CN108628330A - A kind of spacecraft amplitude limit Adaptive Attitude collaboration fault tolerant control method - Google Patents

Abstract

The invention relates to a space vehicle limiting self-adaptive attitude cooperative fault-tolerant control method, which belongs to the technical field of multi-spacecraft formation flight; the redundant fault-tolerant algorithm is used to process the failure of the spacecraft, and the torque saturation controller is controlled to perform torque limiting and self-adaptive control. Algorithm control items compensate for inertia changes and external disturbances, and fast convergence control algorithms enable rapid attitude coordination. A limited adaptive attitude cooperative fault-tolerant control method for spacecraft is proposed. The present invention considers the failure of the torque actuator, the torque limit, the external disturbance and the uncertainty of the inertia change more perfectly, can make the spacecraft cooperative tracking error system converge quickly, and further improves the robustness and practicability of the control system .

Description

A Cooperative Fault-Tolerant Control Method for Spacecraft Limit Adaptive Attitude

technical field

The invention belongs to the technical field of multi-spacecraft formation flight, in particular to a space vehicle limiting adaptive attitude cooperative fault-tolerant control method.

Background technique

With the diversification of space missions, the traditional working mode of a single spacecraft alone can no longer meet the needs of practical engineering. In this context, the research on multi-spacecraft formation flight has developed rapidly and has become one of the research hotspots in recent years.

The so-called multi-spacecraft formation refers to a working system composed of two or more spacecraft with close distances and interactive cooperation. Adjacent individuals in the formation realize information transmission and cooperative attitude control through sensor measurement devices, so as to achieve space detection and maintenance tasks. The formation of multiple small spacecraft solves the physical performance constraints of traditional single spacecraft such as payload volume and mass, and improves the reconfigurability and robustness of the overall system. Attitude coordination of multiple spacecraft is an important feature of spacecraft formation flight control.

With the continuous deepening of human research in the field of aerospace, more and more major space missions have been put into engineering practice. However, due to the special operating environment and complex structure of the spacecraft, sometimes failures inevitably occur, and eventually the mission fails. It has caused serious losses and impacts on sociopolitical, economic and even military aspects, and people are increasingly aware of the importance of reliability and fault handling for spacecraft. In addition, the spacecraft will be subject to disturbance moments caused by gravity gradients and solar radiation, and due to the influence of fuel consumption and the rotation of solar panels, the inertia of the spacecraft is constantly changing and the degree of change is unknown. At the same time, the spacecraft’s The actuator is constrained by its own physical characteristics, and its output torque cannot be any required control force, and there is a torque limit. Based on the above situation, there is an urgent need for a limited adaptive attitude cooperative fault-tolerant control method, which can simultaneously consider the influence of actuator failure, torque limiting, disturbance torque and inertia changes on the spacecraft control performance, and increase the robustness of the attitude cooperative system. sex.

Contents of the invention

The object of the present invention is to provide a space vehicle limitation adaptive attitude cooperative fault-tolerant control method which simultaneously considers actuator failure, torque limitation, disturbance torque and inertia change.

The technical solution to realize the object of the present invention is: a space vehicle limiting self-adaptive attitude cooperative fault-tolerant control method, comprising the following steps:

Step 1. The formation includes n follower spacecraft and 1 leader spacecraft. Taking the rigid body spacecraft as the research object, establish its quaternion attitude kinematics and dynamic equations;

Step 2. Establishing attitude kinematics and dynamic tracking error equations between the follower and the leader according to the coordinate transformation;

Step 3. Use algebraic graph theory to describe the communication topology of the spacecraft formation system; the communication topology of the spacecraft formation system includes a directed spanning tree with the leader as the root node. Through the communication strategy of the directed communication topology graph, each The spacecraft communicates the attitude and angular velocity information of adjacent spacecraft;

Step 4, define the error auxiliary variable;

