CN110502025B - Spacecraft attitude control method considering reactive flywheel characteristics and power limitation - Google Patents

Spacecraft attitude control method considering reactive flywheel characteristics and power limitation Download PDF

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CN110502025B
CN110502025B CN201910707553.3A CN201910707553A CN110502025B CN 110502025 B CN110502025 B CN 110502025B CN 201910707553 A CN201910707553 A CN 201910707553A CN 110502025 B CN110502025 B CN 110502025B
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reaction flywheel
attitude
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胡庆雷
张鑫鑫
董宏洋
郑建英
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Beihang University
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Abstract

The invention discloses a spacecraft attitude control method considering the characteristics and power limitation of a reaction flywheel, which comprises the following steps of: establishing a spacecraft kinematics and dynamics model in a quaternion description mode; establishing a relation between the output power of the spacecraft body-mounted solar array and the solar incident angle; considering the characteristics of the reaction flywheel, establishing angular momentum constraint, control moment constraint and actual available power constraint of the reaction flywheel when the body-mounted solar array fails; designing a target performance function according to task requirements; and finishing the spacecraft attitude control task under the constraint condition based on a model prediction control strategy. The method can well solve the attitude control problem of the spacecraft when the characteristics of the reaction flywheel and the body-mounted solar array are considered and the body-mounted solar array fails, achieves comprehensive optimization of control accuracy and energy consumption through the design of the objective function, and ensures that the spacecraft can still complete high-accuracy attitude control tasks under the condition that the characteristics and the power of the reaction flywheel are limited.

Description

Spacecraft attitude control method considering reactive flywheel characteristics and power limitation
Technical Field
The invention belongs to the technical field of spacecraft attitude control, and particularly relates to a spacecraft attitude control method considering the characteristics of a reaction flywheel and limited power, which is mainly applied to the problem of spacecraft attitude control considering the change of a solar incident angle, the constraint of angular momentum of the flywheel, the constraint of control moment and the limited available power when a body-mounted solar panel fails.
Background
In recent years, with the rapid development of space technology and the trend of more diversification and complication of space flight tasks, the on-orbit attitude control of the spacecraft is an important guarantee for realizing various spacecraft engineering tasks including attitude adjustment operation, and is a key technology. The reaction flywheel has the advantages of fine control moment and no consumption of satellite working media, and gradually becomes one of main actuating mechanisms of the existing spacecraft, but the influence of the problems of angular momentum saturation, control moment saturation and the like which are easy to occur in the working process on the attitude control performance of the spacecraft cannot be ignored. Secondly, for a spacecraft which executes space tasks in orbit, energy sources required for completing tasks such as scientific detection, attitude control and the like are all derived from solar sailboards on the spacecraft, but the solar sailboards can be caused to break down due to a complex space environment. Meanwhile, considering that the energy generated by the solar sailboard needs to be used by the effective load, the attitude control system and other subsystems, the power which can be provided by the spacecraft for the attitude control system is limited and variable, and is mainly related to the spatial position of the spacecraft on the track, the solar incident angle of the sailboard and the attitude angle of the spacecraft body. Therefore, the research on the spacecraft can complete high-precision attitude control under the constraints of the characteristics of a reaction flywheel, the power limitation and the like, simultaneously meet the power consumption requirement and enable the energy consumed by an attitude control system to be as small as possible, thereby ensuring that the spacecraft can complete scientific tasks, and the method has certain engineering significance.
Aiming at the existing spacecraft attitude control method considering the characteristics of a reaction flywheel, patent 201610196190.8 provides a flexible spacecraft attitude control method aiming at the saturation and friction characteristics of the flywheel, but the method only considers the saturation characteristics of the control moment of the flywheel and does not consider the problem of limited power of the flywheel; similarly, patent 201810298997.1 proposes a model prediction control method for spacecraft attitude avoidance considering dynamic characteristics of a flywheel, but the method only considers angular momentum and control torque saturation characteristics of the flywheel, and does not consider the situation that available power of the flywheel is limited, and in actual situations, the actual power limitation of the flywheel will affect attitude control performance of the spacecraft.
Aiming at the research result of the attitude control problem of the spacecraft considering the power of the reaction flywheel at present, most of the existing control strategies are dedicated to realizing the optimal instantaneous total power of the reaction flywheel combination when providing the attitude control torque, but neglecting the condition that the optimal instantaneous total power is still larger than the minimum available power, and under the condition, the reaction flywheel combination still cannot provide the required control torque, thereby influencing the attitude control performance of the spacecraft.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in the process of attitude maneuver of the spacecraft, the angular momentum of the reaction flywheel is saturated, the control moment is saturated but not negligible, and meanwhile, the solar sailboard assembled in the spacecraft is likely to have faults, so that the available power provided by the sailboard is limited. Since this limited power is needed for the payload, attitude control system and other subsystems together, the power available for the attitude control system is only a small fraction of the faulty windsurfing board output power. In order to ensure the normal operation of the spacecraft, the attitude control system can complete high-precision and low-energy-consumption attitude control tasks under the requirement of small and variable available power. The invention provides a spacecraft attitude control method considering the characteristics and power limitation of a reaction flywheel based on a model prediction control strategy. The method can simultaneously process various practical engineering constraints, has good robustness, can enable the spacecraft to complete the attitude control task under the given power requirement, and can design the target performance function according to the task requirement so as to enable the spacecraft to realize the comprehensive optimization of control precision and energy consumption in the attitude control process.
