CN108536014A - A kind of model predictive control method for considering the spacecraft attitude of flywheel dynamic characteristic and evading - Google Patents
A kind of model predictive control method for considering the spacecraft attitude of flywheel dynamic characteristic and evading Download PDFInfo
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Abstract
A kind of model predictive control method for considering the spacecraft attitude of flywheel dynamic characteristic and evading, includes the following steps：The dynamics of attitude dynamics and flywheel based on spacecraft establishes prediction model；Secondly the mathematical model of constraint is established according to the dynamic characteristic and the instrument angle of sight of flywheel；Then the performance index function towards different task demand is designed, control problem is converted into seek the extreme-value problem of object function under the conditions of equation and inequality constraints；Finally, pass through the optimization method based on real-time iterative, the rapid solving above problem, this method can be good at handling posture evasion of the spacecraft under executing agency's restraint condition, it is optimal by reaching the synthesis of energy and time to the design of object function, and by the processing of real-time iterative and hot start method, and the calculation amount of solving-optimizing problem can be reduced.
Description
Technical field
The present invention relates to technical field of spacecraft control is belonged to, it is mainly used in the spacecraft controlled using counteraction flyback
Attitude maneuver evades control, and in particular to a kind of Model Predictive Control for considering the spacecraft attitude of flywheel dynamic characteristic and evading
Method.
Background technology
The development of space technology is at full speed in recent years, and the mission requirements of in-orbit spacecraft are also more and more, so in spacecraft
On all equipped with various optical instruments, such as CCD camera, infrared interferometer, be required for making during these instruments work
Its sight avoids directly opposite strong light, to protect in instrument to illumination and the more sensitive component of temperature ratio.So this requires
Spacecraft makes the direction of these instruments that should get around the direction of strong light during attitude maneuver.Meanwhile most of spacecraft appearances
Executing agency in state control system combines for counteraction flyback, and there is counteraction flyback control accuracy height, output torque only to need
The advantages that consuming electric energy.But counteraction flyback is easy to reach full in use there is also the moment of reaction is smaller
And the problems such as, to influence the gesture stability of spacecraft.So research spacecraft is under the constraints of executing agency's performance
Posture evasion meaning just it is particularly significant.
The method evaded about posture can have the potential function method mentioned in patent 201710521561.X, potential function method can
Effectively to evade constraint, but using the method for Model Predictive Control, it can not only consider that posture evades constraint, and can
Consider the performance constraints of executing agency, can also realize the optimization of energy and time according to performance function, be more suitable for holding in addition
Attitude maneuver control under the constraint of row mechanism performance.
Invention content
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of spacecraft appearances considering flywheel dynamic characteristic
The model predictive control method that state is evaded, existing executing agency's performance constraints and appearance during the attitude maneuver of in-orbit spacecraft
The problem of modal constraint, the present invention provide a kind of Model Predictive Control side for considering the spacecraft attitude of flywheel dynamic characteristic and evading
Method.This method be it is a kind of can handle the performance constraints of executing agency simultaneously and posture evades model predictive control method, it
Real-time iterative and the method for thermal starting have been used in optimization process to improve the solution efficiency for solving optimization problem in MPC, and have been set
Performance function has been counted to realize that energy consumption and the synthesis of time are optimal during attitude maneuver.
The present invention provides a kind of model predictive control method for considering the spacecraft attitude of flywheel dynamic characteristic and evading, packets
Include following steps：
(1) include according to the attitude kinematics of spacecraft and the foundation of the rotational power of kinetic characteristics and flywheel characteristic
Prediction model of the spacecraft attitude model of executing agency as MPC；
(2) it carries the angle of sight of instrument according to spacecraft and evades vector and establish the mathematical model that posture evades constraint,
And the mathematical model of executing agency's constraint is established according to the angular momentum of flywheel saturation and torque saturated characteristic；
(3) corresponding optimization object function is designed according to mission requirements, including the quadratic form of executing agency's input and being
The quadratic form of system state error executes time and energy expenditure to consider；
(4) control problem is converted into the equation and state of system dynamics equation and the inequality constraints of input-bound
Under the conditions of, then the problem of seeking object function extreme value, uses the optimized treatment method rapid solving of real-time iterative, optimization is obtained
It solves and is exported as the controlled quentity controlled variable of system.
