CN104777842B - Satellite single-axis measurement and control integrated method based on magnetic suspension control sensitive gyroscope - Google Patents
Satellite single-axis measurement and control integrated method based on magnetic suspension control sensitive gyroscope Download PDFInfo
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Abstract
The invention relates to a satellite single-axis measurement and control integrated method based on a magnetic suspension control sensitive gyroscope. The attitude angular velocity of the satellite under high-frequency small-amplitude disturbance is detected through a magnetic suspension control sensitive gyroscope, an adaptive notch filter with the central notch frequency changing along with the disturbance frequency is used for identifying and removing the attitude angular velocity generated by the high-frequency small-amplitude disturbance, the compensation moment required by the compensation disturbance is calculated, the radial control moment of a magnetic suspension rotor required by the attitude control is calculated according to a corresponding attitude control law, the integral control law of the magnetic suspension rotor is designed by combining disturbance suppression and attitude control, the rotor rotating shaft deflects to output the required radial two-degree-of-freedom micro-frame effective stress moment, and therefore high-precision attitude control and disturbance suppression of a single shaft of the satellite are achieved.
Description
Technical Field
The invention relates to a satellite single-axis measurement and control integrated method based on a magnetic suspension control sensitive gyroscope, which is suitable for high-precision attitude measurement and control of a satellite.
Technical Field
With the development of high-resolution earth observation technology, the requirements on satellite attitude control and vibration suppression are higher and higher. The detection and control of the traditional attitude control system are separated, the whole attitude control system is of a single closed loop structure, and the bandwidth of the attitude control system is limited. Therefore, the conventional attitude control system is difficult to suppress high-frequency small-amplitude disturbance of the satellite. In addition, the detection and control of the existing attitude control system are separated, and the flexible structure of the satellite is added, so that the problem of out-of-position control is inevitably caused, and the stability and robustness of the whole attitude control system are inevitably influenced.
In order to solve the problems, Zhengshiqiang combines moment execution and attitude measurement through a double-frame magnetic suspension control moment gyroscope, but the research reuses measurement and control in a time-sharing way, the magnetic suspension control moment gyroscope can only work in one state at a certain moment, and the measurement and the control cannot be carried out at the same time; liu bin proposes a design scheme of a magnetic suspension gyro flywheel, although the magnetic suspension gyro flywheel can be controlled and measured at the same time, the method does not obtain an analytic expression of the three-axis attitude angular velocity, not only the practicability is not strong, but also the analysis of the relationship between the attitude angular velocity and the system parameters is inconvenient in mechanism.
The magnetic suspension control sensitive gyroscope is a multifunctional new concept inertial mechanism which integrates the dual functions of angular rate gyroscope rate detection and moment output of an inertial execution mechanism and integrates attitude sensing and control, vibration detection and inhibition. Due to the introduction of the magnetic suspension control sensitive gyroscope, the large closed loop structure of the existing attitude control system is changed, and the topology of the large closed loop structure is changed into a three-closed loop attitude control structure. And each ring is used for carrying out three-ring fusion control on the platform attitude, the platform vibration and the gyroscope self vibration respectively according to different controlled objects and different control bandwidths. The system breaks through the limitation that the existing single closed loop attitude system has limited control stability and cannot carry out active vibration control, and makes high stability and hyperstatic control of the satellite possible.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in order to solve the problems that the existing satellite cannot restrain high-frequency small-amplitude disturbance, and attitude control systems cannot control malposition due to non-co-location detection and control, the satellite single-axis measurement and control integrated method based on the magnetic suspension control sensitive gyroscope is provided. According to the method, the micro-frame effective stress moment can inhibit the high-frequency small-amplitude disturbance of the satellite, and can perform high-precision control on the attitude, so that the integration of attitude detection, disturbance inhibition and attitude control is realized, and a brand-new technical approach is provided for the high-precision attitude control of the satellite.
