CN103224023A - Phase plane self-adaptation control method based on characteristic model - Google Patents

Phase plane self-adaptation control method based on characteristic model Download PDF

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CN103224023A
CN103224023A CN2013101087633A CN201310108763A CN103224023A CN 103224023 A CN103224023 A CN 103224023A CN 2013101087633 A CN2013101087633 A CN 2013101087633A CN 201310108763 A CN201310108763 A CN 201310108763A CN 103224023 A CN103224023 A CN 103224023A
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CN103224023B (en
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解永春
胡军
吴宏鑫
胡海霞
张昊
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Beijing Institute of Control Engineering
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Abstract

Disclosed is a phase plane self-adaptation control method based on a characteristic model. The method comprises the following steps: (1) a speed limit value in a jet control law is designed; (2) an angular speed maximum value of a stepped zone, an angular speed maximum value of a low thrust zone, a dead zone theta D and a stepped threshold value theta v in the jet control law are designed; (3) a high thrust zone threshold value theta B in the jet control law is designed; (4) a low thrust angular speed accelerated speed parameter ac2 and a high thrust angular speed accelerated speed parameter ac1 in the jet control law are calculated according to a golden ratio coefficient; (5) a stepped zone parameter kjj in the jet control law is calculated according to the low thrust angular speed accelerated speed parameter ac2, and a parabola coefficient KX in the jet control law is calculated according to the high thrust angular speed accelerated speed parameter ac1 and other phase plane parameters; (6) the controlled quantity is calculated according to parameters designed in the above-mentioned steps and a phase plane jet control logic, namely, the jet length of an engine is confirmed, and the engine is controlled within a sampling control period according to the confirmed control quantity.

Description

A kind of phase plane self-adaptation control method based on characteristic model
Technical field
The present invention relates to a kind of spacecraft phase plane control method, particularly at flexible spacecraft, the high precision of delaying time when in the intersection docking operation, having interference, systems such as plume, stable jet control method.
Background technology
Technique in Rendezvous and Docking is meant that two spacecrafts join (intersection) by preposition, speed and time in orbit, aims at, draws close the thru-flight course of action until structurally link into an integrated entity (butt joint) through attitude then.Carry out two spacecrafts of Technique in Rendezvous and Docking, common one is known as target aircraft (abbreviation object machine), and another is known as follows the trail of aircraft (abbreviation tracker).In the intersection docking operation, tracker is an actv., generally by changing the intersection butt joint that tracker is realized two spacecrafts stage by stage with respect to the position and the attitude of object machine.The intersection docking operation is generally divided four-stage: remote lead segment, target-seeking section, near section, draw close and the Butt Section.
In the intersection docking operation, tracker need cause propellant expenditure, thereby cause tracker mass property and inertia characteristic constantly to change by driving engine start frequently carrying out track and attitude maneuver; Track and attitude maneuver also can excite the solar array flexible vibration, and this windsurfing flexible vibration characteristic itself exists uncertain; The plume that the driving engine start produces is beaten on solar array can produce exciting force and the disturbance torque that changes with the windsurfing corner to tracker; There was coupling in the control of relative attitude and relative position when this external relative distance was nearer, and the control system life period postpones or the like, and this all makes the accuracy control of intersection butt joint become a difficult problem.
Intelligent adaptive control method based on characteristic model is that the prosperous academician of Wu Hong proposed in 1992, through vicennial research, in theoretical and application, all obtained impressive progress, form complete very strong Adaptive Control Theory and the method for practicality of a cover, mainly comprised the theoretical and contents such as method, calculus golden cut adaptive control method of feature modeling.Referring to document [1] (Wu Hongxin, Hu Jun separate Yongchun. based on the Intelligent Adaptive Control of characteristic model. Beijing, China Science Tech Publishing House, 2009).