It is by the way that the kinetics equation of flywheel is attached to boat in the spacecraft attitude dynamics model described in step (1)
In its device attitude dynamic equations, and sliding-model control arrives, and representation is as follows：
Wherein, ω=[ω1,ω2,ω3]TIndicate the attitude angle of spacecraft relative inertness coordinate system under body coordinate system
Velocity vector, ω1,ω2,ω3Respectively spacecraft is about the angular speed on roll axis, yaw axis and the pitch axis in this system
Component；Indicate derivatives of the ω to the time；J is the total inertia matrix of spacecraft, is simplified shown as diagonal matrix J=diag (J1,J2,
J3), J1,J2,J3For around the rotary inertia of the principal axis of inertia；S (ω) is skew symmetric matrix, and form isτ indicates the output torque of executing agency；Q=[q0,q1,q2,q3]TIndicate the posture list of spacecraft
Position quaternary number,Indicate that the scalar component in the posture unit quaternion of spacecraft, θ expressions are crossed around Euler's shaft rotation
One angle,ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented,
And meet Indicate derivatives of the q to the time；Ω (ω) is skew symmetric matrix, and form is as follows：
The model of counteraction flyback combination is as follows：
Wherein HrwFor the angular momentum of flywheel,For the derivative of the angular momentum relative time of flywheel, by four
The relationship of its angular momentum and rotating speed is as follows in the flywheel of flywheel composition：
Hrw=CJrwN
Wherein C is that 3 × 4 flywheels install matrix, N=[n1,n2,n3,n4]TFor the angular velocity vector of flywheel, n1,n2,n3,n4
The angular speed of each flywheel is indicated respectively；JrwIndicate the moment of inertia matrix of flywheel, form Jrw=JαI4×4, JαTable
Show the rotary inertia of single flywheel, I4×4For 4 rank unit matrixs；
Since executing agency is to control posture by way of exchanging angular momentum with spacecraft, so the angular motion that system is total
Measure conservation：
H=Hrw+Jω
H is the total angular momentum of system, is a constant in no moment of face.
The model integration of the model of executing agency and spacecraft attitude dynamics is got up to obtain：
By above-mentioned model discretization, the setting sampling interval is that Δ t is obtained, and is carved in kth：
ωk+1=J-1ΔtS(ωk)H+J-1JαCΔNk+ωk
Wherein subscript k indicates the value to dependent variable at the kth moment, Δ Nk=Nk-Nk-1, I3×3For three rank unit matrixs.
In step (2)：
(a) counteraction flyback maximum output torque constrains：
The torque output of counteraction flyback is to change the angular momentum realization of flywheel, so there is following form to state：
Wherein TmaxFor maximum output torque vector.It will be obtained after above-mentioned formula discretization：
It is obtained after arrangement：
(b) counteraction flyback maximum angular momentum constrains：
The angular momentum saturation of flywheel is presented as that the rotating speed of flywheel rotor reaches the upper limit, so the full constraint of angular momentum can be used and fly
Angular speed constraint is taken turns to indicate：
-Nmax≤ΔNk+Nk-1≤Nmax
Wherein NmaxFor flywheel maximum angular rate vector.
It is obtained after arrangement：
(c) angle of sight constraint that spacecraft attitude is directed toward：
Consider that the direction of spacecraft will evade certain conical lines-of-sight areas, the following form of posture restraint of design：
Wherein α indicates that the unit vector that spacecraft is directed toward under body coordinate system, β indicate spacecraft under body coordinate system
The unit vector in direction need to be evaded, θ indicates the size for evading the angle of sight in region.
