CN112817233B - Small celestial body detector flying-around segment orbit tracking control method based on iterative learning control - Google Patents

Small celestial body detector flying-around segment orbit tracking control method based on iterative learning control Download PDF

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CN112817233B
CN112817233B CN202110013210.4A CN202110013210A CN112817233B CN 112817233 B CN112817233 B CN 112817233B CN 202110013210 A CN202110013210 A CN 202110013210A CN 112817233 B CN112817233 B CN 112817233B
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disturbance
celestial body
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detector
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姚文龙
杨珂
邵巍
池荣虎
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Qingdao University of Science and Technology
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Abstract

The invention discloses a method for tracking and controlling a small celestial body detector around a flying section orbit based on iterative learning control, which comprises the steps of establishing a small celestial body dynamics model under external disturbance and unmodeled disturbance; designing a nonlinear disturbance observer to estimate external disturbance applied to the detector and compensating the dynamic characteristic of the detector to a controller; designing a feedback controller to inhibit non-periodic disturbance in the process of fly-around; designing an iterative learning controller to inhibit periodic disturbance in the process of fly-around; the output of the controller is combined with the output of the disturbance observer and input to the pseudo-rate modulator to generate a tuned oscillation pulse, the silicon controlled rectifier is conducted after receiving a trigger signal to induce the thruster to generate main discharge, and thrust is generated on the turning shaft, the course shaft and the pitching shaft. The control method disclosed by the invention enables the small celestial body detector to improve the orbit tracking control precision and the system robustness of the flying-around segment under unknown disturbance.

Description

Small celestial body detector flying-around segment orbit tracking control method based on iterative learning control
Technical Field
The invention discloses a small celestial body detector flying around segment track tracking control method based on iterative learning control, and belongs to the technical field of deep space detection.
Background
Under the development background of promoting the innovative development of the aerospace technology and building the aerospace strong country, the small celestial body is detected, so that the solar system origin evolution, the life origin evolution and the celestial body origin evolution can be explored, and the method has important significance for developing the defense research of the small planet in the ground danger and reducing the risk of impacting the earth. The detection of the small celestial body flying around segment can provide prior information for further detection of landing and the like, and can effectively, completely and accurately know information such as the landform, the gravitational environment and the like of the small celestial body.
In the flying section of the small celestial body detector, the detector needs to repeatedly fly hundreds of circles and thousands of circles around the small celestial body, so that the detector needs to simultaneously face periodic and aperiodic complex external environment disturbances such as solar attraction when finishing a series of movements such as landing, flying and the like, and the small celestial body is difficult to operate according to an expected track due to small celestial body volume, small mass and irregular surface attraction when suffering from the disturbances, and the detector can escape more seriously, so that the suppression of the disturbance received by the detector is necessary for track tracking control. In recent years, Ahn and the like propose an iterative learning control scheme for ensuring the flight trajectory of the satellite formation to be kept; aiming at the problem of frequent switching of a constant thrust control engine caused by an irregular gravitational field, such as Juglans and the like, a hovering rail constant thrust control method based on quasi-periodic dynamic switching is provided; the method is characterized in that the feedback control of the orbit and the attitude around the flying celestial body is designed by Mahmut and the like based on a Lyapunov method; wu Baolin and the like propose high-precision satellite attitude tracking control based on iterative gain control; the Wangyue researches the influence of small celestial body gravity moment on the posture of the detector, analyzes the posture stability of the detector when the detector flies around a static orbit, and provides a posture and orbit integrated control method of the detector based on an irregular Hamilton structure in subsequent researches; liyuanchun and the like provide a control method for track attitude analysis and robust self-adaptive backstepping sliding mode of an irregular asteroid detector. The methods are all control aiming at the small celestial body detector attitude or non-periodic disturbance in the detector flying process, but in practice, the periodic disturbance exists for a longer time, the influence on the detector is larger, the precision and the sensitivity of a controller carried by the detector are limited, and the disturbance is controlled according to the period, so that the workload of the controller can be effectively reduced, and the control precision can be ensured.
