CN109507875B - Euler rotary satellite attitude maneuver hierarchical saturation PID control method - Google Patents

Euler rotary satellite attitude maneuver hierarchical saturation PID control method Download PDF

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CN109507875B
CN109507875B CN201910016560.9A CN201910016560A CN109507875B CN 109507875 B CN109507875 B CN 109507875B CN 201910016560 A CN201910016560 A CN 201910016560A CN 109507875 B CN109507875 B CN 109507875B
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郭延宁
祝贺
吕跃勇
李传江
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Harbin Institute of Technology
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Abstract

A hierarchical saturation PID control method for attitude maneuver of Euler rotary satellite belongs to the field of satellite attitude maneuver control. The invention aims to solve the problem that the existing satellite attitude maneuver hierarchical saturation PID control method cannot realize triaxial Euler rotation. The invention firstly establishes a satellite attitude kinematics and an attitude dynamics equation with a flywheel as an actuating mechanism, then analyzes the torque envelope characteristic of a flywheel train, judges a rhombic surface through which an expected torque passes, calculates the maximum output torque of the flywheel along the direction of the expected torque, and determines the maximum flywheel torque vector. And designing a hierarchical saturated PID controller to control the three-axis attitude of the satellite according to the maximum flywheel torque vector and the maneuvering angular speed limit design error limit vector. The invention can enable the flywheel to exert the maximum capability of an expected moment direction when the satellite has large attitude deviation, thereby approaching the near-time optimal Euler rotation attitude maneuver performance. The invention is suitable for controlling the satellite attitude maneuver.

Description

Euler rotary satellite attitude maneuver hierarchical saturation PID control method
Technical Field
The invention belongs to the field of satellite attitude maneuver control, and particularly relates to a satellite attitude maneuver control method.
Background
The euler rotation maneuver strategy is widely applied to satellite attitude maneuver control because the satellite can be guaranteed to maneuver to a desired attitude in the shortest path and the controller is simple and reliable. Meanwhile, the maneuverability of the satellite can be improved by exerting the maximum output capability of the actuating mechanism, and the requirements of large-angle maneuvering and quick maneuvering are further met.
In the design of a wheel-controlled small satellite attitude large-angle maneuver step-by-step saturation controller in the document, under the constraint that the output torque of a reaction wheel is limited and the attitude angular rate is saturated, the step-by-step saturation controller is used for limiting the maximum deviation of each attitude maneuver of the spacecraft so as to eliminate the maximum deviation successively. The literature, namely an on-orbit service spacecraft attitude tracking algorithm based on Euler rotation, aims at a spacecraft rendezvous capture task, decomposes an initial angular velocity into a parallel Euler axis component and a vertical Euler axis component, introduces an actual rotation axis deviating from an expected Euler axis coefficient, and controls the coefficient to be always kept in a preset range after eliminating the vertical component as soon as possible in the initial tracking stage, thereby realizing the near Euler rotation. The document "Rapid Multi-Target Acquisition and Pointing Control of Agile space gradient" designs a hierarchical saturated PID controller considering the angular velocity constraints. However, the problem that the existing satellite attitude maneuver hierarchical saturation PID control method cannot realize triaxial Euler rotation is solved.
Disclosure of Invention
The invention aims to solve the problem that the existing satellite attitude maneuver hierarchical saturation PID control method cannot realize triaxial Euler rotation.
A hierarchical saturation PID control method for attitude maneuver of Euler rotary satellite comprises the following steps:
step one, establishing a satellite attitude kinematics and an attitude dynamics equation of which a flywheel is an actuating mechanism;
analyzing the enveloping characteristics of the moment of the flywheel train, and judging a rhombic surface through which the expected moment passes;
step three, calculating the maximum output torque of the flywheel along the expected torque direction, and determining the maximum flywheel torque vector;
fourthly, designing an error limit vector L according to the maximum flywheel torque vector and the maneuvering angular speed limit;
and step five, designing a hierarchical saturated PID controller to control the satellite triaxial attitude.
