CN112214890A - Tracking control method for small celestial body detector around flying orbit - Google Patents

Tracking control method for small celestial body detector around flying orbit Download PDF

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CN112214890A
CN112214890A CN202011079369.8A CN202011079369A CN112214890A CN 112214890 A CN112214890 A CN 112214890A CN 202011079369 A CN202011079369 A CN 202011079369A CN 112214890 A CN112214890 A CN 112214890A
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CN112214890B (en
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姚文龙
杨珂
邵巍
池荣虎
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Beijing Institute of Technology BIT
Qingdao University of Science and Technology
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Abstract

The invention discloses a tracking control method for a small celestial body detector around-the-fly orbit, which is characterized in that a nonlinear disturbance observer is designed according to a small celestial body detector around-the-fly dynamic model under unknown disturbance to estimate the external disturbance applied to the detector, and the dynamic characteristic of the nonlinear disturbance observer is compensated to a controller; designing a self-adaptive law to estimate an observation error bound output by a disturbance observer; the dynamic surface technology is introduced to solve the problem of differential explosion generated by derivation of virtual control quantity in the self-adaptive law design; designing a controller combined with a hyperbolic tangent function instead of the sign function; the output of the dynamic surface self-adaptive sliding mode controller is used as the input of a pseudo-rate modulator, so that the pseudo-rate modulator outputs tuned oscillation pulses for driving a thruster to work, and the thruster is driven to generate control moments on a turning shaft, a course shaft and a pitching shaft to offset interference moments; the control method disclosed by the invention enables the small celestial body detector to realize high-precision orbit tracking control around the flying section under unknown disturbance.

Description

Tracking control method for small celestial body detector around flying orbit
Technical Field
The invention provides a tracking control method for a small celestial body detector around a flying orbit, and belongs to the technical field of deep space detection.
Background
The small celestial body is used as 'fossil of solar system', and has important significance for human exploration of universe. The detector needs to fly farther, have longer time and have larger communication delay with the ground compared with the detection of moon, Mars and the like; and because the small celestial body is small in size and mass and irregular in surface attraction, the detector can be influenced by various disturbances such as solar attraction when running around the small celestial body. The uncertainty of the small celestial body and the surrounding environment, and the complexity of external environment disturbance in the face of completing a series of movements such as landing, flying around and the like are required, so that the control method also needs to have more excellent robustness and adaptability, and the detection of the small celestial body also faces a plurality of difficulties and challenges.
In recent years, Misra and the like find the resonance radius of a detector around the circular orbit and the elliptical orbit near the small irregular celestial body in subsequent researches, and analyze the influence of the orbit radius, the celestial body spin angular speed and the like on the stability of the around-flying; 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; 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; the Liangchunhui and the like provide a detector attitude control method based on inversion robust self-adaptive sliding mode to ensure the attitude stability of the detector in the active hovering process.
However, the method does not control the influence of external interference in the surrounding motion process of the small celestial body detector, does not account for the influence of disturbance observation errors, and also accounts for the problem of differential explosion easily caused by derivation of virtual control in an inversion method. Therefore, aiming at the problems in motion control of the detector around the flying small celestial body, an adaptive law is designed to estimate an observation error bound output by the disturbance observer, a dynamic surface technology is introduced to solve the problem of differential explosion generated by derivation of a virtual control quantity in adaptive law design, and finally a detector thruster sliding mode control method with the disturbance observer and the adaptive law and the dynamic surface technology is designed to realize high-precision track tracking control of the detector with higher robustness.
Disclosure of Invention
The invention provides a tracking control method for a small celestial body detector around a flying orbit, which solves the problem of influence on trajectory tracking caused by disturbance observation errors in the prior art, and simultaneously introduces a dynamic surface technology to solve the problem of differential explosion generated by derivation of virtual control quantity in self-adaptive law design, thereby improving the robustness of a system.
