, it is not necessary to is optimized.For important control therein
Section, according to its continuous situation, it is assumed that R (R >=1) part can be divided into, r (1≤r≤R) partly includes nr(nr>=2) it is individual continuous
Between control work zone, and the length between its all control work zone meets：
It is as follows to introduce time scale transfer function：
Wherein, τ is new time variable,Represent the maximum integer no more than τ.So, mathematical modeling (4) is new
It can be converted into time scale：
Wherein,
The process that the MCU produces fuel consuming system operating instruction is as follows：
Step D1：Information acquisition module obtain the current decrease speed of lunar orbiter and between moonscape away from
From；
Step D2：Initialization module is run, set initial control lattice number p, fuel consumption rate control strategy just
Beginning conjecture valueSet constant value εe＞ 0, εi∈(0,1]、εs∈ (0,1], maximum iteration l is setmax>=1 and terminate miss
Poor tolJ＞ 0, and make iteration count l=0；
Step D3：Mathematical modeling (2) is converted to mathematical modeling (4) by end time processing module；
Step D4：Dominant vector parameterized module represents fuel consumption rate controlling curve using piece-wise constant strategy,
If l=0, control time domain is divided into p sections and obtains currently controlling grid, and make all control parameter values beOtherwise,
Using ΔlAs current control grid, the parameter value in each control work zone is in corresponding control time domainValue；
Step D5：SQP in NLP problem solver modules solves module operation, and is solved by simultaneous differential equations
Module obtains target function value, object function to the vectorial First-order Gradient information of control parameter, constraint function value, constraint function pair
The First-order Gradient information of control parameter vector, finally give the object function optimal value J under current control grid*lIt is and corresponding
Optimal control parameter
Step D6：End condition judge module is run, for l ＞ 0, if l=lmaxOr
Step D10 is then performed, otherwise, performs step D7；
Step D7：Self Adaptive Control mesh generation module is run, and obtains new control grid Δl+1；
Step D8：Iteration count l=l+1 is made, if l=lmax, then step D9 is performed, otherwise, goes to step D4；
Step D9：Time scale modular converter is converted to mathematical modeling (4) mathematical modeling (23) in new time scale,
Go to step D4；
Step D10：Control instruction output module will currently control time domain to be transformed into actual control time domain by (22), (3), and
The optimum fuel consumption rate control strategy of acquisition is exported.
Beneficial effects of the present invention are mainly manifested in：The moon exploration of adaptive congestion control algorithm grid based on wavelet analysis
Device soft landing optimal control system, the optimal soft landing strategy of detector can be calculated, is adapted to the optimum control of problem
Curve, the discontinuity point of problem is particularly found, higher precision can be obtained；After adaptive strategy, most next time
The initial estimate of excellent controlling curve is the optimal curve of current iteration, it is possible thereby to obtain faster convergence rate, reduces and visits
Survey the calculating time of the optimal soft landing strategy of device.The present invention in the case where ensureing the safe soft landing of lunar orbiter, and
The consumption of fuel can farthest be reduced.
Brief description of the drawings
Fig. 1 is the functional schematic of the present invention；
Fig. 2 is the structural representation of the present invention；
Fig. 3 is MCU internal modules structure chart of the present invention；
Fig. 4 is the fuel consumption rate control strategy figure obtained to embodiment 1；
Fig. 5 is each state variable variation diagram corresponding to fuel consumption rate control strategy in Fig. 4.
Embodiment
As shown in figure 1, the soft landing process of lunar orbiter can be described as：
Wherein t represents time, t0Represent soft landing process time started, tfRepresent soft landing course over time, and tfNo
It is fixed；Be referred to as state variable, represent the speed of lunar orbiter, acceleration,
The physical parameters such as the distance between quality and moonscape, x0It is its initial value,It is its first derivative；U (t) represents the moon
The fuel consumption rate of detector, ul、uuRespectively its lower limit and higher limit；It is according to the conservation of energy and mechanics
The differential equation group that principle is established；It is the constraint bar of the physical parameter foundation to moon detector in flexible landing finish time
Part.nx,ngIt is state variable and the quantity of constraint respectively.
Assuming that with Φ [x (tf)] representing the total flow of fuel, then the mathematical modeling for making fuel consumption minimum is represented by：
Wherein J [u (t)] represents control targe, is determined by fuel consumption rate u (t).It is one optimal in the question essence
Control problem.