Therefore, aiming at the problems in motion control of the detector around the flying small celestial body, the disturbance observer is designed to estimate the disturbance on the detector and is combined with the controller, so that the unknown uncertain disturbance on the detector of the small celestial body estimated by an additional sensor is avoided, the feedback controller is designed to restrain the error generated by the non-periodic disturbance on the detector, meanwhile, the iterative learning controller is designed to restrain the error caused by the periodic disturbance, the influence of the disturbance on the detector is fully considered, and the accuracy of track tracking control of the detector around the flying section is improved.
Disclosure of Invention
The invention provides a small celestial body detector flying around segment track tracking control method based on iterative learning control, and solves the problem of poor detector track tracking control robustness caused by various external unknown disturbances of the small celestial body detector flying around segment in the prior art.
In order to solve the technical problems, the following technical scheme is adopted, and the method mainly comprises the following steps:
(1) establishing a small celestial body dynamics equation under the external disturbance and the unmodeled disturbance:
Figure GDA0003486652380000021
wherein the content of the first and second substances,
r＝[x,y,z]Trepresenting a position vector of the detector under the fixed connection coordinate of the center of the small celestial body;
v＝[vx,vy,vz]Trepresenting the velocity vector of the detector under the fixed connection coordinate of the center of the small celestial body;
ω＝[0,0,ω]Trepresenting the small celestial body rotation angular velocity vector;
g＝[gx,gy,gz]Trepresenting a small celestial body gravity acceleration vector;
a＝[a1,a2,a3]Tthe output of the detector controller is represented and used as the control input of the propeller, and the control force acceleration a on the x, y and z axes is1，a2，a3A control vector of constituents;
d＝[dx,dy,dz]T∈R3is the external disturbance to the small celestial body detector, which mainly comprises non-periodic disturbance dF＝[dFx,dFy,dFz]T∈R3And periodic disturbance dZ＝[dZx,dZy,dZz]T∈R3。
Constructing a gravitational potential function
Figure GDA0003486652380000031
Wherein G is the mass of a celestial body with a small universal gravitation constant,k is GM as a gravitational constant, and M is a disturbance vector;
Figure GDA0003486652380000032
is the length of the position vector r, IU＝(Ixx2+Iyy2+Izz2)/r2，Ix、Iy、IzThe inertia moments of the small celestial bodies around the x, y and z axes respectively, so that the gravitational field of the corresponding position of the small celestial body can be obtained as follows:
Figure GDA0003486652380000033
wherein the disturbance d caused by non-spherical gravitational perturbationp＝[dpx,dpy,dpz]T＝-[uxx,uyy,uzz]T/r5U in the formulax、uy、uzRespectively as follows:
Figure GDA0003486652380000034
(2) according to a small celestial body detector surrounding dynamic model under unknown disturbance, a nonlinear disturbance observer is designed to estimate external environment disturbance on the small celestial body detector, the dynamic characteristic of the small celestial body detector is observed and compensated to a controller:
Figure GDA0003486652380000035
wherein the content of the first and second substances,
Figure GDA0003486652380000036
a vector formed by external disturbance estimated values;
QMan intermediate auxiliary vector of the nonlinear disturbance observer;
Q1∈R3×3is a positive definite parameter matrix.
(3) The feedback controller is designed, so that the closed-loop system can still keep stable after being subjected to non-periodic disturbance;
Figure GDA0003486652380000041
wherein the content of the first and second substances,
aF＝[aF1,aF2,aF3]Tfor the output of the feedback controller, the acceleration a is controlled by the feedback on the three axes x, y and zF1，aF2，aF3Composition is carried out;
Figure GDA0003486652380000042
is a coefficient matrix;
Figure GDA0003486652380000043
A4＝(-β3/β2)I3for feedback of the gain matrix, beta1、β2、β3> 0, wherein I3Is an identity matrix;
rdin order to be able to expect a position vector,
Figure GDA0003486652380000044
a second derivative of the desired position vector;
er＝[erx,ery,erz]T＝r-rdis a position error vector;
ev＝[evx,evy,evz]T＝v-vdis a velocity error vector, vdIs the desired velocity vector.
