CN116923730A - Spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint - Google Patents
Spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint Download PDFInfo
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Abstract
A spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint belongs to the field of aerospace fault diagnosis and flight control. The application solves the problems that the accuracy rate of the fault estimation of the actuator in the existing spacecraft attitude control system is low, the performance index cannot be directly related to the controller parameters, and the preset performance boundary cannot be adjusted on line according to the fault estimation result and the performance constraint of the actuator. Firstly, establishing a kinematic model and a dynamic model of a spacecraft attitude control system; secondly, designing a self-adaptive sliding mode iterative learning observer, and realizing accurate and rapid estimation of equivalent faults by acquiring measurement signals of control moment and angular speed of a spacecraft attitude control system; then, on the basis of obtaining an accurate estimated value of the equivalent fault, a self-adjusting preset performance active fault-tolerant control method is designed. The method can be applied to spacecraft attitude control.
Description
Technical Field
The application belongs to the field of aerospace fault diagnosis and flight control, and particularly relates to an active fault-tolerant control method for a spacecraft attitude with self-adjusting preset performance constraint.
Background
With the continuous development of aerospace technology and space science exploration, tasks such as deep space science exploration, near-earth resource observation, giant communication constellation, global navigation system and the like are continuously increased, a great deal of demands on the aerospace craft are necessarily induced, and in order to pursue higher task efficiency, higher requirements on control performance and safety stability of the craft are also provided. More and more spacecrafts are put into use in the future, and have higher demands on the safety and autonomous processing capacity of the spacecrafts, and the fault-tolerant method of diagnosing loop faults and reformulating a control scheme by a person taking a ground measurement and control center as a core node in the prior art cannot be suitable for the increasingly heavy task requirements in a new period, so that the intensive research on the autonomous fault diagnosis and the autonomous fault-tolerant control method is very necessary. The attitude control system is used as one of the most basic and important subsystems in the spacecraft task, bears the functions of attitude stability control, attitude maneuver and the like, is an indispensable basic capability for realizing the task target, and has the advantages of directly influencing the efficiency of the whole task. It is seen that the safety of the system faults is extremely important as the statistical attitude control system faults account for up to 60% of the historical faults of the spacecraft.
However, when the spacecraft is simultaneously affected by external disturbance and internal uncertainty, an unknown fault occurs to an actuator in the spacecraft attitude control system, and saturation constraint exists to the actuator, the accuracy of the fault estimation of the actuator in the existing spacecraft attitude control system is low, performance indexes of the spacecraft attitude control system under the traditional control method cannot be directly related to controller parameters, and common preset performance control cannot be used for on-line adjustment of preset performance boundaries according to the fault estimation result and the performance constraint of the actuator.
Disclosure of Invention
The application aims to solve the problems that in the existing spacecraft attitude control system, the accuracy of the fault estimation of an actuator is low, performance indexes cannot be directly related to controller parameters, and preset performance boundaries cannot be adjusted on line according to fault estimation results and performance constraints of the actuator.
The technical scheme adopted by the application for solving the technical problems is as follows: a spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint specifically comprises the following steps:
step one, establishing a kinematic equation of a spacecraft attitude control system;
establishing a dynamic equation of a spacecraft attitude control system with system uncertainty, external interference, actuator faults and saturation constraint;
step three, designing an adaptive sliding mode iterative learning observer according to the dynamics equation established in the step two, and obtaining an estimated value of the equivalent fault at each moment by using the designed adaptive sliding mode iterative learning observer;
and step four, designing a spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraint according to the kinematics equation established in the step one and the equivalent fault estimated value obtained in the step three.
Further, the kinematic equation of the spacecraft attitude control system is:
wherein q is the attitude quaternion of the spacecraft, and q= [ q ] 0 ,q 1 ,q 2 ,q 3 ] T ，q 0 Is the scalar portion of the quaternion q,is q 0 First derivative of>Vector part of quaternion q, +.>The upper corner mark T represents a transposition; establishing a spacecraft body reference coordinate system which takes the center of mass of the spacecraft as an origin, takes the rolling axis direction as an x axis, takes the pitching axis direction as a y axis and takes the yaw axis direction as a z axis, wherein omega is an angular velocity component of the spacecraft body reference coordinate system relative to a space inertia reference coordinate system, and omega= [ omega ] 1 ,ω 2 ,ω 3 ] T ，ω 1 Is the angular velocity component, omega, of the axis of rotation 2 Is the angular velocity component of the pitch axis, ω 3 Is the angular velocity component of the yaw axis, I 3×3 Is a 3 x 3 identity matrix; />Is vector->First derivative of>Is vector->Is a cross-over matrix of (c) for the matrix,
further, the dynamic equation of the spacecraft attitude control system is:
in the formula ,J0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 For the nominal moment of inertia matrix portion, aj is the unknown moment of inertia matrix perturbation portion,is the first derivative of ω, is->As a cross-product matrix of the vector omega,D 0 +ΔD is the actual installation matrix of the spacecraft attitude control actuator, D 0 +ΔD is a matrix of 3×n, n representing the number of actuators, D 0 For a nominal installation matrix, Δd is the unknown perturbation of the installation matrix; τ is the actual output torque vector of the actuator, τ= [ τ ] 1 ,τ 2 ,…τ n ] T ，τ i For the actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is the saturation function acting on the output torque vector τ, T d Representing unknown bounded disturbance moment of external space environment acting on the attitude control system;
according toThe kinetic equation is rewritten as follows:
wherein the upper subscript-1 represents the inverse of the matrix,
considering the failure of an actuator in a attitude control system, τ will be i Expressed as:
wherein ,τci For the command torque of the ith actuator, lambda i To the extent of failure loss of the ith actuator,an additive failure of the ith actuator;
the actual output torque vector τ of the actuator is written as:
wherein ,
and then, the sensor measurement noise is considered, and the dynamic equation of the attitude control system is rewritten as follows:
wherein ,fd Representing an equivalent fault of the attitude control system, f d ＝f 1 +d；ω a For the actual value of angular velocity in the attitude control system, η is the angular rate gyro measurement noise.