Technical scheme is used by the present invention solves the problem：Adaptive congestion control algorithm grid is integrated with MCU most
Excellent control method, and a set of optimal control system is constructed based on this.The structure of the control system is as shown in Fig. 2 bag
Velocity sensor, range finder, MCU, fuel consuming system, soft landing regime is included to show.Each part of the system
Connected by data/address bus in lunar orbiter is unified.
The running of the system is as follows：
Step C4：Lunar orbiter prepares opening speed sensor and range finder during soft landing, for surveying in real time
The decrease speed of the current detector of amount and the distance between with moonscape, and send measurement data to MCU；
Step C5：Adaptive congestion control algorithm grid method for optimally controlling inside MCU execution, calculates lunar orbiter of sening as an envoy to
Safe landing and the fuel consumption rate control strategy at least consuming fuel；
Step C6：Obtained fuel consumption rate control strategy is converted to fuel consuming system operating instruction by MCU, transmission
To fuel consuming system, and the current soft landing regime of real-time display.
The MCU for being integrated with adaptive congestion control algorithm grid method for optimally controlling is the core of the present invention, as shown in figure 3, its
Inside includes information acquisition module, initialization module, end time processing module, dominant vector parameterized module, non-linear rule
Draw (Nonlinear Programming, NLP) problem solver module, end condition judge module, Self Adaptive Control mesh generation
Module, time scale modular converter, control instruction output module.
Information acquisition module includes the distance between the collection of current decrease speed and moonscape and gathers two submodules.
End time processing module introduces new time variable υ so that
T=(tf-t0)υ+t0 (28)
So as to by end time tfUnfixed mathematical modeling (2) is converted to the mathematical modeling for controlling time domain to be [0,1], such as
Shown in lower：
Wherein,
Dominant vector parameterized module realizes fuel consumption rate control using piece-wise constant strategy, specific as follows：
Assuming that entirely time domain [0,1] is controlled to be divided into [υ between p (p ＞ 0) individual control work zonek-1,υk) (k=1,2 ...,
P), and
0 ＜ υ1＜ ... ＜ υp-1＜ υp=1 (31)
So,It is represented by：
Wherein,For constant, represent[the υ between control work zonek-1,υk) in parameter value, χk(υ) is that unit switchs letter
Number, it is defined as follows：
So as to which fuel consumption rate control parameter can be by vectorRepresent.
NLP problem solver modules include SQP (Sequential Quadratic Programming, SQP)
Solve, simultaneous differential equations solves two submodules.Simultaneous differential equations includes equation group (9)
With equation group (10)
Wherein,
Simultaneous differential equations (9), (10) are solved using Runge-Kutta algorithm, mathematical modeling (4) can be obtained
Target function valueAnd object function is to the First-order Gradient information of control parameter vector：
It is also possible to obtain the constraint function value in mathematical modeling (4)And constraint function to control parameter to
The First-order Gradient information of amount：
Self Adaptive Control mesh generation module provides a kind of strategy of adaptive division control grid, specific as follows：
Dominant vector is parameterized first with fast wavelet transform (Fast Wavelet Transformation, FWT)
What resume module was crossedIt is transformed into wavelet field, you can obtain
Wherein,For wavelet coefficient column vector,For wavelet function column vector, ΛlIt is one (j, k) to set, is claimed
Index and gather for small echo.
Assuming that obtain optimal solution by the l times iterationIf wavelet coefficient therein meets
|d*l| ＜ εe (41)
Wherein, εe＞ 0 is given threshold value, then the wavelet coefficient can be ignored.The wavelet function being eliminatedIndex
With setTo represent.
Define wavelet function ψj,k-1、ψj,k+1For wavelet function ψj,kHorizontally adjacent function, ψj+1,2k、ψj+1,2k+1Hung down for it
Straight adjacent function.If the wavelet coefficient of at least one adjacent function of a certain wavelet function is zero, it is small that it is referred to as border
Wave function.All border wavelet coefficients byRepresent.
Select the border wavelet function of minimal numberMake its coefficientMeet
Wherein, εi∈ (0,1] represent given selection percentage.So, wavelet functionVertical neighborhood function can quilt
The potential wavelet function being considered as in next iteration, the set of its indexRepresent.
The small echo indexed set for finally giving next iteration is combined into：
Currently the set of small echo index it will potentially gather with next iteration and merge, while the small echo rope that removing is eliminated
Draw.So, with set Λl+1Corresponding time grid is exactly resulting more suitably control grid Δl+1, will be next time
It is employed in iteration.