The optimization object function function V (x in step (3)k,uk) be expressed as：
Wherein xk=[qk,ωk]TThe quantity of state of expression system, physical significance are the posture and angular speed of spacecraft；With
Flywheel rotation speed change amount is as input, i.e. uk=Δ Nk；NPFor the estimation range of MPC；Q and P is that state variable and input become
The weight matrix of amount illustrates that optimization aim is more concerned with the stable time, if Q is larger relative to P if Q relative to P if larger
Illustrate that optimization aim is more concerned with the consumption of energy；
It is organized into compact form：
Wherein
In step (4), control problem is converted to the extreme-value problem for seeking object function under constraints, is used in combination in real time
The method of iteration solves controlled quentity controlled variable.The problem of control input will be solved, is converted to following mathematical problem：
xi,k+1=F (xi,k,ui,k)
L(xi,k,ui,k)≤017×1K=0,1 ..., NP-1
WhereinIndicate the optimization problem in moment i,Indicate the feedback of status in current time i system, xi,k
It indicates by current time state xi,0The system mode at the kth moment of reckoning；ui,kThe estimated input at expression kth moment, 017×1Table
Show 17 × 1 null matrix；F(xi,k,ui,k) it is system state equation, it is embodied as：
L(xi,k,ui,k) it is system restriction, it is embodied as：
Processing procedure using the method for real-time iterative is：Known previous moment optimization problemIt solves
It finds outWithAnd then solving-optimizing problemIt is specifically divided into
Two stages：Preparation stage and response phase：
Preparation phase procedures are：By xi-1And ui-1The displacement for doing a sampling instant keeps the last one element constant, obtains
It arrivesWithAccording toWithCalculate sensitive matrix Ai,k,
Bi,k,Ci,k,Di,kWith error li,k,ri,k, expression is：
By linearisation, the optimization problem of a nonlinear restriction is converted to the quadratic programming problem of linear restriction：
Δui,k=ui,k-ui-1,k
Δxi,k+1=Ai,kΔxi,k+Bi,kΔui,k+ri,k
Ci,kΔxi,k+Di,kΔui,k+li,k≤ 0 k=0,1 ..., NP-1
The process of response phase is：The feedback of status of acquisition systemBring Solve problems intoObtain Δ xi,kAnd Δ
ui,kPass through formula：
Obtain problemSolution (xi,k,ui,k), finally again by ui=ui,0Control as system inputs.
The model predictive control method that the spacecraft attitude of the consideration flywheel dynamic characteristic of the present invention is evaded, can make space flight
Device in the case of executing agency's limited capacity, carries out posture and evades, while can meet energy and time during attitude maneuver
Synthesis it is optimal.The optimization method provided can improve the solution efficiency of MPC, and accelerating solving-optimizing using the thought of thermal starting asks
The speed of topic, the thought that real-time iterative is divided into two stages can make output for the feedback of status at a nearest moment, carry
High system executes the timeliness of control.The present invention has following advantages in summary：
(1) by the model of spacecraft together with the model integration of executing agency, using the knots modification of the rotating speed of flywheel as
Input, control moment is distributed to the control method of each flywheel by control moment again with traditional first obtaining, controlled quentity controlled variable is directly made
For executing agency, the process of the distribution of controlled quentity controlled variable is eliminated, directly whole system process is optimized.
(2) it compared with the potential function method that existing spacecraft attitude is evaded, can will be held using model predictive control method
Posture directing constraint in the performance constraints and attitude of satellite mobile process of row mechanism considers simultaneously, in addition can also be according to task
Corresponding performance function is arranged in demand so that the process of attitude maneuver realizes that energy and the synthesis of time are optimal.
(3) compared with general posture evades optimum control, the method using Model Predictive Control is closed-loop control,
Track optimizing again can be made according to feedback of status after making execution action each time so that control has robustness.
(4) the optimization thought for the real-time iterative and thermal starting that Model Predictive Control of the invention uses, compared to common
The method of Nonlinear Model Predictive Control can reduce operand and optimization efficiency, can be directed to the system shape at a nearest moment
State responds, and the output of control is more time-efficient.
Description of the drawings
Fig. 1 is the flow diagram for the model predictive control method for considering that the spacecraft attitude of flywheel dynamic characteristic is evaded；
Fig. 2 procedural block diagrams that system solution control inputs in order to control；
Specific implementation mode
The following detailed description of the specific implementation of the present invention, it is necessary to it is indicated herein to be, implement to be only intended to this hair below
Bright further explanation, should not be understood as limiting the scope of the invention, and field technology skilled person is according to above-mentioned
Some nonessential modifications and adaptations that invention content makes the present invention, still fall within protection scope of the present invention.