Step 5. Design a fault-tolerant consensus algorithm controller according to the auxiliary variables in step 4 and the obtained attitude and angular velocity state information of adjacent spacecraft;

Step 6, according to its own state information and the obtained state information of adjacent spacecraft, design interference suppression and inertia change compensation controller;

Step 7, designing a fast convergence controller;

Step 8, designing an adaptive attitude cooperative fault-tolerant controller;

Step 9. Design the limiting adaptive attitude cooperative fault-tolerant controller, judge whether the adaptive attitude cooperative fault-tolerant controller reaches the amplitude in step 8, if it reaches saturation, the controller generates torque saturation value, if not, the controller generates the attitude coordination The control torque required for the task is less than the magnitude.

Compared with the prior art, the present invention has the remarkable advantages as follows: (1) it is robust to the complete failure or decay failure of some actuators; (2) it does not separately estimate the unknown time-varying inertia, and the controller has a simple structure and is easy to Engineering implementation; (3) No prior knowledge of inertia and environmental disturbance is required, such as the nominal value of inertia and the upper limit of disturbance; (4) The fast convergence controller can make the error system converge faster and stabilize the error system than the conventional controller; (5) The trajectory path of the leader is time-varying, not a static position, but it is suitable for the case where the path is a fixed point.

Description of drawings

FIG. 1 is a schematic diagram of the clipping adaptive attitude cooperative fault-tolerant control method of the present invention.

Fig. 2 is a communication topology diagram between formation spacecraft in a specific embodiment of the present invention.

Fig. 3 is a diagram of the cooperative tracking error of the attitude and angular velocity of the following spacecraft 1 in the embodiment.

Fig. 4 is a cooperative tracking error diagram of the attitude and angular velocity of the following spacecraft 2 in the embodiment.

Fig. 5 is a diagram of the attitude and angular velocity cooperative tracking error of the following spacecraft 3 in the embodiment.

Fig. 6 is a diagram of the attitude and angular velocity cooperative tracking error of the following spacecraft 4 in the embodiment.

Fig. 7 is a control torque curve diagram of the following spacecraft 1 in the embodiment.

Fig. 8 is a control torque curve diagram of the following spacecraft 2 in the embodiment.

Fig. 9 is a control torque curve diagram of the following spacecraft 3 in the embodiment.

Fig. 10 is a control torque curve diagram of the following spacecraft 4 in the embodiment.

Detailed ways

In conjunction with Fig. 1, a kind of space vehicle limiting self-adaptive attitude cooperative fault-tolerant control method of the present invention comprises the following steps:

Step 1. The formation includes n follower spacecraft and 1 leader spacecraft. Taking the rigid body spacecraft as the research object, establish its quaternion attitude kinematics and dynamics equations as follows:

in, is the attitude unit quaternion vector, ω _i ∈ R ³ represents the angular velocity vector of the spacecraft body coordinate system relative to the inertial coordinate system, represents the derivative of the variable, that is are the derivatives of the attitude quaternion and the angular velocity, respectively, and ^× means the meaning of the oblique symmetric matrix, namely is the oblique symmetric matrix of ω _i =[ω _i1 ,ω _i2 ,ω _i3 ] ^T J _i ∈ R ^3×3 is the spacecraft inertia matrix, Γ _i ∈ R ^3×σ is the moment distribution matrix, M _i =diag{μ _i1 ,μ _i2 ,…,μ _iσ }∈R ^σ×σ is the moment effective matrix , μ _iσ = 1 means that the control torque is normal, μ _iσ = 0 means that the control torque is completely invalid, 0 ≤ μ _iσ ≤ 1 means that the torque begins to age and decline, τ _i ∈ R ^σ and τ _id ∈ R ³ respectively represent the control torque of the spacecraft and external bounded disturbance torque, σ>3, σ is the number of torque actuators, i=0,1,...,n, i=0 means the leader spacecraft, and the others are followers;