Document points out in [1] that so-called feature modeling is exactly to require to carry out modeling according to object dynamic characteristic, environmental characteristic and controller performance.Characteristic model is made of characteristic variable and characteristic parameter.Characteristic variable is the variable of reflection object application force and motion feature, as variablees such as the position of controlling quantity, output, speed, acceleration/accels.Characteristic parameter is the key parameter of reflection application force and motion feature variable relation, comprises gain, delay time, order, relative rank, coefficient and time-varying characteristics parameter thereof.The characteristics of characteristic model are that model has been considered the control requirement, verified in theory: the position of, linear time-varying permanent for linearity, nonlinear constant and some nonlinear and time-varying system keeps and Position Tracking Control, and variation divided equation to describe when its characteristic model was can be with low order slow; Wherein, for open-loop stable system or open-loop unstable but relatively rank are smaller or equal to 2 system, and variation divided equation to describe when its characteristic model was can be with second order slow.Therefore be different from the way as in the methods such as mode truncation high order mode being cast out usually, it is in the characteristic parameter that incorporates characteristic model for information about of high order mode, drop-out not, and the model accuracy height, and simpler than prime power model.The output of characteristic model and the output of practical object remain in dynamic process within the tolerance, and two outputs equate under stable situation.Have a not modeling error between characteristic model and the practical object, under enough little condition of sampling period, this error is approximately the infinitesimal of the same order amount in sampling period.If with the characteristic model be object designs controller to this not modeling error have robustness, so former object is just stable under this controller action.Therefore feature modeling has been broken through control theory bottleneck in actual applications, for the high-order complex object carries out lower order controller design and Design of intelligent controller provides foundation, provide a new technological approaches in particular for the practical application of Adaptive Control Theory.
The golden-section adaptive control rule is a kind of new self-adaptation control method that golden section is combined with the minimum variance adaptive control laws, under certain condition, can guarantee the stability of closed loop system when parameter does not converge on " true value " and to the robust stability of modeling error not, (separate Yongchun referring to document [2], Wu Hongxin. the application of golden section in the self-adaptive robust controller design. the automation journal, 1992,18 (02): 177-185).
But, be linear controller based on the golden-section adaptive control device of characteristic model, can not be directly used in the so jet nonlinear Control problem of intersection butt joint that solves.
Phase plane control is classical jet control method, has obtained using widely in the attitude control of satellite and airship.Document [3] (Tu Shancheng chief editor. " satellite attitude dynam and control ". Yuhang Publishing House .2001 .) chapter 13 introduced the method for designing of phase plane control law.But because phase plane controlling Design parameter is many, and need gather by the artificial examination of experience, so will realize the High Accuracy Control of stable intersection butt joint, the design of phase plane parameter is a difficult problem.
Summary of the invention
Technology of the present invention is dealt with problems and is: overcoming existing phase plane controlling Design parameter needs the people to control examination to gather, the Parameters design of a kind of phase plane control is provided, solves the design of Controller problem that robustness is good, control accuracy is high, adaptive capacity is strong under flexible big, the plume serious interference of windsurfing in the intersection docking operation, attitude and orbit coupling, the big situation of system delay.
Technical solution of the present invention is: a kind of phase plane self-adaptation control method based on characteristic model, and step is as follows:
(1) according to system delay Δ T DelayWith the speed limit in the jet control law of dynamic property requirement design
Figure BDA00002990641600031
(2), and consider step (1) design-calculated speed limit according to the dynamic performance requirement
Figure BDA00002990641600032
Design the stepping district cireular frequency maxim in the jet control law
Figure BDA00002990641600033
With low thrust district cireular frequency maxim
Figure BDA00002990641600034
And according to measured error θ ErrorWith system delay Δ T DelayDesign the dead band threshold values θ in the jet control law DWith stepping threshold values θ v
(3) according to the dead band threshold values θ that determines in control accuracy requirement and the step (2) DDesign the high thrust district threshold values θ in the jet control law B
(4) according to low thrust angular acceleration parameter a in the jet control law of golden section coefficient calculations C2And high thrust angular acceleration parameter a C1
(5) according to low thrust angular acceleration parameter a C2Calculate the stepping district parameter k in the jet control law jAccording to high thrust angular acceleration parameter a C1And the parabola COEFFICIENT K in the jet control law of other phase plane calculation of parameter X
(6) according to design-calculated parameter in above-mentioned five steps, according to the jet control logic calculation control of phase plane amount, promptly determine the jet length of driving engine, according to determined controlling quantity driving engine is controlled in the cycle in this controlling of sampling.
Low thrust angular acceleration parameter in the described step (4)
Figure BDA00002990641600041
Figure BDA00002990641600042
Wherein, k 2∈ [0.5,0.8], k 1∈ [0.2,0.5], Δ T are the controlling of sampling cycle.