The present invention provides a kind of model predictive control methods for considering the spacecraft attitude of flywheel dynamic characteristic and evading, such as
Shown in Fig. 1, the specific steps are：First according to the rotational power of the attitude kinematics and kinetic characteristics and flywheel of spacecraft
Characteristic establishes prediction model of the spacecraft attitude model comprising executing agency as MPC；Secondly instrument is carried according to spacecraft
The angle of sight and evade vector and establish the mathematical model that posture evades constraint, and according to the angular momentum of flywheel saturation and torque
Saturated characteristic establishes the mathematical model of executing agency's constraint.Then corresponding optimization object function, packet are designed according to mission requirements
The quadratic form of the input containing executing agency and the quadratic form of system state amount error, time and energy expenditure are executed to consider
Problem.Control problem is finally converted into the inequality constraints item of the equation and state and input-bound in system dynamics equation
Under part, the mathematical problem of the extreme value of object function is sought；With the optimized treatment method rapid solving of real-time iterative, optimization is obtained
It solves and is exported as the controlled quentity controlled variable of system.The block diagram that control system solves control input process is as shown in Figure 2.
Specific implementation step is as follows：
The first step establishes the mathematical model of attitude control system.The kinetics equation of flywheel is attached to spacecraft attitude
In kinetics equation：
Wherein, ω=[ω1,ω2,ω3]TIndicate the attitude angle of spacecraft relative inertness coordinate system under body coordinate system
Velocity vector, ω1,ω2,ω3Respectively spacecraft is about the angular speed on roll axis, yaw axis and the pitch axis in this system
Component；Indicate the derivative of ω relative times；J is the total inertia matrix of spacecraft, is simplified shown as diagonal matrix J=diag (J1,
J2,J3), J1=30kg/m2,J2=50kg/m2,J3=40kg/m2For around the rotary inertia of the principal axis of inertia；S (ω) is skew symmetry square
Battle array, form areτ indicates the output torque of executing agency；Q=[q0,q1,q2,q3]TIndicate space flight
The posture unit quaternion of device,The scalar component in the posture unit quaternion of spacecraft is indicated, and around Euler's axis
The angle of rotation is related, and θ indicates the angle crossed around Euler's shaft rotation,
ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented, and is met Indicate that q leads the time
Number；Ω (ω) is skew symmetric matrix, and form is
The model of counteraction flyback combination is as follows：
Wherein HrwFor the angular momentum of flywheel,For HrwTo the derivative of time, in the flywheel being made of four flywheels
The relationship of its angular momentum and rotating speed is as follows in combination：
Hrw=CJrwN
WhereinMatrix, N=[n are installed for flywheel1,n2,n3,n4]TFor flywheel angular speed to
Amount, n1,n2,n3,n4The angular speed of each flywheel is indicated respectively；JrwIndicate the moment of inertia matrix of flywheel, form Jrw
=JαI4×4, Jα=0.01608kg/m2Indicate the rotary inertia of single flywheel, I4×4For 4 rank unit matrixs.
Since executing agency is to control posture by way of exchanging angular momentum with spacecraft, so the angular motion that system is total
Measure conservation：
H=Hrw+Jω
H is the total angular momentum of system, is a constant when no moment of face interferes.
The model integration of the model of executing agency and spacecraft attitude dynamics is got up to obtain：
By above-mentioned model discretization, the setting sampling interval is that Δ t=0.2s is obtained, and is carved in kth：
ωk+1=J-1ΔtS(ωk)H+J-1JαCΔNk+ωk
Wherein subscript k indicates the value to dependent variable at the kth moment, Δ Nk=Nk-Nk-1, I3×3For 3 rank unit matrixs.
The initial angular velocity of the initial attitude of spacecraft, initial angular velocity and flywheel is respectively qintial=[-
0.9524,-0.3048,0,0]Tωintial=[0,0,0]TAnd Nintial=[0,0,0,0]T, control desired posture and angle speed
It spends to be not qd=[1,0,0,0]Tωd=[0,0,0]T.Therefore the initial angular momentum H=0 that system is total.