The technical solution of the invention is as follows: the method comprises the following steps of detecting the attitude angular velocity of a satellite under high-frequency small-amplitude disturbance through a magnetic suspension control sensitive gyroscope, using an adaptive notch filter with the central notch frequency changing along with the disturbance frequency to identify and remove the attitude angular velocity generated by the high-frequency small-amplitude disturbance, calculating the compensation moment required by the compensation disturbance, calculating the radial control moment of a magnetic suspension rotor required by the attitude control according to a corresponding attitude control law, designing an integrated control law of the magnetic suspension rotor by combining disturbance suppression and attitude control, deflecting a rotor rotating shaft to output the required radial two-degree-of-freedom micro-frame effective stress moment, and further realizing the high-precision attitude detection, control and disturbance suppression of a satellite single shaft, wherein the method specifically comprises the following steps:
(1) the magnetic suspension rotor dynamic equation according to the rigid body dynamics and the coordinate transformation principle is as follows:
wherein:
Hr＝IΩi
in the formula, MrIndicating the combined external torque of the magnetic levitation rotor, HrRepresenting the angular momentum of the rotor under the rotor train,
the angular momentum change rate of the rotor under the rotor system is shown, I represents the rotational inertia of the rotor rotating around the reference coordinate system of the magnetic suspension control sensitive gyroscope, IrRepresenting the radial moment of inertia of the rotor, IzRepresenting the axial moment of inertia of the rotor, omega representing the axial speed of rotation of the rotor, omegarExpressing the rotor speed, ΩiRepresenting the absolute angular velocity of the rotor,
representing the absolute angular speed rate of change of the rotor,
representing the absolute angular velocity of the rotor coordinate system, i.e. the rotational speed with respect to the inertia space,
indicating the deflection speed of the rotor relative to the magnetic bearings,
for magnetically suspending the speed of the reference system of the control sensitive gyro relative to the inertial space,
is a rotorAngular velocity, omega, relative to inertial spacecmgIn order to be the angular velocity of the frame,
is a transformation matrix from the magnetic bearing coordinate system to the rotor coordinate system,
is a transformation matrix from the frame coordinate system to the magnetic bearing coordinate system,
is a transformation matrix from a reference system of the magnetically suspended control sensitive gyroscope to a frame coordinate system,
a transformation matrix from a star system to a magnetic suspension control sensitive gyroscope reference system;
the magnetic bearing installation system, the frame coordinate system, the magnetic suspension control sensitive gyro reference system are coincided and only the single-axis angular rate of the satellite is available
Under the conditions of (a):
α, β are very small and,
and also
Then:
rotor radial resultant external moment
Expression formulaComprises the following steps:
the magnetic suspension rotor is subjected to the following combined external moment:
the magnetic force applied to the magnetic suspension rotor can be expressed in the following linear form:
fλ＝kiλiλ+khλhλ(λ＝ax,ay,bx,by)
in the formula, kiλAnd khλThe (λ ═ ax, ay, bx, by) respectively represents the current stiffness and the displacement stiffness of radial ax, ay, bx and by channels of the magnetic suspension rotor, and can be calibrated through experiments; i.e. iax、ibx、iayAnd ibyIs the winding current of four radial channels, hax、hbx、hayAnd hbyIs the linear displacement of the magnetic levitation rotor in the ax, bx, ay and by directions, respectively, lmRepresenting the distance from the center of the magnetically levitated rotor to the center of the radial magnetic bearing; h isax、hbx、hay、hbyCan be measured by an eddy current displacement sensor, iax、ibx、iay、ibyCan be measured by a current sensor, thereby calculating the external torque borne by the rotor
The expression for the rotor deflection angle is:
α＝(hay-hby)/(2lm)，β＝(hax-hbx)/(2lm)
hax、hbx、hayand hbyIs the linear displacement of the magnetic suspension rotor in the Ax, Bx, Ay and By directions, respectively, lmDenotes the distance, h, from the center of the magnetically levitated rotor to the center of the radial magnetic bearingax、hbx、hay、hbyCan be measured by an eddy current displacement sensor, so that the deflection information α, β of the rotor can be calculated,
The attitude angular rate and the angular acceleration of the satellite are as follows:
without track angular velocity condition, make
Theta and psi are attitude angles of the satellite coordinate system relative to the orbit coordinate system when no disturbance exists, then
Represents the angular acceleration of each direction attitude,
which represents the angular velocity of each direction and,
indicating the angular acceleration and angular velocity generated by the disturbance,
representing the total angular acceleration and angular velocity, then:
(2) disturbance angular velocity identification and disturbance torque compensation in satellite attitude angular velocity
