CN116923730B - 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 invention 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 invention 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 invention 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 invention 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, q= [ q 0,q1,q2,q3]T,q0 is the scalar part of quaternion q, Is the first derivative of q 0,/>Is the 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 yawing 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, omega= [ omega 1,ω2,ω3]T,ω1 ] is an angular velocity component of the rolling axis, omega 2 is an angular velocity component of the pitching axis, omega 3 is an angular velocity component of the yawing axis, and I 3×3 is a unit matrix of 3 multiplied by 3; /(I)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:
Wherein, J 0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 is the nominal moment of inertia matrix part, deltaJ is the unknown moment of inertia matrix perturbation part, Is the first derivative of ω,/>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 size 3×n, n represents the number of actuators, D 0 is the nominal installation matrix, Δd is the unknown perturbation part of the installation matrix; τ is an actual output torque vector of the actuator, τ= [ τ 1,τ2,…τn]T,τi ] is an actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is a saturation function acting on the output torque vector τ, and T d represents an unknown bounded disturbance torque of the external spatial environment acting on the attitude control system;
According to The 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 i is denoted as:
Wherein τ ci is the command torque of the ith actuator, lambda i is the degree 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 f d represents an equivalent fault of the attitude control system, f d＝f1+d;ωa is an actual value of the angular velocity in the attitude control system, and η is angular rate gyro measurement noise.
Further, the saturation function sat (τ) is:
sat(τ)＝[sat(τ1),sat(τ2),…sat(τn)]T (7)
Where τ max is the maximum output torque of a single actuator, |τ i | represents the absolute value of τ i and sign (τ i) is a sign function.
Further, the sign function sign (τ i) is:
Further, the adaptive sliding mode iterative learning observer is:
Wherein ω (t) represents the value of the angular velocity component ω at time t, Representing an estimate of the observer diagonal velocity component ω (t)/(Is/>First derivative of,/>For/>Cross matrix of,/>Representing the estimated value of the equivalent fault f d (t) at the time t by the adaptive sliding mode iterative learning observer, and defining/>Representing the estimated error of the observer for the angular velocity component ω (t), κ 1,κ3,κ4 being the positive constant gain, sgn [. Cndot ] representing the sign operation on the vector,/>For the estimated value of equivalent fault f d (T-T) of the adaptive sliding mode iterative learning observer, T represents the learning time interval of the adaptive sliding mode iterative learning observer, κ 2(t),κ5 (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, Represents the estimated value of the angular velocity component omega (0) of the self-adaptive sliding mode iterative learning observer at the initial moment, and gamma 1,γ2 is positive gain,/>Delta is an integral variable which is a preliminary rough estimation value;
The specific expression of the adaptive time-varying gain kappa 2(t),κ5 (t, s (t)) of the adaptive sliding mode iterative learning observer is as follows:
In the formula, I II represents taking 2-norm operation, kappa 5 is the minimum value of the adaptive time-varying gain kappa 5 (t, s (t)), Is the first derivative of κ 2 (t), and 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 d＝[qd0,qdv]T＝[qd0,qd1,qd2,qd3]T for spacecraft attitude control, wherein the error quaternion q e is as follows: For quaternion multiplication ,qe＝[qe0,qev]T＝[qe0,qev,1,qev,2,qev,3]T,qe0, the scalar portion of quaternion q e, q ev＝[qev,1,qev,2,qev,3]T, the vector portion of quaternion q e;
The error angular velocity ω e defining the spacecraft attitude control system is: omega e＝ωd-ω,ωd 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 four, calculating a preset performance function ρ j (t') of the jth refresh as follows:
Wherein, beta 1,β2,β3,β4 is a parameter to be designed, t fj represents the terminal time of the jth refreshing, namely the predefining convergence time given by a user, and k and b are adjustable parameters for adjusting the preset performance shape boundary; the preset lower performance bound ρ d,j and the preset upper performance bound ρ u,j for the jth refresh are then:
Wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) is a value of an ith component of an error quaternion vector part at a time t ' =0, ρ ∞,j is a preset performance function steady-state terminal boundary refreshed for the jth time, ψ 1 (t ') is a time-varying self-regulating item of a preset performance upper bound, and ψ 2 (t ') is a time-varying self-regulating item of a preset performance lower bound;
Defining epsilon (t ') as an attitude error under an unconstrained space obtained by error conversion of an error quaternion vector part q ev through a preset performance function, wherein epsilon (t ')= [ epsilon 1(t′),ε2(t′),ε3(t′)]T, epsilon (t ') is specifically as follows:
wherein q ev (t ') is the value of the error quaternion vector portion q ev at time t', Is the first derivative of ε (t')/(Is the first derivative of q ev (t')/(Is the first derivative of ρ u,j (t')/>A first derivative of ρ d,j (t');
The said And/>The method comprises the following steps:
Wherein, Is the first derivative of ψ 1 (t'),/>For/>Is the first derivative of (a);
The calculation method of the virtual control saturation comprises the following steps:
wherein u v (t') is a virtual control quantity to be designed, Is the fault estimated value corresponding to the actual time t j of the jth refreshing;
Where s ' (t ') is a sliding surface, s ' (t ')=λ ' 1ε(t′)+ωe(t′),λ′1,λ′2,λ′3 is a normal number;
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 calculation method of the parameter β 1,β2,β3,β4 to be designed is as follows:
Wherein ρ 0,j is the preset performance function initial error boundary of the jth refresh, and ρ ∞,j is the preset performance function steady-state terminal boundary of the jth refresh.
Further, the time-varying self-adjusting term ψ 1 (t ') of the preset performance upper bound and the time-varying self-adjusting term ψ 2 (t') of the preset performance lower bound are:
Wherein, Is an intermediate variable,/>For the integral initial value, σ 1,σ2,σ3,σ4 is the positive gain parameter, n (delta) is the virtual control saturation,/>Is the first derivative of the attitude error epsilon (delta).
Further, the initial error boundary ρ 0,j of the preset performance function of the jth refresh, the steady-state terminal boundary ρ ∞,j of the preset performance function of the jth refresh, and the terminal time t fj of the jth refresh are:
Wherein c 1,c2 is a positive gain parameter, θ i′ is a difference between an i 'th axis attitude angle target and a current attitude angle, J i′i′ is an i' th diagonal element of a moment of inertia matrix J 0, Representing an estimate of the ith actuator fault, t j is the actual time at the jth refresh.
The beneficial effects of the invention 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 invention 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.
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FIG. 1 is a flow chart of a spacecraft attitude active fault tolerance control method with self-adjusting preset performance constraints of the present invention;
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 inventionin 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 quaternion of the gesture of the spacecraft, and is used for describing gesture information, q= [ q 0,q1,q2,q3]T,q0 is a scalar part of the quaternion q, Is the first derivative of q 0, q v is the vector part of the 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 yawing 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, omega= [ omega 1,ω2,ω3]T,ω1 ] is an angular velocity component of the rolling axis, omega 2 is an angular velocity component of the pitching axis, omega 3 is an angular velocity component of the yawing axis, and I 3×3 is a unit matrix of 3 multiplied by 3; /(I)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:
Wherein, J 0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 is the nominal moment of inertia matrix part, deltaJ is the unknown moment of inertia matrix perturbation part for describing the uncertainty of the internal parameter moment of inertia, Is the first derivative of ω,/>Is a cross-product matrix of vector ω,/>D 0 +Δd is an actual installation matrix of the spacecraft attitude control actuator, D 0 +Δd is a matrix with a size of 3×n, n represents the number of actuators, D 0 is a nominal installation matrix, Δd is an unknown installation matrix perturbation part, and is used for describing the uncertainty of an internal parameter installation matrix; τ is an actual output torque vector of the actuator, τ= [ τ 1,τ2,…τn]T,τi is an actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is a saturation function acting on the output torque vector τ, and is used for describing saturation limiting constraint of the actuator, and T d represents an unknown bounded disturbance torque acting on the attitude control system by an external space environment, and mainly comprises a gravity gradient torque, a aerodynamic torque, a solar radiation pressure torque, a remanence torque and the like, so as to meet ||t d||＜Tmax;
According to The kinetic equation is rewritten as follows:
wherein the upper subscript-1 represents the inverse of the matrix,
Considering the failure of the actuators in the attitude control system (mainly including additive and multiplicative failures), τ i is denoted as:
Wherein τ ci is the command torque of the ith actuator, λ i is the failure loss degree of the ith actuator, satisfying 0.ltoreq.λ i.ltoreq.1, when λ i =0, indicating that the actuator has no failure, when λ i =1, indicating that the actuator has complete failure, 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, f d represents an equivalent fault of the attitude control system, which comprises an actuator multiplicative fault, an additive fault, internal parameter perturbation and external environment disturbance, f d＝f1 +d; ω is the angular rate signal that can be measured by the actual system, ω a is the actual value of the angular velocity in the attitude control system, and η is the angular rate gyro measurement noise.
In order to realize the active fault-tolerant control of the attitude control system, accurate information of the equivalent fault f d is required to be obtained first, and then the fault-tolerant controller can be designed based on the fault information to meet the performance requirement.
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(τ1),sat(τ2),…sat(τn)]T (7)
Where τ max is the maximum output torque of a single actuator, |τ i | represents the absolute value of τ i and sign (τ i) is a sign function.
Other steps and parameters are the same as in one to three embodiments.
Fifth embodiment: this embodiment differs from one to four embodiments in that the sign function sign (τ i) is:
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, Representing an estimate of the observer diagonal velocity component ω (t)/(Is/>First derivative of,/>For/>Cross matrix of,/>Representing the estimated value of the equivalent fault f d (t) at the time t by the adaptive sliding mode iterative learning observer, and defining/>Representing the estimated error of the observer for the angular velocity component ω (t), κ 1,κ3,κ4 being the positive constant gain, sgn [. Cndot ] representing the sign operation on the vector,/>For the estimated value of equivalent fault f d (T-T) of the adaptive sliding mode iterative learning observer, T represents the learning time interval of the adaptive sliding mode iterative learning observer, κ 2(t),κ5 (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 sign operation of vector a= [ a 1,a2,…,an]T, expressed in the form of
Wherein,Represents the estimated value of the angular velocity component omega (0) of the self-adaptive sliding mode iterative learning observer at the initial moment, and gamma 1,γ2 is positive gain,/>Delta is an integral variable which is a preliminary rough estimation value;
The specific expression of the adaptive time-varying gain kappa 2(t),κ5 (t, s (t)) of the adaptive sliding mode iterative learning observer is as follows:
In the formula, I II represents taking 2-norm operation, kappa 5 is the minimum value of the adaptive time-varying gain kappa 5 (t, s (t)), Is the first derivative of κ 2 (t), and α, μ and ε are positive constants.
