CN113220003A - Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft - Google Patents

Abstract

The invention relates to a hybrid non-fragile control method for attitude stability of a non-cooperative flexible composite spacecraft. The invention aims to solve the problem of high-precision and high-stability control of the attitude of a non-cooperative flexible assembly under complex multi-source disturbances, including measurement errors, actuator failures, and controller additive/multiplicative gain perturbations coexisting. 1. Separate unknown and uncertain inertial parameters into synthetic disturbances and model attitude dynamics into state space forms; 2. Construct synthetic disturbance terms including inertial parameters, actuator faults and other complex disturbances, and improve the state space equations in No. 1; 3. . Design a hybrid non-fragile controller considering the coexistence of additive/multiplicative gain perturbation; 4. Substitute three into two to construct a closed-loop attitude control system. 5. Derive the linear matrix inequality conditions that satisfy the stability of the system and use the toolbox to solve it; 6. Realize the attitude/modal integrated control of the non-cooperative flexible assembly under input constraints. The invention is used in the field of spacecraft attitude stability control.

Description

A hybrid non-fragile control method for attitude stability of a non-cooperative flexible composite spacecraft

technical field

The invention relates to a hybrid non-fragile control method for attitude stability of a flexible composite spacecraft after the capture of a space non-cooperative target.

Background technique

With the development of human spaceflight technology and the increase of space activities, space failure targets and space junk have increased year by year, occupying precious orbital resources and threatening the normal operation of other spacecraft. Such space targets cannot actively provide state information and inertia. parameter information, and its stable and high-precision on-orbit operation is affected by complex disturbances, which is a typical non-cooperative target. The capture and processing of such space targets is of great significance to the sustainable development of space activities, and the flexible combination formed after capture The high-precision and high-stability control of the attitude of the spacecraft is a very important link.

Under actual working conditions, the control of the post-capture composite spacecraft not only faces the problem of unknown state information and inertial parameter information, but also the uncertainty of model parameters, external disturbances, measurement errors, actuator failures, input saturation, control However, due to physical and safety constraints, there are limitations in the actual operation of the actuator. These unfavorable factors will lead to the performance degradation or even instability of the control system designed for the ideal situation.

At present, there is no hybrid non-fragile control method for non-cooperative flexible composite spacecraft that considers the above disadvantageous factors at the same time, especially when the controllers coexist with additive/multiplicative perturbations, and the time and accuracy to achieve stability cannot be guaranteed.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problem of non-cooperation in complex situations such as inertia unknown uncertainty, model parameter uncertainty, external disturbance, measurement error, actuator failure, input saturation, controller additive/multiplicative gain perturbation coexistence, etc. To solve the problem of high-precision and high-stability control of the attitude of a flexible composite spacecraft, a hybrid non-fragile control method for attitude stability of a non-cooperative flexible composite spacecraft is proposed.

A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method includes the following steps:

Step 1: Construct and separate the unknown and uncertain terms of inertial parameters, and at the same time consider the uncertainty of model parameters, and rewrite the attitude dynamics model of the non-cooperative flexible composite spacecraft with external interference into the form of state space equation.

Step 2: For the measurement error and actuator fault, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1.

Step 3: Aiming at the coexistence problem of controller gain additive/multiplicative perturbation, define controller parameters and design a hybrid non-fragile controller.

Step 4: Substitute the hybrid non-fragile controller into the attitude dynamics state space model of the non-cooperative flexible assembly including the comprehensive disturbance term, and establish a closed-loop system state space model.

Step 5. According to the Lyapunov stability theory and the linear matrix inequality method, deduce the sufficient conditions of the linear matrix inequality satisfying the system stability to solve the controller parameters in step 3 and substitute them into the controller, so that the state space model in step 4 is complete. .

Step 6: Under the condition of controlling the torque limit, the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible assembly are controlled to quickly achieve stability, and a certain control accuracy is guaranteed.