Time scale modular converter is that current mathematical modeling (4) is transformed into a new time scale, in order to right
The control grid that Self Adaptive Control mesh generation module obtains optimizes, specific as follows：
Select border small echoThe part of middle minimal numberSo that
Wherein, εs∈ (0,1] it is given selection percentage.So, wavelet functionVertical neighborhood function can be considered as
It is important.Time domain corresponding to important vertical neighborhood function is as needed between the important control work zone that optimizes.
Assuming that after the adjustment of Self Adaptive Control mesh generation module, whole control time domain is present between P control work zone
[υk-1,υk) (k=1,2 ..., P), the length θ between each control work zonekRepresent, and its initial value is
For between insignificant control work zone therein, its length is definite value, it is not necessary to is optimized.For important control therein
Section, according to its continuous situation, it is assumed that R (R >=1) part can be divided into, r (1≤r≤R) partly includes nr(nr>=2) it is individual continuous
Between control work zone, and the length between its all control work zone meets：
It is as follows to introduce time scale transfer function：
Wherein, τ is new time variable,Represent the maximum integer no more than τ.So, mathematical modeling (4) is new
It can be converted into time scale：
Wherein,
The process that the MCU produces fuel consuming system operating instruction is as follows：
Step D11：Information acquisition module obtain the current decrease speed of lunar orbiter and between moonscape away from
From；
Step D12：Initialization module is run, set initial control lattice number p, fuel consumption rate control strategy just
Beginning conjecture valueSet constant value εe＞ 0, εi∈(0,1]、εs∈ (0,1], maximum iteration l is setmax>=1 and terminate miss
Poor tolJ＞ 0, and make iteration count l=0；
Step D13：Mathematical modeling (2) is converted to mathematical modeling (4) by end time processing module；
Step D14：Dominant vector parameterized module represents fuel consumption rate controlling curve using piece-wise constant strategy,
If l=0, control time domain is divided into p sections and obtains currently controlling grid, and make all control parameter values beOtherwise,
Using ΔlAs current control grid, the parameter value in each control work zone is in corresponding control time domainValue；
Step D15：SQP in NLP problem solver modules solves module operation, and is solved by simultaneous differential equations
Module obtains target function value, object function to the vectorial First-order Gradient information of control parameter, constraint function value, constraint function pair
The First-order Gradient information of control parameter vector, finally give the object function optimal value J under current control grid*lIt is and corresponding
Optimal control parameter
Step D16：End condition judge module is run, for l ＞ 0, if l=lmaxOr
Step D20 is then performed, otherwise, performs step D17；
Step D17：Self Adaptive Control mesh generation module is run, and obtains new control grid Δl+1；
Step D18：Iteration count l=l+1 is made, if l=lmax, then step D19 is performed, otherwise, goes to step D14；
Step D19：Time scale modular converter is converted to mathematical modeling (4) mathematical modeling in new time scale
(23) step D14, is gone to；
Step D20：Control instruction output module will currently control time domain to be transformed into actual control time domain by (22), (3), and
The optimum fuel consumption rate control strategy of acquisition is exported.
Embodiment 1
The mathematical modeling of certain moon detector in flexible landing is as follows：
Wherein, x1(t)、x2(t)、x3(t) the distance between detector and moonscape (m), decrease speed are represented respectively
(m/s), Fuel Consumption (kg), u (t) represent fuel consumption rate (kg/s).
When detector starts soft landing, velocity sensor, range finder measure the lower reduction of speed of the current detector
It is 10m to spend for the distance between -2m/s and moonscape, and these measurement data are sent to MCU information acquisition module.