Further, the saturation function sat (τ) is:
sat(τ)＝[sat(τ 1 ),sat(τ 2 ),…sat(τ n )] T (7)
wherein ,τmax For maximum output torque of a single actuator, |τ i I represents τ i Is (tau) i ) As a sign function.
Further, the sign function sign (τ i ) The method comprises the following steps:
further, the adaptive sliding mode iterative learning observer is:
wherein ω (t) represents the value of the angular velocity component ω at time t,estimated value representing observer diagonal speed component ω (t), a>Is->First derivative of>Is->Cross matrix of>Representing equivalent fault f of self-adaptive sliding mode iterative learning observer to t moment d An estimated value of (t), defining +.>Representing the estimation error, κ, of the observer diagonal velocity component ω (t) 1 ,κ 3 ,κ 4 For positive constant gain, sgn [. Cndot. ]]Representing the sign operation of the vector,/->Equivalent fault f for adaptive sliding mode iterative learning observer d An estimate of (T-T), T representing adaptive slipLearning time interval, κ of model iterative learning observer 2 (t),κ 5 (t, s (t)) represents the adaptive time-varying gain of the adaptive sliding mode iterative learning observer, and s (t) is the sliding mode surface to be designed;
wherein ,representing the estimated value of the angular velocity component omega (0) of the adaptive sliding mode iterative learning observer to the initial moment, gamma 1 ,γ 2 For positive gain, ++>Delta is an integral variable which is a preliminary rough estimation value;
adaptive time-varying gain kappa of the adaptive sliding mode iterative learning observer 2 (t),κ 5 The specific expression of (t, s (t)) is as follows:
in the formula, I represents 2-norm operation, and K 5 Is adaptive time-varying gain kappa 5 (t, s (t)) minimum values,is kappa 2 The first derivative of (t), α, μ and ε are positive constants.
Further, the design of the spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraint comprises the following specific processes:
step four, defining a target quaternion q for spacecraft attitude control d ＝[q d0 ,q dv ] T ＝[q d0 ,q d1 ,q d2 ,q d3 ] T Error quaternion q e The method comprises the following steps: for quaternion multiplication, q e ＝[q e0 ,q ev ] T ＝[q e0 ,q ev,1 ,q ev,2 ,q ev,3 ] T ，q e0 Is quaternion q e Scalar part, q ev ＝[q ev,1 ,q ev,2 ,q ev,3 ] T Is quaternion q e Is a vector part of (2);
defining the error angular velocity ω of a spacecraft attitude control system e The method comprises the following steps: omega e ＝ω d -ω，ω d Is the target angular velocity;
judging whether a discontinuous control instruction appears in the input control reference instruction at the current moment;
if the discontinuous control command appears in the input control reference command, j=0, and then executing the fourth step;
if the discontinuous control instruction does not appear in the input control reference instruction, executing the fourth step;
step IV, calculating a preset performance function rho of the jth refreshing j (t') is:
in the formula ,β1 ,β 2 ,β 3 ,β 4 For the parameters to be designed, t fj The terminal time of the jth refreshing is represented, namely, the predefined convergence time given by a user, and k and b are adjustable parameters for adjusting the preset performance shape boundary; the j-th refresh is performed by the preset performance lower bound ρ d,j And a preset upper performance bound ρ u,j The method comprises the following steps of:
wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) The i 'th component of the error quaternion vector part takes the value of t' =0, ρ ∞,j The steady-state terminal boundary, ψ, of the preset performance function for the jth refresh 1 (t') is a time-varying self-regulating term of a preset performance upper bound, ψ 2 (t') is a time-varying self-tuning term of a preset performance lower bound;
defining ε (t') as the error quaternion vector portion q ev Attitude error epsilon (t') = [ epsilon ] under unconstrained space obtained by error conversion of preset performance function 1 (t′),ε 2 (t′),ε 3 (t′)] T Epsilon (t') is specifically:
wherein ,qev (t') is the error quaternion vector portion q ev The value at the time t' is taken,is the first derivative of ε (t'),>is q ev First derivative of (t'),>for ρ u,j First derivative of (t'),>for ρ d,j A first derivative of (t');
the said and />The method comprises the following steps:
wherein ,is psi 1 First derivative of (t'),>is->Is the first derivative of (a);
the calculation method of the virtual control saturation comprises the following steps:
wherein ,uv (t') is a virtual control amount to be designed,is the actual time t of the jth refresh j The corresponding fault estimation value;
wherein s '(t') is a sliding surface, s '(t')=λ '' 1 ε(t′)+ω e (t′)，λ′ 1 ,λ′ 2 ,λ′ 3 Is a positive constant;
after calculating the virtual control quantity, executing the fourth and fifth steps;
step four, directly calculating a time-varying self-regulating item, obtaining a virtual control quantity at the current moment according to the calculated time-varying self-regulating item, and executing step four five;
step four, continuously judging whether a discontinuous control instruction appears in the input control reference instruction at the next moment, if so, enabling j=j+1 to return to the step four, otherwise, returning to the step four;
and controlling the attitude of the spacecraft until reaching the termination time of the movement.