Further, the satellite attitude kinematics and attitude dynamics equation with the flywheel as the actuating mechanism in the step one is as follows:
establishing a satellite attitude kinematic equation, namely a satellite error quaternion kinematic equation:
Figure BDA0001939278400000011
wherein,
Figure BDA0001939278400000021
is an attitude error quaternion; omega ═ omega1ω2ω3]TIs the angular velocity, omega, of the rotation of the satellite body system relative to the inertial reference coordinate system×Is the antisymmetric matrix of ω:
Figure BDA0001939278400000022
the flywheel is selected as the actuating mechanism of the satellite by the rigid body moment theorem, the attitude kinetic equation of the satellite is
Figure BDA0001939278400000023
Wherein J ∈ R3×3Is the moment of inertia of the satellite, udIs the disturbance moment u experienced by the satellitewIs the control torque generated by the flywheel.
Further, the process of analyzing the flywheel train wheel torque envelope characteristic and judging the rhombic surface through which the expected torque passes is as follows:
analyzing the moment envelope characteristic of the flywheel system and defining the rhombus w of the corresponding envelope of the flywheels i and jijHas a normal vector of
Figure BDA0001939278400000024
Wherein h isiAnd hjRepresenting the direction vectors of flywheels i and j, respectively;
mapping angular momentum of n-dimensional space into polyhedron of three-dimensional space on rhombic surface w of polyhedronijIn addition to flywheels i and jReach positive or negative saturation with a resultant torque of
Figure BDA0001939278400000025
Wherein, tauwkRepresenting the moment, u, generated by the kth flywheelwmIs the maximum moment amplitude of a single flywheel, sgn (·) represents a sign function;
introduction of parameters
Figure BDA0001939278400000026
Wherein,
Figure BDA0001939278400000027
indicating the desired moment direction auAt wijNormal vector n ofijProjection of (2);
Figure BDA0001939278400000028
denotes wijIn the direction of the diagonal intersection, i.e.
Figure BDA0001939278400000029
In the normal vector nijProjection of (2); by comparing the mu of all rhomboid surfacesijJudgment of auWithin a certain diamond plane.
Further, the process of calculating the maximum output torque of the flywheel in the desired torque direction in step three is as follows:
flywheel system with desired torque auThe maximum torque that can be output is expressed as the vector sum of all saturated and unsaturated flywheel output torques, i.e.
Figure BDA0001939278400000031
Wherein u ismaxRepresenting the maximum torque amplitude, u, that the flywheel train can outputwiAnd uwjRepresenting the moment amplitudes of flywheels i and j, respectively；
Solving the above equation to obtain
Figure BDA0001939278400000032
Will umaxDistributing the maximum flywheel torque vector to each flywheel according to the flywheel saturation condition
Figure BDA0001939278400000033
If umaxGreater than the desired magnitude u of the momentcLinear change is needed to obtain the flywheel command torque
Figure BDA0001939278400000034
Figure BDA0001939278400000035
Further, the process of limiting the design error limit vector L according to the maximum flywheel torque vector and the euler rotation angular velocity in step four is as follows:
design error limit vector
Figure BDA0001939278400000036
Wherein L isaIn (1)
Figure BDA0001939278400000037
Is the maximum angular velocity, L, of the commanded moment direction calculated by the time-optimal control of the second order systembIn an item
Figure BDA0001939278400000038
Is the maximum Euler angular velocity, L, that the flywheel can providecIn an item
Figure BDA0001939278400000039
Is the euler angular velocity limit; p, d are as followsAdjustable parameters of a hierarchical saturated PID controller; | | ae||∞Denotes aeInfinite norm of (d); a iseA direction vector representing the attitude maneuver euler axis,
Figure BDA00019392784000000310
θ represents the euler rotation angle.