Second step, establish posture of spacecraft during attitude maneuver evade constraint and executing agency performance about
Beam：
(1) counteraction flyback maximum output torque constrains：
The torque output of counteraction flyback is to change the angular momentum realization of flywheel, so there is following form to state：
Wherein Tmax=[1 11 1]TNm is maximum output torque vector.It will be obtained after above-mentioned formula discretization：
It is obtained after arrangement：
(2) counteraction flyback maximum angular momentum constrains：
The angular momentum saturation of flywheel is presented as that the rotating speed of flywheel rotor reaches the upper limit, so the full constraint of angular momentum can be used and fly
Angular speed constraint is taken turns to indicate：
-Nmax≤ΔNk+Nk-1≤Nmax
Wherein Nmax=[200 π, 200 π, 200 π, 200 π]TRad/s is maximum angular rate vector.
It is obtained after arrangement：
(3) angle of sight constraint that spacecraft attitude is directed toward：
Consider that the direction of spacecraft will evade certain conical lines-of-sight areas, the following form of posture restraint of design：
Wherein α=[0 0 1]TIndicate that spacecraft is directed toward unit vector under body coordinate system,It indicates
Spacecraft needs the unit vector for evading direction under body coordinate system,Indicate the size for evading the angle of sight in region.
Optimization object function of the third step design based on model predictive controller：
Wherein xk=[qk,ωk]TThe quantity of state of expression system, physical significance are the posture and angular speed of spacecraft；With
Flywheel rotation speed change amount is as input, i.e. uk=Δ Nk；NP=5 be the estimation range of MPC；Q=I7×7And P=I4×4For shape
The weight matrix of state variable and input variable, I7×7For 7 rank unit matrixs, illustrate that optimization aim is more noted if Q is larger relative to P
The stable time is overweighted, illustrates that optimization aim is more concerned with the consumption of energy if larger relative to P if Q.It is organized into compact form：
Wherein
Control problem is converted to the extreme-value problem for seeking object function under constraints, real-time iterative is used in combination by the 4th step
Method solve controlled quentity controlled variable, by restricted model in the system model and second step in the first step and third step in optimization aim
Function Synthesis is got up, and will be solved the problem of control inputs and is converted to following mathematical problem：
xi,k+1=F (xi,k,ui,k)
L(xi,k,ui,k)≤017×1K=0,1 ..., NP-1
WhereinIndicate the optimization problem in moment i,Indicate the feedback of status in current time i system, xi,k
It indicates by current time state xi,0Speculate the system mode at the kth moment；ui,kIndicate the estimated input at the kth moment；F
(xi,k,ui,k) be embodied as the system state equation in the first step：
L(xi,k,ui,k) be second step in system restriction, be embodied as：
Processing procedure using the method for real-time iterative is：Known previous optimization problemSolve ask
OutWithAnd then solving-optimizing problemProcess, tool
Body is divided into two stages：Preparation stage and response phase
Preparation phase procedures are：By xi-1And ui-1The displacement of a sampling instant is done, the last one position is constant, obtainsWithAccording toWithCalculate sensitive square
Battle array Ai,k,Bi,k,Ci,k,Di,kWith error li,k,ri,k, expression is：
By linearisation as above, the optimization problem of a nonlinear restriction is thus converted to the secondary of linear restriction
Planning problem：
Δui,k=ui,k-ui-1,k
Δxi,k+1=Ai,kΔxi,k+Bi,kΔui,k+ri,k
Ci,kΔxi,k+Di,kΔui,k+li,k≤ 0 k=0,1 ..., NP-1
Response phase process is：The feedback of status of acquisition systemBring Solve problems intoObtain Δ xi,kWith Δ ui,k
Pass through formula：
Obtain problemSolution (xi,k,ui,k).Finally again by ui=ui,0Control as system inputs.