In the attitude angular velocity, a high-frequency small-amplitude disturbance moment generates a sinusoidal angular velocity with the same frequency as the disturbance frequency, and the sinusoidal angular velocity can be identified and removed by adopting a self-adaptive notch filter; the core of the wave trap N is a concave feedback element Nf, whereinThe center frequency can be changed according to the change of the disturbance frequency W, epsilon determines the convergence speed and the center trapped wave bandwidth of the wave trap N, Kh/KiA scaling factor compensated for the disturbance;
let ω (t) be the input of the concave feedback element Nf, and c (t) be the output of Nf, then:
c and ω satisfy the following differential equation:
the transfer function of the concave feedback element Nf is:
trap input
Nf output to the sag feedback link
The transfer function No of (1) is:
let s be j ω, considering the frequency characteristic of No, when ≠ 0:
NO(jω)≈0,[ω∈(0,W-Δω)∪(W+Δω,∞)]
NO(jω)＝1,[ω∈(W-Δω,W+Δω)]
that is, when ε ≠ 0, the No output will approach the input
Component of medium frequency W
Output of the debossed feedback link Nf
Comprises the following steps:
namely, the output value of the Nf integrator of the concave feedback link after the convergence of the feedback link is the amplitude of the sine and cosine component with the disturbance frequency quantity in the attitude angular velocity, so that the attitude angular velocity generated by the disturbance in the attitude angular velocity signal is realized
Identifying;
by compensating for the proportionality coefficient Kh/KiIn a
Compensating moment introduced by direction
Eliminating the influence of disturbance on the attitude;
(3) magnetic suspension rotor integrated control law
Under the action of a single-axis high-frequency small-amplitude disturbance moment, a satellite attitude kinetic equation with a magnetic suspension control sensitive gyroscope as an actuating mechanism is as follows:
wherein J represents the satellite moment of inertia matrix, Td＝[Tdx0 0]The method comprises the following steps of representing a single-shaft high-frequency small-amplitude disturbance torque, and taking a magnetic suspension rotor as a satellite attitude kinetic equation of an attitude control actuating mechanism under the condition of a small attitude angle as follows:
wherein, Jx、Jy、JzRepresenting the moment of inertia, h, of each axis of the satelliteyThe dynamic equation of the satellite attitude of the two radial directions of the rotor is shown as follows:
therefore, it is required to
To compensate the disturbance moment of β rotation direction caused by disturbance, so:
order to
The speed of β rotation direction required for posture adjustment,
after compensation, the following steps are carried out:
α, the direction of rotation does not need to be compensated for
α speed of rotation direction required for posture adjustment, so
The dynamic equation of the satellite attitude of the rotor in two radial directions is as follows:
after disturbance compensation is added, according to a satellite kinetic equation, the attitude angle of the attitude adjusting target is
ψrDesigning a decoupling control law as follows:
kpx、kdx、kpz、kdzis a PD controller parameter; the satellite attitude dynamics equation is:
uniaxial attitude angle information under satellite no-disturbance condition
Comprises the following steps:
satellite having only uniaxial angular rate
In the case of (a) in (b),
the satellite attitude control quantity is realized by the rotor radial micro-frame control moment:
therefore, in combination with disturbance compensation, the integrated control law of magnetic suspension rotor control is as follows:
the control reference applied by the magnetic bearing in practice is haxr、hbxr、hayr、hbyrAnd h isbxr＝-haxr，hbyr＝-hayrTherefore:
the principle of the invention is as follows: according to the inertia moment theorem, the change of the angular momentum of the high-speed rotor in the direction of the inertia space only depends on the external moment applied to the high-speed rotor, the moment applied to the magnetic suspension rotor is caused by the rotation of a satellite and the relative deflection of the rotor, the magnitude of the moment applied to the magnetic suspension rotor is uniquely determined by the force of a magnetic bearing, and the attitude angular speed of the satellite under the interference of high frequency and small amplitude can be obtained by detecting the current of the magnetic bearing in real time and accurately and resolving the displacement of the rotor. The attitude angular velocity of the satellite under high-frequency small-amplitude disturbance is detected by the magnetic suspension control sensitive gyroscope, the attitude angular velocity generated by the high-frequency small-amplitude disturbance is identified and removed by using an adaptive notch filter with the central notch frequency changing along with the disturbance frequency, the compensation moment required by the compensation disturbance is calculated, the radial control moment of the magnetic suspension rotor required by the attitude control is calculated according to the corresponding attitude control law, the integrated control law of the magnetic suspension rotor is designed by combining disturbance suppression and attitude control, the rotor rotating shaft deflects to output the required radial two-degree-of-freedom micro-frame effective stress moment, and therefore the attitude control and disturbance suppression of the single shaft of the satellite are achieved.