In order to solve the technical problems, the following technical scheme is adopted, and the method mainly comprises the following steps:
(1) constructing a gravitational potential function U:
Figure BDA0002718148680000021
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; i isU＝(Ixx2+Iyy2+Izz2)/r2，Ix、Iy、IzThe rotational inertia of the small celestial body around the x, y and z axes,
Figure BDA0002718148680000022
is the length of the position vector r; therefore, the gravitational field of the corresponding position of the small celestial body can be obtained as follows:
Figure BDA0002718148680000023
wherein the acceleration z is caused by non-spherical gravitational perturbationp＝[zp,zp,zp]T＝-[uxx,uyy,uzz]T/r5U in the formulax、uy、uzComprises the following steps:
Figure BDA0002718148680000024
under the fixed coordinate system of the small celestial body center, the position vector r of the small celestial body detector is [ x, y, z ]]TVelocity vector v ═ vx,vy,vz]TThe small celestial body detector power system is a high-coupling nonlinear multi-input multi-output system with unknown interference terms, and is as follows:
Figure BDA0002718148680000031
wherein τ ═ τ [ τ ]1,τ2,τ3]TThe output of the sliding mode controller with the adaptive dynamic surface is represented as the control force acceleration tau on the three axes of x, y and z1，τ2，τ3A control vector of constituents; omega is the rotation angular velocity of small celestial body, omega is [0,0, omega ═ 0]TThe small celestial body rotation angular velocity vector is obtained; z is a radical ofd＝[zdx,zdy,zdz]TIs a disturbance vector; z is a radical ofpDisturbance acceleration caused by non-spherical gravitational perturbation;
(2) and designing a nonlinear disturbance observer by a dynamic model to estimate external environment disturbance on the small celestial body detector, observing the dynamic characteristic of the small celestial body detector and compensating the external environment disturbance to a controller:
the method comprises the following specific steps:
(21) for the dynamic system in (1), the error between the actual value of the disturbance and the estimated value of the disturbance observer output can be used to make the estimated value of the disturbance observer output more accurate, so the following equation can be obtained:
Figure BDA0002718148680000032
wherein the content of the first and second substances,
Figure BDA0002718148680000033
estimating a set of values for a disturbanceA vector of (a); q1∈R3×3Is a positive definite parameter matrix;
(22) for the above disturbance observer equation, there are states that are inconvenient to measure
Figure BDA0002718148680000034
The term, the following intermediate vector needs to be employed:
Figure BDA0002718148680000035
wherein M is a middle vector of the nonlinear disturbance observer;
the output estimation value equation of the original disturbance observer can be rewritten as:
Figure BDA0002718148680000041
(3) and designing a self-adaptive law to estimate an observation error bound output by the disturbance observer:
Figure BDA0002718148680000042
ev＝v-vd；
wherein the content of the first and second substances,
evis a velocity error vector;
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3；
ε1、ε2、ε3is an adjustable parameter;
Figure BDA0002718148680000043
for disturbing the observation error, its upper bound is
Figure BDA0002718148680000044
Figure BDA0002718148680000045
By
Figure BDA0002718148680000046
The estimated value composition of (a);
Γ＝diag{γ1,γ2,γ3}∈R3×3、Λ＝diag{σ1,σ2,σ3}∈R3×3are positive fixed parameter diagonal arrays;
wherein, the positive definite parameter matrix is selected to be very small, and simultaneously ensures
Figure BDA0002718148680000047
Does not grow to be unbounded;
Figure BDA0002718148680000048
is composed of
Figure BDA0002718148680000049
X, y, z;
(4) and introducing a dynamic surface technology to solve the problem of differential explosion generated by derivation of virtual control quantity in the self-adaptive law design process:
defining the position error vector of the small celestial body detector:
er＝r-rd；
both sides of the above-mentioned position error vector are simultaneously derived with respect to time:
Figure BDA00027181486800000410
designing a virtual control quantity of the velocity vector of the small celestial body detector:
Figure BDA00027181486800000411
wherein Q is2A positive fixed parameter diagonal matrix is adopted;
defining a velocity error vector according to a traditional inversion method:
ev＝v-α1；
(41) using a first order low pass filter for the virtual control vector alpha1Taking the output of the first order low-pass filter as vd：
Figure BDA0002718148680000051
vd(0)＝α1(0)；
Wherein, TLIs the filter time constant;
by the above formula can
Figure BDA0002718148680000052
The differential explosion problem due to derivation is avoided by the following expression:
Figure BDA0002718148680000053
(42) after the dynamic surface is introduced, the system generates the following filtering error vector:
eL＝vd-α1；
(5) establishing an optimization control law which is combined with a hyperbolic tangent function replacing a symbolic function and comprises a disturbance estimation value and a disturbance observation error upper bound:
(51) selecting a Lyapunov function on the basis of step 4 of the traditional inversion method:
Figure BDA0002718148680000054
simultaneously deriving both sides of the selected Lyapunov function with respect to time:
Figure BDA0002718148680000055
suppose zdAs is known, the following control laws can be designed:
Figure BDA0002718148680000056
it can be obtained that the system can be guaranteed to be stable when the following formula is satisfied:
Figure BDA0002718148680000057
wherein Q is3A positive fixed parameter diagonal matrix is adopted;