Further, the step five process of designing the hierarchical saturated PID controller includes the following steps:
Figure BDA00019392784000000311
the controller parameters p and d and the integral time constant T are adjustable;
Figure BDA00019392784000000312
is defined as
Figure BDA0001939278400000041
Wherein eiAnd LiThe ith component of e and L, respectively;
the controller outputs a resulting command control torque ucIs uc＝τ+ω×Jω+ω×h。
The invention has the following beneficial effects:
the method comprises the steps of analyzing the moment envelope characteristic of a flywheel system by establishing the satellite attitude kinematics and the attitude dynamics equation of an actuating mechanism, and judging a rhombic surface through which an expected moment passes; and then calculating the maximum output moment of the flywheel along the expected moment direction, determining the maximum flywheel moment vector, limiting and designing an error limiting vector L according to the maximum flywheel moment vector and the maneuvering angular speed, and finally designing a hierarchical saturation PID controller to control the three-axis attitude of the satellite. The invention applies the error limiting vector to the hierarchical saturated PID controller, can realize Euler rotation of the spacecraft, and can enable the flywheel to exert the maximum capability of an expected torque direction when the satellite has large attitude deviation if the controller parameters are properly selected, thereby approaching the near-time optimal Euler rotation attitude maneuver performance.
And the method has simple and reliable design and is very easy to realize in engineering.
Drawings
FIG. 1 is a flow chart of a hierarchical saturation PID control method for attitude maneuver of an Euler rotary satellite;
FIG. 2 is a graph of a change in quaternion for satellite attitude;
FIG. 3 is a graph of a change in satellite attitude error quaternion;
FIG. 4 is a graph of the change in angular velocity of the attitude of the satellite;
FIG. 5 is a graph of a change in satellite error attitude angle;
fig. 6 is a graph of control torque variation.
Detailed Description
First embodiment this embodiment will be described with reference to fig. 1,
a hierarchical saturation PID control method for attitude maneuver of Euler rotary satellite comprises the following steps:
step one, establishing a satellite attitude kinematics and an attitude dynamics equation of which a flywheel is an actuating mechanism;
analyzing the enveloping characteristics of the moment of the flywheel train, and judging a rhombic surface through which the expected moment passes;
step three, calculating the maximum output torque of the flywheel along the expected torque direction according to the saturation condition of each flywheel corresponding to the rhombic surface calculated in the step two, and determining the maximum flywheel torque vector;
fourthly, designing an error limit vector L according to the maximum flywheel torque vector and the maneuvering angular speed limit;
and step five, designing a hierarchical saturated PID controller to control the satellite triaxial attitude.
The second embodiment is as follows:
in the first step of the present embodiment, the equation of the satellite attitude kinematics and attitude dynamics with the flywheel as the actuator is as follows:
establishing a satellite attitude kinematic equation, namely a satellite error quaternion kinematic equation:
Figure BDA0001939278400000051
wherein,
Figure BDA0001939278400000052
is a quaternion of attitude error, and the calculation formula is
Figure BDA0001939278400000053
Wherein q isc1,qc2,qc3,qc4Are respectively the desired attitude
Figure BDA0001939278400000054
Component q of1,q2,q3,q4Is the current attitude
Figure BDA0001939278400000055
The component (c). Omega ═ omega1 ω2 ω3]TIs the angular velocity, omega, of the rotation of the satellite body system relative to the inertial reference coordinate system×Is the antisymmetric matrix of ω:
Figure BDA0001939278400000056
the flywheel is selected as the actuating mechanism of the satellite by the rigid body moment theorem, the attitude kinetic equation of the satellite is
Figure BDA0001939278400000057
Wherein J ∈ R3×3Is the moment of inertia of the satellite, udIs the disturbance moment u experienced by the satellitewIs the control torque generated by the flywheel. Since the flywheel uses the rate of change of angular momentum as the reverse control torque, there are
Figure BDA0001939278400000058
hwIs the angular momentum of the flywheel.
Other procedures and parameters are the same as in the first embodiment.
The third concrete implementation mode:
in step two of this embodiment, the process of analyzing the flywheel train torque envelope characteristic and determining the rhombic surface through which the expected torque passes is as follows:
analyzing the moment envelope characteristic of the flywheel system and defining the rhombus w of the corresponding envelope of the flywheels i and jijHas a normal vector of
Figure BDA0001939278400000059
Wherein h isiAnd hjRepresenting the direction vectors of flywheels i and j, respectively;
mapping angular momentum of n-dimensional space into polyhedron of three-dimensional space on rhombic surface w of polyhedronijIn addition, the flywheels except the flywheels i and j reach positive saturation or negative saturation, and the resultant torque is
Figure BDA0001939278400000061
Wherein, tauwkRepresenting the moment, u, generated by the kth flywheelwmIs the maximum moment amplitude of a single flywheel, sgn (·) represents a sign function;
in the determination of the desired moment auOn which diamond surface wijThe parameters are introduced when internal
Figure BDA0001939278400000062
Wherein,
Figure BDA0001939278400000063
indicating the desired moment direction auAt wijNormal vector n ofijProjection of (2);
Figure BDA0001939278400000064
denotes wijIn the direction of the diagonal intersection, i.e.
