CN113485394A - High-precision fixed time convergence relative attitude fault-tolerant tracking control method - Google Patents
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Abstract
A high-precision fixed-time-convergence relative attitude fault-tolerant tracking control method is characterized in that aiming at the particularity of a space intersection butt joint task, a relative attitude tracking error performance constraint boundary capable of being converged in fixed time is designed, a preset performance control method is combined to ensure that the relative attitude tracking error is converged in a steady-state index constraint range in fixed time, in addition, composite uncertainties such as system uncertainty, external interference, executing mechanism faults and the like are estimated and compensated through a self-adaptive control technology, the stability of a closed-loop control system can be ensured in fixed time, fault-tolerant control on faults is realized, meanwhile, external interference suppression control and robust control on model uncertainty can be realized, and the robust fault-tolerant capability of the control system on the executing mechanism faults is enhanced.
Description
Technical Field
The invention relates to a relative attitude fault-tolerant tracking control method with high-precision fixed time convergence, and belongs to the technical field of spacecraft control.
Background
Increasingly complex rendezvous and docking tasks often require a relative attitude tracking control system between a tracking spacecraft and a target spacecraft to have high-precision control performance, but due to the fact that the space environment is severe, various faults cannot be avoided when the on-orbit spacecraft works in the space environment with high and low temperature, strong radiation and strong electromagnetic interference for a long time. Slight faults may cause reduction of control accuracy of the rendezvous and docking tasks, and serious faults may affect stability and reliability of the whole control system and even cause failure of the whole tasks. From the viewpoint of task safety, it is imperative to design a fault-tolerant control scheme capable of dealing with the faults of the executing mechanism for executing the task of the rendezvous and docking operation. Meanwhile, the on-orbit task of the spacecraft is influenced by various space environment interference moments and has system uncertainty, and high-precision and reliable control is required to be realized, so that the control system is required to have stronger robustness and adaptability. Most of the traditional rendezvous and docking fault-tolerant control methods can only ensure the progressive stability of a relative attitude tracking control system, namely, the relative attitude tracking control operation can be completed theoretically for an unlimited time, and the relative attitude is ensured to be converged near a balance point. An infinite convergence time will limit the application of these methods to tasks where fast maneuver control of the pose is required.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the problem that the spacecraft is difficult to realize high-precision and reliable control in the in-orbit task in the prior art, the relative attitude fault-tolerant tracking control test method which takes tracking control of the relative attitude between the spacecraft and the target spacecraft in the rendezvous and docking task as an overall target and fully considers practical problems of model uncertainty, external environment interference, high-precision control, rapid maneuver, executing mechanism fault and the like in the rendezvous and docking task is provided.
The technical scheme for solving the technical problems is as follows:
a relative attitude fault-tolerant tracking control method for high-precision fixed time convergence comprises the following steps:
(1) considering the condition that the executing mechanism has faults, establishing a relative attitude tracking control kinematics and dynamics model of the orbiter and the ascender;
(2) designing a relative attitude tracking error performance function and a relative attitude tracking error fixed time convergence performance function according to the transient and steady performance index requirements of the relative attitude tracking control error in the rendezvous and docking task;
(3) constructing a conversion error variable according to the relative attitude tracking error performance function obtained in the step (2), and constructing an intermediate error variable according to the conversion error variable;
(4) constructing a relative attitude virtual control quantity according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4);
(5) and (3) calculating a derivative of the relative orbit and the attitude virtual control quantity according to the relative attitude virtual control quantity obtained in the step (4), designing a relative attitude fault-tolerant tracking controller with fixed time convergence according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4), and constructing an adaptive law to estimate the external environment interference and the executing mechanism fault condition.