(52) redefining the speed error vector of the small celestial body detector:
ev＝v-vd；
because the traditional inversion method requires that the known conditions of the external environment are difficult to realize, the control law is designed as follows by adopting a sliding mode so as to improve the robustness of the system to the external interference:
Figure BDA0002718148680000061
wherein the content of the first and second substances,
Sgn(ev)＝diag{sgn(evx),sgn(evy),sgn(evz)}∈R3sgn (. cndot.) is a sign function, eviIs evIs a component on the x, y, z axis, i ═ x, y, z;
Figure BDA0002718148680000062
an upper bound for external disturbances;
because the disturbance observer designed in (2) can compensate the unknown disturbance by using the estimated output of the disturbance observer, and further weaken buffeting, in order to avoid adopting buffeting caused by a sign function in a traditional sliding mode, the control law can be rewritten into:
Figure BDA0002718148680000063
considering that the control effect of the control law can be influenced by the error between the output estimation value of the disturbance observer and the actual disturbance, the control law is optimized by combining the self-adaptation law of the hyperbolic tangent function, and the optimized control law is as follows:
Figure BDA0002718148680000064
wherein the content of the first and second substances,
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3，ε1、ε2、ε3is a parameter of the design;
(6) the output tau of the dynamic surface self-adaptive sliding mode controller is used as the input of the pseudo-speed modulator, so that the pseudo-speed modulator outputs a tuned oscillation pulse for driving the thruster to work, and the thruster generates control moment on a turning shaft, a course shaft and a pitching shaft to offset interference moment, thereby effectively weakening the influence of external interference on detection and improving the track tracking control precision;
has the advantages that:
compared with the prior art, the invention has the advantages and positive effects that: the invention relates to a tracking control method for a small celestial body detector around a flying track, which is characterized in that a nonlinear disturbance observer is designed according to a small celestial body detector around dynamic model under unknown disturbance to estimate external disturbance applied to the detector, and disturbance observation errors are estimated
Figure BDA0002718148680000071
Considering the design of the control law; when the adaptive law is designed to estimate the observation error bound output by the disturbance observer, the dynamic surface technology is introduced to solve the problem of solving the virtual control quantity in the adaptive law designThe resulting differential explosion problem; the controller combined with the hyperbolic tangent function replacing the symbolic function is designed, so that the control precision is further improved; the output tau of the dynamic surface self-adaptive sliding mode controller is used as the input of the pseudo-rate modulator to control the thruster to respectively generate corresponding control moments on the turning shaft, the course shaft and the pitching shaft, so that control acceleration is generated, the actual running track of the small celestial body detector is changed, and the external interference on the detector is counteracted.
Therefore, the control method enhances the control capability of the small celestial body detector thruster in a complex disturbance environment through the sliding mode controller with the disturbance observer, and determines the quality of the control performance of the small celestial body detector thruster by estimating the upper bound of external environment disturbance and compensating the controller by the dynamic characteristics of the controller; the disturbance observation error is considered in the control system, so that more accurate control torque is generated on the thruster, and more accurate maneuvering acceleration is generated; the system has stronger anti-interference performance and robustness, 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 tracking and controlling a small celestial body detector around a flying orbit, which is provided by the invention;
FIG. 2 is a structural block diagram of a tracking control method for a small celestial body detector around a flying orbit, which is provided by the invention;
FIG. 3 is an x-axis position tracking curve of a small celestial body detector flying around orbit tracking control method provided by the invention;
FIG. 4 is a y-axis position tracking curve of a small celestial body detector flying around track tracking control method provided by the invention;
FIG. 5 is a z-axis position tracking curve of a small celestial body detector flying around orbit tracking control method provided by the invention;
FIG. 6 is a position error curve under the tracking control method of the small celestial body detector around the flying orbit, which is provided by the invention;
FIG. 7 is a graph of the output acceleration of the controller under the tracking control method of the small celestial body detector around the flying orbit, 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 tracking control method for a small celestial body detector around a flying track by taking the interference factors such as unmodeled dynamic and unknown external perturbation force into consideration, adopting a long-thrust engine as a thruster and combining a small celestial body detector system motion model and the nonlinear dynamic characteristics of a complex actuator. Next, a method for controlling the tracking of the small celestial body detector around the flying orbit will be described in detail with the small celestial body 243Ida as the detector around the flying object.
