CN117682107A - Random axial attitude maneuver stepped saturation angular velocity amplitude limiting method - Google Patents
Random axial attitude maneuver stepped saturation angular velocity amplitude limiting method Download PDFInfo
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Abstract
The invention provides a method for limiting the amplitude of a stepwise saturated angular velocity of any axial attitude maneuver, which comprises the following steps: s1, based on maximum rotational inertia I of satellite max And maximum angular momentum H available to the actuator max Obtaining the limiting value omega of the mechanical angular velocity of any Euler axis direction gesture max The method comprises the steps of carrying out a first treatment on the surface of the S2, based on the maximum control moment T provided by the actuating mechanism max And omega max Respectively designing hierarchical saturation control laws aiming at three body axis directions of a satellite body system, and acquiring control parameters of the three body axis directions for maneuvering tasks; s3, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err According to q err Calculating the current space maneuvering Euler axis direction vector V euler For V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler The method comprises the steps of carrying out a first treatment on the surface of the S4, according to the control parameters and u euler Calculating the current motor Euler axis direction gesture deviation limiting parameter q max_euler The method comprises the steps of carrying out a first treatment on the surface of the S5, calculating based on hierarchical saturation algorithmCalculating a control moment instruction T of the current maneuvering Euler axis direction gesture maneuvering c 。
Description
Technical Field
The invention relates to the technical field of satellite attitude control, in particular to a method for limiting the amplitude of a stepped saturated angular speed of any axial attitude maneuver.
Background
The euler rotation theorem states that the pose of a rigid body can be changed from any given orientation to any other orientation by rotating the rigid body about an axis fixed in the body system and inertial system. The rotation axis is called Euler axis, and its direction is kept unchanged in both the body system and the inertial system. Compared with the traditional maneuvering mode of sequentially rotating around the body shaft according to a certain rotating sequence, the satellite gesture rotates around the Euler shaft when maneuvering, so that the three-axis gesture can move to a target in space according to the shortest path, and maneuvering time is greatly reduced.
The hierarchical saturated PID control law applies proper saturated amplitude limiting treatment to links such as deviation attitude angles, output moment and the like on the basis of a traditional PID control algorithm so as to meet objective constraint that the output moment and angular momentum range of an actuating mechanism are limited. In the single-shaft maneuvering control process, the dynamic performance similar to the time optimum can be realized without planning the maneuvering process in advance, and the method is very suitable for any axial frequent maneuvering tasks in multiple modes.
For satellites with single traditional maneuvering modes, in the process of applying a hierarchical saturation control algorithm, the required maneuvering functions can be realized by completing control parameters and amplitude limiting value design aiming at a specific maneuvering shaft (namely the Euler shaft). The new generation of multimode complex maneuvering task satellite generally needs to have the space arbitrary axial (i.e. arbitrary Euler axis direction) maneuvering capability, the maneuvering axis is continuously changed according to different modes or tasks, parameter design cannot be performed in advance, the use of inherent parameters can lead to mismatching of angular speed amplitude limitation and design values, the saturation of angular momentum of an actuating mechanism can be caused, and serious influence is brought to maneuvering process.
The method for controlling the amplitude limiting of the hierarchical saturated angular velocity, which can adapt to the maneuvering of any axial gesture in space and can be realized by engineering, needs to be designed towards the new maneuvering mode and control requirement.
Disclosure of Invention
The invention aims to provide a random axial attitude maneuver stepped saturation angular velocity amplitude limiting method, which is used for projecting a space random Euler axis direction to three body axis directions of a satellite on the basis of conventional stepped saturation control parameter design on the body axis direction of the satellite, calculating an attitude deviation amplitude limiting value of the space random Euler axis direction through space geometric conversion, and realizing the angular velocity amplitude limiting of the random Euler axis direction. The invention can fully utilize the angular momentum space of the actuating mechanism and effectively avoid the problem that the axial dynamic characteristics of different spaces are inconsistent when the control bandwidth of the directions of all body axes is inconsistent with the design of the damping ratio.