In the step (1), the relative attitude tracking control kinematics and dynamics model of the orbiter and the ascender is specifically as follows:
in the formula (I), the compound is shown in the specification,
to correct for the attitude tracking error described by the rodregs parameters,
in order to be an attitude tracking error,
is a matrix of the rotational inertia of the orbiter,
and
respectively representing disturbance torque and control torque;
matrix G (sigma) in the relative attitude dynamics modele)、CaAnd a non-linear vector haRespectively as follows:
Ca＝S(J(ωe+R(σe)ωt))-S(R(σe)ωt)J-JS(R(σe)ωt)
in the formula I3Is a matrix of the units,
respectively representing the angular velocities of the orbiter and the ascender, and satisfying omegae＝ωs-R(σe)ωtS (·) is a cross multiplier;
coordinate transformation matrix R (sigma) between the orbiter body system and the riser body systeme) Is composed of
For any three-dimensional vector γ ═ γ1 γ2 γ3]TThe cross multiplication matrix S (γ) is specifically:
control moment
The method specifically comprises the following steps:
in the formula, τcA control command torque is to be designed for the relative attitude tracking control system,
the method comprises the following steps that (1) an output torque error caused by a fault of an actuating mechanism of the attitude control system, namely an additive failure fault; diagonal matrix Eσ＝diag{eσ1,eσ2,eσ3The control efficiency matrix of the attitude control system actuating mechanism, namely the multiplicative failure fault, Eσ0For its nominal value, matrix EσDiagonal element satisfies 0<e σi1 or less (i-1, 2,3), wherein, if Eσ0The unit matrix represents that the attitude control system executing mechanism has no fault.
In the step (2), the relative attitude tracking error performance function is as follows:
in the formula, ρσi∞For a steady-state accuracy index of the attitude tracking error of the relative rail, pσAnd q isσTo satisfy pσ<qσPositive odd number of (a)σ>0,βσ>0，ασAnd betaσThe convergence rate of the relative attitude tracking error is influenced;
convergence of relative attitude tracking error to desired stabilityTime T of state indexσThe calculation method comprises the following steps:
according to time TσThe obtained fixed time convergence performance function of the relative attitude tracking error and the preset performance requirements of the relative attitude tracking error specifically comprise:
ρσli≤σei≤ρσui(i＝1,2,3)。
in the step (3), the error variable χ is convertedσ＝[χσ1,χσ2,χσ3]TThe method specifically comprises the following steps:
in the formula, deltauiAnd deltaliRespectively as performance boundary constraint coefficients according to the transformation error variable chiσDesign intermediate error variable eσ1,eσ2The method specifically comprises the following steps:
in the formula, xiσ1And xiσ2For the introduced auxiliary variable, kσ1And k isσ2Are all normal numbers, matrix RσIn particular toComprises the following steps:
in the formula, the filtering tracking error ζσSatisfy ζσ＝ασd-ασc，ασcVirtual control input, alpha, for a relative attitude tracking system to be designedσdThe following filter outputs are specified:
in the formula, gammaσ>0 is the filter parameter.
In the step (4), the relative attitude virtual control quantity is specifically as follows:
ασc＝-(RσG(σe))-1kσ1χσ-G-1(σe)υσ。
in which the auxiliary variable uσ＝[υσ1,υσ2,υσ3]TThe method specifically comprises the following steps:
in the step (5), the adaptive law specifically includes:
in the formula, λσ1,λσ2And
are all normal numbers;
the fixed time relative attitude fault-tolerant tracking controller specifically comprises:
in the formula, kσ2Is a normal number.
Compared with the prior art, the invention has the advantages that:
the invention provides a relative attitude fault-tolerant tracking control test method with high-precision fixed time convergence, aiming at the particularity of a space rendezvous and docking task, firstly, a relative attitude tracking error performance constraint boundary capable of being converged in fixed time is designed, a preset performance control method is combined to ensure that the relative attitude tracking error is converged in a steady-state index constraint range in fixed time, in addition, composite uncertainties such as system uncertainty, external interference, executing mechanism fault and the like are estimated and compensated by an adaptive control technology, the stability of a closed-loop control system can be ensured in fixed time, and the fault-tolerant control of the fault is realized, the method can also realize the external interference suppression control and the robust control of model uncertainty, thereby not only enhancing the robust fault-tolerant capability of the control system to the faults of the actuating mechanism, but also quickening the convergence time of the relative attitude tracking error.