Described k 2Optimum is
Figure BDA00002990641600043
k 1Optimum is
Figure BDA00002990641600044
Stepping district parameter k in the described step (5) j=(1-k 2) a C2Δ T/ (θ Be);
Wherein, Δ T is the controlling of sampling cycle, θ eFor being slightly less than θ DConstant.
Parabola COEFFICIENT K in the described step (5) Xa JL/ a C1, γ span [1,6], a JLBe actual high thrust angular acceleration.
At the intersection butt joint section of drawing close, dead band threshold values θ DWith high thrust district threshold values θ BAccording to following rule automatic compensation:
θ D = θ Dfianal + ( θ Dinitial - θ Dfianal ) ( | X | - X fianal ) ( X initial - X fianal )
θ B = θ Bfinal + ( θ Binitial - θ Bfinal ) ( | X | - X fianal ) ( X initial - X fianl )
Wherein, θ DinitialBe the section of drawing close initial position dead band threshold values, θ DfinalBe terminal location dead band threshold values, θ BinitialBe initial position high thrust district threshold values, θ BfinalBe terminal location high thrust district threshold values, X InitialBe the absolute value of the vertical relative distance of initial position, X FinalBe the absolute value of the vertical relative distance of terminal location, X represents vertical relative distance.
The present invention compared with prior art beneficial effect is:
(1) spacecraft that has a flexible windsurfing belongs to the high-order controlled object.For this controlled object, under the situation that has strong jamming and system delay,, be easy to excite the windsurfing flexible vibration if the design of phase plane controlled variable is improper, cause the control system instability, the very stubborn problem that this problem faces when being airship intersection butt joint Control System Design.This problem, is just solved after the design philosophy that we control golden section is incorporated into phase plane control the comparative studies of distinct methods well through for many years.Its theoretical foundation is: document [2] the is verified robust stability of linear golden-section adaptive control device, and golden section control belongs to careful control, is not easy to excite the windsurfing flexible vibration, therefore can effectively solve windsurfing flexible vibration problem.
(2) according to the golden-section adaptive control theory based on characteristic model, the controlled variable in the jet control law of phase plane is designed and calculates, controlled variable concerns clearly each other, and each parameter is all tried to gather by experience one by one in the prior art.
Therefore (3) considered system delay in the design of controlled variable, effective resolution system delay issue.
(4) the phase plane parameter of adjusting in the jet control law according to characteristic parameter adaptive helps control system satisfies different control accuracys in motion process requirement.
We revise controlled variable according to relative distance according to based on the theoretical phase plane parameter of calculating of the golden-section adaptive control of characteristic model, have proposed the phase plane self-adaptation control method based on characteristic model.This method has advantages such as control accuracy height, consumption of fuel is little, the robust comformability is good, antijamming capability is strong, in the Technique in Rendezvous and Docking of No., No. eight, divine boat, No. nine, divine boat and Heavenly Palace near the section of drawing close successful Application.
Description of drawings
Fig. 1 is the phase plane self-adaptation control method design flow diagram that the present invention is based on characteristic model;
Fig. 2 is the phase plane control zone chart that the present invention is based on the phase plane self-adaptation control method use of characteristic model;
Fig. 3 is an intersection butt joint closed loop control system functional block diagram.
The specific embodiment
The present invention will be further described below in conjunction with accompanying drawing.
Phase plane self-adaptation control method based on characteristic model of the present invention, key content is the method for designing of phase plane parameter, also is included in some performance figure and requires the phase plane parameter to be carried out the method for accommodation according to characteristic parameter in the task of variation.Theoretical foundation of the present invention is based on the golden-section adaptive control theory of characteristic model.
At first the system that this method is suitable for is once simply introduced, and adopts the tracker intersection of jet control to dock the closed loop control system functional block diagram as shown in Figure 3.The each several part implication is as follows among Fig. 3:
Track, attitude dynamics had both comprised tracker absolute orbit and attitude dynamics, comprised relative position and the attitude dynamics of tracker with respect to object machine again, were the controlled objects in the control system.Dynamic disturbance except comprising ambient interference power such as orbit perturbation, atmospheric drag and moment, the plume exciting force and the moment that produce when also comprising the driving engine start.Because the uncertainty that driving engine start and windsurfing rotate causes plume exciting force and moment also to have uncertainty.