Further, the parameter to be designed beta 1 ,β 2 ,β 3 ,β 4 The calculation method of (1) is as follows:
in the formula ,ρ0,j Initial error boundary, ρ, of preset performance function for jth refresh ∞,j And (5) setting a steady-state terminal boundary of the performance function for the jth refreshing.
Further, the time-varying self-regulating term ψ of the preset performance upper bound 1 (t') and a time-varying self-regulating term ψ of a preset performance lower bound 2 (t') is:
wherein ,is an intermediate variable +.>For the initial value of integral, sigma 1 ,σ 2 ,σ 3 ,σ 4 For positive gain parameters, n (delta) is the virtual control saturation, +.>Is the first derivative of the attitude error epsilon (delta).
Further, the preset performance function initial error boundary ρ of the jth refresh 0,j Preset performance function steady-state terminal boundary ρ for jth refresh ∞,j Terminal time t of jth refresh fj The method comprises the following steps:
wherein ,c1 ,c 2 For positive gain parameter, θ i′ For the difference between the target of the ith axis attitude angle and the current attitude angle, J i′i′ For moment of inertia matrix J 0 Is the i' th diagonal element of (c),an estimated value representing the failure of the ith actuator, t j Is the actual time at the jth refresh.
The beneficial effects of the application are as follows:
firstly, establishing a kinematic model of a spacecraft attitude control system and a dynamics model of the spacecraft attitude control system with model uncertainty, spatial environment disturbance, actuator faults and amplitude limiting saturation; secondly, designing a self-adaptive sliding mode iterative learning observer, and realizing accurate and rapid estimation of equivalent faults by acquiring measurement signals of control moment and angular speed of a spacecraft attitude control system; then, on the basis of obtaining an accurate estimated value of the equivalent fault, a self-adjusting preset performance active fault-tolerant control method is designed, and stability and control performance when the system fails and external disturbance exists are ensured. The application can establish direct connection between the performance index requirement of the user and the controller parameter without repeated manual adjustment of the controller parameter, so that the control performance index can be adjusted according to the system state in a self-adaptive way, the controller parameter can be automatically generated according to the performance index, the problem that the system is unstable due to the fact that the traditional preset performance boundary cannot be dynamically adjusted is solved, the user-defined performance requirement comprising convergence time and temporary steady-state performance can be directly met, the controller performance is further improved, the conservation is reduced, and the fault tolerance capability and the robustness to external disturbance are relatively strong.
Drawings
FIG. 1 is a flow chart of a spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of the present application;
FIG. 2 is a flow chart for designing an active fault tolerant controller for spacecraft attitude.
Detailed Description
The application will be described in further detail below with reference to the drawings by means of specific embodiments. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the application. Based on the embodiments of the present application, other embodiments obtained by those skilled in the art without making any inventive effort are within the scope of the present application.
Detailed description of the applicationin the first embodiment, this embodiment will be described with reference to fig. 1. The method for actively controlling the fault tolerance of the attitude of the spacecraft with self-adjusting preset performance constraint, disclosed by the embodiment, specifically comprises the following steps of:
step one, establishing a kinematic equation of a spacecraft attitude control system;
establishing a dynamic equation of a spacecraft attitude control system with system uncertainty (including parameter perturbation and sensor noise), external interference, actuator faults and saturation constraint;
step three, designing an adaptive sliding mode iterative learning observer according to the dynamics equation established in the step two, and obtaining an estimated value of the equivalent fault at each moment by using the designed adaptive sliding mode iterative learning observer;
and step four, introducing a spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint according to the kinematics equation established in the step one and the equivalent fault estimation value obtained in the step three, and designing the spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraint.