Drawings
FIG. 1 is a block diagram of a closed loop structure of a relative attitude tracking control system provided by the present invention;
FIG. 2 is a flow chart of a fixed time relative attitude tracking control method considering actuator faults provided by the invention;
FIG. 3 is a component of the x-axis of the relative attitude tracking error provided by the present invention;
FIG. 4 is a y-axis component of the relative attitude tracking error provided by the present invention;
FIG. 5 is a y-axis component of the relative attitude tracking error provided by the invention;
Detailed Description
A high-precision fixed-time convergence relative attitude fault-tolerant tracking control method can effectively estimate and compensate composite uncertainties such as system uncertainty, external interference, actuator faults and the like through an adaptive control technology, ensures that a relative attitude tracking error converges in a steady-state index constraint range within fixed time by utilizing a relative attitude tracking error performance constraint boundary capable of being converged within fixed time and combining a preset performance control method, enhances the robust fault-tolerant capability of the control system on the actuator faults, and accelerates the convergence time of the relative attitude tracking error, and comprises the following specific steps:
(1) considering the condition that the executing mechanism has faults, establishing a relative attitude tracking control kinematics and dynamics model of the orbiter and the ascender;
the relative attitude tracking control kinematics and dynamics model of the orbiter and the ascender is specifically as follows:
in the formula (I), the compound is shown in the specification,
to correct for the attitude tracking error described by the rodregs parameters,
in order to be an attitude tracking error,
is a matrix of the rotational inertia of the orbiter,
and
respectively representing disturbance torque and control torque;
matrix G (sigma) in the relative attitude dynamics modele)、CaAnd a non-linear vector haRespectively as follows:
Ca＝S(J(ωe+R(σe)ωt))-S(R(σe)ωt)J-JS(R(σe)ωt)
in the formula I3Is a matrix of the units,
respectively representing the angular velocities of the orbiter and the ascender, and satisfying omegae＝ωs-R(σe)ωtS (·) is a cross multiplier;
coordinate transformation matrix R (sigma) between the orbiter body system and the riser body systeme) Can be expressed as
For any three-dimensional vector γ ═ γ1 γ2 γ3]TThe cross multiplication matrix S (γ) is specifically:
control moment
The method specifically comprises the following steps:
in the formula, τcA control command torque is to be designed for the relative attitude tracking control system,
the method comprises the following steps that (1) an output torque error caused by a fault of an actuating mechanism of the attitude control system, namely an additive failure fault; diagonal matrix Eσ＝diag{eσ1,eσ2,eσ3The control efficiency matrix of the attitude control system actuating mechanism, namely the multiplicative failure fault, Eσ0For its nominal value, matrix EσDiagonal element satisfies 0<e σi1 or less (i-1, 2,3), wherein, if Eσ0The attitude control system is a unit array, and indicates that no fault exists in an actuating mechanism of the attitude control system;
(2) designing a relative attitude tracking error performance function and a relative attitude tracking error fixed time convergence performance function according to the transient and steady performance index requirements of the relative attitude tracking control error in the rendezvous and docking task;
wherein the relative attitude tracking error performance function is as follows:
in the formula, ρσi∞For a steady-state accuracy index of the attitude tracking error of the relative rail, pσAnd q isσTo satisfy pσ<qσPositive odd number of (a)σ>0,βσ>0，ασAnd betaσThe convergence rate of the relative attitude tracking error is influenced;
time T for convergence of relative attitude tracking error to expected steady-state indexσThe calculation method comprises the following steps:
according to time TσThe obtained fixed time convergence performance function of the relative attitude tracking error and the preset performance requirements of the relative attitude tracking error specifically comprise:
ρσli≤σei≤ρσui(i＝1,2,3)
(3) constructing a conversion error variable according to the relative attitude tracking error performance function obtained in the step (2), and constructing an intermediate error variable according to the conversion error variable;
wherein, the conversion error variable χσ＝[χσ1,χσ2,χσ3]TThe method specifically comprises the following steps:
in the formula, deltauiAnd deltaliRespectively for performance boundary constraint coefficient, designing an intermediate error variable according to the conversion error variable, specifically:
in the formula, xiσ1And xiσ2For the introduced auxiliary variable, kσ1And k isσ2Are all normal numbers, matrix RσThe method specifically comprises the following steps:
in the formula, the filtering tracking error ζσSatisfy ζσ＝ασd-ασc，ασcVirtual control input, alpha, for a relative attitude tracking system to be designedσdIs the following filter output, specifically：
In the formula, gammaσ>0 is the filter parameter;
(4) constructing a relative attitude virtual control quantity according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4);
the relative attitude virtual control quantity is specifically as follows:
ασc＝-(RσG(σe))-1kσ1χσ-G-1(σe)υσ
in which the auxiliary variable uσ＝[υσ1,υσ2,υσ3]TThe method specifically comprises the following steps:
(5) and (3) calculating a derivative of the relative orbit and the attitude virtual control quantity according to the relative attitude virtual control quantity obtained in the step (4), designing a relative attitude fault-tolerant tracking controller with fixed time convergence according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4), and constructing an adaptive law to estimate the composite uncertainty including the external complex environment interference, the executing mechanism failure and the like.