Referring to fig. 1, the method for controlling the tracking of the small celestial body detector around the flying orbit disclosed by the embodiment includes the following steps:
step S1, designing a nonlinear disturbance observer to estimate external disturbance of the detector according to a small celestial body detector surrounding dynamic model under unknown disturbance:
constructing a gravitational potential function U:
Figure BDA0002718148680000091
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; i isU＝(Ixx2+Iyy2+Izz2)/r2，Ix、Iy、IzThe rotational inertia of the small celestial body around the x, y and z axes,
Figure BDA0002718148680000092
is the length of the position vector r; therefore, the gravitational field of the corresponding position of the small celestial body can be obtained as follows:
Figure BDA0002718148680000093
wherein the acceleration z is caused by non-spherical gravitational perturbationp＝[zp,zp,zp]T＝-[uxx,uyy,uzz]T/r5U in the formulax、uy、uzComprises the following steps:
Figure BDA0002718148680000094
under the fixed coordinate system of the small celestial body center, the position vector r of the small celestial body detector is [ x, y, z ]]TVelocity vector v ═ vx,vy,vz]TThe small celestial body detector power system is a high-coupling nonlinear multi-input multi-output system with unknown interference terms, and is as follows:
Figure BDA0002718148680000095
wherein τ ═ τ [ τ ]1,τ2,τ3]TThe output of the sliding mode controller with the adaptive dynamic surface is represented as the control force acceleration tau on the three axes of x, y and z1，τ2，τ3A control vector of constituents; omega is the rotation angular velocity of small celestial body, omega is [0,0, omega ═ 0]TThe small celestial body rotation angular velocity vector is obtained; z is a radical ofd＝[zdx,zdy,zdz]TIs a disturbance vector; z is a radical ofpDisturbance acceleration caused by non-spherical gravitational perturbation;
step S11, for the dynamic system in (1), the error between the actual value of the disturbance and the estimated value output by the disturbance observer can be used to make the estimated value output by the disturbance observer more accurate, so the following equation can be obtained:
Figure BDA0002718148680000101
wherein the content of the first and second substances,
Figure BDA0002718148680000102
a vector formed by disturbance estimated values; q1∈R3×3Is a positive definite parameter matrix;
step S12, for the above disturbance observer equation, there is a state that is not convenient to measure
Figure BDA00027181486800001010
The term, the following intermediate vector needs to be employed:
Figure BDA0002718148680000103
wherein M is a middle vector of the nonlinear disturbance observer;
the output estimation value equation of the original disturbance observer can be rewritten as:
Figure BDA0002718148680000104
step S2, designing adaptive law to estimate the observation error bound output by the disturbance observer
Figure BDA0002718148680000105
ev＝v-vd； (9)
Wherein the content of the first and second substances,
evis a velocity error vector;
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3； (10)
ε1、ε2、ε3is an adjustable parameter;
Figure BDA0002718148680000106
for disturbing the observation error, its upper bound is
Figure BDA0002718148680000107
Figure BDA0002718148680000108
By
Figure BDA0002718148680000109
The estimated value composition of (a);
Γ＝diag{γ1,γ2,γ3}∈R3×3、Λ＝diag{σ1,σ2,σ3}∈R3×3are positive fixed parameter diagonal arrays;
wherein, the positive definite parameter matrix is selected to be very small, and simultaneously ensures
Figure BDA0002718148680000111
Does not grow to be unbounded;
Figure BDA0002718148680000112
is composed of
Figure BDA0002718148680000113
X, y, z;
step S3; the dynamic surface technology is introduced to solve the problem of differential explosion generated by derivation of virtual control quantity in the adaptive law design:
defining the position error vector of the small celestial body detector:
er＝r-rd； (11)
both sides of the above-mentioned position error vector are simultaneously derived with respect to time:
Figure BDA0002718148680000114
designing a virtual control quantity of the velocity vector of the small celestial body detector:
Figure BDA0002718148680000115
wherein Q is2A positive fixed parameter diagonal matrix is adopted;
defining a velocity error vector according to a traditional inversion method:
ev＝v-α1； (14)
step S31, adopting a first-order low-pass filter to the virtual control vector alpha1Taking the output of the first order low-pass filter as vd：
Figure BDA0002718148680000116
vd(0)＝α1(0)； (16)
Wherein, TLIs the filter time constant;
by the above formula can
Figure BDA0002718148680000117
The differential explosion problem due to derivation is avoided by the following expression:
Figure BDA0002718148680000118
after introducing the dynamic surface in step S32, the system generates the following filtering error vector:
eL＝vd-α1； (18)
step S4; designing a controller in combination with a hyperbolic tangent function instead of a sign function:
step S41, selecting a Lyapunov function on the basis of the step S3 of the traditional inversion method:
Figure BDA0002718148680000121
simultaneously deriving both sides of the selected Lyapunov function with respect to time:
Figure BDA0002718148680000122
suppose zdAs is known, the following control laws can be designed:
Figure BDA0002718148680000123