The beneficial effects of the present invention are:

Compared with the prior art, the present invention has the beneficial effects of unknown uncertainty of inertial parameters, uncertainty of model parameters, external disturbances, measurement errors, failures of actuators, input saturation, and additive/multiplicative gain perturbation of the controller. In the case of coexistence, the non-cooperative flexible composite spacecraft can quickly reach a high-precision and high-stability state, and the stabilization time does not exceed 150s, the attitude angle control accuracy is less than 0.01rad, the attitude angular velocity control accuracy is less than 0.01rad/s, and the modal displacement The control precision is less than 0.01, and the size of the control torque does not exceed 15Nm throughout the control process.

The hybrid non-fragile control method designed by the invention enables the flexible composite spacecraft to have unknown inertial parameters, model parameter uncertainties, external disturbances, measurement errors, actuator failures, input saturation, etc. The controller can quickly reach a stable state under complex disturbances such as the coexistence of additive/multiplicative gain perturbations to meet mission requirements.

Description of drawings

1 is a flowchart of a non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method of the present invention;

θ、ψ分别表示航天器的滚动角、偏航角和俯仰角，rad表示角度的单位为弧度；Fig. 2 is the change curve of the attitude angle of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller in the present invention,

θ and ψ represent the roll angle, yaw angle and pitch angle of the spacecraft, respectively, and rad represents the unit of the angle in radians;

Fig. 3 is the change curve of the attitude angular velocity of the non-cooperative flexible composite spacecraft under the action of the hybrid non-fragile controller in the present invention, ω _x , ω _y , ω _z respectively represent the components of the angular velocity on the three axes of the body coordinate system, rad/s indicates that the unit of angular velocity is radians per second;

Fig. 4 is the variation curve of the modal displacement of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller in the present invention, η ₁ , η ₂ , η ₃ , η ₄ are the four components of the modal displacement respectively;

Fig. 5 is the curve of the attitude angle accuracy of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller of the present invention, and the accuracy is represented by the two-norm of the attitude angle vector;

6 is a curve of the attitude angular velocity accuracy of the non-cooperative flexible composite spacecraft under the action of the hybrid non-fragile controller according to the present invention, and the accuracy is represented by the two-norm of the attitude angular velocity vector;

Fig. 7 is the curve of the modal displacement accuracy of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller according to the present invention, and the accuracy is represented by the two-norm of the modal displacement vector;

Fig. 8 is the change curve of the control torque in the present invention, u _x , u _y , and u _z respectively represent the components of the control torque on the three axes of the body coordinate system, and Nm represents the unit of the control torque is Newton meters.

Detailed ways

Specific embodiment 1: This embodiment is described with reference to FIG. 1 . A non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of this embodiment is characterized in that:

A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method includes the following steps:

Step 1. Construct and separate the unknown uncertainties of inertial parameters by introducing the nominal inertia matrix. At the same time, considering the uncertainties of model parameters, there will be irregularities of external disturbance moments (such as aerodynamic moments, gravity gradient moments, and geomagnetic moments). The attitude dynamics equation of the cooperative flexible assembly spacecraft is rewritten into the state space form;

Step 2: For the measurement error and the actuator fault, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1;

Step 3: Define the controller parameters and design a hybrid non-fragile controller when there is an additive/multiplicative perturbation in the controller at the same time;

Step 4. Substitute the controller model into the flexible spacecraft attitude dynamics state space model including the comprehensive interference term, and establish a closed-loop control state space model;

Step 5: According to the linear matrix inequality principle and the Lyapunov stability principle, solve the controller parameters in the third step and substitute them into the controller model, so that the state space model in the fourth step is complete.

Step 6. Under the condition that the control input limit is 15Nm, the attitude angle, attitude angular velocity and modal displacement of the controlled non-cooperative flexible composite spacecraft can be stabilized within 150s, and the stability accuracy of the attitude angle is less than 0.01 radian, The stabilization accuracy of attitude angular velocity is less than 0.01 radians per second, and the stabilization accuracy of modal displacement is less than 0.01.