(4) An iterative learning controller is designed to inhibit the influence of periodic disturbance on the small celestial body detector:
Figure GDA0003486652380000045
wherein the content of the first and second substances,
t is the current moment, and T is the operation period of the small celestial body detector;
aILC(t) an iteratively controlled acceleration vector at time t, aILC(T-T) iteratively controlling the acceleration vector for a previous cycle;
L＝[lrI3,lvI3]·diag{Lr,Lvis the iterative control gain, Lr,Lv∈R3×3，lr、lvDependent on position tracking error and velocity tracking error:
Figure GDA0003486652380000051
tanh(x)＝(ex-e-x)/(ex+e-x) Is a hyperbolic tangent function,/r1、lr2、lv1、lv2Are all constants greater than zero;
e＝[er,ev]Tto track the error vector, e (T-T) is the previous cycle tracking error vector.
(5) The outputs of the controllers are added to obtain a composite acceleration vector:
a＝aF+aILC；
wherein the content of the first and second substances,
aILCcontrolling the acceleration vector for iteration;
and the synthesized acceleration vector a (t) at the time t is used as the output of a controller consisting of a feedback controller and an iterative learning controller and the output of a disturbance observer to be combined and input to a pseudo-rate modulator to generate a tuned oscillation pulse, and 220V alternating current is transformed and subjected to half-wave rectification to charge an energy storage capacitor. When the controllable silicon receives a trigger signal sent by a control system and is conducted, the energy storage capacitor discharges through the primary side of the pulse transformer to form a single pulse current, high voltage is formed on the secondary side of the transformer to discharge the spark plug, the follow current loop is conducted at the moment, the energy storage capacitor continuously provides larger current for the spark plug, the spark plug generates electric sparks of a large current channel, and therefore more plasmas are generated through excitation, the thruster is induced to generate main discharge, and thrust is generated on the overturning shaft, the course shaft and the pitching shaft.
Further, the step (2) specifically comprises the following steps:
(21) based on the small celestial body fly-around power equation, in order to further improve the accuracy of the output estimation value of the disturbance observer by considering the error between the actual value of the disturbance and the estimation value output by the disturbance observer, the output value of the disturbance observer is designed to meet the following equation:
Figure GDA0003486652380000052
(22) for the disturbance observer equation above, the derivative due to velocity
Figure GDA0003486652380000067
Terms cannot be measured, so the following intermediate vector is used:
Figure GDA0003486652380000061
and (3) performing derivation on two sides of the intermediate vector, and combining the equation in the step (21) to obtain an output value equation of the disturbance observer as follows:
Figure GDA0003486652380000062
further, the output of the controller after estimation compensation by the disturbance observer satisfies:
Figure GDA0003486652380000063
further, the external aperiodic perturbation in the kinetic equation of step (1) is described by a first-order markov process:
Figure GDA0003486652380000064
wherein the content of the first and second substances,
dF∈R3the non-periodic disturbance of the detector under the fixed central coordinate system of the small celestial body is detected;
r (t) is a rotation matrix from the inertial to the fixed coordinate system:
Figure GDA0003486652380000065
Figure GDA0003486652380000066
the non-periodic disturbance of the detector under the inertial center coordinate system of the small celestial body;
Qcis a time constant diagonal matrix;
dn∈R3is a zero mean Gaussian white noise vector;
rho is a matrix formed by the amplitudes of the zero-mean Gaussian white noise vector.
Further, the external disturbance in the kinetic equation of step (1) is divided into two parts:
d＝dF+dZ；
dFfor non-periodic disturbances experienced by the small celestial body probe in flight, dZThe periodic disturbance is the disturbance d caused by the non-spherical gravitational perturbationPThus having dZ＝dP。
Has the advantages that:
compared with the prior art, the invention has the advantages and positive effects that: according to the orbit tracking control method for the small celestial body detector around the flying section, the nonlinear disturbance observer is designed to estimate the external disturbance received by the detector according to the surrounding dynamic model of the small celestial body detector under unknown disturbance, and the dynamic characteristic of the external disturbance is compensated to the controller, so that the detector can timely cope with other unknown external disturbances; and based on an iterative learning control method, the detector can better cope with non-periodic disturbance in the process of repeated flying around, the influence caused by the non-periodic disturbance can be effectively inhibited by iterative learning control, the output of the controller and the output of the disturbance observer are combined and input into the pseudo-velocity modulator, tuned oscillation pulses for driving the thruster to work are output, the silicon controlled rectifier receives a trigger signal to be conducted, the thruster is induced to generate main discharge, thrust is generated on the roll-over shaft, the course shaft and the pitch shaft, and the actual position of the small celestial body detector is adjusted to track to an expected track.