The invention provides a spacecraft attitude control method considering the characteristics and power limitation of a reaction flywheel, which comprises the following steps of:
s1: aiming at the problem of spacecraft attitude control, establishing a spacecraft attitude kinematics and dynamics model in a quaternion description mode, discretizing the spacecraft attitude kinematics and dynamics model, and establishing a prediction model of a model prediction control method;
s2: establishing a relation between output power of the spacecraft body-mounted solar array and a solar incident angle, and converting the relation into an expression related to a spacecraft attitude angle;
s3: based on the characteristics of a reaction flywheel of a spacecraft actuating mechanism, establishing angular momentum constraint and control moment constraint of the reaction flywheel, and simultaneously establishing actual available power constraint of the reaction flywheel when the spacecraft-mounted solar panel fails;
s4: designing a target performance function according to task requirements;
s5: and (4) finishing the spacecraft attitude control task under the constraint established in the step S3 based on the prediction model of the model prediction control method established in the step S1.
Further, the spacecraft attitude kinematics and dynamics model in the quaternion description mode in the step S1 is as follows:
Figure BDA0002152648190000031
wherein J ∈ R3×3Is a spacecraft inertia matrix; ω ═ ω (ω)1，ω2，ω3)TThe three-axis angular velocity of the spacecraft body; h is belonged to R3The total angular momentum of the spacecraft is H ═ J omega + HRWA，HRWA∈R3Combining the projection of the angular momentum on the main axis of the inertia of the spacecraft for the reaction flywheel; u. ofc∈R3Controlling moment for the attitude of the spacecraft; q ═ q0，q1，q2，q3)TIs a quaternion for describing the attitude of the spacecraft and satisfies
Figure BDA0002152648190000032
Xi (ω) is a skew antisymmetric matrix of specific form:
Figure BDA0002152648190000033
for any vector x ∈ R3Its corresponding oblique antisymmetric array x×The form is as follows:
Figure BDA0002152648190000034
when the influence of the orbital angular velocity of the spacecraft on the angular momentum of the reaction flywheel is neglected, the dynamic model of the reaction flywheel combination is as follows:
Figure BDA0002152648190000035
wherein, tauRWA∈RLIs the control moment generated by the L reaction flywheels; h isRWA∈RLIn order to counteract the angular momentum of the flywheel assembly,
Figure BDA0002152648190000036
combining derivatives of angular momentum with respect to time for the reaction flywheel; j. the design is a squareRWA∈RL×LA matrix of moments of inertia in the form of a reaction flywheel assembly
Figure BDA0002152648190000037
The moment of inertia of each reaction flywheel;
Figure BDA0002152648190000038
for the rotational speed of the respective reaction flywheel,
Figure BDA0002152648190000039
a derivative with respect to time for each reaction flywheel rotational speed;
based on a dynamic model of the reaction flywheel combination and a reaction flywheel combination configuration, the attitude control moment of the reaction flywheel combination applied to the spacecraft is obtained as follows:
Figure BDA0002152648190000041
wherein C ∈ R3×LInstalling a matrix for the reaction flywheel assembly;
acting on attitude control moment u of spacecraft according to the law of conservation of angular momentumcIs composed of
Figure BDA0002152648190000042
Substituting formula (5) into formula (1) to obtain a spacecraft attitude kinematics and dynamics model taking a reaction flywheel combination as an actuating mechanism:
Figure BDA0002152648190000043
discretizing the spacecraft attitude kinematics and dynamics model, taking a sampling time interval as delta t, and taking the spacecraft attitude kinematics and dynamics model as a prediction model of a model prediction control method, wherein the discretized spacecraft attitude kinematics and dynamics model is as follows:
Figure BDA0002152648190000044
subscripts k and k +1 represent time k and time k + 1; hkThe total angular momentum of the spacecraft at the moment k;
Figure BDA0002152648190000045
I4×4is a fourth order identity matrix; the superscript x is an oblique antisymmetric matrix;
let xk＝(qk，ωk)TThe state quantity of the spacecraft attitude control system at the kth moment represents the attitude and the angular speed of the spacecraft,
Figure BDA0002152648190000046
and (3) simplifying the discretized spacecraft attitude kinematics and dynamics model (7) into the following form for the system control quantity at the kth moment:
Figure BDA0002152648190000047
definition of
Figure BDA0002152648190000051
Then
xk+1＝F(xk，uk) (10)
Further, the relationship between the output power of the spacecraft-mounted solar array and the solar incident angle, which is established in step S2, is as follows:
Figure BDA0002152648190000052
wherein, PtotalThe total output power of the m individual solar sailboards on the spacecraft is obtained;
Figure BDA0002152648190000053
the output power of the ith solar panel;
Figure BDA0002152648190000054
the effective area of the ith solar array; thetaiThe solar incident angle represents the included angle between the normal of the ith solar sailboard and sunlight; pEOL(θi) Is the angle of incidence theta of the suniThe specific relation of the function of (b) represents the power per unit area of the ith solar sailboard, and is as follows:
Figure BDA0002152648190000055
wherein, PsIs incident solar radiation; eta is the photoelectric conversion rate of the solar sailboard; i isdIs an inherent degradation factor of the solar sailboard; l isdIs a solar panel life degradation factor;
however, considering that the solar incident angle is not a fixed value when the spacecraft operates on orbit and changes with the orbit of the spacecraft, the attitude angle of the spacecraft at the current moment and the position of the orbit, in order to obtain the instantaneous available total power of the spacecraft at any position on the orbit, a solar incident angle model is established as follows:
θi＝arccos<ni，rsb>，i＝1，2，...，m (13)
wherein n isi∈R3，|ni1 is a unit normal vector of the ith solar array in a spacecraft body coordinate system;<·，·>representing an inner product operation; r issb∈R3The projection of the sun unit vector in the spacecraft body coordinate system has the following conversion relationship:
rsb＝RbIrsI (14)
wherein r issI＝rs/|rs|∈R3Is a position vector r of the sun under the earth center inertial coordinate systems∈R3A unit vector of (a); rbIA transformation matrix from the geocentric inertial coordinate system to the spacecraft body coordinate system is related to the Euler rotation sequence and the attitude Euler angle;
converting the relation between the output power of the spacecraft-mounted solar array and the solar incident angle into an expression related to the attitude angle of the spacecraft:
Figure BDA0002152648190000061
wherein, Psolar∈RmThe vector of the output power of the body-mounted solar sailboard is output.