Embodiment 2: This mode is different from Embodiment 1 in that:

2. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 1, it is characterized in that: described step 1 builds and separates the unknown uncertainty item of inertial parameter, considers model parameter uncertainty simultaneously , and rewrite the attitude dynamics equation of the flexible assembly with external disturbance torque (such as aerodynamic torque, gravity gradient torque, geomagnetic torque) into the state space form, and the specific process is as follows:

Define the local horizontal and local vertical coordinate system F _o (X _o , Y _o , Z _o ) (LVLH) as the reference coordinate system, the origin of the coordinate system is located at the center of mass of the non-cooperative composite body, the roll axis is along the flight direction, and the yaw axis points to the center of the earth , the pitch axis completes the right-handed coordinate system. Define the composite spacecraft body coordinate system _{FB (X B , Y B , Z B ) , the} origin is located at the center of mass of the non-cooperative composite body, and the three coordinate axes coincide with the inertial main axis of the composite body respectively.

Then the attitude kinematics equation of the flexible composite spacecraft is:

θ和ψ分别表示柔性组合体航天器的三个分量，即滚转、俯仰和偏航姿态角，ω₀表示柔性组合体所在的轨道角速度。在高轨组合体进行小角度姿态调整时，有：in,

θ and ψ represent the three components of the flexible assembly spacecraft, namely roll, pitch and yaw attitude angles, respectively, and ω ₀ represents the orbital angular velocity where the flexible assembly is located. When the high-orbit assembly performs small-angle attitude adjustment, there are:

If a piezoelectric actuator is coupled to the surface of the composite flexible attachment to provide an input voltage _up , resulting in a deformation that results in a control torque, the composite body and flexibility dynamics equations can be expressed as follows:

表示组合体本体的惯性矩阵，ω＝[ω_x ω_y ω_z]表示姿态角速度矢量，包含滚转、俯仰和偏航姿态角变化率，

表示刚体与组合体柔性结构之间的耦合系数矩阵，

表示相对组合体本体的模态坐标矢量，

和

表示控制输入力矩和外界干扰力矩；

表示模态阻尼矩阵，其中

和Ω_i,i＝1,2,…,m分别表示阻尼比和固有频率，

表示刚度矩阵，而m是所考虑的柔性模态的个数。此处，T_d包括重力梯度力矩、太阳辐射压力矩和空气动力矩，u_p表示压电输入电压，而

是对应的耦合系数矩阵。in,

represents the inertia matrix of the combined body, ω=[ω _x ω _y ω _z ] represents the attitude angular velocity vector, including the roll, pitch and yaw attitude angle change rates,

represents the coupling coefficient matrix between rigid body and composite flexible structure,

represents the modal coordinate vector relative to the assembly body,

and

Indicates the control input torque and external disturbance torque;

represents the modal damping matrix, where

and Ω _i , i=1,2,...,m represent damping ratio and natural frequency, respectively,

represents the stiffness matrix, and m is the number of flexible modes considered. Here, T _d includes gravity gradient moment, solar radiation pressure moment and aerodynamic moment, u _p represents the piezoelectric input voltage, and

is the corresponding coupling coefficient matrix.

得到：define auxiliary variables

get:

Substitute into the second equation in the non-cooperative flexible assembly attitude dynamics equations to get the rewritten equation:

Using real value feedback, the piezoelectric input u _p is expressed as:

代入辅助变量导数

和改写后的柔性组合体姿态动力学方程，得到：where F _a and F _b are measurement feedback coefficients. Will

Substitute the auxiliary variable derivative

and the rewritten attitude dynamics equation of the flexible assembly, we get:

可将上述两式改写为状态空间形式：make

The above two equations can be rewritten in state space form:

输出变量

u(t)＝T_c为控制力矩，

是综合干扰。系数矩阵：where the state variable

output variable

u(t)=T _c is the control torque,

is the combined interference. Coefficient matrix:

C＝I_6+2m

C=I6 _+2m

The unknown inertial parameter information is all reduced to the following coefficient matrix:

J_n为标称惯量矩阵。in

J _n is the nominal inertia matrix.

△A _p represents the model parameter uncertainty (except inertial uncertainty), which is norm bound and satisfies the matching condition:

where M ₁ and N ₁ are real constant matrices of suitable dimensions, and F ₁ (t) is a Lebesgue-measurable matrix function.

Other steps and parameters are the same as in the first embodiment.

Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that:

3. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 2, it is characterized in that: in the described step 2, for the existence of measurement error and actuator failure situation, construct actuator failure interference term and together with the unknown uncertainty term of inertial parameters and the external disturbance moment term in step 1 to form a comprehensive disturbance term; the specific process is as follows:

Improper action of the actuator will seriously affect the performance of the attitude control system, let E with full rank (its structure is similar to B1) represent the distribution matrix _of the fault signal f(t) appearing in the input. If E≠B ₁ , it means a process failure; if E=B ₁ , it means an actuator failure.

The above complex disturbance factors are constructed as synthetic disturbances:

是B₂的伪逆，步骤一中状态空间方程改写为：where the matrix

is the pseudo-inverse of B ₂ , and the state space equation in step 1 is rewritten as:

where v(t) represents the measurement error.

Other steps and parameters are the same as in the first or second embodiment.

Specific embodiment four: this embodiment is different from one of specific embodiments one to three in that:

4. a kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 3, is characterized in that: in the described step 3, when there is additive/multiplicative perturbation for the controller at the same time, define the controller parameters, design a hybrid non-fragile controller; the specific process is:

When the controller has additive/multiplicative perturbations at the same time, the form of designing the controller is as follows:

是控制器引入的状态变量，

是不考虑测量误差对输出变量的估计值，A_c、B_c是具有合适维度的控制器系数矩阵，K为控制器增益矩阵。控制器错误和未知的执行机构动力学特性会导致摄动问题，当△K是加法式摄动时，其数学表达式为△K＝M₂F₂(t)N₂,||F₂(t)||≤1，当△K是乘法式摄动时，其数学表达式为△K＝M₃F₃(t)N₃K,||F₃(t)||≤1。

is the state variable introduced by the controller,

is the estimated value of the output variable without considering the measurement error, A _c , B _c are the controller coefficient matrices with appropriate dimensions, and K is the controller gain matrix. Controller errors and unknown actuator dynamics can lead to perturbation problems. When △K is an additive perturbation, its mathematical expression is △K=M ₂ F ₂ (t)N ₂ ,||F ₂ ( t)||≤1, when ΔK is a multiplicative perturbation, its mathematical expression is ΔK=M ₃ F ₃ (t)N ₃ K,||F ₃ (t)||≤1.

Considering the above two perturbation problems in the controller at the same time, the expressions are:

△K=M ₂ F ₂ (t)N ₂ +M ₃ F ₃ (t)N ₃ K,||F ₂ (t)||≤1,||F ₃ (t)||≤1

M ₂ , N ₂ , M ₃ , N ₃ are real constant matrices of suitable dimensions, and F ₂ (t), F ₃ (t) are Lebesgue-measurable matrix functions.

Other steps and parameters are the same as one of the first to third embodiments.

Embodiment 5: This embodiment is different from one of Embodiments 1 to 4 in that:

5. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 4, it is characterized in that: described step 4 substitutes the controller into the non-cooperative flexible composite spacecraft attitude that includes comprehensive interference term The dynamic state space equation is used to establish the state space model of the closed-loop attitude control system; the specific process is as follows:

Substitute the controller obtained in step 3 into the attitude dynamics model of the non-cooperative flexible composite spacecraft including the comprehensive interference term in step 2 to obtain:

B₁＝B₂＝B，有：in

B ₁ =B ₂ =B, there are:

y(t)=Cx(t)=[C 0]ζ(t)

The coefficient matrix is:

具体数学表达式为：When the additive perturbation △K _α and the multiplicative perturbation △K _m coexist, the coefficient matrix

The specific mathematical expression is:

where σ∈(0,1) is a given constant.

写成：put the matrix

written as:

The control torque u(t) is written as:

Other steps and parameters are the same as one of the first to fourth embodiments.

Embodiment 6: This embodiment is different from one of Embodiments 1 to 5 in that:

6. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 5, it is characterized in that: in described step 5, according to Lyapunov stability theory and linear matrix inequality method, deriving satisfy system The sufficient condition of the linear matrix inequality of stability is to solve the controller parameters in step 3 and substitute them into the controller, so that the state space model in step 4 is complete; the specific process is:

γ>0，求解线性矩阵不等式：When there are controller additive/multiplicative perturbations at the same time, the state space model in step 2 has quadratic stability under the action of the controller in step 3, then the output y(t) satisfies the H _∞ performance constraint, and for a given The constant ξ>0,

γ>0, solve the linear matrix inequality:

in

和

进而求得步骤三中的控制器参数矩阵：The positive definite symmetric matrices P ₁₁ , Q ₁₁ and the matrix Q ₂₁ can be obtained,

and

Then, the controller parameter matrix in step 3 is obtained:

Substitute into the closed-loop system state space equation in step 4.