Figure BDA0001939278400000065
In the normal vector nijProjection of (1), muijDenotes auAt wijNormal vector n ofijThe result of the normalization of the projection on;
when a isuWhen the intersection line of the two diamond surfaces to be judged is just intersected with the connection line of the original points, the mu corresponding to the two diamond surfacesijEqual; on the contrary, when auPoint to a certain wijWhen, the corresponding μijIncrease, therefore, can be obtained by comparing the μ of all rhomboid facesijJudgment of auWithin which diamond plane.
Other procedures and parameters are the same as in the first or second embodiment.
The fourth concrete implementation mode:
in the third step of this embodiment, the process of calculating the maximum output torque of the flywheel along the expected torque direction according to whether each flywheel corresponding to the rhombic surface calculated in the second step is saturated or not is as follows:
on the rhombic surface wijIn the above, the flywheels i and j are not saturated, and the other flywheels are saturated, so that the flywheel system has the expected moment auThe maximum torque that can be output is expressed as the vector sum of all saturated and unsaturated flywheel output torques, i.e.
Figure BDA0001939278400000066
Wherein u ismaxRepresenting the maximum torque amplitude, u, that the flywheel train can outputwiAnd uwjRepresenting the moment amplitudes of flywheels i and j, respectively;
solving the above equation to obtain
Figure BDA0001939278400000067
Will umaxDistributing the maximum flywheel torque vector to each flywheel according to the flywheel saturation condition
Figure BDA0001939278400000068
If umaxGreater than the desired magnitude u of the momentcLinear change is needed to obtain the flywheel command torque
Figure BDA0001939278400000069
Figure BDA0001939278400000071
Other procedures and parameters are the same as in one of the first to third embodiments.
The fifth concrete implementation mode:
the process of designing the error limit vector L based on the maximum flywheel torque vector and the euler rotation angular velocity limit described in step four of the present embodiment is as follows:
and limiting a design error limiting vector L according to the maximum flywheel torque vector and the rotation angular velocity of Euler rotation, and respectively setting the angular acceleration vector and the attitude error vector from the flywheel as a | | a if the satellite always rotates in EulereAnd
Figure BDA0001939278400000072
from a and e, an error limit vector can be designed
Figure BDA0001939278400000073
Wherein L isaIn (1)
Figure BDA0001939278400000074
Is the maximum angular velocity, L, of the commanded moment direction calculated by the time-optimal control of the second order systembIn an item
Figure BDA0001939278400000075
Is the maximum Euler angular velocity, L, that the flywheel can providecIn an item
Figure BDA0001939278400000076
Is the euler angular velocity limit; p and d are adjustable parameters of the following hierarchical saturated PID controller; | | ae||∞Denotes aeInfinite norm of (d); a iseA direction vector representing the attitude maneuver euler axis,
Figure BDA0001939278400000077
θ represents the Euler rotation angle;
in effect, the sum of a in the designed error-limited vector L
Figure BDA0001939278400000078
Calculating the maximum flywheel moment vector obtained in the third step to obtain:
Figure BDA0001939278400000079
Figure BDA00019392784000000710
wherein, lambda is a conservative coefficient and represents the degree of exerting the maximum output capacity of the flywheel system, uwm,HwmThe saturation moment and the saturation angular momentum of the flywheel, J is the rotational inertia of the satellite, CwThe three-axis coordinate of the ith row of the configuration matrix is the three-axis projection of the moment direction of the ith flywheel in the satellite body coordinate system.