it can be obtained that the system can be guaranteed to be stable when the following formula is satisfied:
Figure BDA0002718148680000124
wherein Q is3A positive fixed parameter diagonal matrix is adopted;
step S42, redefining the speed error vector of the small celestial body detector:
ev＝v-vd； (23)
because the traditional inversion method requires that the known conditions of the external environment are difficult to realize, the control law is designed as follows by adopting a sliding mode so as to improve the robustness of the system to the external interference:
Figure BDA0002718148680000125
wherein the content of the first and second substances,
Sgn(ev)＝diag{sgn(evx),sgn(evy),sgn(evz)}∈R3sgn (. cndot.) is a sign function, eviIs evThe x-axis, the y-axis, the components on the z-axis, i ═ x, y, z;
Figure BDA0002718148680000126
an upper bound for external disturbances;
since the disturbance observer designed in step S2 can compensate the unknown disturbance by using its estimated output, and further weaken the buffeting, in order to avoid the buffeting caused by the sign function in the conventional sliding mode, the control law can be rewritten by using the disturbance observer designed in step S2 as:
Figure BDA0002718148680000131
considering that the control effect of the control law can be influenced by the error between the output estimation value of the disturbance observer and the actual disturbance, the control law is optimized by combining the self-adaptation law of the hyperbolic tangent function, and the optimized control law is as follows:
Figure BDA0002718148680000132
wherein the content of the first and second substances,
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3，ε1、ε2、ε3is a parameter of the design;
and step S5, taking the output tau of the dynamic surface self-adaptive sliding mode controller as the input of a pseudo-speed modulator, and outputting a tuned oscillation pulse for driving a thruster to work by the pseudo-speed modulator so that the thruster can generate control torque on a turning shaft, a course shaft and a pitching shaft to offset interference torque.
According to the tracking control method for the small celestial body detector around the flying orbit, the nonlinear disturbance observer is designed to estimate the external disturbance applied to the detector according to the surrounding dynamic model of the small celestial body detector under unknown disturbance, and the disturbance observation error is estimated
Figure BDA0002718148680000133
Considering the design of the control law; when the adaptive law is designed to estimate an observation error bound output by a disturbance observer, a dynamic surface technology is introduced to solve the problem of differential explosion generated by derivation of virtual control quantity in the adaptive law design; designing and replacing symbolic functionsThe controller combining the hyperbolic tangent function is beneficial to further improving the control precision; the output tau of the dynamic surface self-adaptive sliding mode controller is used as the input of the pseudo-rate modulator to control the thruster to respectively generate corresponding control moments on the turning shaft, the course shaft and the pitching shaft, so that control acceleration is generated, the actual running track of the small celestial body detector is changed, and the external interference on the detector is counteracted. Therefore, the control method of the embodiment enhances the control capability of the small celestial body detector thruster in a complex disturbance environment through the sliding mode controller with the disturbance observer, and determines the quality of the control performance of the small celestial body detector thruster by estimating the upper bound of external environment disturbance and compensating the dynamic characteristics of the controller; the disturbance observation error is considered in the control system, so that more accurate control torque is generated on the thruster, and more accurate maneuvering acceleration is generated; the system has stronger anti-interference performance and robustness, and the track tracking control precision of the small celestial body detector can be improved.
The control method of the embodiment is a small celestial body detector track tracking control method based on sliding mode control and self-adaptive control algorithm, can effectively solve the problem of track tracking control of the small celestial body detector with known related small celestial body parameters at present, has strong robustness to external unknown disturbance on the small celestial body detector, has high controllability, stability and robustness of the algorithm, and can realize track tracking control of the small celestial body detector with the known related small celestial body parameters at present.
The method has strong anti-interference performance and robustness, the disturbance of the external environment which can be possibly suffered is considered for the complexity of the environment of the small celestial body detector in the space, and a sliding mode control method based on disturbance upper and lower bounds is designed. On the basis, a disturbance observer is adopted to estimate the disturbance in real time, and the disturbance observation error is utilized to perform feedforward compensation on the control quantity, so that switching action is avoided, buffeting is further eliminated, and control precision is improved.