Further, the step S3 specifically includes the following steps:
the specific forms of the angular momentum constraint and the control moment constraint of the spacecraft actuating mechanism reaction flywheel are as follows:
1) the angular momentum constraint is expressed in terms of the rotational speed constraint as:
Figure BDA0002152648190000062
wherein the content of the first and second substances,
Figure BDA0002152648190000063
the maximum rotating speed vector of the reaction flywheel combination;
transforming equation (16) into incremental form:
Figure BDA0002152648190000064
2) the control torque constraint is expressed as:
Figure BDA0002152648190000065
wherein the content of the first and second substances,
Figure BDA0002152648190000066
the maximum control moment vector of the reaction flywheel combination;
because the spacecraft attitude control system is in a discrete system form, the following angular acceleration is used for controlling the moment constraint
Figure BDA0002152648190000067
Approximately represents:
Figure BDA0002152648190000068
3) the actual available power of the reaction flywheel when the body-mounted solar panel fails is restricted:
firstly, the time of the spacecraft entering the ground shadow area is assumed to be negligible, namely, the body-mounted solar sailboard on the spacecraft is approximately considered to be always irradiated by sunlight;
secondly, considering that the output power of the upper body-mounted solar array of the spacecraft needs to be used by an effective load, an actuating mechanism and other subsystems; meanwhile, when the spacecraft runs to different orbit positions, the output power provided by the solar sailboard changes along with the solar incident angle or the attitude angle of the satellite of the spacecraft, and the solar sailboard possibly fails due to a complex space environment, so that the actual power available for an actuating mechanism is limited;
therefore, the expression of the actual power constraint available for the reactive flywheel in the case of a failure of the body-mounted solar panel is as follows:
Figure BDA0002152648190000071
wherein the content of the first and second substances,
Figure BDA0002152648190000072
instantaneous power vectors which can be provided for all the body-mounted solar sailboards at the moment k; kappa is the power ratio available for the actuator; ek＝(e1，e2，…，em) A fault factor sequence of each solar array at the moment k, wherein e is more than or equal to 0i≤1，i＝1，2，…，m；
Figure BDA0002152648190000073
For moment k reaction flywheel combinationThe total power required to provide the desired attitude control torque is specified in the form:
Figure BDA0002152648190000074
wherein the content of the first and second substances,
Figure BDA0002152648190000075
the derivative of the combined angular momentum with respect to time for the moment k reaction flywheel,
Figure BDA0002152648190000076
for the angular acceleration of the reaction flywheel combination at time k, the superscript T indicates transposition,
discretizing the formula (21) to obtain
Figure BDA0002152648190000077
By substituting formula (22) into formula (20):
Figure BDA0002152648190000078
and the angular momentum constraint and the control moment constraint of the reaction flywheel and the actual available power constraint of the reaction flywheel when the body-mounted solar array fails are organized into the following forms:
Figure BDA0002152648190000081
wherein the content of the first and second substances,
Figure BDA0002152648190000082
04L+1represents a 4L + 1-dimensional zero vector; and L is the total number of the reaction flywheels in the reaction flywheel combination.
Further, in the case of reducing the energy consumption as much as possible while satisfying the high control accuracy in the spacecraft attitude control process, the target performance function designed in step S4 is:
Figure BDA0002152648190000083
wherein, N is the prediction step length, and the subscript j | k represents the j prediction time at the k time; x is the number of0|kPredicting initial state quantity x in step length for spacecraft attitude control system at kth momentj|k＝(qj|k，ωj|k)TPredicting the attitude control system state quantity of the spacecraft in the jth step in the step length at the kth moment, and representing the attitude and the angular speed of the spacecraft;
Figure BDA0002152648190000084
is a desired state of the control system;
Figure BDA0002152648190000085
predicting the system control quantity of the jth step in the step length at the kth moment; q and P are constant positive definite weight matrixes of the state quantity and the control quantity.
Further, the step S5 specifically includes the following steps:
based on the prediction model of the model predictive control method established in the step S1, the target performance function designed in the step S4, the angular momentum constraint and the control moment constraint of the reaction flywheel established in the step S3, and the actual available power constraint condition of the reaction flywheel when the body-mounted solar array fails, the spacecraft attitude control problem is converted into the following optimization problem:
Figure BDA0002152648190000086
subject to xj+1|k＝F(xj|k，uj|k) (27)
K(xj|k，uj|k)≤04L+1 (28)
wherein x isj+1|k＝F(xj|k，uj|k) The spacecraft attitude control system state equation is obtained; k (x)j|k，uj|k) To compriseThe system comprises angular momentum constraint and control moment constraint of a reaction flywheel and system constraint of actual available power constraint of the reaction flywheel when the body-mounted solar panel fails; the specific form of the state equation and the system constraint of the jth step in the k moment prediction step length of the spacecraft attitude control system is as follows:
Figure BDA0002152648190000091
Figure BDA0002152648190000092
solving the optimization problem to obtain an optimal control sequence of the system meeting constraint conditions at the moment k:
Figure BDA0002152648190000093
wherein the superscript denotes the optimal solution,
taking the first item in the optimal control sequence as the optimal control input quantity of the attitude control system of the spacecraft at the moment k, namely
Figure BDA0002152648190000094
Finally, let
Figure BDA0002152648190000095
And solving the optimal control input quantity of the spacecraft attitude control system at the next moment, and completing the spacecraft attitude control task under the constraint established in the step S3.