The installation of the satellite and the magnetic suspension control sensitive gyroscope is shown in figure 1, the installation positions of the radial magnetic bearings are symmetrical relative to the mass center of the rotor, the rotor realizes suspension control through the magnetic bearing with 5 degrees of freedom, the radial 4 magnetic bearings (respectively represented by ax, ay, bx and by) control two radial translational degrees of freedom and two rotational degrees of freedom of the magnetic suspension rotor, the axial bearing (represented by z) controls one translational degree of freedom, and the rotational degree of freedom is driven by a motor to provide angular momentum of the rotor. By applying the Euler kinetic equation, the magnetic suspension rotor kinetic equation under the rotor system can be obtained as follows:
wherein:
Hr＝IΩi
the magnetic bearing installation system, the frame coordinate system, the magnetic suspension control sensitive gyro reference system are coincided and only the single-axis angular rate of the satellite is available
Under the conditions of (a):
α, β are very small and,
and also
Then:
rotor radial resultant external moment
The expression is as follows:
according to the principle of moment balance, the rotor radial-to-outer moment can also be expressed as:
the magnetic force applied to the magnetic suspension rotor can be expressed in the following linear form:
fλ＝kiλiλ+khλhλ(λ＝ax,ay,bx,by)
hax、hbx、hay、hbycan be measured by an eddy current displacement sensor, iax、ibx、iay、ibyCan be measured by a current sensor, thereby calculating the external torque borne by the rotor
The expression for the rotor deflection angle is:
α＝(hay-hby)/(2lm)，β＝(hax-hbx)/(2lm)
hax、hbx、hay、hbycan be measured by an eddy current displacement sensor, so that the deflection information α, β of the rotor can be calculated,
The attitude angular rate and the angular acceleration of the satellite are as follows:
without track angular velocity condition, make
Theta and psi are attitude angles of the satellite coordinate system relative to the orbit coordinate system when no disturbance exists, then
Represents the angular acceleration of each direction attitude,
which represents the angular velocity of each direction and,
indicating the angular acceleration and angular velocity generated by the disturbance,
representing the total angular acceleration and angular velocity, then:
in the attitude angular velocity, a high-frequency small-amplitude disturbance moment generates a sinusoidal angular velocity with the same frequency as the disturbance frequency, and the sinusoidal angular velocity can be identified and removed by adopting a self-adaptive notch filter; the core of the wave trap N is a concave feedback link Nf, the central frequency of which can be changed according to the change of disturbance frequency W, epsilon determines the convergence speed and the central wave-trapping bandwidth, K of the wave trap Nh/KiA scaling factor compensated for the disturbance;
let ω (t) be the input of the concave feedback element Nf, and c (t) be the output of Nf, then:
c and ω satisfy the following differential equation:
the transfer function of the concave feedback element Nf is:
trap input
Nf output to the sag feedback link
The transfer function No of (1) is:
let s be j ω, considering the frequency characteristic of No, when ≠ 0:
NO(jω)≈0,[ω∈(0,W-Δω)∪(W+Δω,∞)]
NO(jω)＝1,[ω∈(W-Δω,W+Δω)]
that is, when ε ≠ 0, the No output will approach the input
Component of medium frequency W
Output of the debossed feedback link Nf
Comprises the following steps:
namely, the output value of the Nf integrator of the concave feedback link after the convergence of the feedback link is the amplitude of the sine and cosine component with the disturbance frequency quantity in the attitude angular velocity, so that the attitude angular velocity generated by the disturbance in the attitude angular velocity signal is realized
Identifying;
by compensating for the proportionality coefficient Kh/KiIn a
Compensating moment introduced by direction
Eliminating the influence of disturbance on the attitude;
under the action of a single-axis high-frequency small-amplitude disturbance moment, a satellite attitude kinetic equation with a magnetic suspension control sensitive gyroscope as an actuating mechanism is as follows:
wherein J represents the satellite moment of inertia matrix, Td＝[Tdx0 0]The method comprises the following steps of representing a single-shaft high-frequency small-amplitude disturbance torque, and taking a magnetic suspension rotor as a satellite attitude kinetic equation of an attitude control actuating mechanism under the condition of a small attitude angle as follows:
wherein, Jx、Jy、JzRepresenting the moment of inertia, h, of each axis of the satelliteyThe dynamic equation of the satellite attitude of the rotor in two radial directions is represented as follows:
therefore, it is required to
To compensate the disturbance moment of β rotation direction caused by disturbance, so:
order to
The speed of β rotation direction required for posture adjustment,
after compensation, the following steps are carried out:
α, the direction of rotation does not need to be compensated for
α speed of rotation direction required for posture adjustment, so
The dynamic equation of the satellite attitude of the rotor in two radial directions is as follows:
after disturbance compensation is added, according to a satellite kinetic equation, the attitude angle of the attitude adjusting target is
ψrDesigning a decoupling control law as follows:
kpx、kdx、kpz、kdzis a PD controller parameter; the satellite attitude dynamics equation is:
uniaxial attitude angle information under satellite no-disturbance condition
Comprises the following steps:
satellite having only uniaxial angular rate
In the case of (a) in (b),
the satellite attitude control quantity is realized by the rotor radial micro-frame control moment:
therefore, in combination with disturbance compensation, the integrated control law of magnetic suspension rotor control is as follows:
the control reference applied by the magnetic bearing in practice is haxr、hbxr、hayr、hbyrAnd h isbxr＝-haxr，hbyr＝-hayrTherefore:
therefore, measurement and control integration of the single-axis attitude of the satellite is realized by controlling the displacement of the magnetic bearing rotor to output the micro-frame effective moment.