Based on the design of a sliding mode control method with a disturbance observer, the embodiment provides a tracking control method for a small celestial body detector around a flying track, which includes: the system comprises an adaptive law sliding mode controller module, a pseudo-rate modulator module, a thruster module, a disturbance observer module and the like.
The self-adaptive law sliding mode controller module is used for designing a sliding mode controller based on self-adaptive law; specifically comprises a sliding mode control law calculation unit,
Figure BDA0002718148680000141
A vector estimation unit and a dynamic surface design unit.
The sliding mode control law calculation unit is used for establishing a sliding mode control law considering the dynamic characteristics of the disturbance error:
Figure BDA0002718148680000142
sign function Sgn (e)v) Using hyperbolic tangent function theta (e)v) Instead, a bound for disturbance observation error derived from the adaptive law is introduced at the same time
Figure BDA0002718148680000151
Can obtain
Figure BDA0002718148680000152
The formula is used for calculating the upper bound estimated value of disturbance observation error
Figure BDA0002718148680000153
The sliding mode control law of (1).
Figure BDA0002718148680000154
A vector estimation unit for estimating a boundary vector of the disturbance observation error by using an adaptive law
Figure BDA0002718148680000155
And (3) estimating:
Figure BDA0002718148680000156
wherein
Figure BDA0002718148680000157
Is composed of
Figure BDA0002718148680000158
A priori estimate of i ═ x, y, z, epsilon1、ε2、ε3For adjustable parameters, Γ, Λ ∈ R3×3All positive definite parameter diagonal arrays are selected to be very small, and simultaneously, the positive definite parameter diagonal arrays are ensured
Figure BDA0002718148680000159
Does not grow to be unbounded;
dynamic surface design unit for constructing
Figure BDA00027181486800001510
The dynamic surface control expression of (1):
using a first order low pass filter for the virtual control vector alpha1Taking the output of the first order low-pass filter as vdIs provided with
Figure BDA00027181486800001511
Wherein v isd(0)＝α1(0)，TLIs a filter time constant, and therefore can be
Figure BDA00027181486800001512
Is shown as
Figure BDA00027181486800001513
To avoid the problem of differential explosion caused by derivation.
And the pseudo-rate modulator module is used for receiving the output tau of the dynamic surface self-adaptive sliding mode controller and further outputting a tuned oscillation pulse for driving the thruster to work.
And the thruster module is used for generating control moments for counteracting the interference moments on the turning shaft, the course shaft and the pitching shaft respectively so as to generate control acceleration, and adjusting the actual position and speed of the small celestial body detector to enable the small celestial body detector to operate according to an expected track.
A disturbance observer module for estimating and compensating to the controller disturbances of the external environment: correcting the estimated output value of the disturbance observation according to the error between the actual value of the disturbance and the estimated output value of the disturbance observation, and designing to obtain the target
Figure BDA00027181486800001514
Thereby estimating the actual disturbance, wherein
Figure BDA00027181486800001515
For vectors formed by disturbance estimates, Q1∈R3×3For positively determining a parameter matrix, perturbing an observer equation, having states that are inconvenient to measure
Figure BDA00027181486800001516
Term, need to adopt intermediate vector
Figure BDA00027181486800001517
The output estimation value equation of the original disturbance observer can be rewritten as:
Figure BDA00027181486800001518
the working process of the specific control system has been described in detail in the above control method, and is not described herein again.