The active fault-tolerant control method for the spacecraft attitude with the self-adjustment preset performance constraint is an active fault-tolerant control scheme with both fault estimation and self-adjustment preset performance boundary constraint, and is designed to solve the problem of rapid and accurate estimation of the actuator fault in the spacecraft attitude control system, and an equivalent fault of an adaptive sliding mode iterative learning observer estimated actuator is designed; in order to solve the problems that an actuator in a spacecraft attitude control system is likely to have unknown faults, the actuator has saturation constraint, sensor noise and internal and external interference are influenced simultaneously, a self-adjusting preset performance control method is designed to realize active fault-tolerant control, the performance index requirements of a user can be directly connected with the parameters of a controller without repeated parameter adjustment, and meanwhile, the preset performance boundary can be adjusted on line according to a fault estimation result and the performance constraint of the actuator, so that the problem that the system is unstable due to incapability of adjusting the performance boundary in the traditional preset performance control is solved, and the control performance and the robustness of active fault tolerance of the spacecraft attitude control system are ensured.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is that the kinematic equation of the spacecraft attitude control system is:
wherein q is a gesture quaternion of the spacecraft and is used for describing gesture information, and q= [ q ] 0 ,q 1 ,q 2 ,q 3 ] T ，q 0 Is the scalar portion of the quaternion q,is q 0 First derivative of q v Vector part of quaternion q, +.>The upper corner mark T represents a transposition; establishing a spacecraft body reference coordinate system which takes the center of mass of the spacecraft as an origin, takes the rolling axis direction as an x axis, takes the pitching axis direction as a y axis and takes the yaw axis direction as a z axis, wherein omega is an angular velocity component of the spacecraft body reference coordinate system relative to a space inertia reference coordinate system, and omega= [ omega ] 1 ,ω 2 ,ω 3 ] T ，ω 1 Is the angular velocity component, omega, of the axis of rotation 2 Is the angular velocity component of the pitch axis, ω 3 Is the angular velocity component of the yaw axis, I 3×3 Is a 3 x 3 identity matrix; />Is vector->First derivative of>Is a vectorCross matrix of>
Other steps and parameters are the same as in the first embodiment.
And a third specific embodiment: the difference between the present embodiment and the first or second embodiment is that the kinetic equation of the spacecraft attitude control system is:
in the formula ,J0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 For the nominal moment of inertia matrix portion, Δj is the unknown moment of inertia matrix perturbation portion, describing the uncertainty of the internal parameter moment of inertia,is the first derivative of ω, is->Is a cross matrix of vector ω, +.>D 0 +ΔD is the actual installation matrix of the spacecraft attitude control actuator, D 0 +ΔD is a matrix of 3×n, n representing the number of actuators, D 0 For a nominal installation matrix, Δd is an unknown installation matrix perturbation portion for describing the uncertainty of the internal parameter installation matrix; τ is the actual output torque vector of the actuator, τ= [ τ ] 1 ,τ 2 ,…τ n ] T ，τ i For the actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is the saturation function acting on the output torque vector τ, describing the saturation clipping constraints of the actuator, T d Representing the effect of external spatial environment on attitude controlThe unknown bounded disturbance moment of the system mainly comprises gravity gradient moment, aerodynamic moment, solar radiation pressure moment, residual magnetic moment and the like, and meets the specification T d ||＜T max ；
According toThe kinetic equation is rewritten as follows:
wherein the upper subscript-1 represents the inverse of the matrix,
considering faults (mainly including additive faults and multiplicative faults) of actuators in attitude control system, tau is calculated i Expressed as:
wherein ,τci For the command torque of the ith actuator, lambda i For the failure loss degree of the ith actuator, the lambda is more than or equal to 0 i Not more than 1, when lambda i When=0, the actuator has no fault, λ i When=1 indicates that the actuator is completely disabled,an additive failure of the ith actuator;
the actual output torque vector τ of the actuator is written as:
wherein ,
And then, the sensor measurement noise is considered, and the dynamic equation of the attitude control system is rewritten as follows:
wherein ,fd Representing an equivalent fault of the attitude control system, including an actuator multiplicative fault, an additive fault, an internal parameter perturbation, and an external environmental disturbance, f d ＝f 1 +d; omega is the angular rate signal which can be measured by the actual system a For the actual value of angular velocity in the attitude control system, η is the angular rate gyro measurement noise.
In order to realize the active fault-tolerant control of the attitude control system, the equivalent fault f needs to be obtained first d And then the fault tolerant controller can be designed based on the fault information to meet the performance requirements.
Other steps and parameters are the same as in the first or second embodiment.
The specific embodiment IV is as follows: this embodiment differs from one to three embodiments in that the saturation function sat (τ) is:
sat(τ)＝[sat(τ 1 ),sat(τ 2 ),…sat(τ n )] T (7)
wherein ,τmax For maximum output torque of a single actuator, |τ i I represents τ i Is (tau) i ) As a sign function.
Other steps and parameters are the same as in one to three embodiments.
Fifth embodiment: this embodiment differs from the embodiments by one to four in that the sign function sign (τ i ) The method comprises the following steps:
other steps and parameters are the same as in one to four embodiments.