The kinematic parameter of controlled object is measured by the measurement sensor that is installed on the tracker, measure sensor and both comprised infrared earth sensor, star sensor, inertia measurement sensor, also comprise intersection butt joint relative measurement sensors such as CCD optical imagery sensor, laser radar, microwave radar, satellite navigational equipment.According to the output of measuring sensor, by attitude, the attitude angular velocity of position and attitude estimator estimation tracker, and tracker is with respect to the status informations such as relative position, relative velocity, relative attitude angle and relative attitude cireular frequency of object machine.
Select different guidance rules in the different stage of intersection butt joint, as multiple pulse guidance, CW guidance, Line of Sight Guidance etc.Targeted attitude according to the output of guidance rule requires and the attitude estimated result, calculates the required torque command of deviation of revising the relative targeted attitude of the actual attitude of tracker by attitude controller.In the translation section of drawing close, require and the location estimation result according to the target location, calculate the required power instruction of deviation of revising the relative target location of tracker actual position by positioner; In other stage, the guidance rule directly provides the size and Orientation that becomes the rail velocity increment.Power, torque command and velocity increment require to select which driving engine start and start duration (or jet length) by the decision of thruster command assignment algorithm.
The control executing mechanism of tracker is made up of tens to tens of thrusters.Separate unit rail control thruster is because thrust not by barycenter, can produce the attitude disturbance torque, and separate unit appearance control thruster also can produce the track exciting force, and therefore, attitude control and track control are coupled.In order accurately to realize thrust or the moment on certain direction, need one group of thruster to work simultaneously and offset the effect of thruster other direction.The thruster combination that can realize above-mentioned requirements is selected in given control thrust and moment requirement in all thrusters, and calculates the work-hours of every thruster in this combination, just is called command assignment.Concrete thruster command assignment algorithm has special document introduction.Require the attitude control channel high, that dynamic range is big for control accuracy, usually by the large and small two kinds of thrusters of configuration.
Actual control system, all need the time owing to measure sensor response, signal transmission, data handing, guidance, navigation and control law calculating etc., it is generally also bigger under present engineering factor therefore to output to the time delay of thruster generation control effort and moment from the measurement sensor.
Secondly, incorporated by reference document [3] is controlled phase plane and is simply introduced.Phase plane shown in Figure 2 is divided into 14 control areas by some switching lines, and therefore the phase plane switching line only is illustrated RHP below about initial point O center symmetry.The meaning of basic symbol is referring to table 1, the switching line GC of RHP 1C 2The equation of D can be designed to
Figure BDA00002990641600071
Also can replace with straight line is approximate.R1 is high thrust standard-sized sheet district, and R2 is low thrust standard-sized sheet district, and R3 is low thrust stepping district, and R4 and R6 are high thrust speed limit district, and R5 is anti-outer skating area, and R7 is the complete shut-down district.Phase plane R1, R2, R3, R4, R5, R6 district are deceleration area, oppositely driving engine start.Correspondingly R ' 1, R ' 2, R ' 3, R ' 4, R ' 5, R ' 6 districts are accelerating region, the start of forward driving engine.R ' 7 also is the complete shut-down district.Need to prove,, can regard this thruster standard-sized sheet as high thrust, regard low thrust as and this thruster is opened N% if only dispose a kind of thruster.N determines according to actual needs.
Table 1 basic symbol meaning
Figure BDA00002990641600072
Embodiment 1
Performing step of the present invention is as follows:
(1) according to system delay Δ T DelayWith the speed limit in the jet control law of dynamic property requirement design
Figure BDA00002990641600073
The system of setting up departments postpones to be Δ T Delay, high thrust angular acceleration a JL, the angular velocity range that controller performance requires to allow is Then can design speed limit in the jet control law
Figure BDA00002990641600082
It is satisfied
Figure BDA00002990641600083
And θ · L = [ θ · min , θ · max ] .
(2), and consider step (1) design-calculated speed limit according to the dynamic performance requirement
Figure BDA00002990641600085
Design the stepping district cireular frequency maxim in the jet control law
Figure BDA00002990641600086
With low thrust district cireular frequency maxim
Figure BDA00002990641600087
And according to measured error θ ErrorWith system delay Δ T DelayDesign the dead band threshold values θ in the jet control law DWith stepping threshold values θ v
Stepping district cireular frequency maxim With low thrust district cireular frequency maxim Determined the height in R2 and R3 district, its principle of design is to raise the height in R2 and R3 district to avoid exciting flexible vibration under the prerequisite that satisfies the system response time requirement as far as possible.On this basis, can design
Figure BDA000029906416000810
Or
Figure BDA000029906416000811
After making that the phase path enters RHP from left half-plane, directly enter the R3 district, enter the R3 district again after perhaps entering the R2 district from the R7 district from the R7 district.