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 ω
Numerical value 5.1732×1016kg 50.85m 178.85m 185.6m 3.77×10-4rad/s
In the inertial coordinate system of the small celestial body center, the track inclination angle omegad0.5rad and ascension node right ascension id1 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. The time constant of the filter is TL＝0.3，ε1＝ε2＝0.005，ε3＝0.0001，
Figure BDA0002718148680000161
γ1＝1×10-4，γ2＝6×10-6Controller related parameter setting Q1＝diag{2,2,2}，Q2＝diag{2,2,2}，Q3＝diag{106,106,109Positive fixed parameter diagonal matrix Λ biag {10 }-8,10-8,10-11}，Γ＝diag{106,106,109}。
Under the fixed coordinate system of the small celestial body center, the target orbit is as follows:
Figure BDA0002718148680000162
wherein xi (t) is a desired direction angle of the detector in a desired orbital plane in an inertial coordinate system of the small celestial body center;
R(t)、RΩ、Riis a rotation matrix, and the expression is as follows:
Figure BDA0002718148680000163
Figure BDA0002718148680000164
Figure BDA0002718148680000165
the unknown external disturbances are represented using a first order Markov process as follows:
Figure BDA0002718148680000171
wherein the content of the first and second substances,
b∈R3the small celestial body is fixedly connected with a central coordinate system and is subjected to external environment disturbance;
Tc＝diag{103,103,103is a time constant diagonal matrix;
n∈R3is a zero mean Gaussian white noise vector;
ρ＝diag{5×104,5×104,5×105the is a matrix formed by the amplitudes of n;
establishing a track tracking control system of the small celestial body detector under the MATLAB/Simulink simulation environment, and regarding the actual position of the small celestial body detector on the x axis in the figure 3Rapidly increasing from 0km initial position, approaching to the expected track, and reaching 2 × 10 at 40 s4A km position, wherein the actual position track of the detector on the x axis is overlapped with the expected position track in 100 seconds, so that the track tracking from the initial position to the expected track is realized; after 100 seconds, the actual position of the small celestial body detector is always basically coincident with the position of the expected track, and the track is not deviated; with respect to fig. 4, the actual position of the small celestial detector on the y-axis is rapidly adjusted from an initial position of 60km, moving towards the desired trajectory, reaching 6.4 × 10 seconds at 30 seconds4A km position, wherein the actual position track of the detector on the y axis is overlapped with the expected position track in 90 seconds, so that the track tracking from the initial position to the expected track is realized; after 90 seconds, the actual position of the small celestial body detector is always basically coincident with the position of the expected track, and the track is not deviated; with respect to fig. 5, the actual position of the small celestial detector on the z-axis increases rapidly from an initial position of 0m, moving closer to the desired trajectory, reaching 7 × 10 at 50 seconds4A km position, wherein the actual position track of the detector on the z axis is overlapped with the expected position track in 100 seconds, so that the track tracking from the initial position to the expected track is realized; after 100 seconds, the actual position of the small celestial body detector is always basically coincident with the position of the expected track, and the track is not deviated; it can be seen that: under the influence of disturbance, the operation positions of the small celestial body detector on the x axis, the y axis and the z axis can stably operate according to an expected track, and the operation track is free from oscillation jitter or deviation. With respect to fig. 6, the orbit tracking position error decreases rapidly from the initial error, and after 100 seconds the error changes consistently at a lower level, indicating that the small celestial detector trajectory tracking error is effectively eliminated. Fig. 7 shows that after the disturbance observer is used to estimate the disturbance and the disturbance observation error is compensated by the self-adaptation law combined with the hyperbolic tangent function, the output of the controller is smooth and no buffeting occurs.
The control method provided by the invention can ensure that the small celestial body detector has better speed tracking precision and better anti-interference capability under the influence of unknown external disturbance. The embodiment provides a tracking control method for a small celestial body detector around a flying track, external disturbance applied to the detector is estimated through a designed nonlinear disturbance observer, dynamic characteristics of the external disturbance are compensated to a controller, meanwhile, a dynamic surface technology and a designed self-adaptation law are introduced to estimate an observation error boundary output by the disturbance observer, a symbolic function in a traditional sliding mode control method is replaced by a hyperbolic tangent function, buffeting can be effectively eliminated, and control accuracy is improved. The result shows that the control method is used for controlling the influence of external interference in the surrounding motion process of the small celestial body detector, considering the influence from disturbance observation errors and the problem of differential explosion easily caused by derivation of virtual control in an inversion method, so that the control method with strong anti-interference performance and robustness can be obtained, and the track tracking control of the small celestial body detector with high precision is realized.