Specifically, the adaptive law specifically includes:
in the formula, λσ1,λσ2And
are all normal numbers;
the fixed time relative attitude fault-tolerant tracking controller specifically comprises:
in the formula, kσ2Is a normal number.
The following is further illustrated with reference to specific examples:
the method firstly establishes a relative attitude tracking dynamics and kinematics model between the orbiter and the ascender in the rendezvous and docking task, and considers model uncertainty, executing mechanism faults and external disturbance torque disturbance. Performance boundaries with fixed time convergence characteristics are then designed to constrain relative attitude tracking errors. And finally, designing a self-adaptive updating law to estimate composite uncertainty including model uncertainty, executing mechanism faults and external disturbance moment disturbance, and thus obtaining a final relative attitude tracking control law between the orbiter and the ascender.
In this embodiment, as shown in fig. 1 and fig. 2, a fixed-time relative attitude fault-tolerant tracking control method is provided for a problem of tracking control of a relative attitude between a tracking spacecraft and a target spacecraft in a rendezvous and docking task, and specifically includes the steps of:
(1) and under the condition of considering the fault of the actuating mechanism, establishing the relative attitude tracking control kinematics and dynamics between the orbiter and the ascender.
In the formula (I), the compound is shown in the specification,
to correct for the attitude tracking error described by the rodregs parameters,
in order to be an attitude tracking error,
is a matrix of the rotational inertia of the orbiter,
and
respectively representing the disturbance torque and the control torque. Matrix G (sigma) in the relative attitude dynamics modele)、CaAnd a non-linear vector haAre respectively represented as
Ca＝S(J(ωe+R(σe)ωt))-S(R(σe)ωt)J-JS(R(σe)ωt)
In the formula I3Is a matrix of the units,
respectively representing the angular velocities of the orbiter and the ascender, and satisfying omegae＝ωs-R(σe)ωtS (-) is a cross product, defining: for any three-dimensional vector γ ═ γ1 γ2 γ3]TThe cross multiplication matrix S (gamma) is
Coordinate transformation matrix R (sigma) between the orbiter body system and the riser body systeme) Can be expressed as
The control torque is caused by possible fault conditions of the actual actuator
Satisfy the requirement of
In the formula, τcA control command torque is to be designed for the relative attitude tracking control system,
the error of the output torque caused by the fault of the attitude control system actuating mechanism is an additive failure fault; diagonal matrix Eσ＝diag{eσ1,eσ2,eσ3The control efficiency matrix of the attitude control system actuating mechanism is a multiplicative failure fault Eσ0For its nominal value, matrix EσDiagonal element satisfies 0<eσi1 (i-1, 2,3) or less. If E isσ0The unit matrix represents that the attitude control system executing mechanism has no fault.