Compared with the prior art, the scheme of the invention has the main advantages that: in order to solve the problems that the existing satellite is difficult to inhibit high-frequency small-amplitude disturbance, and attitude control systems are subjected to ex-situ control due to the fact that detection and control are not in co-location, the method for integrating single-axis attitude measurement and control of the satellite under the high-frequency small-amplitude disturbance based on the magnetically suspended control sensitive gyroscope is provided. On the basis of realizing high-precision detection of the attitude angular rate, the method can inhibit high-frequency small-amplitude disturbance of the satellite through the micro-frame effective stress moment, can perform attitude control, realizes integration of the attitude angular rate detection, the attitude control and the disturbance inhibition of the satellite, and provides a brand-new technical approach for the high-precision attitude control of the satellite.
Drawings
FIG. 1 is a schematic diagram of a mounting structure of a magnetic suspension control sensitive gyroscope on a satellite;
figure 2 is a diagram of a trap structure;
FIG. 3 is a functional block diagram of the present invention;
FIG. 4 is a diagram of PD control disturbance-free suppression compensation satellite single-axis attitude angle;
FIG. 5 is a diagram of PD control disturbance-free suppression compensation satellite single-axis attitude angular rate;
FIG. 6 is a diagram illustrating PD control of a perturbation suppression compensation satellite single-axis attitude angle;
FIG. 7 is a diagram of PD control with disturbance rejection compensation for satellite single axis attitude angular rate.
Detailed description of the preferred embodiments
The implementation object of the invention is shown in fig. 1, the installation positions of the radial magnetic bearings are symmetrical relative to the center of mass of the rotor, the radial 4 magnetic bearings (respectively represented by ax, ay, bx, by) control two radial translational degrees of freedom and two rotational degrees of freedom of the magnetic suspension rotor, the structure of the designed wave trap is shown in fig. 2, the specific implementation scheme of the invention is shown in fig. 3, and the specific implementation steps are as follows:
(1) the magnetic suspension rotor dynamic equation according to the rigid body dynamics and the coordinate transformation principle is as follows:
wherein:
Hr＝IΩi
in the formula, MrIndicating the combined external torque of the magnetic levitation rotor, HrRepresenting the angular momentum of the rotor under the rotor train,
the angular momentum change rate of the rotor under the rotor system is shown, I represents the rotational inertia of the rotor rotating around the reference coordinate system of the magnetic suspension control sensitive gyroscope, IrRepresenting the radial moment of inertia of the rotor, IzRepresenting the axial moment of inertia of the rotor, omega representing the axial speed of rotation of the rotor, omegarExpressing the rotor speed, ΩiRepresenting the absolute angular velocity of the rotor,
representing the absolute angular speed rate of change of the rotor,
representing the absolute angular velocity of the rotor coordinate system, i.e. the rotational speed with respect to the inertia space,
indicating the deflection speed of the rotor relative to the magnetic bearings,
for magnetically suspending the speed of the reference system of the control sensitive gyro relative to the inertial space,
is the angular velocity, ω, of the rotor relative to the inertial spacecmgIn order to be the angular velocity of the frame,
is a transformation matrix from the magnetic bearing coordinate system to the rotor coordinate system,
is a transformation matrix from the frame coordinate system to the magnetic bearing coordinate system,
is a transformation matrix from a reference system of the magnetically suspended control sensitive gyroscope to a frame coordinate system,
a transformation matrix from a star system to a magnetic suspension control sensitive gyroscope reference system;
the magnetic bearing installation system, the frame coordinate system, the magnetic suspension control sensitive gyro reference system are coincided and only the single-axis angular rate of the satellite is available
Under the conditions of (a):
α, β are very small and,
and also
Then:
rotor radial resultant external moment
The expression is as follows:
the rotor radial-external moment can also be expressed as:
the magnetic force applied to the magnetic suspension rotor can be expressed in the following linear form:
fλ＝kiλiλ+khλhλ(λ＝ax,ay,bx,by)
in the formula, kiλAnd khλThe (λ ═ ax, ay, bx, by) respectively represents the current stiffness and the displacement stiffness of radial ax, ay, bx and by channels of the magnetic suspension rotor, and can be calibrated through experiments; i.e. iax、ibx、iayAnd ibyIs the winding current of four radial channels, hax、hbx、hayAnd hbyIs the linear displacement of the magnetic levitation rotor in the ax, bx, ay and by directions, respectively, lmRepresenting the distance from the center of the magnetically levitated rotor to the center of the radial magnetic bearing; h isax、hbx、hay、hbyCan be measured by an eddy current displacement sensor, iax、ibx、iay、ibyCan be measured by a current sensor, thereby calculating the external torque borne by the rotor