If measured error is θ Error, then can design threshold values θ in dead band in the jet control law DIt is satisfied θ D > θ error + Δ T delay θ · V , θ v>θ error
(3) according to the dead band threshold values θ that determines in control accuracy requirement and the step (2) DDesign the high thrust district threshold values θ in the jet control law B
If control accuracy requires to be θ Desired, then can design high thrust district threshold values θ in the jet control law BMake it satisfy θ D<θ B<θ DesiredPrerequisite under as far as possible big.
(4) according to low thrust angular acceleration parameter a in the jet control law of golden section coefficient calculations C2And high thrust angular acceleration parameter a C1
Low thrust angular acceleration parameter
Figure BDA000029906416000813
High thrust angular acceleration parameter
Wherein, k 2∈ [0.5,0.8], k 1∈ [0.2,0.5], Δ T are the controlling of sampling cycle, k 2Optimum is
Figure BDA000029906416000815
k 1Optimum is 3 - 5 2 .
(5) according to low thrust angular acceleration parameter a C2Calculate the stepping district parameter k in the jet control law jAccording to high thrust angular acceleration parameter a C1And the parabola COEFFICIENT K in the jet control law of other phase plane calculation of parameter Xk j=(1-k 2) a C2Δ T/ (θ Be), K Xa JL/ a C1, γ span [1,6], θ eFor being slightly less than θ DConstant.
(6) according to design-calculated parameter in above-mentioned five steps, according to the jet control logic calculation control of phase plane amount, promptly determine the jet length of driving engine, according to determined controlling quantity driving engine is controlled in the cycle in this controlling of sampling.
Be example with the deceleration area below, provide the jet calculation methods of length of calculative driving engine of each controlling of sampling cycle.
The R1 district: reverse high thrust motor standard-sized sheet, jet length is slightly larger than the controlling of sampling cycle.
The R2 district: reverse thrustor standard-sized sheet, jet length is slightly larger than the controlling of sampling cycle.
R3 district: the reverse jet length T of thrustor NComputing formula:
T N 1 = | θ · ^ | a c 2 , T N 2 = K j | θ ^ | - θ e a c 2 , T N=T N1+T N2
R4 district: the reverse jet length T of high thrust motor NComputing formula:
Figure BDA00002990641600093
R5 district: the reverse jet length T of thrustor NComputing formula: T N=T Min
R6 district: the reverse jet length T of high thrust motor NComputing formula:
Figure BDA00002990641600094
R7 district: shutdown.
Embodiment 2
Provide the method for the phase plane parameter being carried out accommodation according to characteristic parameter below.
If change the transverse axis and the longitudinal axis of phase plane into relative position and relative velocity, the phase plane control method also can be applicable to translation control.In the intersection butt joint section of drawing close, tracker is approaching to object machine along the butt joint corridor.Along with the minimizing of vertical relative distance, require the horizontal position control accuracy to improve gradually.At this moment can select vertical relative distance is characteristic parameter, according to this characteristic parameter the phase plane parameter that influences control accuracy is carried out the self adaptation adjustment, to realize controlled target.
With reference to embodiment 1 design phase plane parameter.Along with the minimizing of vertical relative distance, the horizontal position control accuracy requires to improve gradually to be mainly reflected in θ DAnd θ BReduce gradually.If the section of drawing close initial position dead band threshold values θ DBe designed to θ Dinitial, terminal location dead band threshold values θ DBe designed to θ Dfinal, initial position high thrust district threshold values θ BBe designed to θ Binitial, terminal location high thrust district threshold values θ BBe designed to θ Bfinal, the absolute value of the vertical relative distance of initial position is X Initial, the absolute value of the vertical relative distance of terminal location is X Final, then in moving closer to process, along with the variation of vertical relative distance X, phase plane parameter θ DAnd θ BCan be by following rule automatic compensation:
θ D = θ Dfianal + ( θ Dinitial - θ Dfianal ) ( | X | - X fianal ) ( X initial - X fianal )
θ B = θ Bfinal + ( θ Binitial - θ Bfinal ) ( | X | - X fianal ) ( X initial - X fianl )
The inventive method has advantages such as control accuracy height, consumption of fuel is little, the robust comformability is good, antijamming capability is strong, in the Technique in Rendezvous and Docking of No., No. eight, divine boat, No. nine, divine boat and Heavenly Palace near the section of drawing close successful Application.