(2) According to the transient and steady performance index requirements of the relative attitude tracking control error, the fixed time convergence performance function derivative of the relative attitude tracking error is designed as
In the formula, ρσi∞Representing the steady-state accuracy index, p, of the tracking error of the attitude of the relative railσAnd q isσTo satisfy pσ<qσPositive odd number of (a)σ>0,βσ>0, and ασAnd betaσThe convergence speed of the relative attitude tracking error is affected. Relative attitude tracking errorWill be at time TσConverge to a desired steady state index, where TσIs composed of
(3) Constructing a fixed time convergence performance function of the relative attitude tracking error as
The preset performance requirements for the relative attitude tracking error may then be expressed as
ρσli≤σei≤ρσui(i＝1,2,3)
(4) The conversion error variable for constructing the relative attitude tracking controller is
In the formula, deltauiAnd deltaliThe performance boundary constraint coefficients are respectively, and are generally 1.
(5) Constructing intermediate error variables for subsequent relative attitude tracking controller design
In the formula, the auxiliary variable xiσ1And xiσ2Respectively, the state variables of the following auxiliary compensating system.
In the formula, kσ1And k isσ2Are all normal numbers, matrix RσIs composed of
In the formula, the filtering tracking error ζσSatisfy ζσ＝ασd-ασc，ασcTracking system virtual for relative attitude to be designed
Pseudo control input, ασdIs the following filter output
In the formula, gammaσ>0 is the filter parameter.
(6) Based on the relative attitude conversion error variable in the step (1), designing a relative attitude virtual control quantity as
ασc＝-(RσG(σe))-1kσ1χσ-G-1(σe)υσ
In which the auxiliary variable uσ＝[υσ1,υσ2,υσ3]TThe method specifically comprises the following steps:
(7) and (5) designing the upper bound of the composite terms of uncertainty, external interference, actuator fault and the like of the self-adaptive law estimation system by using the intermediate error variable in the step (5).
In the formula, λσ1,λσ2And
are all normal numbers;
(8) designing relative attitude tracking control quantity based on the relative attitude tracking kinematics in the step (1), the relative attitude intermediate error variable in the step (5) and the composite uncertainty item upper bound estimation value in the step (7);
in the formula, kσ2Is a normal number.
As shown in fig. 3, 4 and 5, simulation examples of the invention are given, and fig. 3-5 show the relative attitude tracking error time-varying curves between the tracking spacecraft and the target spacecraft. 3-5, the relative attitude tracking error can be converged to the vicinity of the equilibrium point in a short time, and in the whole transient process, the relative attitude tracking error is within the performance boundary constraint range determined by the relative attitude tracking performance index requirement.
In summary, the relative attitude fault-tolerant tracking control test method with high-precision fixed time convergence, which is designed by the invention, firstly, the composite uncertainties such as system uncertainty, external interference, actuator fault and the like are effectively estimated and compensated through the self-adaptive control technology; in addition, a relative attitude tracking error performance constraint boundary capable of being converged within fixed time is designed, and a preset performance control method is combined to ensure that the relative attitude tracking error is converged within a steady-state index constraint range within the fixed time. In a word, the method not only enhances the robust fault-tolerant capability of the control system to the faults of the executing mechanism, but also accelerates the convergence time of the relative attitude tracking error.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (7)
1. A relative attitude fault-tolerant tracking control method for high-precision fixed time convergence is characterized by comprising the following steps:
(1) considering the condition that the executing mechanism has faults, establishing a relative attitude tracking control kinematics and dynamics model of the orbiter and the ascender;
(2) designing a relative attitude tracking error performance function and a relative attitude tracking error fixed time convergence performance function according to the transient and steady performance index requirements of the relative attitude tracking control error in the rendezvous and docking task;
(3) constructing a conversion error variable according to the relative attitude tracking error performance function obtained in the step (2), and constructing an intermediate error variable according to the conversion error variable;
(4) constructing a relative attitude virtual control quantity according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4);
(5) and (3) calculating a derivative of the relative orbit and the attitude virtual control quantity according to the relative attitude virtual control quantity obtained in the step (4), designing a relative attitude fault-tolerant tracking controller with fixed time convergence according to the relative attitude tracking control kinematics and dynamics model constructed in the step (1) and the intermediate error variable obtained in the step (4), and constructing an adaptive law to estimate the external environment interference and the executing mechanism fault condition.