Compared with the traditional observer, the method of the invention 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 d＝[qd0,qdv]T＝[qd0,qd1,qd2,qd3]T for spacecraft attitude control, wherein the target quaternion is used for describing attitude instruction information, and the error quaternion q e is as follows: For quaternion multiplication ,qe＝[qe0,qev]T＝[qe0,qev,1,qev,2,qev,3]T,qe0, the scalar portion of quaternion q e, q ev＝[qev,1,qev,2,qev,3]T, the vector portion of quaternion q e;
The error angular velocity ω e defining the spacecraft attitude control system is: omega e＝ωd-ω,ωd 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 gesture position of the system at the current moment and the position of the newly received target gesture instruction, namely calculating an error quaternion, converting the error quaternion into an error Euler angle omega e＝[Ωe1,Ωe2,Ωe3]T, and if I omega e||∞ is more than or equal to 0.0001, considering that a discontinuous control instruction appears;
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 four, calculating a preset performance function ρ j (t') of the jth refresh as follows:
Wherein, beta 1,β2,β3,β4 is a parameter to be designed, t fj represents the terminal time of the jth refreshing, namely the predetennined convergence time given by a user, namely the settable terminal time when the performance function reaches a steady-state value, k and b are adjustable parameters for adjusting the preset performance shape boundary, and the adjustable parameters can be selected according to actual conditions, and other constants in the invention can be selected according to actual conditions; each time the preset performance function ρ j (t ') is refreshed, the time t ' therein starts from 0, which only represents that the time in the preset performance function starts from 0 time, for example, for the jth refresh, the control amount of the actual time t j at the present refresh is output based on the preset performance function after the jth refresh, and not represents that the actual control time at the present time is 0, which can be understood as that the time t ' =0 corresponds to t=t j; the preset lower performance bound ρ d,j and the preset upper performance bound ρ u,j for the jth refresh are then:
Wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) is a value of an ith component of an error quaternion vector part at a time t ' =0, ρ ∞,j is a preset performance function steady-state terminal boundary refreshed for the jth time, ψ 1 (t ') is a time-varying self-regulating item of a preset performance upper bound, and ψ 2 (t ') is a time-varying self-regulating item of a preset performance lower bound;
Defining epsilon (t ') as an attitude error under an unconstrained space obtained by error conversion of an error quaternion vector part q ev through a preset performance function, wherein epsilon (t ')= [ epsilon 1(t′),ε2(t′),ε3(t′)]T, epsilon (t ') is specifically as follows:
wherein q ev (t ') is the value of the error quaternion vector portion q ev at time t', Is the first derivative of ε (t')/(Is the first derivative of q ev (t')/(Is the first derivative of ρ u,j (t')/>A first derivative of ρ d,j (t');
The said And/>The method comprises the following steps:
Wherein, Is the first derivative of ψ 1 (t'),/>For/>Is the first derivative of (a);
The calculation method of the virtual control saturation comprises the following steps:
wherein u v (t') is a virtual control quantity to be designed, Is the fault estimated value corresponding to the actual time t j of the jth refreshing;
Where s ' (t ') is a sliding surface, s ' (t ')=λ ' 1ε(t′)+ωe(t′),λ′1,λ′2,λ′3 is a normal number;
sig(s(t))r＝[|s1(t)|rsign(s1(t)),|s2(t)|rsign(s2(t)),|s3(t)|rsign(s3(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 ev of the systematic error quaternion is always within the performance boundary constraint given by user definition, namely ρ d(t)＜qev,i′(t)＜ρu (t), i' =1, 2,3, and 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: the difference between this embodiment and one of the first to seventh embodiments is that the method for calculating the parameter β 1,β2,β3,β4 to be designed is as follows:
Wherein ρ 0,j is the preset performance function initial error boundary of the jth refresh, ρ ∞,j is the preset performance function steady-state terminal boundary of the jth refresh, and ρ 0,j and ρ ∞,j are manually specified by the user when j=0 is the initial operation stage of the system.
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 specific embodiments in that the time-varying self-adjustment term ψ 1 (t ') of the upper preset performance bound and the time-varying self-adjustment term ψ 2 (t') of the lower preset performance bound are:
/>
Wherein, Is an intermediate variable,/>For the integral initial value, σ 1,σ2,σ3,σ4 is the positive gain parameter, 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: the difference between this embodiment and one of the first to ninth embodiments is that the initial error boundary ρ 0,j of the preset performance function of the jth refresh, the steady-state terminal boundary ρ ∞,j of the preset performance function of the jth refresh, and the terminal time t fj of the jth refresh are:
Wherein c 1,c2 is a positive gain parameter, θ i′ is a difference between an i 'th axis attitude angle target and a current attitude angle, J i′i′ is an i' th diagonal element of a moment of inertia matrix J 0, 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 invention are only for describing the calculation model and calculation flow of the present invention in detail, and are not limiting of the embodiments of the present invention. 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 invention.