The invention has the beneficial effects that:
(1) compared with the existing spacecraft attitude control method considering the characteristics of the reaction flywheel, the method considers the problem that the actual available power of the reaction flywheel is limited when the bulk solar panel fails on the basis of considering the angular momentum saturation and the moment saturation of the reaction flywheel, and more comprehensively analyzes the actual constraint which is possibly met when the reaction flywheel provides attitude control moment for the spacecraft in space;
(2) compared with the existing spacecraft attitude control method with the optimal instantaneous power of the reaction flywheel, the instantaneous optimal power obtained by the existing optimal method is possibly still larger than the maximum available power provided by the solar sailboard when the solar sailboard fails.
(3) The actual available power constraint of the reaction flywheel described in the invention is a dynamic constraint, which is not only related to the possible faults of the solar sailboard, but also closely related to the current orbit position and the current attitude angle of the spacecraft, so that the spacecraft attitude control problem under the dynamic constraint is solved, and the method has more engineering significance.
Drawings
FIG. 1 is a flow chart of a spacecraft attitude control method of the present invention that considers reactive flywheel characteristics and power constraints.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and embodiments.
The spacecraft attitude control method considering the characteristics of the reaction flywheel and the power limitation is based on a model prediction control strategy, and considers the spacecraft attitude control problem under the condition that the angular momentum, the control moment and the power of the reaction flywheel are limited. As shown in fig. 1, the method firstly establishes a spacecraft kinematics and dynamics model in a quaternion description mode; secondly, establishing a relation between the output power of the spacecraft body-mounted solar array and the solar incident angle; then, considering the characteristics of the reaction flywheel to establish angular momentum constraint and control moment constraint, and establishing the actual available power constraint of the reaction flywheel when the three-dimensional assembled solar array fails according to the relation between the output power of the spacecraft assembled solar array and the solar incident angle; then designing a target performance function to ensure that the spacecraft can meet high-precision control in the attitude maneuver process and reduce energy consumption as much as possible; and finally, solving the optimal control moment based on a model predictive control strategy, thereby completing the spacecraft attitude control task under the constraint condition.
The specific operation steps are as follows:
firstly, establishing a spacecraft attitude kinematics and dynamics model in a quaternion description mode as follows:
Figure BDA0002152648190000111
wherein J ═ diag (1, 0.5, 0.8) kg · m2∈R3×3Is a spacecraft inertia matrix; ω ═ ω (ω)1，ω2，ω3)TThe three-axis angular velocity of the spacecraft body; h is belonged to R3The total angular momentum of the spacecraft is H ═ J omega + HRWAAnd H isRWA∈R3Combining the projection of the angular momentum on the main axis of the inertia of the spacecraft for the reaction flywheel; u. ofc∈R3In order to act on the attitude control moment of the spacecraft, the attitude control moment is provided by a reaction flywheel combination; q ═ q0，q1，q2，q3)TIs a quaternion for describing the attitude of the spacecraft and satisfies
Figure BDA0002152648190000112
Xi (ω) is a skew antisymmetric matrix of specific form:
Figure BDA0002152648190000113
for any vector x ∈ R3Its corresponding oblique antisymmetric array x×The form is as follows:
Figure BDA0002152648190000114
if the influence of the orbital angular velocity of the spacecraft on the angular momentum of the flywheel is neglected, a counteractive flywheel combined dynamic model is given:
Figure BDA0002152648190000115
wherein, tauRWA∈RLIs the control moment generated by the L reaction flywheels; h isRWA∈RLIn order to counteract the angular momentum of the flywheel assembly,
Figure BDA0002152648190000116
combining derivatives of angular momentum with respect to time for the reaction flywheel; j. the design is a squareRWA∈RL×LA matrix of moments of inertia in the form of a reaction flywheel assembly
Figure BDA0002152648190000117
The moment of inertia of each reaction flywheel;
Figure BDA0002152648190000121
the rotational speed of each reaction flywheel. In this embodiment, the number of flywheels L is 4, and the reaction flywheel combination is configured as a three-orthogonal one-slant assembly.
According to the dynamic model of the reaction flywheel combination and the reaction flywheel combination configuration, the attitude control moment applied to the spacecraft by the reaction flywheel combination is as follows:
Figure BDA0002152648190000122
wherein C ∈ R3×4A matrix is assembled and installed for the reaction flywheel, and the concrete form is as follows;
Figure BDA0002152648190000123
according to the law of conservation of angular momentum, the total angular momentum of the spacecraft system is conserved under the action of no external moment, so that the attitude control moment acting on the spacecraft is
Figure BDA0002152648190000124
Substituting the attitude control torque provided by the reaction flywheel into the spacecraft attitude dynamics model can obtain a spacecraft attitude kinematics and dynamics model which takes the reaction flywheel combination as an actuating mechanism:
Figure BDA0002152648190000125
in order to use the above-described kinetic model as a prediction model of the model prediction control method, it is necessary to discretize the model, and when the sampling time interval Δ t is 0.4s, the discretized kinetic model is:
Figure BDA0002152648190000126
subscripts k and k +1 represent time k and time k + 1; hkThe total angular momentum of the spacecraft at the moment k;
Figure BDA0002152648190000127
I4×4is a fourth order identity matrix; the superscript x is a skewed antisymmetric matrix.