Specific embodiment six: the difference between this embodiment and one to fifth embodiments is that the adaptive sliding mode iterative learning observer is:
wherein ω (t) represents the value of the angular velocity component ω at time t,estimated value representing observer diagonal speed component ω (t), a>Is->First derivative of>Is->Cross matrix of>Representing equivalent fault f of self-adaptive sliding mode iterative learning observer to t moment d An estimated value of (t), defining +.>Representing the estimation error, κ, of the observer diagonal velocity component ω (t) 1 ,κ 3 ,κ 4 For positive constant gain, sgn [. Cndot. ]]Representing the sign operation of the vector,/->Equivalent fault f for adaptive sliding mode iterative learning observer d An estimated value of (T-T), T representing a learning time interval, κ, of the adaptive sliding mode iterative learning observer 2 (t),κ 5 (t, s (t)) represents the adaptive time-varying gain of the adaptive sliding mode iterative learning observer, and s (t) is the sliding mode surface to be designed;
sgn (·) represents the pair vector a= [ a ] 1 ,a 2 ,…,a n ] T Performing symbol operation in the form of
wherein ,representing the estimated value of the angular velocity component omega (0) of the adaptive sliding mode iterative learning observer to the initial moment, gamma 1 ,γ 2 For positive gain, ++>Delta is an integral variable which is a preliminary rough estimation value;
adaptive time-varying gain kappa of the adaptive sliding mode iterative learning observer 2 (t),κ 5 The specific expression of (t, s (t)) is as follows:
in the formula, I represents 2-norm operation, and K 5 Is adaptive time-varying gain kappa 5 (t, s (t)) minimum values,is kappa 2 The first derivative of (t), α, μ and ε are positive constants.
Compared with the traditional observer, the method of the application requires less online calculation amount, and can effectively reduce energy consumption. The equivalent faults consisting of partial failure faults, installation deviation and external disturbance can be estimated at the same time, so that the problem that the faults are difficult to decouple from disturbance and uncertainty is avoided; meanwhile, a novel sliding mode gain self-adaptive law is introduced, so that better estimation precision and rapidity can be considered at the same time; and the method is introduced into an active fault-tolerant controller, so that the active fault-tolerant controller has better fault-tolerant capability and robustness and has stronger engineering value.
Other steps and parameters are the same as in one of the first to fifth embodiments.
Seventh embodiment: this embodiment will be described with reference to fig. 2. The difference between the present embodiment and one to six embodiments is that the design of the spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraint includes the following specific procedures:
step four, defining a target quaternion q for spacecraft attitude control d ＝[q d0 ,q dv ] T ＝[q d0 ,q d1 ,q d2 ,q d3 ] T The target quaternion is used for describing gesture instruction information, and then the error quaternion q e The method comprises the following steps: for quaternion multiplication, q e ＝[q e0 ,q ev ] T ＝[q e0 ,q ev,1 ,q ev,2 ,q ev,3 ] T ，q e0 Is quaternion q e Scalar part, q ev ＝[q ev,1 ,q ev,2 ,q ev,3 ] T Is quaternion q e Is a vector part of (2);
defining the error angular velocity ω of a spacecraft attitude control system e The method comprises the following steps: omega e ＝ω d -ω，ω d Is the target angular velocity;
judging whether a discontinuous control instruction appears in the input control reference instruction at the current moment;
calculating the difference between the actual attitude position of the system at the current moment and the newly received target attitude instruction position, namely calculating an error quaternion, and converting the error quaternion into an error Euler angle omega e ＝[Ω e1 ,Ω e2 ,Ω e3 ] T If I omega e || ∞ More than or equal to 0.0001, a discontinuous control instruction is considered to appear;
if the discontinuous control command appears in the input control reference command, j=0, and then executing the fourth step;
if the discontinuous control instruction does not appear in the input control reference instruction, executing the fourth step;
step IV, calculating a preset performance function rho of the jth refreshing j (t') is:
in the formula ,β1 ,β 2 ,β 3 ,β 4 To be treatedDesign parameters, t fj The terminal time representing the jth refreshing, namely the preset convergence time given by a user, namely the settable terminal time when the performance function reaches a steady-state value, wherein k and b are adjustable parameters for adjusting the preset performance shape boundary and can be selected according to actual conditions, and other constants in the application can be selected according to actual conditions; every refresh preset performance function ρ j At (t'), all of which start at 0, which represents only that the time in the preset performance function starts at 0, e.g., for the jth refresh, the actual time t at the present refresh is output based on the preset performance function after the jth refresh j The control amount of (2) does not represent the actual control time at this time being 0, and it is understood that the time t' =0 corresponds to t=t j The method comprises the steps of carrying out a first treatment on the surface of the The j-th refresh is performed by the preset performance lower bound ρ d,j And a preset upper performance bound ρ u,j The method comprises the following steps of:
wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) The i 'th component of the error quaternion vector part takes the value of t' =0, ρ ∞,j The steady-state terminal boundary, ψ, of the preset performance function for the jth refresh 1 (t') is a time-varying self-regulating term of a preset performance upper bound, ψ 2 (t') is a time-varying self-tuning term of a preset performance lower bound;