The control method improves the capability of the small celestial body detector thruster under the external unknown disturbance to adjust the actual position to the expected track through the iterative learning controller with the disturbance observer, and the control performance of the small celestial body detector is determined by the estimation value and the feedback compensation of the disturbance observer and the compensation gain of the iterative learning controller and the feedback controller; the disturbance observation error is considered in the control system, so that more accurate thrust is generated on the thruster; the external unknown disturbance of the small celestial body detector is described through a first-order Markov process, and compared with other methods in which the disturbance is restricted within a certain small value range, the method has higher randomness and better accords with the actual operating environment; compared with the traditional iterative learning control method, the output of the iterative learning controller is not stored by different iteration times but stored by different periods, so that the initial values of each iteration are required to be the same without the traditional iterative learning null method, and the actual operation condition is better met; the problem that track tracking control is easy to be disturbed by external unknown and is low in precision in the prior art is solved, the anti-interference performance and robustness are higher, and the track tracking control precision of the small celestial body detector can be improved.
Other features and advantages of the present invention will become more apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a method for controlling orbit tracking of a small celestial body detector around a flying segment based on iterative learning control, which is provided by the invention;
FIG. 2 is a structural block diagram of a tracking control structure of a small celestial body detector around a flying section based on iterative learning control, which is provided by the invention;
FIG. 3 is an x-axis position tracking curve of a small celestial body detector flying around section orbit tracking control method based on iterative learning control, which is provided by the invention;
FIG. 4 is a y-axis position tracking curve of a small celestial body detector flying around section orbit tracking control method based on iterative learning control, which is provided by the invention;
FIG. 5 is a z-axis position tracking curve of the orbital tracking control method of the small celestial body detector around the flying section based on iterative learning control, which is provided by the invention;
Detailed Description
To better illustrate the objects and advantages of the present invention, the following detailed description is given with reference to the accompanying drawings.
The invention provides a small celestial body detector fly-around segment orbit tracking control method based on iterative learning control by considering external interference factors such as periodic disturbance and non-periodic disturbance, adopting a pulse plasma thruster and combining a small celestial body detector fly-around segment dynamic model and the nonlinear dynamic characteristics of a complex actuator. A detailed description will be given below of a small celestial body detector orbit tracking control method based on iterative learning control, with the small celestial body 243Ida as a detector orbit target.
Referring to fig. 1, the method for controlling the orbit tracking of the small celestial body detector around the flying segment based on iterative learning control disclosed by the embodiment includes the following steps:
and step S1, establishing a small celestial body dynamics equation under the external disturbance and the unmodeled disturbance.
The dynamic equation of the small celestial body detector around the flying section is given by taking unknown external disturbance and control input of a propeller into consideration
Figure GDA0003486652380000091
Wherein the content of the first and second substances,
r＝[x,y,z]Trepresenting a position vector of the detector under the fixed connection coordinate of the center of the small celestial body;
v＝[vx,vy,vz]Trepresenting the velocity vector of the detector under the fixed connection coordinate of the center of the small celestial body;
ω＝[0,0,ω]Trepresenting the small celestial body rotation angular velocity vector;
g＝[gx,gy,gz]Trepresenting a small celestial body gravity acceleration vector;
a＝[a1,a2,a3]Tthe output of the detector controller is represented and used as the control input of the propeller, and the control force acceleration a on the x, y and z axes is1，a2，a3A control vector of constituents;
d＝[dx,dy,dz]T∈R3is the external disturbance to the small celestial body detector, which mainly comprises non-periodic disturbance dF＝[dFx,dFy,dFz]T∈R3And periodic disturbance dZ＝[dZx,dZy,dZz]T∈R3。
Constructing a gravitational potential function
Figure GDA0003486652380000092
Wherein G is the mass of a small celestial body with a universal gravitation constant, k is GM is the gravitation constant, and M is a disturbance vector;
Figure GDA0003486652380000093
is the length of the position vector r, IU＝(Ixx2+Iyy2+Izz2)/r2，Ix、Iy、IzThe rotational inertia of the small celestial body around the x, y and z axes respectively, so that the gravitational field of the corresponding position of the small celestial body is obtained
Figure GDA0003486652380000094
Wherein the disturbance d caused by non-spherical gravitational perturbationp＝[dpx,dpy,dpz]T＝-[uxx,uyy,uzz]T/r5U in the formulax、uy、uzRespectively as follows:
Figure GDA0003486652380000101
specifically, the method comprises the following steps:
s11, the external non-periodic disturbance in the dynamic equation is described as a first-order Markov process
Figure GDA0003486652380000102
Wherein the content of the first and second substances,
dF∈R3the non-periodic disturbance of the detector under the fixed central coordinate system of the small celestial body is detected;
r (t) is a rotation matrix from the inertial to the fixed coordinate system:
Figure GDA0003486652380000103
Figure GDA0003486652380000104
the non-periodic disturbance of the detector under the inertial center coordinate system of the small celestial body;
Qcis a time constant diagonal matrix;
dn∈R3is a zero mean Gaussian white noise vector;
rho is a matrix formed by the amplitudes of the zero-mean Gaussian white noise vector.