In order to achieve the above purpose, the present invention provides a method for limiting the amplitude of a stepwise saturated angular velocity of a maneuver in any axial posture, comprising the steps of:
s1, based on maximum rotational inertia I of satellite max And the maximum angular momentum H that the actuator can provide max Obtaining the limiting value omega of the maneuvering angular speed of any maneuvering Euler axis direction gesture maneuvering max ；
S2, based on maximum control moment T which can be provided by the actuating mechanism max And the angular velocity limit value omega max Respectively designing hierarchical saturation control laws for three body axis directions of a satellite body system, and acquiring control parameters of the three body axis directions for on-orbit maneuvering tasks;
s3, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err According to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis directionVector V euler The method comprises the steps of carrying out a first treatment on the surface of the For the spatial maneuver Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
S4, according to the control parameters of the three body axis directions and the spatial maneuvering Euler axis direction unit vector u euler Calculating the current motor Euler axis direction gesture deviation limiting value q max_euler ；
S5, calculating a control moment instruction T of the current maneuver Euler axis direction gesture maneuver based on a hierarchical saturation algorithm c The method comprises the steps of carrying out a first treatment on the surface of the By the control moment command T c Realizing that the attitude maneuver angular speed of the current maneuver Euler axis direction does not exceed the limiting value omega max 。
Optionally, in step S1:
the angular velocity limiting value
k is a coefficient of 1 or less, and the symbol "·" represents multiplication.
Optionally, in step S2, the hierarchical saturation control law is:
wherein: i=x, Y, Z, representing the satellite body axis direction; t (T) ci For controlling moment command in the i-axis direction, K pi 、K Ii 、K di For the control parameter of the i-axis direction, q ei 、ω ei 、q maxi Control attitude error, control angular velocity error, attitude deviation limit value, q in the i-axis direction, respectively maxi The calculation method is as follows:
the sat function is a saturated function, defined for any vector a and clipping value b as:
optionally, step S3 includes:
s31, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err ，
q 0 、q mb Quaternion of the current gesture and the target gesture respectively;
s32, according to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis direction vector V euler ；
Wherein sign (·) is a sign function, q err (0) For the attitude deviation quaternion q err Standard part, q err (1)、q err (2)、q err (3) For the attitude deviation quaternion q err Is defined by the vector portion of (a).
S33, the spatial maneuvering Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
Wherein, I represent and calculating vector modular length.
Optionally, step S4 includes:
s41, in satellite body coordinate system Ox b y b z b In the inner part, all maneuvering Euler axes of the traversing space are traversed, and the Euler axis direction gesture deviation limiting value q max_euler Forming an ellipse in the spaceSphere, in coordinate system Ox b y b z b The equation of the ellipsoid is
Wherein:(x, y, z) is the coordinates of any point on the ellipsoid;
wherein alpha is E [0, pi ]]、β∈[-π,π]Respectively represent the points (x, y, z) in the coordinate system Ox b y b z b Azimuth and elevation angles within;
the attitude deviation limiting valueWill q max_euler Expressed in matrix form to obtain
Wherein the symbol "×" denotes matrix multiplication.
Optionally, the control moment command T in step S5 c The expression of (2) is:
wherein: t (T) c 、q e 、ω e Are 3 x 1 dimensional space vectors; q e 、ω e Respectively representing three-axis attitude errors and three-axis angular velocity errors of any Euler axis direction attitude maneuver in space; k (K) p 、K I 、K d In order to control the matrix of parameters,
compared with the prior art, the invention has the beneficial effects that:
the method for limiting the stepped saturated angular velocity of any axial gesture maneuver is popularized to any spatial Euler axis direction, and the problem that the angular velocity limiting is incorrect when the uniaxial control parameter is used for any spatial Euler axis direction maneuver is avoided. On the basis of independently completing control parameter design for each body axis of a satellite, through the projection relation of the actual Euler axis direction in the satellite body axis direction, the attitude maneuver control of the same angular velocity amplitude limitation in any axial direction (namely, any Euler axis direction) of the space can be realized by utilizing the control parameters on the body axis, the problem that the angular momentum of an actuating mechanism is saturated due to incorrect angular velocity amplitude limitation is effectively avoided, and the reliability of executing the attitude maneuver task is improved. The invention is especially suitable for satellite frequent arbitrary axial large-angle attitude maneuver tasks, can ensure equal amplitude limiting control of the angular speeds of different maneuver axial (i.e. Euler axial) attitudes, ensures that the angular momentum of the control moment gyro group cannot exceed the usable range, and improves the reliability of a control system.