Let xk＝(qk，ωk)TThe state quantity of the spacecraft attitude control system at the kth moment represents the attitude and the angular speed of the spacecraft,
Figure BDA0002152648190000128
for the system control quantity at the kth moment, the discrete dynamic model can be simplified into the following form:
Figure BDA0002152648190000131
if defined, are
Figure BDA0002152648190000132
Then there is
xk+1＝F(xk，uk) (10)
Secondly, establishing the relation between the output power of the spacecraft body-mounted solar array and the solar incident angle:
Figure BDA0002152648190000133
wherein, PtotalThe method comprises the following steps of providing the total output power of m individual solar sailboards on a spacecraft, providing energy for the spacecraft to complete tasks such as scientific detection, attitude control and the like, wherein m is 4;
Figure BDA0002152648190000134
the output power of the ith solar panel;
Figure BDA0002152648190000135
the effective area of the ith solar array; thetaiThe solar incident angle represents the included angle between the normal of the ith solar sailboard and sunlight; pEOL(θi) Is the angle of incidence theta of the suniThe specific relation of the function of (b) represents the power per unit area of the ith solar sailboard, and is as follows:
Figure BDA0002152648190000136
wherein, Ps＝1358W/m2Is incident solar radiation; eta is 0.14, which is the photoelectric conversion rate of the solar sailboard; i isd0.77 is the inherent degradation factor of the solar sailboard; l isd0.625 is the solar panel life degradation factor.
However, considering that the solar incident angle is not a fixed value when the spacecraft operates on orbit and changes with the orbit of the spacecraft, the attitude angle of the spacecraft at the current moment and the position of the orbit, in order to obtain the instantaneous available total power of the spacecraft at any position on the orbit, a solar incident angle model is established as follows:
θi＝arccos<ni，rsb>，i＝1，2，...，m (13)
wherein n isi∈R3，|ni1 is a unit normal vector of the ith solar array in a spacecraft body coordinate system;<·，·>representing an inner product operation; r issb∈R3The projection of the sun unit vector in the spacecraft body coordinate system has the following conversion relation:
rsb＝RbIrsI (14)
wherein r issI＝rs/|rs|∈R3Is a position vector r of the sun under the earth center inertial coordinate systems∈R3A unit vector of (a); rbIA transformation matrix from the geocentric inertial coordinate system to the spacecraft body coordinate system is related to the Euler rotation sequence and the attitude Euler angle;
converting the relation between the output power of the spacecraft-mounted solar array and the solar incident angle into an expression related to the attitude angle of the spacecraft:
Figure BDA0002152648190000141
wherein, Psolar∈RmThe vector of the output power of the body-mounted solar sailboard is output.
If the Euler rotation sequence is 2-3-1, the transformation matrix R from the geocentric inertial coordinate system to the spacecraft body coordinate systembIThe form of (A) is as follows:
Figure BDA0002152648190000142
wherein R isx(γ) is a primitive transformation matrix that rotates through a roll angle γ around the ox axis; ry(ψ) is a primitive transformation matrix that rotates through the yaw angle ψ about the oy axis;
Figure BDA0002152648190000143
for turning over pitch angle about oz axis
Figure BDA0002152648190000144
The primitive transformation matrix of (2); the three primitive transformation matrices are of the form:
Figure BDA0002152648190000145
unfolding to obtain:
Figure BDA0002152648190000146
at this time, the relational expression (15) of the output power of the spacecraft-mounted solar panel and the solar incident angle can be converted into an expression related to the attitude angle of the spacecraft:
Figure BDA0002152648190000151
wherein the amount of the component phi, psi,
Figure BDA0002152648190000152
gamma represents the Euler angles of the yaw, pitch and roll attitudes of the spacecraft respectively.