defining ε (t') as the error quaternion vector portion q ev Attitude error epsilon (t') = [ epsilon ] under unconstrained space obtained by error conversion of preset performance function 1 (t′),ε 2 (t′),ε 3 (t′)] T Epsilon (t') is specifically:
wherein ,qev (t') is the error quaternion vector portion q ev The value at the time t' is taken,is the first derivative of ε (t'),>is q ev First derivative of (t'),>for ρ u,j First derivative of (t'),>for ρ d,j A first derivative of (t');
the said and />The method comprises the following steps:
wherein ,is psi 1 First derivative of (t'),>is->Is the first derivative of (a);
the calculation method of the virtual control saturation comprises the following steps:
wherein ,uv (t') is a virtual to be designedThe control amount of the liquid is controlled,is the actual time t of the jth refresh j The corresponding fault estimation value;
wherein s '(t') is a sliding surface, s '(t')=λ '' 1 ε(t′)+ω e (t′)，λ′ 1 ,λ′ 2 ,λ′ 3 Is a positive constant;
sig(s(t)) r ＝[|s 1 (t)| r sign(s 1 (t)),|s 2 (t)| r sign(s 2 (t)),|s 3 (t)| r sign(s 3 (t))] T r is the order;
after calculating the virtual control quantity, executing the fourth and fifth steps;
step four, directly calculating a time-varying self-regulating item, obtaining a virtual control quantity at the current moment according to the calculated time-varying self-regulating item (the method of the step four three is adopted, wherein if a discontinuous control instruction does not appear at the current moment, a preset performance function is not required to be refreshed, the time-varying self-regulating item and the virtual control quantity are calculated based on the preset performance function after the last refreshing, and an error quaternion vector part at the actual moment is utilized during calculation), and then executing the step four five;
step four, continuously judging whether a discontinuous control instruction appears in the input control reference instruction at the next moment, if so, enabling j=j+1 to return to the step four, otherwise, returning to the step four;
and controlling the attitude of the spacecraft until reaching the termination time of the movement.
According to the definition of the preset performance control, the controller needs to be designed so that the vector part q of the systematic error quaternion ev Always within the user-defined given performance boundary constraint, i.e., ρ d (t)＜q ev,i′ (t)＜ρ u (t), i' =1, 2,3, so that the system can meet the convergence time requirement, the transient performance requirement and the steady state performance requirement specified by the user.
Other steps and parameters are the same as in one of the first to sixth embodiments.
Eighth embodiment: this embodiment differs from one of the embodiments one to seven in that the parameter β to be designed 1 ,β 2 ,β 3 ,β 4 The calculation method of (1) is as follows:
in the formula ,ρ0,j Initial error boundary, ρ, of preset performance function for jth refresh ∞,j The preset performance function steady-state terminal boundary for the jth refreshing is the first operation stage of the system when j=0, at this time ρ 0,j and ρ∞,j Is manually specified by the user.
Other steps and parameters are the same as those of one of the first to seventh embodiments.
Detailed description nine: this embodiment differs from one to eight of the embodiments in that the time-varying self-adjustment term ψ of the upper bound of the preset performance 1 (t') and a time-varying self-regulating term ψ of a preset performance lower bound 2 (t') is:
/>
wherein ,is an intermediate variable +.>For the initial value of integral, sigma 1 ,σ 2 ,σ 3 ,σ 4 For positive gain parameters, n (delta) is the virtual control saturation, +.>Is the first derivative of the attitude error epsilon (delta).
Other steps and parameters are the same as in one to eight of the embodiments.
Detailed description ten: this embodiment differs from one of the embodiments one through nine in that the preset performance function initial error boundary ρ of the jth refresh 0,j Preset performance function steady-state terminal boundary ρ for jth refresh ∞,j Terminal time t of jth refresh fj The method comprises the following steps:
wherein ,c1 ,c 2 For positive gain parameter, θ i′ For the difference between the target of the ith axis attitude angle and the current attitude angle, J i′i′ For moment of inertia matrix J 0 Is the i' th diagonal element of (c),representing an estimate of the ith actuator fault,t j is the actual time at the jth refresh.
Other steps and parameters are the same as in one of the first to ninth embodiments.
The above examples of the present application are only for describing the calculation model and calculation flow of the present application in detail, and are not limiting of the embodiments of the present application. Other variations and modifications of the above description will be apparent to those of ordinary skill in the art, and it is not intended to be exhaustive of all embodiments, all of which are within the scope of the application.
Claims (10)
1. The spacecraft attitude active fault-tolerant control method with the self-adjusting preset performance constraint is characterized by comprising the following steps of:
step one, establishing a kinematic equation of a spacecraft attitude control system;
establishing a dynamic equation of a spacecraft attitude control system with system uncertainty, external interference, actuator faults and saturation constraint;
step three, designing an adaptive sliding mode iterative learning observer according to the dynamics equation established in the step two, and obtaining an estimated value of the equivalent fault at each moment by using the designed adaptive sliding mode iterative learning observer;
and step four, designing a spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraint according to the kinematics equation established in the step one and the equivalent fault estimated value obtained in the step three.