Claims (9)
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;
the dynamic equation of the spacecraft attitude control system is as follows:
Wherein, J 0 +DeltaJ is the actual moment of inertia matrix of the spacecraft, J 0 is the nominal moment of inertia matrix part, deltaJ is the unknown moment of inertia matrix perturbation part, Is the first derivative of ω, ω is the angular velocity component of the spacecraft body reference frame relative to the spatial inertial reference frame, ω= [ ω 1,ω2,ω3]T, ω x is the cross-multiplication matrix of the vector ω,D 0 +Δd is the actual installation matrix of the spacecraft attitude control actuator, D 0 +Δd is a matrix of size 3×n, n represents the number of actuators, D 0 is the nominal installation matrix, Δd is the unknown perturbation part of the installation matrix; τ is an actual output torque vector of the actuator, τ= [ τ 1,τ2,…τn]T,τi ] is an actual output torque of the ith actuator, i=1, 2, …, n, sat (τ) is a saturation function acting on the output torque vector τ, and T d represents an unknown bounded disturbance torque of the external spatial environment acting on the attitude control system;
According to The kinetic equation is rewritten as follows:
wherein the upper subscript-1 represents the inverse of the matrix, D＝D0+ΔD；
Considering the failure of an actuator in a attitude control system, τ i is denoted as:
Wherein τ ci is the command torque of the ith actuator, lambda i is the degree 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 f d represents an equivalent fault of the attitude control system, f d＝f1+d;ωa is an actual value of angular velocity in the attitude control system, and eta is angular rate gyro measurement noise;
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, q= [ q 0,q1,q2,q3]T,q0 is the scalar part of quaternion q, Is the first derivative of q 0,/>Is the 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 yawing 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, omega= [ omega 1,ω2,ω3]T,ω1 ] is an angular velocity component of the rolling axis, omega 2 is an angular velocity component of the pitching axis, omega 3 is an angular velocity component of the yawing axis, and I 3×3 is a unit matrix of 3 multiplied by 3; /(I)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 saturation function sat (τ) is:
sat(τ)＝[sat(τ1),sat(τ2),…sat(τn)]T (7)
Where τ max is the maximum output torque of a single actuator, |τ i | represents the absolute value of τ i and sign (τ i) is a sign function.
4. A spacecraft attitude initiative fault tolerance control method with self-adjusting preset performance constraints according to claim 3, wherein the sign function sign (τ i) is:
5. The spacecraft attitude initiative fault-tolerant control method with self-adjusting preset performance constraints of claim 4, wherein the adaptive sliding mode iterative learning observer is:
Wherein ω (t) represents the value of the angular velocity component ω at time t, Representing an estimate of the observer diagonal velocity component ω (t)/(Is/>First derivative of,/>For/>Cross matrix of,/>Representing the estimated value of the equivalent fault f d (t) at the time t by the adaptive sliding mode iterative learning observer, and defining/> Representing the estimated error of the observer for the angular velocity component ω (t), κ 1,κ3,κ4 is the positive constant gain, sgn [ · ] represents the sign operation of the vector,For the estimated value of equivalent fault f d (T-T) of the adaptive sliding mode iterative learning observer, T represents the learning time interval of the adaptive sliding mode iterative learning observer, κ 2(t),κ5 (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, Represents the estimated value of the angular velocity component omega (0) of the self-adaptive sliding mode iterative learning observer at the initial moment, and gamma 1,γ2 is positive gain,/>Delta is an integral variable which is a preliminary rough estimation value;
The specific expression of the adaptive time-varying gain kappa 2(t),κ5 (t, s (t)) of the adaptive sliding mode iterative learning observer is as follows:
In the formula, I II represents taking 2-norm operation, kappa 5 is the minimum value of the adaptive time-varying gain kappa 5 (t, s (t)), Is the first derivative of κ 2 (t), and α, μ and ε are positive constants.