Other procedures and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode:
the process of designing a hierarchical saturated PID controller described in step five of this embodiment includes the following steps:
Figure BDA0001939278400000081
the controller parameters p and d and the integral time constant T are adjustable;
Figure BDA0001939278400000082
the element in (A) is defined as
Figure BDA0001939278400000083
Wherein eiAnd LiThe ith component of e and L, respectively;
the controller outputs a resulting command control torque ucIs uc＝τ+ω×Jω+ω×h。
Other procedures and parameters are the same as in one of the first to fifth embodiments.
Examples
And carrying out simulation experiments by using the implementation contents of all the first to sixth specific embodiments.
The following is the verification and validity analysis of the control method of the invention, and the simulation parameters are designed as follows:
moment of inertia of satellite J ═ diag (1000,750,800) kg · m2。
Six flywheel mounting matrix
Figure BDA0001939278400000084
The saturation angular momentum of the flywheel is 20Nms, and the saturation rotating speed is +/-1800 rpm.
Euler angular velocity limitation
Figure BDA0001939278400000085
Initial attitude quaternion qbe＝[1 0 0 0]TInitial attitude angular velocity w0＝[0 0 0]T rad/s。
And (3) grading saturated PID controller parameters, wherein p is 9.54, and d is 5.5.
Multiple attitude maneuver simulations are performed under the above simulation conditions, and the obtained satellite attitude quaternion, attitude error quaternion, attitude angular velocity, error attitude angle and control moment graph lines are shown in fig. 2 to 6.
By designing error limiting conditions, Euler rotation is kept in the process of multiple attitude maneuvers, and it can be seen from figure 6 that the control torque respectively reaches saturation in the acceleration section and the deceleration section, and the control torque is not output in the uniform speed section, so that the near-time optimal characteristic of acceleration at the maximum angular acceleration and deceleration at the maximum angular acceleration is realized.
In summary, the present invention ensures euler rotation of the satellite while considering the maximum output capability of the flywheel system in the expected torque direction by designing the error limiting vector on the premise of not significantly increasing the complexity of the original PID controller.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (6)

1. A hierarchical saturation PID control method for attitude maneuver of Euler rotary satellite is characterized by comprising the following steps:
step one, establishing a satellite attitude kinematics and an attitude dynamics equation of which a flywheel is an actuating mechanism;
analyzing the enveloping characteristics of the moment of the flywheel train, and judging a rhombic surface through which the expected moment passes;
step three, calculating the maximum output torque of the flywheel along the expected torque direction, and determining the maximum flywheel torque vector;
fourthly, designing an error limit vector L according to the maximum flywheel torque vector and the maneuvering angular speed limit; the process of limiting the design error limit vector L according to the maximum flywheel torque vector and the Euler rotation angular velocity in the fourth step is as follows:
design error limit vector
Figure FDA0003363832830000011
Wherein L isaIn (1)
Figure FDA0003363832830000012
Is the maximum angular velocity, L, of the commanded moment direction calculated by the time-optimal control of the second order systembIn an item
Figure FDA0003363832830000013
Is the maximum Euler angular velocity, L, that the flywheel can providecIn an item
Figure FDA0003363832830000014
Is the euler angular velocity limit; p and d are adjustable parameters of the following hierarchical saturated PID controller; | | ae||∞Denotes aeInfinite norm of (d); a iseA direction vector representing the attitude maneuver euler axis,
Figure FDA0003363832830000015
θ represents the Euler rotation angle;
Figure FDA0003363832830000016
Figure FDA0003363832830000017
wherein, lambda is a conservative coefficient and represents the degree of exerting the maximum output capacity of the flywheel system, uwm,HwmThe saturation moment and the saturation angular momentum of the flywheel, J is the rotational inertia of the satellite, CwThe method is characterized in that the method is a configuration matrix of the flywheel, and the triaxial coordinate of the ith row of the configuration matrix is the triaxial projection of the moment direction of the ith flywheel under a satellite body coordinate system;
Figure FDA0003363832830000018
to obtain the maximum flywheel torque vector;
and step five, designing a hierarchical saturated PID controller to control the satellite triaxial attitude.