The expression for the rotor deflection angle is:
α＝(hay-hby)/(2lm)，β＝(hax-hbx)/(2lm)
hax、hbx、hayand hbyIs the linear displacement of the magnetic levitation rotor in the ax, bx, ay and by directions, respectively, lmDenotes the distance, h, from the center of the magnetically levitated rotor to the center of the radial magnetic bearingax、hbx、hay、hbyCan be measured by an eddy current displacement sensor, so that the deflection information α, β of the rotor can be calculated,
The attitude angular rate and the angular acceleration of the satellite are as follows:
without track angular velocity condition, make
Theta and psi are attitude angles of the satellite coordinate system relative to the orbit coordinate system when no disturbance exists, then
Represents the angular acceleration of each direction attitude,
which represents the angular velocity of each direction and,
indicating the angular acceleration and angular velocity generated by the disturbance,
representing the total angular acceleration and angular velocity, then:
(2) disturbance angular velocity identification and disturbance torque compensation in satellite attitude angular velocity
In the attitude angular velocity, a high-frequency small-amplitude disturbance moment generates a sinusoidal angular velocity with the same frequency as the disturbance frequency, and the sinusoidal angular velocity can be identified and removed by adopting a self-adaptive notch filter; the core of the wave trap N is a concave feedback link Nf, the central frequency of which can be changed according to the change of disturbance frequency W, epsilon determines the convergence speed and the central wave-trapping bandwidth, K of the wave trap Nh/KiA scaling factor compensated for the disturbance;
let ω (t) be the input of the concave feedback element Nf, and c (t) be the output of Nf, then:
c and ω satisfy the following differential equation:
the transfer function of the concave feedback element Nf is:
trap input
Nf output to the sag feedback link
The transfer function No of (1) is:
let s be j ω, considering the frequency characteristic of No, when ≠ 0:
NO(jω)≈0,[ω∈(0,W-Δω)∪(W+Δω,∞)]
NO(jω)＝1,[ω∈(W-Δω,W+Δω)]
that is, when ε ≠ 0, the No output will approach the input
Component of medium frequency W
Output of the debossed feedback link Nf
Comprises the following steps:
namely, the output value of the Nf integrator of the concave feedback link after the convergence of the feedback link is the amplitude of the sine and cosine component with the disturbance frequency quantity in the attitude angular velocity, so that the attitude angular velocity generated by the disturbance in the attitude angular velocity signal is realized
Identifying;
by compensating for the proportionality coefficient Kh/KiIn a
Compensating moment introduced by direction
Eliminating the influence of disturbance on the attitude;
(3) magnetic suspension rotor integrated control law
Under the action of a single-axis high-frequency small-amplitude disturbance moment, a satellite attitude kinetic equation with a magnetic suspension control sensitive gyroscope as an actuating mechanism is as follows:
wherein J represents the satellite moment of inertia matrix, Td＝[Tdx0 0]The method comprises the following steps of representing a single-shaft high-frequency small-amplitude disturbance torque, and taking a magnetic suspension rotor as a satellite attitude kinetic equation of an attitude control actuating mechanism under the condition of a small attitude angle as follows:
wherein, Jx、Jy、JzRepresenting the moment of inertia, h, of each axis of the satelliteyThe dynamic equation of the satellite attitude of the two radial directions of the rotor is shown as follows:
therefore, it is required to
To compensate the disturbance moment of β rotation direction caused by disturbance, so:
order to
The speed of β rotation direction required for posture adjustment,
after compensation, the following steps are carried out:
α, the direction of rotation does not need to be compensated for
α speed of rotation direction required for posture adjustment, so
The dynamic equation of the satellite attitude of the rotor in two radial directions is as follows:
after disturbance compensation is added, according to a satellite kinetic equation, the attitude angle of the attitude adjusting target is
ψrDesigning a decoupling control law as follows:
kpx、kdx、kpz、kdzis a PD controller parameter; the satellite attitude dynamics equation is:
uniaxial attitude angle information under satellite no-disturbance condition
Comprises the following steps:
satellite having only uniaxial angular rate
In the case of (a) in (b),
the satellite attitude control quantity is realized by the rotor radial micro-frame control moment:
therefore, in combination with disturbance compensation, the integrated control law of magnetic suspension rotor control is as follows:
the control reference applied by the magnetic bearing in practice is haxr、hbxr、hayr、hbyrAnd h isbxr＝-haxr，hbyr＝-hayrTherefore:
in order to verify the effect of this method, the attitude angle and the attitude angular velocity before and after disturbance suppression compensation were compared, and the test results are shown in fig. 4, 5, 6, and 7, respectively.
