CN108508751A - A kind of input saturation Adaptive Attitude collaboration tracking and controlling method - Google Patents

Abstract

The invention relates to an input saturation adaptive attitude cooperative tracking control method, which belongs to the technical field of multi-spacecraft formation flight; the method absorbs the double power algorithm to make the formation system fast and stable, and dynamically adjusts the function to optimize the control gain to reduce the occurrence rate of saturation. Based on the advantages of saturation function control, input saturation limit, adaptive law to suppress interference, and compensation for inertia time-varying uncertainty, an input saturation adaptive attitude cooperative tracking control method is proposed, which can enable spacecraft formation members to quickly complete attitude coordination track. The invention comprehensively considers the influence of input saturation, interference, inertia time variation, etc., improves the input saturation cooperative tracking control strategy, can quickly stabilize the cooperative tracking error system, and further improves the robustness and practicability of the control system.

Description

An Input Saturation Adaptive Attitude Cooperative Tracking Control Method

technical field

The invention belongs to the technical field of multi-spacecraft formation flight, in particular to an input saturation adaptive attitude cooperative tracking control method.

Background technique

With the development of society, space missions such as earth observation, on-orbit maintenance, and deep space exploration are booming, and the system scale of a single spacecraft is becoming larger and larger. For some load systems that require long baselines and multi-point synchronous work The task of ability cannot be completed at all. Multiple spacecraft working together in formation can not only reduce the cost of the task, but also have stronger robustness, and can even complete tasks that a single spacecraft could not complete in the past. When performing space missions, multiple spacecraft can cooperate to achieve functional reorganization, not just the function superposition of a single spacecraft, and more optimized control effects can be obtained in terms of resources and efficiency. Cooperative tracking of spacecraft attitude is an important feature of spacecraft formation flight control.

In recent years, scholars at home and abroad have carried out extensive research on the cooperative control of spacecraft formation flight attitude, and proposed robust adaptive consensus control, finite-time attitude cooperative control, fast terminal sliding mode surface control and switched topology attitude tracking control, etc. method. Due to the complex space environment in which the spacecraft is located, it will be subject to external interference such as gravity gradients and solar radiation. At the same time, 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. In addition, , the actuator torque mechanism of the spacecraft is constrained by its own physical characteristics, and its output torque cannot be any required control force. There is a saturation limit of the actuator, that is, the spacecraft input saturation constraint.

Based on the above situation, there is an urgent need for an adaptive attitude cooperative control method with input saturation constraints, which can consider the influence of input saturation, external disturbance and inertia changes on the spacecraft control performance, and increase the robustness of the attitude system tracking system.

Contents of the invention

The purpose of the present invention is to provide an input saturation adaptive posture cooperative tracking control method.

The technical solution to realize the object of the present invention is: an input saturation adaptive posture cooperative tracking control method, comprising the following steps:

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

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

Step 3, define error auxiliary variable;

Step 4. The communication topology of the spacecraft formation system includes a directed spanning tree, and the virtual leader is the root node. Through the communication strategy of the directed communication topology graph, the attitude and angular velocity information of each spacecraft communicating with adjacent spacecraft is obtained;

Step 5, according to the auxiliary variables in step 3 and the state information such as the attitude and angular velocity of the adjacent spacecraft obtained, design the attitude cooperative consistency control algorithm controller;

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. Design a fast and stable controller according to its own state information;

Step 8, designing dynamic optimization parameters to obtain an adaptive attitude cooperative tracking controller;

Step 9. Design and input the saturated adaptive attitude cooperative tracking controller, and judge whether the adaptive attitude cooperative tracking controller reaches saturation in step 8. If it reaches saturation, the controller inputs the torque saturation limit value. If it does not reach the saturation value, the controller The input value is the control torque less than the limit value required to complete the task.

The present invention considers input mechanism saturation, external disturbance and inertia change more perfectly, and has the advantages compared with the prior art: (1) no separate estimation of unknown time-varying inertia, simple controller structure, and easy engineering implementation; 2) No prior knowledge of inertia and disturbance is required, such as the nominal value of inertia and the upper limit of disturbance; (3) Dynamic optimization of parameters can reduce the frequency of saturation; (4) Fast and stable controllers can use The error system is more rapid and stable; (5) The trajectory of the leader is time-varying, not a static position.

Description of drawings

FIG. 1 is a schematic diagram of the input saturation adaptive attitude cooperative tracking 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 cooperative tracking error diagram of the attitude and angular velocity of the following spacecraft 1 in a specific embodiment.

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

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

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

Fig. 7 is a curve diagram of input control torques of following spacecraft 1 and 2 in a specific embodiment.