6. The spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraints according to claim 5, 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 d＝[qd0,qdv]T＝[qd0,qd1,qd2,qd3]T for spacecraft attitude control, wherein the error quaternion q e is as follows: For quaternion multiplication ,qe＝[qe0,qev]T＝[qe0,qev,1,qev,2,qev,3]T,qe0, the scalar portion of quaternion q e, q ev＝[qev,1,qev,2,qev,3]T, the vector portion of quaternion q e;
The error angular velocity ω e defining the spacecraft attitude control system is: omega e＝ωd-ω,ωd 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 four, calculating a preset performance function ρ j (t') of the jth refresh as follows:
where beta 1,β2,β3,β4 is the parameter to be designed, 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 preset lower performance bound ρ d,j and the preset upper performance bound ρ u,j for the jth refresh are then:
Wherein a is a performance boundary shape parameter given by a user, q ev,i′ (0) is a value of an ith component of an error quaternion vector part at a time t ' =0, ρ ∞,j is a preset performance function steady-state terminal boundary refreshed for the jth time, ψ 1 (t ') is a time-varying self-regulating item of a preset performance upper bound, and ψ 2 (t ') is a time-varying self-regulating item of a preset performance lower bound;
Defining epsilon (t ') as an attitude error under an unconstrained space obtained by error conversion of an error quaternion vector part q ev through a preset performance function, wherein epsilon (t ')= [ epsilon 1(t′),ε2(t′),ε3(t′)]T, epsilon (t ') is specifically as follows:
wherein q ev (t ') is the value of the error quaternion vector portion q ev at time t', Is the first derivative of epsilon (t'),Is the first derivative of q ev (t')/(Is the first derivative of ρ u,j (t')/>A first derivative of ρ d,j (t');
The said And/>The method comprises the following steps:
Wherein, Is the first derivative of ψ 1 (t'),/>For/>Is the first derivative of (a);
The calculation method of the virtual control saturation comprises the following steps:
wherein u v (t') is a virtual control quantity to be designed, Is the fault estimated value corresponding to the actual time t j of the jth refreshing;
where s ' (t ') is a sliding surface, s ' (t ')=λ ' 1ε(t′)+ωe(t′),λ′1,λ′2,λ′3 is a normal number;
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.
7. The spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraints according to claim 6, wherein the calculation method of the parameter β 1,β2,β3,β4 to be designed is as follows:
Wherein ρ 0,j is the preset performance function initial error boundary of the jth refresh, and ρ ∞,j is the preset performance function steady-state terminal boundary of the jth refresh.
8. The spacecraft attitude initiative fault tolerance control method with self-adjusting preset performance constraints of claim 7, wherein the time-varying self-adjusting term ψ 1 (t ') for the upper preset performance bound and the time-varying self-adjusting term ψ 2 (t') for the lower preset performance bound are:
Wherein, Is an intermediate variable,/>For the integral initial value, σ 1,σ2,σ3,σ4 is the positive gain parameter, n (delta) is the virtual control saturation,/>Is the first derivative of the attitude error epsilon (delta).
9. The spacecraft attitude initiative fault-tolerant control method with self-adjusting preset performance constraints of claim 8, wherein the jth refreshed preset performance function initial error boundary ρ 0,j, the jth refreshed preset performance function steady-state terminal boundary ρ ∞,j, and the jth refreshed terminal timeThe method comprises the following steps:
Wherein c 1,c2 is a positive gain parameter, θ i′ is a difference between an i 'th axis attitude angle target and a current attitude angle, J i′i′ is an i' th diagonal element of a moment of inertia matrix J 0, Representing an estimate of the ith actuator fault, t j is the actual time at the jth refresh.
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