2. The spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of claim 1, wherein the kinematic equations of the spacecraft attitude control system are:
wherein q is the attitude quaternion of the spacecraft, and q= [ q ] 0 ,q 1 ,q 2 ,q 3 ] T ，q 0 Is the scalar portion of the quaternion q,is q 0 First derivative of>Vector part of quaternion q, +.>The upper corner mark T represents a transposition; establishing a spacecraft body reference coordinate system which takes the center of mass of the spacecraft as an origin, takes the rolling axis direction as an x axis, takes the pitching axis direction as a y axis and takes the yaw axis direction as a z axis, wherein omega is an angular velocity component of the spacecraft body reference coordinate system relative to a space inertia reference coordinate system, and omega= [ omega ] 1 ,ω 2 ,ω 3 ] T ，ω 1 Is the angular velocity component, omega, of the axis of rotation 2 Is the angular velocity component of the pitch axis, ω 3 Is the angular velocity component of the yaw axis, I 3×3 Is a 3 x 3 identity matrix; />Is vector->First derivative of>Is vector->Is a cross-over matrix of (c) for the matrix,
3. the spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of claim 2, wherein the dynamic equation of the spacecraft attitude control system is:
in the formula ,J0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 For the nominal moment of inertia matrix portion, aj is the unknown moment of inertia matrix perturbation portion,is the first derivative of ω, is->As a cross-product matrix of the vector omega,D 0 +ΔD is the actual installation matrix of the spacecraft attitude control actuator, D 0 +ΔD is a matrix of 3×n, n representing the number of actuators, D 0 For a nominal installation matrix, Δd is the unknown perturbation of the installation matrix; τ is the actual output torque vector of the actuator, τ= [ τ ] 1 ,τ 2 ,…τ n ] T ，τ i For the actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is the saturation function acting on the output torque vector τ, T d Representing unknown bounded disturbance moment of external space environment acting on the attitude control system;
according toThe kinetic equation is rewritten as follows:
wherein the upper subscript-1 represents the inverse of the matrix,D＝D 0 +ΔD；
considering the failure of an actuator in a attitude control system, τ will be i Expressed as:
wherein ,τci For the command torque of the ith actuator, lambda i To the extent of failure loss of the ith actuator,an additive failure of the ith actuator;
the actual output torque vector τ of the actuator is written as:
wherein ,τ c ＝[τ c1 ,τ c2 ,…τ cn ] T ，
and then, the sensor measurement noise is considered, and the dynamic equation of the attitude control system is rewritten as follows:
wherein ,fd Representing an equivalent fault of the attitude control system, f d ＝f 1 +d；ω a For the actual value of angular velocity in the attitude control system, η is the angular rate gyro measurement noise.
4. A spacecraft attitude initiative fault tolerance control method with self-adjusting preset performance constraints according to claim 3, wherein the saturation function sat (τ) is:
sat(τ)＝[sat(τ 1 ),sat(τ 2 ),…sat(τ n )] T (7)
wherein ,τmax For maximum output torque of a single actuator, |τ i I represents τ i Is (tau) i ) As a sign function.
5. The spacecraft attitude initiative fault-tolerant control with self-tuning preset performance constraints of claim 4, wherein the sign function sign (τ i ) The method comprises the following steps:
6. the spacecraft attitude initiative fault-tolerant control method with self-adjusting preset performance constraints of claim 5, wherein the adaptive sliding mode iterative learning observer is:
wherein ω (t) represents the value of the angular velocity component ω at time t,estimated value representing observer diagonal speed component ω (t), a>Is->First derivative of>Is->Cross matrix of>Representing equivalent fault f of self-adaptive sliding mode iterative learning observer to t moment d An estimated value of (t), defining +.> Representing the estimation error, κ, of the observer diagonal velocity component ω (t) 1 ,κ 3 ,κ 4 For positive constant gain, sgn [. Cndot. ]]The representation is a sign operation on the vector,equivalent fault f for adaptive sliding mode iterative learning observer d An estimated value of (T-T), T representing a learning time interval, κ, of the adaptive sliding mode iterative learning observer 2 (t),κ 5 (t, s (t)) represents the adaptive time-varying gain of the adaptive sliding mode iterative learning observer, and s (t) is the sliding mode surface to be designed;
wherein ,representing the estimated value of the angular velocity component omega (0) of the adaptive sliding mode iterative learning observer to the initial moment, gamma 1 ,γ 2 For positive gain, ++>Delta is an integral variable which is a preliminary rough estimation value;
adaptive time-varying gain kappa of the adaptive sliding mode iterative learning observer 2 (t),κ 5 The specific expression of (t, s (t)) is as follows:
in the formula, I II represents taking 2 norms for transportationThe calculation is carried out to obtain the calculation result,κ 5 is adaptive time-varying gain kappa 5 (t, s (t)) minimum values,is kappa 2 The first derivative of (t), α, μ and ε are positive constants.