And thirdly, based on the relation between the output power of the body-mounted solar array of the spacecraft and the attitude angle of the spacecraft in the second step, further considering the characteristic of a reaction flywheel of an actuating mechanism of the spacecraft, and establishing angular momentum constraint, control moment constraint and actual available power constraint of the reaction flywheel when the body-mounted solar array fails:
because the reaction flywheel belongs to a mechanical structure, angular momentum constraint and control moment constraint exist, and the specific form is as follows:
1) and (3) angular momentum constraint: the angular momentum of the reaction flywheel is reflected in the flywheel speed, and the angular momentum constraint can be expressed in terms of a speed constraint, i.e. the angular momentum constraint is expressed in terms of the flywheel speed
Figure BDA0002152648190000153
Wherein the content of the first and second substances,
Figure BDA0002152648190000154
for counteracting the maximum speed vector of the flywheel combination, take
Figure BDA0002152648190000155
Transforming the above into incremental form:
Figure BDA0002152648190000156
2) controlling torque constraint:
Figure BDA0002152648190000157
wherein the content of the first and second substances,
Figure BDA0002152648190000158
for the maximum control moment vector of the counteracting flywheel combination, taken here
Figure BDA0002152648190000159
Because the spacecraft attitude control system is in a discrete system form, the control moment constraint can be realized by the following angular acceleration
Figure BDA00021526481900001510
Approximately represents:
Figure BDA00021526481900001511
3) the actual available power of the reaction flywheel when the body-mounted solar panel fails is restricted:
firstly, the time of the spacecraft entering the ground shadow area is assumed to be negligible, namely, the body-mounted solar sailboard on the spacecraft is approximately considered to be always irradiated by sunlight;
secondly, considering that the output power of the upper body-mounted solar array of the spacecraft needs to be used by an effective load, an actuating mechanism and other subsystems; meanwhile, when the spacecraft runs to different orbit positions, the output power provided by the solar sailboard changes along with the solar incident angle or the spacecraft attitude angle, and the solar sailboard possibly fails due to a complex space environment, so that the actual power available for an actuating mechanism is limited;
therefore, the expression of the actual power constraint available for the reactive flywheel combination in the case of a failure of the body-mounted solar panel is as follows:
Figure BDA0002152648190000161
wherein the content of the first and second substances,
Figure BDA0002152648190000162
the yaw angle phi at the moment k is used as the instantaneous power vector which can be provided by each body-mounted solar array at the moment kkAnd a pitch angle
Figure BDA0002152648190000163
And roll angle gammakThe instantaneous power vector which can be provided by each body-mounted solar array of the spacecraft at the current k moment and the current attitude can be obtained by specific substitution
Figure BDA0002152648190000164
The concrete form is shown as a formula (15-3); kappa is the power ratio available for the actuator; ek＝(e1，e2，…，em) A fault factor sequence of each solar array at the moment k, wherein e is more than or equal to 0i≤1，i＝1，2，...，m；
Figure BDA0002152648190000165
The total power required for generating the expected attitude control torque for the reaction flywheel combination at the moment k is specifically as follows:
Figure BDA0002152648190000166
wherein the content of the first and second substances,
Figure BDA0002152648190000167
the derivative of the combined angular momentum with respect to time for the moment k reaction flywheel,
Figure BDA0002152648190000168
for the angular acceleration of the reaction flywheel combination at time k, the superscript T indicates transposition,
discretizing the above formula to obtain the product
Figure BDA0002152648190000169
The actual power constraint for the combination of the reaction flywheel when the assembled solar panel fails after the arrangement is as follows:
Figure BDA0002152648190000171
wherein the Euler angle psik，
Figure BDA0002152648190000172
γkAnd quaternion qkThere is a mutual conversion relationship between them, so the above formula can be expressed as:
Figure BDA0002152648190000173
according to the above definition
Figure BDA0002152648190000174
Restrain the angular momentum of the reaction flywheel,The control moment constraint and the actual power constraint which can be used by the combination of the reaction flywheel when the body-mounted solar panel has a fault are organized into the following forms:
Figure BDA0002152648190000175
wherein, 04L+1Represents a 4L + 1-dimensional zero vector; and L is 4, which is the total number of the reaction flywheels in the reaction flywheel combination.
Fourthly, considering that the energy consumption is reduced as much as possible while meeting high control precision in the spacecraft attitude control process, the target performance function in the design step S4 is:
Figure BDA0002152648190000176
where N ═ 5 is the prediction step size, and the subscript j | k denotes the j-th prediction time at the k-th time; x is the number of0|kPredicting initial state quantity x in step length for spacecraft attitude control system at kth momentj|k＝(qj|k，ωj|k)TPredicting the attitude control system state quantity of the spacecraft in the jth step in the step length at the kth moment, and representing the attitude and the angular speed of the spacecraft;
Figure BDA0002152648190000177
the form of the control system is determined by the specific task in order to control the desired state of the system;
Figure BDA0002152648190000178
predicting the system control quantity of the jth step in the step length at the kth moment; q is 0.7I7×7，P＝0.3I4×4The weighting matrix is positively determined for the constant values of the state quantities and the control quantities.
And fifthly, based on the constraint conditions in the third step and the target performance function designed in the fourth step, completing the constrained spacecraft attitude control task based on the model prediction control strategy:
from the discretized dynamical model, the objective performance function and the constraint conditions, the control problem can be converted into the following optimization problem:
Figure BDA0002152648190000181
subject to xj+1|k＝F(xj|k，uj|k) (27)
K(xj|k，uj|k)≤04L+1 (28)
wherein x isj+1|k＝F(xj|k，uj|k) The spacecraft attitude control system state equation is obtained; k (x)j|k，uj|k) The method comprises the following steps of performing system constraint, wherein the system constraint comprises reaction flywheel angular momentum constraint, control moment constraint and actual available power constraint of a reaction flywheel when a body-mounted solar array fails; the specific form of the state equation and the system constraint of the jth step in the k moment prediction step length of the spacecraft attitude control system is as follows:
Figure BDA0002152648190000182
Figure BDA0002152648190000183
solving the optimization problem can obtain an optimal control sequence of the system meeting the constraint condition at the moment k:
Figure BDA0002152648190000184
taking the first item in the optimal control sequence as the optimal control input quantity of the attitude control system of the spacecraft at the moment k, namely