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For a clearer description of the technical solutions of the present invention, the drawings that are needed in the description will be briefly introduced below, it being obvious that the drawings in the following description are one embodiment of the present invention, and that, without inventive effort, other drawings can be obtained by those skilled in the art from these drawings:
FIG. 1 is a flow chart of a method for clipping an arbitrary axial attitude maneuver stepped saturation angular velocity of the present invention;
FIG. 2 is a schematic illustration of the present invention implementing attitude maneuver about a spatial Euler axis;
FIG. 3 shows the limit value of the attitude deviation of the Euler axis direction in the body coordinate system Ox b y b z b Formed space ellipsoidA schematic face view;
FIG. 4 is a motor Euler axis direction unit vector u of the present invention euler In the satellite body coordinate system Ox b y b z b Schematic representation of the inner projection.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
As used in this specification and the appended claims, the term "if" may be interpreted as "when..once" or "in response to a determination" or "in response to detection" depending on the context. Similarly, the phrase "if a determination" or "if a [ described condition or event ] is detected" may be interpreted in the context of meaning "upon determination" or "in response to determination" or "upon detection of a [ described condition or event ]" or "in response to detection of a [ described condition or event ]".
In addition, in the description of the present application, the terms "first," "second," "third," etc. are used merely to distinguish between descriptions and are not to be construed as indicating or implying relative importance.
The invention provides a method for limiting amplitude of a stepwise saturated angular velocity of any axial attitude maneuver, which is shown in figure 1 and comprises the following steps:
s1, based on maximum rotational inertia I of satellite max And the maximum angular momentum H that the actuator can provide max Obtaining the limiting value omega of the maneuvering angular speed of any maneuvering Euler axis direction gesture maneuvering max ；
The angular velocity limiting value
k is a coefficient of 1 or less for setting the angular momentum range margin, and the symbol "·" represents multiplication. Through mathematical simulation or ground test, the parameter K pi 、K Ii 、K di And (5) correcting to obtain control parameters which can be used for on-orbit maneuvering tasks.
For the agile motor satellite with compact structure, the rotational inertia parameter of the satellite can be accurately calculated after the control system completes the single-machine product matching, the whole-satellite structural design and the layout design, and the maximum rotational inertia I of the satellite max And can be obtained therewith. At the same time, the angular momentum envelope range of the actuating mechanism is also determined, and the maximum angular momentum H for attitude maneuver can be provided max Maximum control torque T that can be output max And is accordingly determined as an input to the clipping method of the present invention.
S2, based on maximum control moment T which can be provided by the actuating mechanism max And the angular velocity limit value omega max Respectively designing hierarchical saturation control laws for three body axis directions of a satellite body system, and acquiring control parameters of the three body axis directions for on-orbit maneuvering tasks;
the hierarchical saturation control law in step S2 is:
wherein: i=x, Y, Z, representing the satellite body axis direction; t (T) ci For controlling moment command in the i-axis direction, K pi 、K Ii 、K di For the control parameter of the i-axis direction, q ei 、ω ei 、q maxi The control attitude error, the control angular velocity error and the attitude deviation limit value of the i-axis direction are respectively; q maxi The calculation method is as follows:
the sat function is a saturated function, defined for any vector a and clipping value b as:
s3, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err According to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis direction vector V euler The method comprises the steps of carrying out a first treatment on the surface of the For the spatial maneuver Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
As shown in fig. 2, the satellite body system is derived from the current coordinate system Ox according to the euler theorem 0 y 0 z 0 Maneuvering to target coordinate system Ox mb y mb z mb This can be accomplished by one rotation about the euler axis.