Other steps and parameters are the same as one of the specific embodiments one to five.

Embodiment 7: The difference between this embodiment and one of Embodiments 1 to 6 is:

7. a kind of non-cooperative flexible assembly spacecraft attitude stability hybrid non-fragile control method according to claim 6, is characterized in that: under the condition of control input amplitude limit, control the attitude angle, attitude angular velocity of flexible assembly spacecraft and modal displacement quickly reach stability and ensure a certain accuracy; the specific process is:

Due to physical and safety constraints, actuator constraints exist and control inputs are saturated, negatively impacting the stability and performance of attitude control systems designed for "ideal" conditions. For a positive scalar λ:

||u||<λ

Indicates that the two-norm saturation value of the control input is λ. Adding saturation limit to the controller obtained in step 5, that is, the actual control torque can be described as:

sat(u _i=1,2,3 (t))=sign(u _i (t))min{|u _i (t)|,u _mi }

Where u _mi is the upper limit of the control torque provided by the actuator.

Other steps and parameters are the same as one of Embodiments 1 to 6.

Adopt the following examples to verify the beneficial effects of the present invention:

Example 1:

A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method of the present embodiment is specifically prepared according to the following steps:

Step 1: Construct and separate the unknown and uncertain terms of inertial parameters, and at the same time consider the uncertainty of model parameters, and rewrite the attitude dynamics equation of the non-cooperative flexible spacecraft with external interference into the form of state space equation.

The attitude dynamics equation of the flexible composite spacecraft can be expressed in the following form:

可将上述两式改写为状态空间形式：make

The above two equations can be rewritten in state space form:

输出变量

u(t)＝T_c为控制力矩，

是外界干扰。系数矩阵：where the state variable

output variable

u(t)=T _c is the control torque,

outside interference. Coefficient matrix:

C＝I_6+2m

C=I6 _+2m

The unknown and uncertain inertial parameter information is all reduced to the following coefficient matrix:

J_n为标称惯性矩阵。in

J _n is the nominal inertia matrix.

△A _p represents the uncertainty of the model parameters (except inertial uncertainty), which has norm bounds and satisfies the matching condition:

Step 2: In the presence of measurement errors and actuator faults, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1.

The above complex disturbance is constructed as a synthetic disturbance:

Substitute into the state space model in step 1:

v(t) is the measurement error.

Step 3: Define the controller parameters and design a hybrid non-fragile controller when there are additive/multiplicative perturbations in the controller at the same time.

When the controller has additive/multiplicative perturbations at the same time, the form of designing the controller is as follows:

是控制器引入的状态变量，

是不考虑测量误差对输出变量的估计值，A_c、B_c是具有合适维度的控制器参数矩阵，K为控制器增益矩阵。同时考虑控制器存在上述两种摄动，其表达式为：

is the state variable introduced by the controller,

is the estimated value of the output variable without considering the measurement error, A _c , B _c are the controller parameter matrices with appropriate dimensions, and K is the controller gain matrix. Considering the existence of the above two kinds of perturbation in the controller at the same time, its expression is:

△K=M ₂ F ₂ (t)N ₂ +M ₃ F ₃ (t)N ₃ K,||F ₂ (t)||≤1,||F ₃ (t)||≤1

M ₂ , N ₂ , M ₃ , N ₃ are real constant matrices of suitable dimensions, and F ₂ (t), F ₃ (t) are Lebesgue-measurable matrix functions.

Step 4: Substitute the controller into the state space equation of the attitude dynamics of the non-cooperative flexible composite spacecraft including the comprehensive interference term, and establish the state space equation of the closed-loop attitude control system.