S12, dividing the external disturbance in the kinetic equation into two parts:
d＝dF+dZ；
dFfor non-periodic disturbances experienced by the small celestial body probe in flight, dZThe periodic disturbance is the disturbance d caused by the non-spherical gravitational perturbationPThus having dZ＝dP。
And step S2, designing a nonlinear disturbance observer.
According to a small celestial body detector surrounding dynamic model under unknown disturbance, a nonlinear disturbance observer is designed to estimate external environment disturbance on the small celestial body detector, the dynamic characteristic of the small celestial body detector is observed and compensated to a controller:
Figure GDA0003486652380000111
wherein the content of the first and second substances,
Figure GDA0003486652380000112
the vector is composed of non-periodic disturbance estimated values;
QMan intermediate auxiliary vector of the nonlinear disturbance observer;
Q1∈R3×3is a positive definite parameter matrix.
Specifically, the method comprises the following steps:
s21, based on the small celestial body around-flying dynamic equation, considering the error between the actual value of the disturbance and the estimated value output by the disturbance observer, and in order to further improve the accuracy of the estimated value output by the disturbance observer, designing the output value of the disturbance observer to satisfy the following equation:
Figure GDA0003486652380000113
s22, for the disturbance observer equation above, due to the derivative of the velocity
Figure GDA0003486652380000114
Term cannot be measured and is therefore taken asAn inter vector:
Figure GDA0003486652380000115
and (3) performing derivation on two sides of the intermediate vector, and combining the equation in the step 2.1 to obtain an output value equation of the disturbance observer as follows:
Figure GDA0003486652380000116
and step S3, designing a feedback controller.
The feedback controller is designed, so that the closed-loop system can still keep stable after being subjected to non-periodic disturbance;
Figure GDA0003486652380000121
wherein the content of the first and second substances,
aF＝[aF1,aF2,aF3]Tfor the output of the feedback controller, the acceleration a is controlled by the feedback on the three axes x, y and zF1，aF2，aF3Composition is carried out;
Figure GDA0003486652380000122
is a coefficient matrix;
Figure GDA0003486652380000123
A4＝(-β3/β2)I3for feedback of the gain matrix, beta1,β2,β3> 0, wherein I3As an identity matrix);
rdin order to be able to expect a position vector,
Figure GDA0003486652380000124
a second derivative of the desired position vector;
er＝[erx,ery,erz]T＝r-rdis a position error vector;
ev＝[evx,evy,evz]T＝v-vdis a velocity error vector, vdIs a desired velocity vector;
and step S4, designing an iterative learning controller.
In order to inhibit the influence caused by periodic disturbance on the small celestial body detector, an iterative learning controller is designed:
Figure GDA0003486652380000125
wherein the content of the first and second substances,
t is the current moment, and T is the operation period of the small celestial body detector;
aILC(t) an iteratively controlled acceleration vector at time t, aILC(T-T) iteratively controlling the acceleration vector for a previous cycle;
L＝[lrI3,lvI3]·diag{Lr,Lvis the iterative control gain, Lr,Lv∈R3×3，lr、lvDependent on position tracking error and velocity tracking error:
Figure GDA0003486652380000126
tanh(x)＝(ex-e-x)/(ex+e-x) Is a hyperbolic tangent function,/r1、lr2、lv1、lv2Are all constants greater than zero;
e＝[er,ev]Tto track the error vector, e (T-T) is the previous cycle tracking error vector.