Fig. 8 is a curve diagram of input control torques of following spacecraft 3 and 4 in a specific embodiment.

Detailed ways

In conjunction with Fig. 1, a kind of input saturation adaptive posture cooperative tracking control method of the present invention comprises the following steps:

Step 1. The formation includes n follower spacecraft and 1 virtual 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, I represents the identity matrix, J _i ∈ ^{R 3×3} is the spacecraft inertia matrix, τ _i ∈ R ³ and τ _id ∈ R ³ represent the control moment of the spacecraft and the external bounded disturbance moment respectively, and represent the derivative of the variable, namely are the derivatives of attitude quaternion and angular velocity respectively, and × means the meaning of oblique symmetric matrix, namely is the oblique symmetric matrix of ω _i =[ω _i1 ,ω _i2 ,ω _i3 ] ^T

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 and satisfies ω _ie ＝ω _i -N _i ω _r is the angular velocity error, and ω _r ∈ R ³ are the attitude unit quaternion vector and angular velocity vector of the leader, respectively, is the coordinate rotation matrix;

Step 3. Define the error auxiliary variable S _i =βq _ie +ω _ie , and its time derivative is In the formula, and satisfied φ _i ＝1+||ω _i ||+||ω _i || ² ;

Step 4. The communication topology of the spacecraft formation system includes a directed spanning tree, and the virtual leader is the root node. It is set that the leader information can be obtained by the followers, and a _ij is an adjacency matrix element. If there is In the communication of i, a _ij >0; on the contrary, a _ij =0; b _i =a _i0 is the leader adjacency matrix element;

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 5. According to the auxiliary variables in step 3 and the obtained state information such as the attitude and angular velocity of adjacent spacecraft, design the attitude cooperative consistency control algorithm controller

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 In the formula is the estimated value of the uncertainty parameter c _i ;

Step 7. Design a fast and stable controller according to its own state information, In 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 _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, sign( ) is a sign function,

Step 8. Design dynamic optimization parameters It can reduce the probability of input saturation and make the system stable quickly. Therefore, the adaptive attitude cooperative tracking controller is

Step 9. Design the input saturated adaptive attitude cooperative tracking controller, and judge whether the adaptive attitude cooperative tracking controller is saturated in step 8. If it is saturated, τ _i =-T _imax S _i /||S _i ||, if did not reach saturation which is:

In the formula, ρ represents the ρth actuator of any spacecraft, T _imax =diag[τ _i1max ,τ _i2max ,τ _i3max ], k _i >0, k _i1 >0, 0<α=α ₁ /α ₂ <1, α ₁ and α ₂ are relatively prime positive odd numbers, 0<δ _i ≤0.5, 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 virtual leader is used as the research object, and the specific parameters are as follows:

Table 1. Spacecraft inertia matrix and initial attitude

The desired trajectory of the spacecraft: q _r =0.2[cos(0.2t),sin(0.2t),2sin(0.2t)] ^T , The angular velocity can be obtained by formula (2). The input torque saturation value is τ _1max ＝[4,5,3] ^T Nm, τ _2max ＝[5,5,6] ^T Nm, τ _3max ＝[7.5,6,6.5] ^T Nm, τ _4max ＝[3, 5.5,4.5] ^T Nm. External disturbance τ _id =(5+10||ω _i || ² )[0.02sin(t), 0.05cos(t), 0.03cos(t)] ^T . The controller parameters are k ₁ =k ₂ =k ₃ =k ₄ =50, k ₁₁ =k ₂₁ =k ₃₁ =k ₄₁ =50, α=7/9, β=1, β ₁₁ =β ₂₁ =β ₃₁ =β ₄₁ =0.01, β ₁₂ =80, β ₁₄ =β ₂₄ =β ₃₄ =β ₄₄ =0.1, β ₂₂ =60 and β ₃₂ =β ₄₂ =100.

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 virtual 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 realized the tracking of the leader spacecraft with a time-varying reference trajectory , it can be seen from the error magnification diagram that the error precision reaches 3×10 ^-4 .

Figure 7 and Figure 8 show the input control torque curves of spacecraft 1, 2, 3, and 4. It can be seen that during the entire cooperative tracking process of the spacecraft, the input saturation only occurs between 0 and 2s, and then the Quickly adjust the spacecraft to track the navigator.

From the above embodiments, it can be verified that the present invention improves the input saturation cooperative tracking control strategy, compensates the influence of inertia change and external disturbance by designing an adaptive law, and can make the cooperative tracking error system quickly stable, further improving the control system. robustness and practicality.