The step S3 comprises the following steps:
s31, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err ，
q 0 、q mb Quaternion of the current gesture and the target gesture respectively;
s32, according to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis direction vector V euler ；
Wherein sign (·) is a sign function, q err (0) For the attitude deviation quaternion q err Standard part, q err (1)、q err (2)、q err (3) For the attitude deviation quaternion q err Is defined by the vector portion of (a).
S33, the spatial maneuvering Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
Wherein, I represent and calculating vector modular length.
S4, according to the control parameters of the three body axis directions and the spatial maneuvering Euler axis direction unit vector u euler Calculating the current motor Euler axis direction gesture deviation limiting value q max_euler ；
As shown in fig. 3, step S4 includes:
s41, in satellite body coordinate system Ox b y b z b In the inner part, all maneuvering Euler axes of the traversing space are traversed, and the Euler axis direction gesture deviation limiting value q max_euler Forming an ellipsoid in space, in a coordinate system Ox b y b z b The equation of the ellipsoid is
Wherein:(x, y, z) is the coordinates of any point on the ellipsoid;
as shown in fig. 4, according to the polar coordinate representation method of points on an ellipsoid, any motorized euler axis direction posture deviation limit value can be represented as
Wherein alpha is E [0, pi ]]、β∈[-π,π]Respectively represent the points (x, y, z) in the coordinate system Ox b y b z b Azimuth and elevation angles within;
the attitude deviation limiting valueWill q max_euler Expressed in matrix form to obtain
Wherein the symbol "×" denotes matrix multiplication.
S5, calculating a control moment instruction T of the current maneuver Euler axis direction gesture maneuver based on a hierarchical saturation algorithm c The method comprises the steps of carrying out a first treatment on the surface of the By the control moment command T c Realizing that the attitude maneuver angular speed of the current maneuver Euler axis direction does not exceed the limiting value omega max 。
The control moment command T in step S5 c The expression of (2) is:
wherein: t (T) c 、q e 、ω e Are 3 x 1 dimensional space vectors; q e 、ω e Respectively representing three-axis attitude errors and three-axis angular velocity errors of any Euler axis direction attitude maneuver in space; k (K) p 、K I 、K d In order to control the matrix of parameters,
the method for limiting the stepped saturated angular velocity of any axial gesture maneuver is popularized to any spatial Euler axis direction, and the problem that the angular velocity limiting is incorrect when the uniaxial control parameter is used for any spatial Euler axis direction maneuver is avoided. On the basis of independently completing control parameter design for each body axis of a satellite, through the projection relation of the actual Euler axis direction in the satellite body axis direction, the control parameters on the body axis can be utilized to realize attitude maneuver control of the same angular velocity amplitude limitation of any maneuvering axis (namely, any maneuvering Euler axis direction) in space, so that the problem of saturation of angular momentum of an actuating mechanism possibly caused by incorrect angular velocity amplitude limitation is effectively avoided, and the reliability of executing attitude maneuver tasks is improved. The invention is especially suitable for satellite frequent arbitrary axial large-angle attitude maneuver tasks, can ensure equal amplitude limiting control of different maneuver axial attitude angular speeds, ensures that the angular momentum of the control moment gyro group cannot exceed the usable range, and improves the reliability of a control system.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic of each process, and should not limit the implementation process of the embodiment of the present application in any way.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (6)
1. The amplitude limiting method for the arbitrary axial posture maneuver stepped saturation angular velocity is characterized by comprising the following steps:
s1, based on maximum rotational inertia I of satellite max And the maximum angular momentum H that the actuator can provide max Obtaining the limiting value omega of the maneuvering angular speed of any maneuvering Euler axis direction gesture maneuvering max ；