Step 2, establish the posture kinematics and dynamics error equation between the follower and the leader according to the coordinate transformation as follows:

in, and is the attitude quaternion error, ω _ie =ω _i -N _i ω ₀ is the angular velocity error, i=1,2,…,n, is the coordinate rotation matrix;

Step 3, describe the communication topology of the spacecraft formation system with algebraic graph theory, in order to reduce the communication path and avoid waste of resources, the present invention adopts a directed communication that includes a directed spanning tree and the leader is the root node with less traffic Topological structure, setting the leader information can be obtained by followers, a _ij is the adjacency matrix element, if there is communication from spacecraft j to i, a _ij >0; on the contrary, a _ij =0; b _i =a _i0 is Leader adjacency matrix elements;

Through the communication strategy of the directed communication topology graph, the spacecraft can obtain the attitude of each communicating adjacent spacecraft through the sensor and angular velocity information ω _j ∈ R ³ ;

Step 4. Define error auxiliary variable S _i =βq _ie +ω _ie , In the formula, β>0, and satisfied φ _i ＝1+||ω _i ||+||ω _i || ² ;

Step 5. Design a fault-tolerant consensus algorithm controller according to the auxiliary variables in step 4 and the obtained state information such as attitude and angular velocity of adjacent spacecraft In the formula, the parameter k _i >0;

Step 6. Design the disturbance suppression and inertia change compensation controller according to its own state information and the obtained state information of adjacent spacecraft Among them, the parameter is the estimated value of c _i , φ _i ＝1+||ω _i ||+||ω _i || ² , β _i3 >0;

Step 7. Design a fast-converging controller Where sig ^α (S _i )＝[sign(S _i1 )|S _i1 | ^α ,sign(S _i2 )|S _i2 | ^α ,sign(S _i3 )|S _i3 | ^α ] ^T , S _ix means S _i The xth element of , 0<α=α ₁ /α ₂ <1, α ₁ and α ₂ are coprime positive odd numbers, k _i1 >0, sign( ) is a sign function,

Step 8. Design the adaptive attitude cooperative fault-tolerant controller as

Step 9. Design the limiting adaptive attitude cooperative fault-tolerant controller, and judge whether the adaptive attitude cooperative fault-tolerant controller reaches the amplitude in step 8, and if it reaches τ _imax ＝diag(τ _i1max ,τ _i2max ,…,τ _iσmax ), if the saturation value is not reached That is, the controller is

In the formula, j represents the jth torque actuator of any spacecraft, _ki >0, β _i1 >0, β _i2 >0 and β _i4 >0.

Below in conjunction with embodiment the present invention is described in further detail:

Example

A formation system consisting of 4 follower spacecraft and 1 leader is used as the research object, and the specific parameters are as follows:

Table 1. Spacecraft inertia matrix and initial attitude

Leader trajectory: ω ₀ =[0.1sin(0.2t), 0.1cos(0.2t), 0.1cos(0.5t)] ^T , q ₀ and q ₀₀ can be obtained by kinematic equation (1). The total number of actuators σ = 6, the torque limit is τ _1max = [4,4,5,5,6,6] ^T Nm, τ _2max = [7,7,8,8,5,5] ^T Nm, τ _3max = [8,8,5,5,6,6] ^T Nm, τ _4max =[6,6,4,4,5,5] ^T Nm. External disturbance τ _id =(0.5+||ω _i || ² )[0.02sin(t), 0.05cos(t), 0.03cos(t)] ^T , i=1,2,3,4. The controller parameters are k ₁ =k ₂ =k ₃ =k ₄ =15, k ₁₁ =k ₂₁ =k ₃₁ =k ₄₁ =2, α=1/3, β=1, β ₁₁ =β ₂₁ =β ₃₁ =β ₄₁ =0.01, β ₁₄ =β ₂₄ =β ₃₄ =β ₄₄ =0.1, β ₁₂ =80, β ₃₂ =50, β ₂₂ =β ₄₂ =100.