In fig. 4 and 6, the abscissa indicates time in units of s, the ordinate indicates roll angle in units of s, and in fig. 5 and 7, the abscissa indicates time in units of s, and the ordinate indicates roll angular velocity in units of °/s. Compared with the attitude angle and the attitude angular velocity before and after disturbance suppression compensation, the method and the device can well realize suppression of high-frequency small-amplitude disturbance, and have the advantages of simple calculation and strong engineering.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (1)
1. The invention relates to a satellite single-axis measurement and control integrated method based on a magnetic suspension control sensitive gyroscope, which is characterized in that the attitude angular velocity of a satellite under high-frequency small-amplitude disturbance is detected through the magnetic suspension control sensitive gyroscope, an adaptive notch filter with the central notch frequency changing along with the disturbance frequency is used for identifying and removing the attitude angular velocity generated by the high-frequency small-amplitude disturbance, a compensation moment required by the compensation disturbance is calculated, a magnetic suspension rotor radial control moment required by the attitude control is calculated according to a corresponding attitude control law, an integrated control law of the magnetic suspension rotor is designed by combining disturbance suppression and attitude control, a rotor rotating shaft deflects to output a required radial two-degree-of-freedom micro-frame effective stress moment, and therefore the attitude control and disturbance suppression of a satellite single axis are realized, and the method specifically comprises the following steps:
(1) the magnetic suspension rotor dynamic equation according to the rigid body dynamics and the coordinate transformation principle is as follows:
wherein:
Hr＝IΩi
in the formula, MrIndicating the combined external torque of the magnetic levitation rotor, HrRepresenting the angular momentum of the rotor under the rotor train,
the angular momentum change rate of the rotor under the rotor system is shown, I represents the rotational inertia of the rotor rotating around the reference coordinate system of the magnetic suspension control sensitive gyroscope, IrRepresenting the radial moment of inertia of the rotor, IzRepresenting the axial moment of inertia of the rotor, omega representing the axial speed of rotation of the rotor, omegarExpressing the rotor speed, ΩiRepresenting the absolute angular velocity of the rotor,
representing the absolute angular speed rate of change of the rotor,
representing the absolute angular velocity of the rotor coordinate system, i.e. the rotational speed with respect to the inertia space,
indicating the deflection speed of the rotor relative to the magnetic bearings,
for magnetically suspending the speed of the reference system of the control sensitive gyro relative to the inertial space,
is the angular velocity, ω, of the rotor relative to the inertial spacecmgIn order to be the angular velocity of the frame,
is a transformation matrix from the magnetic bearing coordinate system to the rotor coordinate system,
is a transformation matrix from the frame coordinate system to the magnetic bearing coordinate system,
is a transformation matrix from a reference system of the magnetically suspended control sensitive gyroscope to a frame coordinate system,
a transformation matrix from a star system to a magnetic suspension control sensitive gyroscope reference system;
the magnetic bearing installation system, the frame coordinate system, the magnetic suspension control sensitive gyro reference system are coincided and only the single-axis angular rate of the satellite is available
Under the conditions of (a):
α, β are very small and,
and also
Then:
rotor radial resultant external moment
The expression is as follows:
according to the principle of moment balance, the rotor radially closes the external moment
Can also be expressed as:
the magnetic force applied to the magnetic suspension rotor can be expressed in the following linear form:
fλ＝kiλiλ+khλhλ(λ＝ax,ay,bx,by)
in the formula, kiλAnd khλThe (λ ═ ax, ay, bx, by) respectively represents the current stiffness and the displacement stiffness of radial ax, ay, bx and by channels of the magnetic suspension rotor, and can be calibrated through experiments; i.e. iax、ibx、iayAnd ibyIs the winding current of four radial channels, hax、hbx、hayAnd hbyIs the linear displacement of the magnetic levitation rotor in the ax, bx, ay and by directions, respectively, lmRepresenting the distance from the center of the magnetically levitated rotor to the center of the radial magnetic bearing; h isax、hbx、hay、hbyCan be measured by an eddy current displacement sensor, iax、ibx、iay、ibyCan be measured by a current sensor, thereby calculating the external torque M borne by the rotorx r、Mz r；
The expression for the rotor deflection angle is:
α＝(hay-hby)/(2lm)，β＝(hax-hbx)/(2lm)