S2, based on maximum control moment T which can be provided by the actuating mechanism max And the angular velocity limit value omega max Respectively designing hierarchical saturation control laws for three body axis directions of a satellite body system, and acquiring control parameters of the three body axis directions for on-orbit maneuvering tasks;
s3, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err According to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis direction vector V euler The method comprises the steps of carrying out a first treatment on the surface of the For the spatial maneuver Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
S4, according to the control parameters of the three body axis directions and the spatial maneuvering Euler axis direction unit vector u euler Calculating the current motor Euler axis direction gesture deviation limiting value q max_euler ；
S5, calculating a control moment instruction T of the current maneuver Euler axis direction gesture maneuver based on a hierarchical saturation algorithm c The method comprises the steps of carrying out a first treatment on the surface of the By the control moment command T c Realizing that the attitude maneuver angular speed of the current maneuver Euler axis direction does not exceed the limiting value omega max 。
2. The arbitrary axial pose maneuver stepped saturation angular velocity clipping method as claimed in claim 1, wherein in step S1:
the angular velocity limiting value
k is a coefficient of 1 or less, and the symbol "·" represents multiplication.
3. The method for limiting the angular velocity of stepwise saturation of any axial posture maneuver according to claim 2, wherein the stepwise saturation control law in step S2 is:
wherein: i=x, Y, Z, representing the satellite body axis direction; t (T) ci For controlling moment command in the i-axis direction, K pi 、K Ii 、K di For the control parameter of the i-axis direction, q ei 、ω ei 、q maxi Control attitude error, control angular velocity error, attitude deviation limit value, q in the i-axis direction, respectively maxi The calculation method is as follows:
the sat function is a saturated function, defined for any vector a and clipping value b as:
4. a method of clipping arbitrary axial attitude maneuver stepped saturation angular velocity as claimed in claim 3, wherein step S3 comprises:
s31, calculating an attitude deviation quaternion q of the satellite from the current attitude to the target attitude err ，
q 0 、q mb Respectively the currentA quaternion of the gesture and the target gesture;
s32, according to the attitude deviation quaternion q err Calculating the current space maneuvering Euler axis direction vector V euler ；
Wherein sign (·) is a sign function, q err (0) For the attitude deviation quaternion q err Standard part, q err (1)、q err (2)、q err (3) For the attitude deviation quaternion q err Is defined by the vector portion of (a).
S33, the spatial maneuvering Euler axis direction vector V euler Normalization processing is carried out to obtain a spatial maneuvering Euler axis direction unit vector u euler ；
Wherein, I represent and calculating vector modular length.
5. The arbitrary axial pose maneuver stepped saturation angular velocity clipping method as claimed in claim 4, wherein step S4 comprises:
s41, in satellite body coordinate system Ox b y b z b In the inner part, all maneuvering Euler axes of the traversing space are traversed, and the Euler axis direction gesture deviation limiting value q max_euler Forming an ellipsoid in space, in a coordinate system Ox b y b z b The equation of the ellipsoid is
Wherein:(x, y, z) is the coordinates of any point on the ellipsoid;
wherein alpha is E [0, pi ]]、β∈[-π,π]Respectively represent the points (x, y, z) in the coordinate system Ox b y b z b Azimuth and elevation angles within;
the attitude deviation limiting valueWill q max_euler Expressed in matrix form to obtain
Wherein the symbol "×" denotes matrix multiplication.
6. The method for limiting the angular velocity of stepwise saturation of any axial posture maneuver as defined in claim 5, wherein said control moment command T in step S5 c The expression of (2) is:
wherein: t (T) c 、q e 、ω e Are 3 x 1 dimensional space vectors; q e 、ω e Respectively representing three-axis attitude errors and three-axis angular velocity errors of any Euler axis direction attitude maneuver in space; k (K) p 、K I 、K d In order to control the matrix of parameters,
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