The outputs of the controllers are added to obtain a composite acceleration vector:
a＝aF+aILC。
wherein the content of the first and second substances,
aILCcontrolling the acceleration vector for iteration;
and step S5, combining the output of a controller consisting of a feedback controller and an iterative learning controller and the output of a disturbance observer, inputting the resultant acceleration vector a (t) at the time t into a pseudo-rate modulator to generate a tuned oscillation pulse, and charging an energy storage capacitor after the 220V alternating current is subjected to voltage transformation and half-wave rectification. When the controllable silicon receives a trigger signal sent by a control system and is conducted, the energy storage capacitor discharges through the primary side of the pulse transformer to form a single pulse current, and forms a high voltage on the secondary side of the transformer to discharge the spark plug, at the moment, the follow current loop is conducted, the energy storage capacitor continuously provides a larger current for the spark plug to enable the spark plug to generate electric sparks of a large current channel, so that more plasmas are excited to be generated, the thruster is induced to generate main discharge, and thrust is generated on the overturning shaft, the course shaft and the pitching shaft;
according to the orbit tracking control method of the small celestial body detector around the flying segment based on iterative learning control, according to a dynamic model of the small celestial body detector around the flying segment under unknown disturbance, a nonlinear disturbance observer is designed to estimate external unknown disturbance borne by the detector, and the dynamic characteristic of the external unknown disturbance is compensated to a controller; the output of the controller is combined with the output of the disturbance observer and then input to the pseudo-speed modulator, and then tuned oscillation pulses for driving the thruster to work are output, so that the thruster generates control moments on the turning shaft, the course shaft and the pitching shaft to offset interference moments. Therefore, in the control method of the embodiment, the control capability of the thruster of the small celestial body detector under the unknown external disturbance environment is enhanced through the iterative learning controller with the disturbance observer and the feedback controller, and the estimation value and the feedback compensation of the disturbance observer and the compensation gain of the iterative learning controller and the feedback controller play a decisive role in the performance of track tracking control of the small celestial body detector; disturbance observation errors are further considered in the process of designing the disturbance observer, so that more accurate control torque is generated on the thruster; the method can avoid using an additional sensor to estimate the external unknown disturbance received by the detector, can enable the small celestial body detector to better inhibit errors caused by various external disturbances, and can accurately track the expected track under the condition that the external unknown disturbance exists compared with the existing control method.
The embodiment provides a method for tracking and controlling a small celestial body detector flying around segment orbit based on a small celestial body detector flying around segment orbit tracking and controlling method with a disturbance observer, which comprises the following steps: the device comprises a feedback control module, an iterative learning control module, a disturbance observer module, a pseudo-rate modulator module and the like.
The feedback control module is used for inhibiting the non-periodic disturbance d suffered by the small celestial body detector in the flying around processF：
Construction feedback controller
Figure GDA0003486652380000141
The stability of the system can be ensured when the whole closed-loop system is in an environment with non-periodic disturbance, and the system can operate within a limited influence range.
The iterative learning control module is used for inhibiting the periodic disturbance d suffered by the small celestial body detector in the process of flying aroundZ: the method specifically comprises an error memory unit and an iteration controller output memory unit:
the error memory unit is used for storing error vectors collected at all sampling time of each period in the process of the detector historical period flying around, and the error vectors comprise position error vectors and speed error vectors;
the iteration controller output memory unit is used for storing an iteration controller output vector acquired at each sampling time of each period in the process of the detector historical period around the fly;
reading the error vector and the output vector of the iteration controller of the last period through the error memory unit and the output memory unit of the iteration controller, and performing iterative learning control through the structure
Figure GDA0003486652380000142
To obtain the iterative controller output required for the current cycle.
A disturbance observer module for estimating the external unknown disturbance experienced by the detector and compensating its dynamics to the controller: based on the small celestial body fly-around power equation, in consideration of the error between the actual value of the disturbance and the estimated value output by the disturbance observer, in order to further improve the accuracy of the estimated value output by the disturbance observer, the output value of the disturbance observer is designed to meet the equation
Figure GDA0003486652380000151
Due to derivative of velocity
Figure GDA0003486652380000152
Terms cannot be measured, so intermediate vectors are used
Figure GDA0003486652380000153
The two sides of the intermediate vector are derived, and the equation in the step 2.1 is combined to obtain an output estimation value equation of the disturbance observer
Figure GDA0003486652380000154
And the pseudo-rate modulator module is used for receiving the output a of the controller and further outputting a tuned oscillation pulse for driving the thruster to work.