MCU immediately begins to run adaptive congestion control algorithm grid method for optimally controlling, and its running is as shown in figure 3, be：
Step E1：Initialization module 2 is run, and sets initial control lattice number p=4, fuel consumption rate control strategy
Initial guessSet constant value εe=10-4、εi=0.9999, εs=0.97, maximum iteration l is setmax
=2 and termination error tolJ=10-6, and make iteration count l=0；
Step E2：End time processing module 3 is run, and mathematical modeling (51) is converted to the form of mathematical modeling (4)；
Step E3：Dominant vector parameterized module 4 represents fuel consumption rate controlling curve using piece-wise constant strategy,
If l=0, control time domain is divided into p sections and obtains currently controlling grid, and make all control parameter values beOtherwise,
Using ΔlAs current control grid, the parameter value in each control work zone is in corresponding control time domainValue；
Step E4：SQP in NLP problem solver modules 5 solves module operation, and is solved by simultaneous differential equations
Module obtains target function value, object function to the vectorial First-order Gradient information of control parameter, constraint function value, constraint function pair
The First-order Gradient information of control parameter vector, finally give the object function optimal value J under current control grid*lIt is and corresponding
Optimal control parameter
Step E5：End condition judge module 6 is run, for l ＞ 0, if l=lmaxOr
Step E9 is then performed, otherwise, performs step E6；
Step E6：Self Adaptive Control mesh generation module 7 is run, and obtains new control grid Δl+1；
Step E7：Iteration count l=l+1 is made, if l=lmax, then step E8 is performed, otherwise, goes to step E3；
Step E8：Time scale modular converter 8 is converted to mathematical modeling (4) mathematical modeling in new time scale
(23) step E3, is gone to；
Step E9：Control instruction output module 9 will currently control time domain to be transformed into actual control time domain by (22), (3), and
The optimum fuel consumption rate control strategy of acquisition is exported.
Optimum fuel consumption speed control curve such as Fig. 4 institutes that adaptive congestion control algorithm grid method for optimally controlling obtains
Show, fully meet control and require.Fig. 5 shows the change curve of distance between lunar orbiter and moonscape, decrease speed,
It can be seen that its value is 0 at the end of soft landing.
Finally, obtained fuel consumption rate control strategy is converted to fuel consuming system operating instruction by MCU, is sent to
Fuel consuming system, and the current soft landing regime of real-time display.
Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and
In scope of the claims, to any modifications and changes of the invention made, protection scope of the present invention is both fallen within.
Claims (1)
1. a kind of moon detector in flexible landing optimal control system based on adaptive congestion control algorithm grid, can be calculated optimal
Soft landing strategy, with ensure detector safe landing and farthest reduce fuel consumption.It is characterized in that：By speed
Spend sensor, range finder, MCU, fuel consuming system, soft landing regime display composition.The running bag of the system
Include：
Step A1：Lunar orbiter prepares opening speed sensor and range finder during soft landing, works as measuring in real time
The decrease speed of the preceding detector and the distance between with moonscape, and send measurement data to MCU；
Step A2：Adaptive congestion control algorithm grid method for optimally controlling inside MCU execution, calculate lunar orbiter safety of sening as an envoy to
Landing and the fuel consumption rate control strategy at least consuming fuel；
Step A3：Obtained fuel consumption rate control strategy is converted to fuel consuming system operating instruction by MCU, sends combustion to
Expect consumption system, and the current soft landing regime of real-time display.
Described MCU, including information acquisition module, initialization module, end time processing module, dominant vector parametrization mould
It is block, Non-Linear Programming (Nonlinear Programming, NLP) problem solver module, end condition judge module, adaptive
Control mesh generation module, time scale modular converter, control instruction output module.
The soft landing process of lunar orbiter can be described as：
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Wherein t represents time, t0Represent soft landing process time started, tfRepresent soft landing course over time, and tfIt is not solid
It is fixed；It is referred to as state variable, represents speed, acceleration, the matter of lunar orbiter
The physical parameters such as the distance between amount and moonscape, x0It is its initial value,It is its first derivative；U (t) represents moon talent scout
Survey the fuel consumption rate of device, ul、uuRespectively its lower limit and higher limit；It is former according to the conservation of energy and mechanics
Manage the differential equation group established；It is the constraint bar of the physical parameter foundation to moon detector in flexible landing finish time
Part.nx,ngIt is state variable and the quantity of constraint respectively.
Assuming that with Φ [x (tf)] representing the total flow of fuel, then the mathematical modeling for making fuel consumption minimum is represented by：
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Wherein J [u (t)] represents control targe, is determined by fuel consumption rate u (t).
Information acquisition module includes the distance between the collection of current decrease speed and moonscape and gathers two submodules.
End time processing module introduces new time variable υ so that
T=(tf-t0)υ+t0 (3)
So as to by end time tfUnfixed mathematical modeling (2) is converted to the mathematical modeling for controlling time domain to be [0,1], following institute
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Dominant vector parameterized module realizes fuel consumption rate control using piece-wise constant strategy, specific as follows：
Assuming that entirely time domain [0,1] is controlled to be divided into [υ between p (p ＞ 0) individual control work zonek-1,υk) (k=1,2 ..., p), and
0 ＜ υ1＜ ... ＜ υp-1＜ υp=1 (6)
So,It is represented by：
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So as to which fuel consumption rate control parameter can be by vectorRepresent.