The case where control method more than utilization can make spacecraft during attitude maneuver, executing agency's limited capacity
Under, it carries out posture and evades, while the synthesis that can meet energy and time is optimal.The optimization method provided can improve the solution of MPC
Efficiency accelerates the speed of solving-optimizing problem using the thought of thermal starting, and the thought that real-time iterative is divided into two stages can
Control output is made for the feedback of status at a nearest moment, improves the timeliness that system executes control, the flow of optimization
As shown in Figure 2.
Although for illustrative purposes, it has been described that exemplary embodiments of the present invention, those skilled in the art
Member it will be understood that, can be in form and details in the case of not departing from the scope and spirit invented disclosed in appended claims
On the change that carry out various modifications, add and replace etc., and all these changes should all belong to appended claims of the present invention
Protection domain, and each step in the claimed each department of product and method, can be in any combination
Form is combined.Therefore, to disclosed in this invention the description of embodiment be not intended to limit the scope of the invention,
But for describing the present invention.Correspondingly, the scope of the present invention is not limited by embodiment of above, but by claim or
Its equivalent is defined.
Claims (7)
1. a kind of model predictive control method for considering the spacecraft attitude of flywheel dynamic characteristic and evading, which is characterized in that including
Following steps：
(1) it is established comprising execution according to the attitude kinematics of spacecraft and the rotational power of kinetic characteristics and flywheel characteristic
Prediction model of the spacecraft attitude model of mechanism as MPC；
(2) it carries the angle of sight of instrument according to spacecraft and evades vector and establish the mathematical model that posture evades constraint, and root
The mathematical model of executing agency's constraint is established according to the angular momentum saturation and torque saturated characteristic of flywheel；
(3) corresponding optimization object function is designed according to mission requirements, includes the quadratic form and system shape of executing agency's input
The quadratic form of state error executes time and energy expenditure to consider；
(4) control problem is converted into the inequality constraints condition of the equation and state and input-bound in system dynamics equation
Under, the extreme value of object function is sought, with the optimized treatment method rapid solving of real-time iterative, the solution that optimization is obtained is as system
Controlled quentity controlled variable exports.
2. according to the method described in claim 1, it is characterized in that：The kinetics equation of flywheel is attached to spacecraft attitude to move
In mechanical equation, and sliding-model control, establish the prediction model of MPC.
3. according to the method described in claim 2, it is characterized in that：Spacecraft attitude dynamics model in step (1) is as follows
It indicates：
Wherein, ω=[ω1,ω2,ω3]TIndicate spacecraft relative inertness coordinate system under body coordinate system attitude angular velocity to
Amount, ω1,ω2,ω3Respectively spacecraft is about the angular velocity component on roll axis, yaw axis and the pitch axis in this system；
Indicate derivatives of the ω to the time；J is the total inertia matrix of spacecraft, is simplified shown as diagonal matrix J=diag (J1,J2,J3), J1,
J2,J3For around the rotary inertia of the principal axis of inertia；S (ω) is skew symmetric matrix, and form isτ
Indicate the output torque of executing agency；Q=[q0,q1,q2,q3]TIndicate the posture unit quaternion of spacecraft,Table
Show that the scalar component in the posture unit quaternion of spacecraft, θ indicate the angle crossed around Euler's shaft rotation,ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented, and full
Foot Indicate derivatives of the q to the time；Ω (ω) is skew symmetric matrix, and form is as follows：
The model of counteraction flyback combination is as follows：
Wherein HrwFor the angular momentum of flywheel,For the derivative of the angular momentum relative time of flywheel, by four flywheels
The relationship of its angular momentum and rotating speed is as follows in the flywheel of composition：
Hrw=CJrwN
Wherein C is that 3 × 4 flywheels install matrix, N=[n1,n2,n3,n4]TFor the angular velocity vector of flywheel, n1,n2,n3,n4Respectively
Indicate the angular speed of each flywheel；JrwIndicate the moment of inertia matrix of flywheel, form Jrw=JαI4×4, JαIndicate single
The rotary inertia of a flywheel, I4×4For 4 rank unit matrixs；
Since executing agency is to control posture by way of exchanging angular momentum with spacecraft, so the total angular momentum of system is kept
It is permanent：
H=Hrw+Jω
H is the total angular momentum of system, is a constant in no moment of face；
The model integration of the model of executing agency and spacecraft attitude dynamics is got up to obtain：
By above-mentioned model discretization, the setting sampling interval is that Δ t is obtained, and is carved in kth：
ωk+1=J-1ΔtS(ωk)H+J-1JαCΔNk+ωk
Wherein subscript k indicates the value to dependent variable at the kth moment, Δ Nk=Nk-Nk-1, I3×3For three rank unit matrixs.