The parameter values for the small celestial body 243Ida used in the examples are given in Table 1.
TABLE 1 parameters table of small celestial body
Parameter(s) m Ix Iy Iz T
Numerical value 5.1732×1016kg 50.85m 178.85m 185.6m 333360s
In the inertial coordinate system of the small celestial body center, the track inclination angle omegad0.5rad and ascension node right ascension i d1 rad. The initial position of the small celestial body detector is r0＝[0,60,0]Tkm, initial velocity v0＝[0,0,v0]Tm/s, wherein v0The velocity corresponding to the initial position of the detector. ILC gain is L ═ diag { -3 × 10-12I3,-3×10-10I3Q, disturbance observer dependent parameter setting1＝diag{2,2,2}，Qc＝diag{103,103,103Is a time constant diagonal matrix, feedback controller gain A3＝-3×10-3I3，A4＝-3×10-4I3，ρ＝diag{0.01,0.01,0.01}；
As can be seen from fig. 3, 4 and 5: under the same initial condition and external disturbance influence, the feedback iterative learning controller without the disturbance observer can enable the detector to track to an expected track in 10000s or so; under the action of a feedback iterative learning controller with a disturbance observer, the detector can track the expected track within 1000s or so. Therefore, under the same initial conditions and under the same external disturbance conditions, the feedback iterative learning controller without the disturbance observer and the closed-loop orbit tracking control system with the disturbance observer, which are respectively operated by the feedback iterative learning controller, can stably track the desired orbit, but the latter can more quickly track the detector to the desired orbit but has a faster response speed based on the feedback iterative learning controller of the disturbance observer, and can track the detector to the desired orbit in a shorter time. It can be seen that the motor control method provided by the invention enables the small celestial body detector to have better speed tracking accuracy and better anti-interference capability under the influence of unknown external disturbance.
The above detailed description further illustrates the objects, technical solutions and advantages of the present invention, and it should be understood that the embodiments are only used for explaining the present invention and not for limiting the scope of the present invention, and modifications, equivalent substitutions, improvements and the like under the same principle and concept of the present invention should be included in the scope of the present invention.

Claims (5)

1. A method for tracking and controlling a small celestial body detector around a flying section orbit based on iterative learning control is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a small celestial body dynamics equation under external disturbance and unmodeled disturbance:
Figure FDA0003486652370000011
wherein the content of the first and second substances,
r＝[x,y,z]Trepresenting a position vector of the detector under the fixed connection coordinate of the center of the small celestial body;
v＝[vx,vy,vz]Trepresenting the velocity vector of the detector under the fixed connection coordinate of the center of the small celestial body;
ω＝[0,0,ω]Trepresenting the small celestial body rotation angular velocity vector;
g＝[gx,gy,gz]Trepresenting a small celestial body gravity acceleration vector;
a＝[a1,a2,a3]Tthe output of the detector controller is represented and used as the control input of the propeller, and the control force acceleration a on the x, y and z axes is1，a2，a3A control vector of constituents;
d＝[dx,dy,dz]T∈R3is an external disturbance to the small celestial body detector, which mainly comprises a periodic disturbance dZ＝[dZx,dZy,dZz]T∈R3And non-periodic disturbance dF＝[dFx,dFy,dFz]T∈R3；
Step 2, designing a nonlinear disturbance observer to estimate the external environment disturbance on the small celestial body detector according to a small celestial body detector surrounding dynamic model under unknown disturbance, observing the dynamic characteristic of the small celestial body detector and compensating the dynamic characteristic to a controller:
Figure FDA0003486652370000012
wherein the content of the first and second substances,
Figure FDA0003486652370000013
a vector formed by external disturbance estimated values;
QMan intermediate auxiliary vector of the nonlinear disturbance observer;
Q1∈R3×3is a positive definite parameter matrix;
step 3, designing a feedback controller to ensure that the closed-loop system can still keep the system stable after being subjected to non-periodic disturbance;