In addition the present invention can be applied to a class high-order, the time change, non-linear, big delay, strong jamming and uncertain object jet control problem.Such as the attitude control of the LIQUID-FILLED SATELLITE that has flexible solar array when becoming rail.Also can be applicable to the attitude control of general satellite.
The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (6)

1. phase plane self-adaptation control method based on characteristic model is characterized in that step is as follows:
(1) according to system delay Δ T DelayWith the speed limit in the jet control law of dynamic property requirement design
Figure FDA00002990641500011
(2), and consider step (1) design-calculated speed limit according to the dynamic performance requirement
Figure FDA00002990641500012
Design the stepping district cireular frequency maxim in the jet control law
Figure FDA00002990641500018
With low thrust district cireular frequency maxim
Figure FDA00002990641500013
And according to measured error θ ErrorWith system delay Δ T DelayDesign the dead band threshold values θ in the jet control law DWith stepping threshold values θ v
(3) according to the dead band threshold values θ that determines in control accuracy requirement and the step (2) DDesign the high thrust district threshold values θ in the jet control law B
(4) according to low thrust angular acceleration parameter a in the jet control law of golden section coefficient calculations C2And high thrust angular acceleration parameter a C1
(5) according to low thrust angular acceleration parameter a C2Calculate the stepping district parameter k in the jet control law jAccording to high thrust angular acceleration parameter a C1And the parabola COEFFICIENT K in the jet control law of other phase plane calculation of parameter X
(6) according to design-calculated parameter in above-mentioned five steps, according to the jet control logic calculation control of phase plane amount, promptly determine the jet length of driving engine, according to determined controlling quantity driving engine is controlled in the cycle in this controlling of sampling.
2. a kind of phase plane self-adaptation control method based on characteristic model according to claim 1 is characterized in that: the low thrust angular acceleration parameter in the described step (4)
Figure FDA00002990641500014
a c 1 = θ · L / ( k 1 ΔT ) ;
Wherein, k 2∈ [0.5,0.8], k 1∈ [0.2,0.5], Δ T are the controlling of sampling cycle.
3. a kind of phase plane self-adaptation control method based on characteristic model according to claim 2 is characterized in that: described k 2Optimum is
Figure FDA00002990641500016
k 1Optimum is
Figure FDA00002990641500017
4. a kind of phase plane self-adaptation control method based on characteristic model according to claim 1 is characterized in that: stepping district parameter k in the described step (5) j=(1-k 2) a C2Δ T/ (θ Be);
Wherein, Δ T is the controlling of sampling cycle, θ eFor being slightly less than θ DConstant.
5. a kind of phase plane self-adaptation control method based on characteristic model according to claim 1 is characterized in that: parabola COEFFICIENT K in the described step (5) Xa JL/ a C1, γ span [1,6], a JLBe actual high thrust angular acceleration.
6. a kind of phase plane self-adaptation control method based on characteristic model according to claim 1 is characterized in that: at the intersection butt joint section of drawing close, dead band threshold values θ DWith high thrust district threshold values θ BAccording to following rule automatic compensation:
θ D = θ Dfianal + ( θ Dinitial - θ Dfianal ) ( | X | - X fianal ) ( X initial - X fianal )
θ B = θ Bfinal + ( θ Binitial - θ Bfinal ) ( | X | - X fianal ) ( X initial - X fianl )
Wherein, θ DinitialBe the section of drawing close initial position dead band threshold values, θ DfinalBe terminal location dead band threshold values, θ BinitialBe initial position high thrust district threshold values, θ BfinalBe terminal location high thrust district threshold values, X InitialBe the absolute value of the vertical relative distance of initial position, X FinalBe the absolute value of the vertical relative distance of terminal location, X represents vertical relative distance.
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CN105843239A (en) * 2016-04-06 2016-08-10 北京理工大学 Attitude control thruster layout optimization method for combined spacecraft
CN107966901A (en) * 2017-11-06 2018-04-27 北京控制工程研究所 With reference to continuous control and the RLV thrust reversers control method and system of phase plane method
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