Substitute the controller obtained in step 3 into the attitude dynamics equation of the flexible assembly including the comprehensive interference term in step 2, and obtain:

in:

The coefficient matrix is:

具体数学表达式为：Uncertainty coefficient matrix when additive perturbation △K _α and multiplicative perturbation △K _m coexist

The specific mathematical expression is:

where σ∈(0,1) is a given constant.

Step 5: According to the Lyapunov stability theory and the linear matrix inequality method, deduce the sufficient conditions of the linear matrix inequality satisfying the system stability to solve the controller parameters in step 3 and substitute them into the controller, so that the state space model in step 4 is complete. .

γ>0，求解线性矩阵不等式：When there are additive/multiplicative perturbations at the same time, the state space model in step 2 has quadratic stability under the action of the controller in step 3, then the output y(t) satisfies the H _∞ performance constraint, and for a given constant ξ>0,

γ>0, solve the linear matrix inequality:

in

和

进而求得步骤三中的控制器参数矩阵：The positive definite symmetric matrices P ₁₁ , Q ₁₁ and the matrix Q ₂₁ can be obtained,

and

Then, the controller parameter matrix in step 3 is obtained:

Step 6: Control the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible composite spacecraft under the condition of limiting the control input to quickly achieve stability and ensure a certain accuracy.

Adding a limiter to the controller obtained in step 5, that is, the actual control torque can be described as:

sat(u _i=1,2,3 (t))=sign(u _i (t))min{|u _i (t)|,u _mi }

Where u _mi is the upper limit of the control torque provided by the actuator.

A non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of the present embodiment is verified by numerical simulation as follows:

Nominal inertial parameters of the non-cooperative flexible composite spacecraft:

The unknown uncertain inertia matrix is: △J=(0.05+0.01sin(πt))J _n

Number of flexible modes considered: m=4

Coupling coefficient matrix between rigid body and flexible structure:

Damping ratio: [ξ ₁ ξ ₂ ξ ₃ ξ ₄ ]＝[0.005607 0.008620 0.01283 0.02516]

Natural frequency: [Ω ₁ Ω ₂ Ω ₃ Ω ₄ ]＝[0.7681 1.1038 1.8733 2.5496]

Coupling matrix:

Feedback coefficient matrix: F _a = [3.1533 -0.5714 5.3674 9.3389], F _b = [1.0976 0.19651.8086 3.0873]

External environment torque:

Lebesgue matrix functions and their corresponding real constant matrices:

M ₁ =0.01×[8 11 13 15 16 -18 8 11 13 15 16 18 8 11] ^T ,

N ₁ =0.01×[1 2 3 4 2 10 1 2 3 4 2 10 1 2], F ₁ (t)=sin(0.11πt)

M ₂ =0.1×ones(3,1) N ₂ =0.01×ones(1,14), F ₂ (t)=sin(0.11πt+π/4)

M ₃ =0.1×ones(3,1) N ₃ =0.01×ones(1,3), F ₃ (t)=cos(0.11πt)

Angle initial value: Θ(0)=[0.18,0.15,-0.15] ^T rad

Initial value of angular velocity: ω(0)＝[-0.02,-0.02,0.02] ^T rad/s

Modal displacement initial value:

Initial value of the modal displacement derivative:

Actuator failure signal:

ξ₁＝0.025,ξ₂＝0.025,γ＝3.2,σ＝0.5.Relevant normals:

ξ ₁ =0.025,ξ ₂ =0.025,γ=3.2,σ=0.5.

Measurement error:

v(t)=10 ^-4 ×[4 5 6 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.2]sin(0.01πt)

Control torque limiter: u _m1 =u _m2 =u _m3 =15Nm

Solving the linear matrix inequalities with the LMI toolbox gives:

Under the designed hybrid non-fragile controller, Figures 2 to 8 are the corresponding simulation results, in which Figure 2 is the attitude angle change curve of the non-cooperative flexible composite spacecraft, and Figure 3 is the attitude angular velocity of the non-cooperative flexible composite spacecraft. Figure 4 is the change curve of the modal displacement of the non-cooperative flexible composite spacecraft, Figure 5 is the attitude angle accuracy curve of the non-cooperative flexible composite spacecraft, and Figure 6 is the attitude angular velocity accuracy of the non-cooperative flexible composite spacecraft. Figure 7 is the curve of the modal displacement accuracy of the non-cooperative flexible composite spacecraft, and Figure 8 is the change curve of the control torque during the entire attitude stabilization control process. It can be seen from the observation that the convergence time of the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible composite spacecraft are all less than 150s, the accuracy is less than 0.01rad, 0.01rad/s and 0.01 respectively, and the control torque is always within the limit of 15Nm. .