Figure FDA0003486652370000021
wherein the content of the first and second substances,
aF＝[aF1,aF2,aF3]Tfor feedback controlThe output of the controller controls the acceleration a by feedback on three axes x, y and zF1，aF2，aF3Composition is carried out;
Figure FDA0003486652370000022
is a coefficient matrix;
Figure FDA0003486652370000023
A4＝(-β3/β2)I3for feedback of the gain matrix, beta1，β2，β3> 0, wherein I3Is an identity matrix;
rdin order to be able to expect a position vector,
Figure FDA0003486652370000024
a second derivative of the desired position vector;
er＝[erx,ery,erz]T＝r-rdis a position error vector;
ev＝[evx,evy,evz]T＝v-vdis a velocity error vector, vdIs a desired velocity vector;
step 4, designing an iterative learning controller to inhibit the influence of periodic disturbance on the small celestial body detector:
Figure FDA0003486652370000025
wherein the content of the first and second substances,
t is the current moment, and T is the operation period of the small celestial body detector;
aILC(t) an iteratively controlled acceleration vector at time t, aILC(T-T) iteratively controlling the acceleration vector for a previous cycle;
L＝[lrI3,lvI3]·diag{Lr,Lvas the iterative control gain, a constant matrix Lr,Lv∈R3×3，lr、lvDependent on position tracking error and velocity tracking error:
Figure FDA0003486652370000026
tanh(x)＝(ex-e-x)/(ex+e-x) Is a hyperbolic tangent function,/r1、lr2、lv1、lv2Are all constants greater than zero;
e＝[er,ev]Tis the tracking error vector, e (T-T) is the tracking error vector of the previous period;
and 5, adding the outputs of the controllers to obtain a synthetic acceleration vector:
a＝aF+aILC；
wherein the content of the first and second substances,
aILCcontrolling the acceleration vector for iteration;
and the synthesized acceleration vector a (t) at the time t is used as the output of a controller consisting of a feedback controller and an iterative learning controller and the output of a disturbance observer to be combined and input to a pseudo-rate modulator to generate a tuned oscillation pulse, the controllable silicon is conducted after receiving a trigger signal to induce the thruster to generate main discharge, and thrust is generated on the roll axis, the course axis and the pitch axis.
2. The method of claim 1, further comprising: the main design process of the nonlinear disturbance observer in the step 2 comprises the following steps:
step 2.1, based on the small celestial body orbit flight power equation, considering the error between the actual value of the disturbance and the estimated value output by the disturbance observer, and in order to further improve the accuracy of the estimated value output by the disturbance observer, designing the output value of the disturbance observer to meet the following equation:
Figure FDA0003486652370000031
step 2.2, for the above disturbance observer equation, due to the derivative of the velocity
Figure FDA0003486652370000034
Terms cannot be measured, so the following intermediate vector is used:
Figure FDA0003486652370000032
and (3) performing derivation on two sides of the intermediate vector, and combining the equation in the step 2.1 to obtain an output value equation of the disturbance observer as follows:
Figure FDA0003486652370000033
3. the method of claim 2, further comprising: the controller output after estimation compensation by the disturbance observer satisfies:
Figure FDA0003486652370000041
4. the method of claim 1, further comprising: the external non-periodic disturbance in the kinetic equation of step 1 is described by a first order markov process:
Figure FDA0003486652370000042
wherein the content of the first and second substances,
dF∈R3the external non-periodic disturbance on a detector under a small celestial body fixed connection center coordinate system;
r (t) is a rotation matrix from the inertial to the fixed coordinate system:
Figure FDA0003486652370000043
Figure FDA0003486652370000044
external non-periodic disturbance on a detector under a small celestial body inertia center coordinate system;
Qcis a time constant diagonal matrix;
dn∈R3is a zero mean Gaussian white noise vector;
rho is a matrix formed by the amplitudes of the zero-mean Gaussian white noise vector.
5. The method of claim 1, further comprising: dividing the external disturbance in the kinetic equation of the step 1 into two parts:
d＝dF+dZ；
dFfor non-periodic disturbances experienced by the small celestial body probe in flight, dZThe periodic disturbance is the disturbance d caused by the non-spherical gravitational perturbationPThus having dZ＝dP。
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