2. The method according to claim 1, wherein the method comprises the following steps:
in the step (1), the trajectory tracking control kinematics and dynamics model of the relative posture of the orbiter and the ascender is specifically as follows:
in the formula (I), the compound is shown in the specification,
to correct for the attitude tracking error described by the rodregs parameters,
in order to be an attitude tracking error,
is a matrix of the rotational inertia of the orbiter,
and
respectively representing disturbance torque and control torque;
matrix G (sigma) in the relative attitude dynamics modele)、CaAnd a non-linear vector haRespectively as follows:
Ca＝S(J(ωe+R(σe)ωt))-S(R(σe)ωt)J-JS(R(σe)ωt)
in the formula I3Is a matrix of the units,
respectively representing the angular velocities of the orbiter and the ascender, and satisfying omegae＝ωs-R(σe)ωtS (·) is a cross multiplier;
coordinate transformation matrix R (sigma) between the orbiter body system and the riser body systeme) Is composed of
3. The method according to claim 2, wherein the method comprises the following steps:
for any three-dimensional vector γ ═ γ1 γ2 γ3]TThe cross multiplication matrix S (γ) is specifically:
control moment
The method specifically comprises the following steps:
in the formula, τcA control command torque is to be designed for the relative attitude tracking control system,
the method comprises the following steps that (1) an output torque error caused by a fault of an actuating mechanism of the attitude control system, namely an additive failure fault; diagonal matrix Eσ＝diag{eσ1,eσ2,eσ3The control efficiency matrix of the attitude control system actuating mechanism, namely the multiplicative failure fault, Eσ0For its nominal value, matrix EσDiagonal element satisfies 0<eσi1 or less (i-1, 2,3), wherein, if Eσ0The unit matrix represents that the attitude control system executing mechanism has no fault.
4. The method according to claim 1, wherein the method comprises the following steps:
in the step (2), the relative attitude tracking error performance function is as follows:
in the formula, ρσi∞For a steady-state accuracy index of the attitude tracking error of the relative rail, pσAnd q isσTo satisfy pσ<qσPositive odd number of (a)σ>0,βσ>0，ασAnd betaσThe convergence rate of the relative attitude tracking error is influenced;
time T for convergence of relative attitude tracking error to expected steady-state indexσThe calculation method comprises the following steps:
according to time TσThe obtained fixed time convergence performance function of the relative attitude tracking error and the preset performance requirements of the relative attitude tracking error specifically comprise:
ρσli≤σei≤ρσui(i＝1,2,3)。
5. the method according to claim 1, wherein the method comprises the following steps:
in the step (3), the error variable chi is convertedσ＝[χσ1,χσ2,χσ3]TThe method specifically comprises the following steps:
in the formula, deltauiAnd deltaliRespectively, performance boundaryBeam coefficient according to transformation error variable χσDesign intermediate error variable eσ1,eσ2The method specifically comprises the following steps:
in the formula, xiσ1And xiσ2For the introduced auxiliary variable, kσ1And k isσ2Are all normal numbers, matrix RσThe method specifically comprises the following steps:
in the formula, the filtering tracking error ζσSatisfy ζσ＝ασd-ασc，ασcVirtual control input, alpha, for a relative attitude tracking system to be designedσdThe following filter outputs are specified:
in the formula, gammaσ>0 is the filter parameter.
6. The method according to claim 1, wherein the method comprises the following steps:
in the step (4), the relative attitude virtual control quantity specifically includes:
ασc＝-(RσG(σe))-1kσ1χσ-G-1(σe)υσ。
in which the auxiliary variable uσ＝[υσ1,υσ2,υσ3]TThe method specifically comprises the following steps:
7. the method according to claim 1, wherein the method comprises the following steps:
in the step (5), the adaptive law specifically includes:
in the formula, λσ1,λσ2And
are all normal numbers;
the fixed time relative attitude fault-tolerant tracking controller specifically comprises:
in the formula, kσ2Is a normal number.
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