2. The Euler rotary satellite attitude maneuver hierarchical saturation PID control method according to claim 1, wherein the satellite attitude kinematics and attitude dynamics equations with the flywheel as an actuator in step one are as follows:
establishing a satellite attitude kinematic equation, namely a satellite error quaternion kinematic equation:
Figure FDA0003363832830000019
wherein,
Figure FDA00033638328300000110
is an attitude error quaternion; omega ═ omega1 ω2 ω3]TIs the angular velocity, omega, of the rotation of the satellite body system relative to the inertial reference coordinate system×Is the antisymmetric matrix of ω:
Figure FDA0003363832830000021
the flywheel is selected as the actuating mechanism of the satellite by the rigid body moment theorem, the attitude kinetic equation of the satellite is
Figure FDA0003363832830000022
Wherein J ∈ R3×3Is the moment of inertia of the satellite, udIs the disturbance moment u experienced by the satellitewIs the control moment generated by the flywheel; the above-mentioned
Figure FDA0003363832830000023
Wherein q isc1,qc2,qc3,qc4Are respectively the desired attitude
Figure FDA0003363832830000024
Component q of1,q2,q3,q4Is the current attitude
Figure FDA0003363832830000025
The component (c).
3. The Euler rotary satellite attitude maneuver hierarchical saturation PID control method according to claim 2, wherein the Euler rotary satellite attitude maneuver hierarchical saturation PID control method is characterized in that
Figure FDA0003363832830000026
hwIs the angular momentum of the flywheel.
4. The Euler rotary satellite attitude maneuver hierarchical saturation PID control method according to claim 1, 2 or 3, wherein the process of analyzing the flywheel train torque envelope characteristic and judging the rhombic surface through which the expected torque passes is as follows:
analyzing the moment envelope characteristic of the flywheel system and defining the rhombus w of the corresponding envelope of the flywheels i and jijHas a normal vector of
Figure FDA0003363832830000027
Wherein h isiAnd hjRepresenting the direction vectors of flywheels i and j, respectively;
mapping angular momentum of n-dimensional space into polyhedron of three-dimensional space on rhombic surface w of polyhedronijIn addition, the flywheels except the flywheels i and j reach positive saturation or negative saturation, and the resultant torque is
Figure FDA0003363832830000028
Wherein，τwkRepresenting the moment, u, generated by the kth flywheelwmIs the maximum moment amplitude of a single flywheel, sgn (·) represents a sign function;
introduction of parameters
Figure FDA0003363832830000029
Wherein,
Figure FDA00033638328300000210
indicating the desired moment direction auAt wijNormal vector n ofijProjection of (2);
Figure FDA00033638328300000211
denotes wijIn the direction of the diagonal intersection, i.e.
Figure FDA0003363832830000031
In the normal vector nijProjection of (2); by comparing the mu of all rhomboid surfacesijJudgment of auWithin a certain diamond plane.
5. The Euler rotary satellite attitude maneuver hierarchical saturation PID control method according to claim 4, wherein the process of calculating the maximum output torque of the flywheel in the desired torque direction in step three is as follows:
flywheel system with desired torque auThe maximum torque that can be output is expressed as the vector sum of all saturated and unsaturated flywheel output torques, i.e.
Figure FDA0003363832830000032
Wherein u ismaxRepresenting the maximum torque amplitude, u, that the flywheel train can outputwiAnd uwjRepresenting the moment amplitudes of flywheels i and j, respectively;
solving the above equation to obtain
Figure FDA0003363832830000033
Will umaxDistributing the maximum flywheel torque vector to each flywheel according to the flywheel saturation condition
Figure FDA0003363832830000034
If umaxGreater than the desired magnitude u of the momentcLinear change is needed to obtain the flywheel command torque
Figure FDA0003363832830000035
Figure FDA0003363832830000036
6. The Euler rotary satellite attitude maneuver hierarchical saturation PID control method according to claim 2, wherein the process of designing the hierarchical saturation PID controller in step five comprises the steps of:
Figure FDA0003363832830000037
the controller parameters p and d and the integral time constant T are adjustable;
Figure FDA0003363832830000038
is defined as
Figure FDA0003363832830000039
Wherein eiAnd LiThe ith component of e and L, respectively;
the command control torque generated by the controller outputucIs uc＝τ+ω×Jω+ω×hw，hwIs the angular momentum of the flywheel.
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