Claims (10)

1. An input saturation adaptive posture cooperative tracking control method is characterized by comprising the following steps:

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

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

step 3, defining an error auxiliary variable;

step 4, the communication topology of the spacecraft formation system comprises a directed spanning tree, the virtual leader is a root node, and the attitude and angular velocity information of each spacecraft communication adjacent spacecraft is obtained through a directed communication topological graph communication strategy;

step 5, designing a posture cooperative consistency control algorithm controller according to the auxiliary variables in the step 3 and the obtained state information of the adjacent spacecrafts such as the postures and the angular speeds;

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 rapid and stable controller according to the self state information;

step 8, designing dynamic optimization parameters to obtain a self-adaptive posture cooperative tracking controller;

and 9, designing an input saturation adaptive attitude cooperative tracking controller, judging whether the adaptive attitude cooperative tracking controller in the step 8 is saturated, inputting a torque saturation amplitude limit value by the controller if the adaptive attitude cooperative tracking controller is saturated, and inputting a control torque which is smaller than the amplitude limit value and is required for completing a task by the controller if the adaptive attitude cooperative tracking controller is not saturated.

2. The input saturation adaptive attitude collaborative tracking control method according to claim 1, wherein the quaternion attitude kinematics and kinetic equations established in step 1 are:

wherein,is a quaternion vector of attitude units, ω_i∈R³Representing angular velocity vector of a spacecraft body coordinate system relative to an inertia coordinate system, I representing an identity matrix, J_i∈R^3×3Is a spacecraft inertia matrix, tau_i∈R³And τ_id∈R³Respectively representing the control moment and the externally bounded disturbance moment of the spacecraft; derivatives of the representative 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 of

3. The input saturation adaptive attitude collaborative tracking control method according to claim 2, wherein the attitude kinematic and dynamic error equations in step 2 are as follows:

wherein,andis an attitude quaternion error and satisfiesω_ie＝ω_i-N_iω_rIs the error in the angular velocity of the object,and ω_r∈R³Respectively the attitude unit quaternion vector and the angular velocity vector of the leader,is a coordinate rotation matrix.

4. The input saturation adaptive posture cooperative tracking control method according to claim 3, wherein the step 3 is specifically:

defining an error auxiliary variable S_i＝βq_ie+ω_ieHaving a time derivative ofwherein, beta is more than 0,and satisfyφ_i＝1+||ω_i||+||ω_i||²。

5. The input saturation adaptive posture cooperative tracking control method according to claim 4, wherein the step 4 is specifically:

the communication topology of the spacecraft formation system comprises a directed spanning tree, a virtual leader is a root node, and a leading node is setLeader information can be obtained by the 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;

obtaining the attitude of each spacecraft communicating with the adjacent spacecraft through a communication strategy of a directed communication topological graphAnd angular velocity information ω_j∈R³。

6. The input saturation adaptive posture cooperative tracking control method according to claim 5, wherein the step 5 is specifically:

designing a posture cooperative consistency control algorithm controller according to the auxiliary variables obtained in the step 3 and the obtained posture and angular speed state information of the adjacent spacecrafts

7. The input saturation adaptive posture cooperative tracking control method according to claim 6, wherein step 6 specifically is:

designing an interference suppression and inertia change compensation controller according to the self state information and the acquired state information of the adjacent spacecraftIn the formulaIs an uncertainty parameter c_iAn estimate of (d).

8. The input saturation adaptive posture cooperative tracking control method according to claim 7, wherein the step 7 is specifically:

according to the self state information, a fast stable controller is designed,in 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 alpha₂Is a relatively prime odd number, sign (·) is a sign function,

9. the input saturation adaptive posture cooperative tracking control method according to claim 8, wherein step 8 is specifically:

designing dynamic optimization parametersThe adaptive attitude cooperative tracking controller is characterized in that the input saturation occurrence probability is reduced and the system can be rapidly stabilized

10. The input saturation adaptive posture cooperative tracking control method according to claim 9, wherein step 9 is specifically:

designing an input saturation self-adaptive posture cooperative tracking controller, judging whether the self-adaptive posture cooperative tracking controller in the step 8 is saturated, and if so, determining tau_i＝-T_imaxS_i/||S_iIf the saturation value is not reachedNamely:

where ρ represents the ρ -th actuator of any spacecraft, T_imax＝diag[τ_i1max,τ_i2max,τ_i3max]，k_i＞0，k_i1＞0，0＜α＝α₁/α₂＜1，α₁and alpha₂Is a prime odd number of each other, 0 < delta_i≤0.5，β_i1＞0，β_i2> 0 and β_i4＞0。