Figure BDA0002152648190000185
Finally, let
Figure BDA0002152648190000186
And solving the optimal control input quantity of the spacecraft attitude control system at the next moment, thus finishing the constrained spacecraft attitude control task.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (4)

1. A spacecraft attitude control method considering the characteristics and power limitation of a reaction flywheel is characterized by comprising the following steps:
s1: aiming at the problem of spacecraft attitude control, establishing a spacecraft attitude kinematics and dynamics model in a quaternion description mode, discretizing the spacecraft attitude kinematics and dynamics model, and establishing a prediction model of a model prediction control method;
s2: establishing a relation between output power of the spacecraft body-mounted solar array and a solar incident angle, and converting the relation into an expression related to a spacecraft attitude angle;
s3: based on the characteristics of a reaction flywheel of a spacecraft actuating mechanism, establishing angular momentum constraint and control moment constraint of the reaction flywheel, and simultaneously establishing actual available power constraint of the reaction flywheel when the spacecraft-mounted solar panel fails;
s4: designing a target performance function according to task requirements;
s5: based on the prediction model of the model prediction control method established in the step S1, completing the spacecraft attitude control task under the constraint established in the step S3;
the spacecraft attitude kinematics and dynamics model in the quaternion description mode in step S1 is as follows:
Figure FDA0002620031530000011
wherein J ∈ R3×3Is a spacecraft inertia matrix, R3×3Representing a set of 3 x 3 matrices; ω ═ ω (ω)1,ω2,ω3)TThe three-axis angular velocity of the spacecraft body; h is belonged to R3Is the total angular momentum of the spacecraft, R3Represents a 3-dimensional real vector space, which is embodied in the form of H ═ J ω + HRWA，HRWA∈R3Combining the projection of the angular momentum on the main axis of the inertia of the spacecraft for the reaction flywheel; u. ofc∈R3Controlling moment for the attitude of the spacecraft; q ═ q0,q1,q2,q3)TIs a quaternion for describing the attitude of the spacecraft and satisfies
Figure FDA0002620031530000012
Xi (ω) is a skew antisymmetric matrix of specific form:
Figure FDA0002620031530000013
for any vector x ∈ R3Its corresponding oblique antisymmetric array x×The form is as follows:
Figure FDA0002620031530000021
when the influence of the orbital angular velocity of the spacecraft on the angular momentum of the reaction flywheel is neglected, the dynamic model of the reaction flywheel combination is as follows:
Figure FDA0002620031530000022
wherein, tauRWA∈RLFor control torque produced by L reaction flywheels, RLRepresenting an L-dimensional real vector space; h isRWA∈RLIn order to counteract the angular momentum of the flywheel assembly,
Figure FDA0002620031530000023
combining derivatives of angular momentum with respect to time for the reaction flywheel; j. the design is a squareRWA∈RL×LIs a matrix of moments of inertia of the counteracting flywheel combination,in the form of
Figure FDA0002620031530000024
For the moment of inertia of each reaction flywheel, RL×LRepresenting a set of L × L matrices;
Figure FDA0002620031530000025
for the rotational speed of the respective reaction flywheel,
Figure FDA0002620031530000026
a derivative with respect to time for each reaction flywheel rotational speed;
based on a dynamic model of the reaction flywheel combination and a reaction flywheel combination configuration, the attitude control moment of the reaction flywheel combination applied to the spacecraft is obtained as follows:
Figure FDA0002620031530000027
wherein C ∈ R3×LMounting matrices, R, for reaction flywheel combinations3×LRepresenting a 3 × L matrix set;
acting on attitude control moment u of spacecraft according to the law of conservation of angular momentumcIs composed of
Figure FDA0002620031530000028
Substituting formula (5) into formula (1) to obtain a spacecraft attitude kinematics and dynamics model taking a reaction flywheel combination as an actuating mechanism:
Figure FDA0002620031530000029
discretizing the spacecraft attitude kinematics and dynamics model, taking a sampling time interval as delta t, and taking the spacecraft attitude kinematics and dynamics model as a prediction model of a model prediction control method, wherein the discretized spacecraft attitude kinematics and dynamics model is as follows:
Figure FDA0002620031530000031
subscripts k and k +1 respectively represent the k time and the k +1 time; hkThe total angular momentum of the spacecraft at the moment k;
Figure FDA0002620031530000032
I4×4is a fourth order identity matrix; the superscript x is an oblique antisymmetric matrix;
let xk＝(qk,ωk)TThe state quantity of the spacecraft attitude control system at the kth moment represents the attitude and the angular speed of the spacecraft,
Figure FDA0002620031530000033
and (3) simplifying the discretized spacecraft attitude kinematics and dynamics model (7) into the following form for the system control quantity at the kth moment:
Figure FDA0002620031530000034
definition of
Figure FDA0002620031530000035
Then
xk+1＝F(xk,uk) (10)；
The relationship between the output power of the spacecraft-mounted solar array and the solar incident angle, which is established in the step S2, is as follows:
Figure FDA0002620031530000036
wherein, PtotalThe total output power of the m individual solar sailboards on the spacecraft is obtained;
Figure FDA0002620031530000037
the output power of the ith solar panel;
Figure FDA0002620031530000038
the effective area of the ith solar array; thetaiThe solar incident angle represents the included angle between the normal of the ith solar sailboard and sunlight; pEOL(θi) Is the angle of incidence theta of the suniThe specific relation of the function of (b) represents the power per unit area of the ith solar sailboard, and is as follows:
Figure FDA0002620031530000039
wherein, PsIs incident solar radiation; eta is the photoelectric conversion rate of the solar sailboard; i isdIs an inherent degradation factor of the solar sailboard; l isdIs a solar panel life degradation factor;
the solar incident angle changes with the orbit of the spacecraft, the attitude angle of the spacecraft at the current moment and the position of the orbit, and in order to obtain the instantaneous available total power of the spacecraft at any position on the orbit, a solar incident angle model is established as follows:
θi＝arccos<ni,rsb>,i＝1,2,...,m (13)
wherein n isi∈R3,|ni1 is a unit normal vector of the ith solar array in a spacecraft body coordinate system;<·,·>representing an inner product operation; r issb∈R3The projection of the sun unit vector in the spacecraft body coordinate system has the following conversion relationship:
rsb＝RbIrsI (14)
wherein r issI＝rs/|rs|∈R3Is a position vector r of the sun under the earth center inertial coordinate systems∈R3A unit vector of (a); rbIA transformation matrix from the geocentric inertial coordinate system to the spacecraft body coordinate system is related to the Euler rotation sequence and the attitude Euler angle;
converting the relation between the output power of the spacecraft-mounted solar array and the solar incident angle into an expression related to the attitude angle of the spacecraft:
Figure FDA0002620031530000041
wherein, Psolar∈RmFor the output power vector, R, of the body-mounted solar panelmRepresenting an m-dimensional real vector space.