It can be seen that a non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of the present invention can be used in the unknown uncertainty of inertial parameters, model parameter uncertainty, external disturbance, measurement error, actuator failure, input saturation, control Under the influence of complex disturbances such as additive/multiplicative perturbation coexistence, the attitude of the non-cooperative flexible composite spacecraft has been successfully controlled with high precision and high stability.

The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (7)

1. A non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method is characterized by comprising the following steps: a hybrid non-fragile attitude stabilization control method of a flexible assembly spacecraft is specifically carried out according to the following steps:

the method comprises the steps of firstly, constructing and separating an unknown uncertainty item of an inertia parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form.

And step two, aiming at the measurement error and the fault of the actuating mechanism, constructing a fault interference item of the actuating mechanism and forming a comprehensive interference item with the unknown inertial parameter item, the uncertain model parameter interference item and the external interference moment item in the step one.

And step three, aiming at the problem of coexistence of gain addition/multiplication perturbation of the controller, defining controller parameters and designing a hybrid non-fragile controller.

And step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing the comprehensive interference item to establish a closed-loop system state space model.

And step five, deducing sufficient conditions of the linear matrix inequality meeting the system stability according to the Lyapunov stability theory and the linear matrix inequality method to solve the controller parameters in the step three and substitute the controller parameters into the controller, so that the state space model in the step four is complete.

And step six, under the condition of controlling torque amplitude limiting, controlling the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly to quickly reach stability, and ensuring certain control precision.

2. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method according to claim 1, characterized by comprising the following steps: the method comprises the following steps of firstly, constructing and separating an unknown uncertainty item of an inertia parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly attitude dynamics equation with external disturbance moment into a state space equation form, wherein the specific process comprises the following steps:

defining a local horizontal and local vertical coordinate system F_o(X_o,Y_o,Z_o) (LVLH) as a reference coordinate system with an origin at the non-cooperative composite centroid, a roll axis along the flight direction, a yaw axis pointing towards the geocentric, and a pitch axis completing the right hand coordinate system. Defining a body coordinate system F of the combined spacecraft_B(X_B,Y_B,Z_B) The origin is located at the center of mass of the non-cooperative combination, and the three coordinate axes are respectively superposed with the inertia main axis of the combination.

The attitude kinematic equation of the flexible assembly spacecraft is as follows:

wherein,

theta and psi represent the three components of the flexible composite spacecraft, i.e., roll, pitch and yaw attitude angles, omega, respectively₀Indicating the angular velocity of the track on which the flexible assembly is located. When high rail assembly carries out the small-angle attitude adjustment, have:

if a piezoelectric actuator is incorporated into the surface of a flexible attachment of the combination to provide the input voltage u_pAnd thus the deformation that results in the control moment, the body of the assembly and the compliance kinetics equation can be expressed as follows:

wherein,

an inertia matrix representing the body of the assembly, ω ═ ω_x ω_y ω_z]Representing attitude angular velocity vectors, including roll, pitch, and yaw attitude angle rates of change,

representing a matrix of coupling coefficients between the rigid body and the flexible structure of the combination,

a modal coordinate vector representing the relative composition ontology,

and

representing a control input torque and an external disturbance torque;

representing a modal damping matrix, wherein

And Ω_iI is 1,2, …, m represents damping ratio and natural frequency respectively,

the stiffness matrix is represented and m is the number of flexural modes considered. Here, T_dIncluding gravity gradient moment, solar radiation pressure moment and aerodynamic moment u_pRepresents a piezoelectric input voltage, and

is the corresponding coupling coefficient matrix.