4. according to the method described in claim 3, it is characterized in that：In step (2)：
(a) counteraction flyback maximum output torque constrains：
The torque output of counteraction flyback is to change the angular momentum realization of flywheel, so there is following form to state：
Wherein TmaxFor maximum output torque vector；
It will be obtained after above-mentioned formula discretization：
It is obtained after arrangement：
(b) counteraction flyback maximum angular momentum constrains：
The angular momentum saturation of flywheel is presented as that the rotating speed of flywheel rotor reaches the upper limit, so angular momentum constraint of saturation can use flywheel
Angular speed constraint indicates：
-Nmax≤ΔNk+Nk-1≤Nmax
Wherein NmaxFor flywheel maximum angular rate vector；
It is obtained after arrangement：
(c) angle of sight constraint that spacecraft attitude is directed toward：
Consider that the direction of spacecraft will evade certain conical lines-of-sight areas, the following form of posture restraint of design：
Wherein α indicates that the unit vector that spacecraft is directed toward under body coordinate system, β indicate that spacecraft needs to advise under body coordinate system
The unit vector in direction is kept away, θ indicates the size for evading the angle of sight in region.
5. according to the method described in claim 4, it is characterized in that：Optimization object function V (x in step (3)k,uk) be expressed as：
Wherein xk=[qk,ωk]TThe quantity of state of expression system, physical significance are the posture and angular speed of spacecraft；With flywheel group
Rotation speed change amount is closed as input, i.e. uk=Δ Nk；NPFor the estimation range of MPC；Q and P is the power of state variable and input variable
Weight matrix, illustrate that optimization aim is more concerned with the stable time if larger relative to P if Q, if Q relative to P it is larger illustrate it is excellent
Change the consumption that target is more concerned with energy；
It is organized into compact form：
Wherein
6. according to the method described in claim 5, it is characterized in that：Control problem is converted to and seeks target letter under constraints
Several extreme-value problem, the method that real-time iterative is used in combination solve controlled quentity controlled variable.
7. according to the method described in claim 6, it is characterized in that：The problem of control input will be solved, is converted to following mathematics and asks
Topic：
xi,k+1=F (xi,k,ui,k)
L(xi,k,ui,k)≤017×1K=0,1 ..., NP-1
WhereinIndicate the optimization problem in moment i,Indicate the feedback of status in current time i system, xi,kTable
Show by current time state xi,0The system mode at the kth moment of reckoning；ui,kThe estimated input at expression kth moment, 017×1It indicates
17 × 1 null matrix；F(xi,k,ui,k) it is system state equation, it is embodied as：
L(xi,k,ui,k) it is system restriction, it is embodied as：
Processing procedure using the method for real-time iterative is：Known previous moment optimization problemSolve find out
ComeWithAnd then solving-optimizing problemSpecific point
For two stages：Preparation stage and response phase：
Preparation phase procedures are：By xi-1And ui-1The displacement for doing a sampling instant keeps the last one element constant, obtainsWithAccording toWithCalculate sensitive square
Battle array Ai,k,Bi,k,Ci,k,Di,kWith error li,k,ri,k, expression is：
By linearisation, the optimization problem of a nonlinear restriction is converted to the quadratic programming problem of linear restriction：
Δui,k=ui,k-ui-1,k
Δxi,k+1=Ai,kΔxi,k+Bi,kΔui,k+ri,k
Ci,kΔxi,k+Di,kΔui,k+li,k≤ 0k=0,1 ..., NP-1
The process of response phase is：The feedback of status of acquisition systemBring Solve problems intoObtain Δ xi,kWith Δ ui,kIt is logical
Cross formula：
Obtain problemSolution (xi,k,ui,k), finally again by ui=ui,0Control as system inputs.
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