thereby the rotor deflection information α, β,
The attitude angular rate and the angular acceleration of the satellite are as follows:
without track angular velocity condition, make
Theta and psi are attitude angles of the satellite coordinate system relative to the orbit coordinate system when no disturbance exists, then
Represents the angular acceleration of each direction attitude,
which represents the angular velocity of each direction and,
indicating the angular acceleration and angular velocity generated by the disturbance,
representing the total angular acceleration and angular velocity, then:
(2) disturbance angular velocity identification and disturbance torque compensation in satellite attitude angular velocity
In the attitude angular velocity, a high-frequency small-amplitude disturbance moment generates a sinusoidal angular velocity with the same frequency as the disturbance frequency, and the sinusoidal angular velocity can be identified and removed by adopting a self-adaptive notch filter; the core of the wave trap N is a concave feedback link Nf, the central frequency of which can be changed according to the change of disturbance frequency W, epsilon determines the convergence speed and the central wave-trapping bandwidth, K of the wave trap Nh/KiA scaling factor compensated for the disturbance;
let ω (t) be the input of the concave feedback element Nf, and c (t) be the output of Nf, then:
c and ω satisfy the following differential equation:
the transfer function of the concave feedback element Nf is:
trap input
Nf output to the sag feedback link
The transfer function No of (1) is:
let s be j ω, considering the frequency characteristic of the transfer function No, when ∈ 0,
NO(jω)≈0,[ω∈(0,W-Δω)∪(W+Δω,∞)］
NO(jω)＝1,[ω∈(W-Δω,W+Δω)]
that is, when ε ≠ 0, the No output will approach the input
Component of medium frequency W
Output of the debossed feedback link Nf
Comprises the following steps:
therefore, the output value of the Nf integrator of the concave feedback link after the convergence of the feedback link is the amplitude of the sine and cosine component with the disturbance frequency quantity in the attitude angular velocity, and the attitude angular velocity generated by the disturbance in the attitude angular velocity signal is realized
Identifying;
by compensating for the proportionality coefficient Kh/KiIn a
Compensating moment introduced by direction
Eliminating the influence of disturbance on the attitude;
(3) magnetic suspension rotor integrated control law
Under the action of a single-axis high-frequency small-amplitude disturbance moment, a satellite attitude kinetic equation with a magnetic suspension control sensitive gyroscope as an actuating mechanism is as follows:
wherein J represents the satellite moment of inertia matrix, Td＝[Tdx0 0]The method comprises the following steps of representing a single-shaft high-frequency small-amplitude disturbance torque, and taking a magnetic suspension rotor as a satellite attitude kinetic equation of an attitude control actuating mechanism under the condition of a small attitude angle as follows:
wherein, Jx、Jy、JzRepresenting the moment of inertia, h, of each axis of the satelliteyThe dynamic equation of the satellite attitude of the two radial directions of the rotor is shown as follows:
therefore, it is required to
To compensate the disturbance moment of β rotation direction caused by disturbance, so:
order to
The speed of β rotation direction required for posture adjustment,
after compensation, the following steps are carried out:
α without need for compensation of direction of rotationLet us order
α speed of rotation direction required for posture adjustment, so
The dynamic equation of the satellite attitude of the rotor in two radial directions is as follows:
after disturbance compensation is added, according to a satellite kinetic equation, the attitude angle of the attitude adjusting target is
ψrDesigning a decoupling control law as follows:
kpx、kdx、kpz、kdzis a PD controller parameter; the satellite attitude dynamics equation is:
uniaxial attitude angle information under satellite no-disturbance condition
Comprises the following steps:
satellite having only uniaxial angular rate
In the case of (a) in (b),
the satellite attitude control quantity is realized by the rotor radial micro-frame control moment:
therefore, in combination with disturbance compensation, the integrated control law of magnetic suspension rotor control is as follows:
the control reference applied by the magnetic bearing in practice is haxr、hbxr、hayr、hbyrAnd h isbxr＝-haxr，hbyr＝-hayrTherefore:
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| CN115574819A (en) * | 2022-09-05 | 2023-01-06 | 中国人民解放军战略支援部队航天工程大学 | Spacecraft attitude measurement and control method based on variable speed magnetic suspension control sensitive gyroscope |
| CN115598969B (en) * | 2022-10-20 | 2024-11-29 | 北京控制工程研究所 | An adaptive suppression system for periodic disturbances of rotors in magnetically suspended rotating joints |
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