7. The spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraints according to claim 6, wherein the design of the spacecraft attitude active fault-tolerant controller with self-adjusting preset performance constraints comprises the following specific processes:
step four, defining a target quaternion q for spacecraft attitude control d ＝[q d0 ,q dv ] T ＝[q d0 ,q d1 ,q d2 ,q d3 ] T Error quaternion q e The method comprises the following steps:for quaternion multiplication, q e ＝[q e0 ,q ev ] T ＝[q e0 ,q ev,1 ,q ev,2 ,q ev,3 ] T ，q e0 Is quaternion q e Scalar part, q ev ＝[q ev,1 ,q ev,2 ,q ev,3 ] T Is quaternion q e Is a vector part of (2);
defining the error angular velocity ω of a spacecraft attitude control system e The method comprises the following steps: omega e ＝ω d -ω，ω d Is the target angular velocity;
judging whether a discontinuous control instruction appears in the input control reference instruction at the current moment;
if the discontinuous control command appears in the input control reference command, j=0, and then executing the fourth step;
if the discontinuous control instruction does not appear in the input control reference instruction, executing the fourth step;
step IV, calculating a preset performance function rho of the jth refreshing j (t') is：
in the formula ,β1 ,β 2 ,β 3 ,β 4 For the parameters to be designed, t fj The terminal time of the jth refreshing is represented, namely, the predefined convergence time given by a user, and k and b are adjustable parameters for adjusting the preset performance shape boundary; the j-th refresh is performed by the preset performance lower bound ρ d,j And a preset upper performance bound ρ u,j The method comprises the following steps of:
wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) The i 'th component of the error quaternion vector part takes the value of t' =0, ρ ∞,j The steady-state terminal boundary, ψ, of the preset performance function for the jth refresh 1 (t') is a time-varying self-regulating term of a preset performance upper bound, ψ 2 (t') is a time-varying self-tuning term of a preset performance lower bound;
defining ε (t') as the error quaternion vector portion q ev Attitude error epsilon (t') = [ epsilon ] under unconstrained space obtained by error conversion of preset performance function 1 (t′),ε 2 (t′),ε 3 (t′)] T Epsilon (t') is specifically:
wherein ,qev (t') is the error quaternion vector portion q ev The value at the time t' is taken,is the first derivative of epsilon (t'),is q ev First derivative of (t'),>for ρ u,j First derivative of (t'),>for ρ d,j A first derivative of (t');
the said and />The method comprises the following steps:
wherein ,is psi 1 First derivative of (t'),>is->Is the first derivative of (a);
the calculation method of the virtual control saturation comprises the following steps:
wherein ,uv (t') is a virtual control amount to be designed,is the actual time t of the jth refresh j The corresponding fault estimation value;
wherein s '(t') is a sliding surface, s '(t')=λ '' 1 ε(t′)+ω e (t′)，λ′ 1 ,λ′ 2 ,λ′ 3 Is a positive constant;
after calculating the virtual control quantity, executing the fourth and fifth steps;
step four, directly calculating a time-varying self-regulating item, obtaining a virtual control quantity at the current moment according to the calculated time-varying self-regulating item, and executing step four five;
step four, continuously judging whether a discontinuous control instruction appears in the input control reference instruction at the next moment, if so, enabling j=j+1 to return to the step four, otherwise, returning to the step four;
and controlling the attitude of the spacecraft until reaching the termination time of the movement.
8. The spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of claim 7, wherein the parameter to be designed is beta 1 ,β 2 ,β 3 ,β 4 The calculation method of (1) is as follows:
in the formula ,ρ0,j Initial error boundary, ρ, of preset performance function for jth refresh ∞,j And (5) setting a steady-state terminal boundary of the performance function for the jth refreshing.
9. A self-adjusting device as defined in claim 8The spacecraft attitude active fault-tolerant control method with preset performance constraint is characterized in that the time-varying self-adjusting term psi of the preset performance upper bound 1 (t') and a time-varying self-regulating term ψ of a preset performance lower bound 2 (t') is:
wherein ,is an intermediate variable +.>For the initial value of integral, sigma 1 ,σ 2 ,σ 3 ,σ 4 For positive gain parameters, n (delta) is the virtual control saturation, +.>Is the first derivative of the attitude error epsilon (delta).
10. The spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of claim 9, wherein said jth refreshed preset performance function initial error boundary ρ 0,j Preset performance function steady-state terminal boundary ρ for jth refresh ∞,j Terminal time of jth refreshThe method comprises the following steps:
wherein ,c1 ,c 2 For positive gain parameter, θ i′ For the difference between the target of the ith axis attitude angle and the current attitude angle, J i′i′ For moment of inertia matrix J 0 Is the i' th diagonal element of (c),an estimated value representing the failure of the ith actuator, t j Is the actual time at the jth refresh.
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| CN117572780B (en) * | 2024-01-17 | 2024-04-30 | 安徽大学 | Self-adaptive fault-tolerant control method for flexible spacecraft faults |
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| CN117572780B (en) * | 2024-01-17 | 2024-04-30 | 安徽大学 | Self-adaptive fault-tolerant control method for flexible spacecraft faults |
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