NLP problem solver modules are asked including SQP (Sequential Quadratic Programming, SQP)
Solution, simultaneous differential equations solve two submodules.Simultaneous differential equations includes equation group (9)
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<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mo>&part;</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
Simultaneous differential equations (9), (10) are solved using Runge-Kutta algorithm, the mesh of mathematical modeling (4) can be obtained
Offer of tender numerical valueAnd object function is to the First-order Gradient information of control parameter vector：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>J</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>&Phi;</mi>
<mo>&lsqb;</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>&part;</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msub>
<mo>|</mo>
<mrow>
<mi>&upsi;</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
It is also possible to obtain the constraint function value in mathematical modeling (4)And constraint function is to control parameter vector
First-order Gradient information：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>G</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>G</mi>
<mo>&lsqb;</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mo>&part;</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>|</mo>
<mover>
<mi>u</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<msub>
<mo>|</mo>
<mrow>
<mi>&upsi;</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
Self Adaptive Control mesh generation module provides a kind of strategy of adaptive division control grid, specific as follows：
First with fast wavelet transform (Fast Wavelet Transformation, FWT) by dominant vector parameterized module
TreatedIt is transformed into wavelet field, you can obtain
<mrow>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<msup>
<mi>&Lambda;</mi>
<mi>l</mi>
</msup>
<mi>T</mi>
</msubsup>
<msub>
<mi>&Psi;</mi>
<msup>
<mi>&Lambda;</mi>
<mi>l</mi>
</msup>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,For wavelet coefficient column vector,For wavelet function column vector, ΛlIt is one (j, k) to set, is referred to as small
Ripple index set.
Assuming that obtain optimal solution by the l times iterationIf wavelet coefficient therein meets
|d*l| ＜ εe (16)
Wherein, εe＞ 0 is given threshold value, then the wavelet coefficient can be ignored.The wavelet function being eliminatedIndex collection
CloseTo represent.
Define wavelet function ψj,k-1、ψj,k+1For wavelet function ψj,kHorizontally adjacent function, ψj+1,2k、ψj+1,2k+1For its vertical phase
Adjacent function.If the wavelet coefficient of at least one adjacent function of a certain wavelet function is zero, it is referred to as border small echo letter
Number.All border wavelet coefficients byRepresent.
Select the border wavelet function of minimal numberMake its coefficientMeet
Wherein, εi∈ (0,1] represent given selection percentage.So, wavelet functionVertical neighborhood function can be considered as
Potential wavelet function in next iteration, the set of its indexRepresent.
The small echo indexed set for finally giving next iteration is combined into：
<mrow>
<msup>
<mi>&Lambda;</mi>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>&Lambda;</mi>
<mi>l</mi>
</msup>
<mo>&cup;</mo>
<msup>
<mover>
<mi>&Lambda;</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>\</mo>
<msup>
<mover>
<mi>&Lambda;</mi>
<mo>~</mo>
</mover>
<mrow>
<mi>l</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
Currently the set of small echo index it will potentially gather with next iteration and merges, while the eliminated small echo of removing indexes.
So, with set Λl+1Corresponding time grid is exactly resulting more suitably control grid Δl+1, will be changed next time
It is employed in generation.
Time scale modular converter is that current mathematical modeling (4) is transformed into a new time scale, in order to adaptive
The control grid that mesh generation module should be controlled to obtain optimizes, specific as follows：
Select border small echoThe part of middle minimal numberSo that
Wherein, εs∈ (0,1] it is given selection percentage.So, wavelet functionVertical neighborhood function can be considered as weight
Want.Time domain corresponding to important vertical neighborhood function is as needed between the important control work zone that optimizes.