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 (3)

1. A tracking control method for a small celestial body detector around a flying orbit is characterized by comprising the following steps: the method comprises the following steps:
step 1, designing a nonlinear disturbance observer to estimate external environment disturbance on a small celestial body detector according to a small celestial body detector surrounding dynamic model with unknown disturbance, observing the dynamic characteristic of the small celestial body detector and compensating the small celestial body detector to a controller:
Figure RE-FDA0002771288750000011
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]Tto representThe detector is fixedly connected with a velocity vector under the coordinate at the center of the small celestial body;
τ＝[τ1,τ2,τ3]Tthe output of the sliding mode controller with the adaptive dynamic surface is represented as the control force acceleration tau on the three axes of x, y and z1，τ2，τ3A control vector of constituents;
Figure RE-FDA0002771288750000012
a vector formed by disturbance estimated values;
m is a middle vector of the nonlinear disturbance observer;
Q1∈R3×3is a positive definite parameter matrix;
step 2, designing a self-adaptive law to estimate an observation error bound output by the disturbance observer:
Figure RE-FDA0002771288750000013
ev＝v-vd；
Figure RE-FDA0002771288750000014
wherein the content of the first and second substances,
evis a velocity error vector;
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3；
ε1、ε2、ε3is an adjustable parameter;
Γ＝diag{γ1,γ2,γ3}∈R3×3、Λ＝diag{σ1,σ2,σ3}∈R3×3are positive fixed parameter diagonal arrays;
Figure RE-FDA0002771288750000021
is composed of
Figure RE-FDA0002771288750000022
X, y, z;
Figure RE-FDA0002771288750000023
a vector composed of disturbance observation errors;
Figure RE-FDA0002771288750000024
a vector composed of an upper bound of disturbance observation errors;
Figure RE-FDA0002771288750000025
a vector consisting of estimated values for the upper bound of disturbance observation errors;
and 3, solving the problem of differential explosion generated by derivation of the virtual control quantity in the self-adaptive law design process by a dynamic surface technology:
Figure RE-FDA0002771288750000026
wherein the content of the first and second substances,
TLis the filter time constant;
step 4, designing a controller combined with the hyperbolic tangent function replacing the symbolic function:
Figure RE-FDA0002771288750000027
er＝r-rd；
wherein the content of the first and second substances,
Θ(ev)＝diag{tanh(evx/ε1),tanh(evy/ε2),tanh(evz/ε3)}∈R3；
ε1、ε2、ε3is an adjustable parameter;
Q3∈R3×3is a positive definite parameter matrix;
eris a position error vector;
and 5, taking the output tau of the dynamic surface self-adaptive sliding mode controller as the input of the pseudo-speed modulator, so that the pseudo-speed modulator outputs a tuned oscillation pulse for driving the thruster to work, and the thruster generates control moments on the turning shaft, the course shaft and the pitching shaft to offset interference moments, thereby effectively weakening the influence of external interference on detection and improving the track tracking control precision.
2. The method of claim 1, further comprising: the design process of the nonlinear disturbance observer in the step 2 mainly comprises the following steps:
step 2.1, for the power system, the error between the actual value of the disturbance and the estimated value output by the disturbance observer can be used to make the estimated value output by the disturbance observer more accurate, so that the following equation can be obtained:
Figure RE-FDA0002771288750000031
step 2.2, for the above disturbance observer equation, for the state inconvenient for measurement
Figure RE-FDA0002771288750000038
The term, the following intermediate vector needs to be employed:
Figure RE-FDA0002771288750000032
the output estimation value equation of the original disturbance observer can be rewritten as:
Figure RE-FDA0002771288750000033
3. the method of claim 1, further comprising: in a conventional sliding mode, a sign function is usually adopted to design a control law, but buffeting occurs to a system, and adverse effects are caused to the system, so that the control law is designed by combining an adaptive law of a hyperbolic tangent function, and the buffeting is weakened, and the control law design of the step 5 mainly comprises the following steps:
step 3.1, selecting a Lyapunov function on the basis of the step 4 of the traditional inversion method:
Figure RE-FDA0002771288750000034
simultaneously deriving both sides of the selected Lyapunov function with respect to time:
Figure RE-FDA0002771288750000035
suppose zdAs is known, the following control laws can be designed:
Figure RE-FDA0002771288750000036
it can be obtained that the system can be guaranteed to be stable when the following formula is satisfied:
Figure RE-FDA0002771288750000037
wherein Q is3A positive fixed parameter diagonal matrix is adopted;
step 3.2, redefining the speed error vector of the small celestial body detector:
ev＝v-vd；
because the traditional inversion method requires that the known conditions of the external environment are difficult to realize, the control law is designed as follows by adopting a sliding mode so as to improve the robustness of the system to the external interference:
Figure RE-FDA0002771288750000041
wherein the content of the first and second substances,
Sgn(ev)＝diag{sgn(evx),sgn(evy),sgn(evz)}∈R3sgn (. cndot.) is a sign function, eviIs evThe x-axis, the y-axis, the components on the z-axis, i ═ x, y, z;
Figure RE-FDA0002771288750000042
an upper bound for external disturbances;
since the disturbance observer designed in claim 2 can compensate the unknown disturbance by using the estimated output thereof, and further attenuate the buffeting, in order to avoid the buffeting caused by the sign function in the conventional sliding mode, the control law can be rewritten by using the disturbance observer designed in claim 2 as follows:
Figure RE-FDA0002771288750000043
considering that the control effect of the control law can be influenced by the error between the output estimation value of the disturbance observer and the actual disturbance, the control law is optimized by combining the self-adaptation law of the hyperbolic tangent function, and the optimized control law is as follows:
Figure RE-FDA0002771288750000044
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