Select the moment distribution matrix The moment effective matrix is

First, build the spacecraft formation system model in MATLAB/Simulink, and the simulation time is 20s.

Figure 2 shows a directed communication topology, including 4 follower spacecraft and 1 leader. The attitude and angular velocity collaborative tracking error curves of the spacecraft are shown in Figure 3, Figure 4, Figure 5, and Figure 6. From the error curves, it can be seen that the follower has achieved a fast tracking of the leader spacecraft with a time-varying reference trajectory. Tracking, from the error magnification diagram (embedded diagram), it can be seen that the error accuracy reaches the order of 10 ^-4 .

Figure 7, Figure 8, Figure 9, and Figure 10 show the control torque curves of spacecraft 1, 2, 3, and 4. It can be seen that during the entire cooperative fault-tolerant tracking process of the spacecraft, torque limiting occurs in the early stage of tracking , in addition, it can be seen from the moment effective matrix that when time t>12s, M ₁ (2), M ₂ (4), M ₃ (5), M ₄ (6) are 0, which means that the first 2 torque actuators, the 4th torque actuator of spacecraft 2, the 5th torque actuator of spacecraft 3, and the 6th torque actuator of spacecraft 4 have complete failures. Similarly, when time t＞ At 13s, M ₁ (4), M ₂ (2), M ₃ (1), and M ₄ (2) are 0, indicating that the fourth torque actuator of spacecraft 1 and the second torque actuator of spacecraft 2 Mechanisms, the first torque actuator of spacecraft 3, and the second torque actuator of spacecraft 4 have completely failed; the rest of the actuators have aging failures of varying degrees.

From the above-mentioned embodiments, it can be verified that the present invention improves the fault-tolerant control strategy of clipping adaptive attitude cooperative tracking, realizes the redundant fault-tolerant control method through reasonable torque distribution, and at the same time, designs the adaptive law to compensate the influence of inertia change and disturbance, Moreover, the spacecraft cooperative tracking error system can be quickly converged, and the robustness and practicability of the control system are further improved.

Claims (10)

1. A spacecraft amplitude limiting self-adaptive attitude collaborative fault-tolerant control method is characterized by comprising the following steps:

step 1, a formation comprises n following spacecrafts and 1 leader spacecrafts, and a quaternion attitude kinematics and a kinetic equation are established by taking a rigid body spacecraft as a research object;

step 2, establishing an attitude kinematics and dynamics tracking error equation between the follower and the leader according to coordinate transformation;

step 3, describing a communication topological structure of the spacecraft formation system by using an algebraic graph theory; the communication topological structure of the spacecraft formation system comprises a directed spanning tree, a leader is a root node, and attitude and angular velocity information of adjacent spacecrafts communicated by each spacecraft can be obtained through a directed communication topological graph communication strategy;

step 4, defining an error auxiliary variable;

step 5, designing a fault-tolerant consistency algorithm controller according to the auxiliary variables in the step 4 and the obtained attitude and angular speed state information of the adjacent spacecraft;

step 6, designing an interference suppression and inertia variation compensation controller according to the self state information and the obtained state information of the adjacent spacecraft;

step 7, designing a fast convergence controller;

step 8, designing a self-adaptive attitude cooperative fault-tolerant controller;

and 9, designing an amplitude limiting self-adaptive attitude cooperative fault-tolerant controller, judging whether the self-adaptive attitude cooperative fault-tolerant controller in the step 8 reaches the amplitude, if so, generating a torque saturation value by the controller, and if not, generating a control torque which is smaller than the amplitude and is required by the attitude cooperative task by the controller.

2. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 1, wherein quaternion attitude kinematics and kinetic equations established in the step 1 are as follows:

wherein,is a quaternion vector of attitude units, ω_i∈R³Representing the angular velocity vector of the spacecraft body coordinate system relative to the inertia coordinate systemRepresenting derivatives of variables, i.e.Are derivatives of the attitude quaternion and angular velocity, respectively, and x denotes the skew-symmetric matrix meaning, i.e.Is omega_i＝[ω_i1,ω_i2,ω_i3]^TIs diagonally symmetrical matrix ofI denotes an identity matrix, J_i∈R^3×3Is a spacecraft inertia matrix, Γ_i∈R^3×σIs a moment distribution matrix, M_i＝diag{μ_i1,μ_i2,…,μ_iσ}∈R^σ×σIs a moment effective matrix, mu_iσ1 denotes normal control torque, μ_iσ0 means complete failure of the control torque, 0. ltoreq. mu_iσ1 or less indicates that the moment begins to age and decline, tau_iE.g. R σ and τ_id∈R³The control torque and the externally bounded disturbance torque of the spacecraft are respectively represented, sigma is the number of torque actuators, sigma is more than 3, i is 0,1, …, n, i is 0, and the leader spacecraft and the others are followers.

3. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 2, wherein the attitude kinematic and dynamic error equations in the step 2 are as follows:

wherein,andis the attitude quaternion error, ω_ie＝ω_i-N_iω₀Is the angular velocity error, i ═ 1,2, …, n,is a coordinate rotation matrix.

4. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 3, wherein the step 3 specifically comprises:

describing a communication topology structure of a spacecraft formation system by using algebraic graph theory, wherein the communication topology comprises a directed spanning tree, a virtual leader is a root node, and leader information is set to be obtained by a follower, a_ijIs an element of the adjacency matrix, a if there is a communication from spacecraft j to i_ijIs greater than 0; in contrast, a_ij＝0；b_i＝a_i0Adjoining the matrix elements for the leader;

through a communication strategy of the directed communication topological graph, the spacecraft can obtain the postures of the adjacent communication spacecrafts through the sensorAnd angular velocity information ω_j∈R³。

5. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 4, wherein the step 4 specifically comprises: defining an error auxiliary variable S_i＝βq_ie+ω_ie，Wherein β is greater than 0,and satisfyφ_i＝1+||ω_i||+||ω_i||²。

6. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 5, wherein the step 5 specifically comprises: designing a fault-tolerant consistency algorithm controller according to the auxiliary variables in the step 4 and the obtained state information of the adjacent spacecrafts, such as the attitude, the angular velocity and the likeIn the formula, the parameter k_i＞0。

7. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 6, wherein the step 6 specifically comprises: designing an interference suppression and inertia change compensation controller according to the self state information and the acquired state information of the adjacent spacecraftWherein the parametersIs c_iIs estimated by_i＝1+||ω_i||+||ω_i||²，β_i3＞0。

8. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 7, wherein the step 7 specifically comprises: designing a fast convergence controllerIn the formula sig^α(S_i)＝[sign(S_i1)|S_i1|^α,sign(S_i2)|S_i2|^α,sign(S_i3)|S_i3|^α]^T，S_ixDenotes S_i0 < α ═ α₁/α₂＜1，α₁And α₂Is a prime odd number, k, of relative prime_i1> 0, sign (·) is a sign function,

9. the spacecraft amplitude limiting adaptive attitude cooperative fault-tolerant control method according to claim 8, wherein the adaptive attitude cooperative fault-tolerant controller is designed in step 8 as

10. The spacecraft amplitude limiting adaptive attitude collaborative fault-tolerant control method according to claim 9, wherein the step 9 specifically comprises:

designing an amplitude limiting self-adaptive attitude cooperative fault-tolerant controller, judging whether the self-adaptive attitude cooperative fault-tolerant controller in the step 9 reaches the amplitude value, and if so, judging whether the self-adaptive attitude cooperative fault-tolerant controller reaches the amplitude valueτ_imax＝diag(τ_i1max,τ_i2max,…,τ_iσmax) If the saturation value is not reachedThat is, the controller is

Wherein j represents the jth moment actuating mechanism of any spacecraft, k_i＞0、β_i1＞0、β_i2> 0 and β_i4＞0。