2. The method according to claim 1, wherein step S3 is implemented as follows:
the specific forms of the angular momentum constraint and the control moment constraint of the spacecraft actuating mechanism reaction flywheel are as follows:
1) the angular momentum constraint is expressed in terms of the rotational speed constraint as:
Figure FDA0002620031530000042
wherein the content of the first and second substances,
Figure FDA0002620031530000043
the maximum rotating speed vector of the reaction flywheel combination;
transforming equation (16) into incremental form:
Figure FDA0002620031530000051
2) the control torque constraint is expressed as:
Figure FDA0002620031530000052
wherein the content of the first and second substances,
Figure FDA0002620031530000053
the maximum control moment vector of the reaction flywheel combination;
because the spacecraft attitude control system is in a discrete system form, the following angular acceleration is used for controlling the moment constraint
Figure FDA0002620031530000054
Approximately represents:
Figure FDA0002620031530000055
3) the actual available power of the reaction flywheel when the body-mounted solar panel fails is restricted:
under the condition that the body-mounted solar array on the spacecraft is always irradiated by sunlight, the actual power constraint expression of the reactive flywheel when the body-mounted solar array fails is as follows:
Figure FDA0002620031530000056
wherein the content of the first and second substances,
Figure FDA0002620031530000057
instantaneous power vectors which can be provided for all the body-mounted solar sailboards at the moment k; kappa is the power ratio available for the actuator; ek＝(e1,e2,…,em) A fault factor sequence of each solar array at the moment k, wherein e is more than or equal to 0i≤1,i＝1,2,…,m；
Figure FDA0002620031530000058
For moment-k reaction flywheel combinationThe total power required to expect the attitude control moment is specifically formed as follows:
Figure FDA0002620031530000059
wherein the content of the first and second substances,
Figure FDA00026200315300000510
the derivative of the combined angular momentum with respect to time for the moment k reaction flywheel,
Figure FDA00026200315300000511
for the angular acceleration of the reaction flywheel combination at time k, the superscript T indicates transposition,
discretizing the formula (21) to obtain
Figure FDA00026200315300000512
By substituting formula (22) into formula (20):
Figure FDA00026200315300000513
and the angular momentum constraint and the control moment constraint of the reaction flywheel and the actual available power constraint of the reaction flywheel when the body-mounted solar array fails are organized into the following forms:
Figure FDA0002620031530000061
wherein the content of the first and second substances,
Figure FDA0002620031530000062
04L+1represents a 4L + 1-dimensional zero vector; and L is the total number of the reaction flywheels in the reaction flywheel combination.
3. The method according to claim 2, wherein the target performance function designed in step S4 is, in the spacecraft attitude control process, as much as possible while satisfying high control accuracy, the following:
Figure FDA0002620031530000063
wherein, N is the prediction step length, and the subscript j | k represents the j prediction time at the k time; x is the number of0|kPredicting initial state quantity x in step length for spacecraft attitude control system at kth momentj|k＝(qj|k,ωj|k)TPredicting the attitude control system state quantity of the spacecraft in the jth step in the step length at the kth moment, and representing the attitude and the angular speed of the spacecraft;
Figure FDA0002620031530000064
is a desired state of the control system;
Figure FDA0002620031530000065
predicting the system control quantity of the jth step in the step length at the kth moment; q and P are constant positive definite weight matrixes of the state quantity and the control quantity.
4. The method according to claim 3, wherein step S5 is implemented as follows:
based on the prediction model of the model predictive control method established in the step S1, the target performance function designed in the step S4, the angular momentum constraint and the control moment constraint of the reaction flywheel established in the step S3, and the actual available power constraint condition of the reaction flywheel when the body-mounted solar array fails, the spacecraft attitude control problem is converted into the following optimization problem:
Figure FDA0002620031530000066
satisfies the following conditions:
xj+1|k＝F(xj|k,uj|k) (27)
K(xj|k,uj|k)≤04L+1 (28)
wherein x isj+1|k＝F(xj|k,uj|k) The spacecraft attitude control system state equation is obtained; k (x)j|k,uj|k) The system constraint comprises angular momentum constraint and control moment constraint of a reaction flywheel and actual available power constraint of the reaction flywheel when the body-mounted solar sailboard fails; the specific form of the state equation and the system constraint of the jth step in the k moment prediction step length of the spacecraft attitude control system is as follows:
Figure FDA0002620031530000071
Figure FDA0002620031530000072
solving the optimization problem to obtain an optimal control sequence of the system meeting constraint conditions at the moment k:
Figure FDA0002620031530000073
wherein the superscript denotes the optimal solution,
taking the first item in the optimal control sequence as the optimal control input quantity of the attitude control system of the spacecraft at the moment k, namely
Figure FDA0002620031530000074
Finally, let
Figure FDA0002620031530000075
Solving optimal control of spacecraft attitude control system at next momentAnd inputting the quantity, and finishing the spacecraft attitude control task under the constraint established in the step S3.
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