Assuming that after the adjustment of Self Adaptive Control mesh generation module, it is whole to control time domain [υ between P control work zone to be presentk-1,υk)
(k=1,2 ..., P), the length θ between each control work zonekRepresent, and its initial value is
<mrow>
<msubsup>
<mi>&theta;</mi>
<mi>k</mi>
<mn>0</mn>
</msubsup>
<mo>=</mo>
<msub>
<mi>&upsi;</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&upsi;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
For between insignificant control work zone therein, its length is definite value, it is not necessary to is optimized.For important control work zone therein
Between, according to its continuous situation, it is assumed that R (R >=1) part can be divided into, r (1≤r≤R) partly includes nr(nr>=2) individual continuous control
System section, and the length between its all control work zone meets：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
</msub>
<mo>+</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mo>...</mo>
<mo>+</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<msub>
<mi>n</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msubsup>
<mi>&theta;</mi>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>0</mn>
</msubsup>
<mo>+</mo>
<mn>...</mn>
<mo>+</mo>
<msubsup>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<msub>
<mi>n</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>0</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
</msub>
<mo>,</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>&theta;</mi>
<mrow>
<msub>
<mi>k</mi>
<mi>r</mi>
</msub>
<mo>+</mo>
<msub>
<mi>n</mi>
<mi>r</mi>
</msub>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&GreaterEqual;</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>21</mn>
<mo>)</mo>
</mrow>
</mrow>
It is as follows to introduce time scale transfer function：
Wherein, τ is new time variable,Represent the maximum integer no more than τ.So, mathematical modeling (4) is in the new time
It can be converted on yardstick：
Wherein,
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&upsi;</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>u</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&upsi;</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>f</mi>
<mo>~</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&tau;</mi>
<mo>,</mo>
<mover>
<mi>x</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mover>
<mi>u</mi>
<mo>~</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>=</mo>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
<mo>{</mo>
<mi>&upsi;</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&upsi;</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>,</mo>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&upsi;</mi>
<mrow>
<mo>(</mo>
<mi>&tau;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>=</mo>
<mover>
<mi>f</mi>
<mo>&OverBar;</mo>
</mover>
<mo>&lsqb;</mo>
<mi>&upsi;</mi>
<mo>,</mo>
<mover>
<mi>x</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mover>
<mi>u</mi>
<mo>&OverBar;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>&upsi;</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>24</mn>
<mo>)</mo>
</mrow>
</mrow>
The process that the MCU produces fuel consuming system operating instruction is as follows：
Step B1：Information acquisition module obtains the current decrease speed of lunar orbiter and the distance between with moonscape；
Step B2：Initialization module is run, and sets initial control lattice number p, the initial of fuel consumption rate control strategy to guess
Measured valueSet constant value εe＞ 0, εi∈(0,1]、εs∈ (0,1], maximum iteration l is setmax>=1 and terminate error
tolJ＞ 0, and make iteration count l=0；
Step B3：End time unfixed moon detector in flexible landing mathematical modeling is converted to control by end time processing mould
Time domain is the mathematical modeling of [0,1]；
Step B4：Dominant vector parameterized module represents fuel consumption rate controlling curve using piece-wise constant strategy, if l
=0, then control time domain is divided into p sections and obtains currently controlling grid, and make all control parameter values beOtherwise, use
ΔlAs current control grid, the parameter value in each control work zone is in corresponding control time domainValue；
Step B5：SQP in NLP problem solver modules solves module operation, and solves module by simultaneous differential equations
Target function value, object function are obtained to the First-order Gradient information, constraint function value, constraint function of control parameter vector to control
The First-order Gradient information of parameter vector, finally give the object function optimal value J under current control grid*lIt is and corresponding optimal
Control parameter
Step B6：End condition judge module is run, for l ＞ 0, if l=lmaxOr
<mrow>
<mo>|</mo>
<mfrac>
<mrow>
<msup>
<mi>J</mi>
<mrow>
<mo>*</mo>
<mi>l</mi>
</mrow>
</msup>
<mo>-</mo>
<msup>
<mi>J</mi>
<mrow>
<mo>*</mo>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
<msup>
<mi>J</mi>
<mrow>
<mo>*</mo>
<mi>l</mi>
</mrow>
</msup>
</mfrac>
<mo>|</mo>
<mo>&le;</mo>
<msub>
<mi>tol</mi>
<mi>J</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>25</mn>
<mo>)</mo>
</mrow>
</mrow>
Step B10 is then performed, otherwise, performs step B7；
Step B7：Self Adaptive Control mesh generation module is run, and obtains new control grid Δl+1；
Step B8：Iteration count l=l+1 is made, if l=lmax, then step B9 is performed, otherwise, goes to step B4；
Step B9：Mathematical modeling is transformed into new time scale by time scale modular converter, goes to step B4；
Step B10：Control instruction output module will current control time domain by being transformed into actual control time domain, and by the optimal of acquisition
Fuel consumption rate control strategy exports.
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| 朱建丰等: "基于自适应模拟退火遗传算法的月球软着陆轨道优化", 《航空学报》 * |
| 王立伟: "自适应控制向量参数化动态优化研究", 《中国优秀硕士学位论文全文数据库 基础科学辑》 * |
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| CN107703759B (en) | 2020-05-08 |
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