Defining auxiliary variables

Obtaining:

substituting the second equation in the non-cooperative flexible assembly attitude dynamics equation set to obtain a rewritten equation:

using feedback of true values, piezoelectric input u_pExpressed as:

in the formula F_a，F_bTo measure the feedback coefficient. Will be provided with

Substituting the derivative of the auxiliary variable

And the flexible assembly attitude kinetic equation after rewriting is obtained:

order to

The two equations above can be rewritten as a state space form:

wherein the state variable is

Output variable

u(t)＝T_cIn order to control the torque, the torque is controlled,

is an external disturbance. Coefficient matrix：

C＝I_6+2m

The unknown uncertain inertial parameter information is all normalized to the following coefficient matrix:

wherein

J_nIs a nominal inertia matrix.

△A_pRepresenting model parameter uncertainty (except inertial uncertainty), which has a norm bound and satisfies the matching condition:

wherein M is₁And N₁Is a real constant matrix of suitable dimensions, F₁(t) is a measurable matrix function of Leeberg.

3. The method of claim 2, wherein the non-cooperative flexible assembly attitude stabilization hybrid non-fragile control method comprises: in the second step, aiming at the conditions of measurement errors and actuator faults, an actuator fault interference item is constructed and forms a comprehensive interference item together with the unknown inertial parameter item and the external interference moment item in the first step; the specific process is as follows:

improper actuation of the actuator can seriously affect the performance of the attitude control system, allowing the matrix E (its structure and B) with full rank₁Similarly) represents the distribution matrix of the fault signals f (t) present in the input. If E ≠ B₁Then a process fault is indicated; if E is equal to B₁Then an actuator failure is indicated.

Constructing the complex disturbance as a comprehensive disturbance:

wherein the matrix

Is B₂The state space equation in the step one is rewritten as:

where v (t) represents the measurement error vector.

4. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 3, characterized by comprising the following steps: in the third step, when the addition/multiplication perturbation exists in the controller at the same time, the controller parameters are defined, and a hybrid non-fragile controller is designed; the specific process is as follows:

when the controller has additive/multiplicative perturbation, the form of the controller is designed as follows:

is a state variable introduced by the controller,

is an estimate of the output variable without taking into account the measurement error, A_c，B_cIs a matrix of controller coefficients with appropriate dimensions, and K is a matrix of controller gains. Controller errors and unknown actuator dynamics can cause perturbation problems, and when Δ K is an additive perturbation, the mathematical expression is:

△K＝M₂F₂(t)N₂,||F₂(t)||≤1

when Δ K is a multiplicative perturbation, the mathematical expression is:

△K＝M₃F₃(t)N₃K,||F₃(t)||≤1

considering the existence of the two disturbances of the controller at the same time, the expression is:

△K＝M₂F₂(t)N₂+M₃F₃(t)N₃K,||F₂(t)||≤1,||F₃(t)||≤1

M₂、N₂、M₃、N₃is a real constant matrix of suitable dimensions, F₂(t)、F₃(t) is a measurable matrix function of Leeberg.

5. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 4, characterized in that: substituting the controller model into a non-cooperative flexible assembly attitude dynamics state space equation containing a comprehensive interference item, and establishing a closed-loop attitude control system state space equation; the specific process is as follows:

substituting the controller obtained in the third step into the flexible assembly attitude dynamics equation containing the comprehensive interference item in the second step to obtain:

wherein:

the coefficient matrix is:

when-added perturbation Δ K_αMultiplication-by-sum perturbation Δ K_mMatrix of uncertainty coefficients when all exist

The specific mathematical expression is as follows:

where σ ∈ (0,1) is a given constant.

6. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 5, characterized in that: deducing a linear matrix inequality sufficient condition meeting the system stability in the step five, solving the controller parameters in the step three and substituting the controller parameters into the hybrid non-fragile controller to complete the state space equation in the step four; the specific process is as follows:

when the additive/multiplicative perturbation exists at the same time, the state space model of the non-cooperative combination attitude system in the step two has secondary stability under the action of the controller in the step three, and the output y (t) meets the requirement of H_∞Performance constraint, for a given constant xi>0，

γ>0, solving a linear matrix inequality:

wherein

Obtaining positive definite symmetric matrix P₁₁，Q₁₁And matrix Q₂₁，

And

and further solving a controller parameter matrix in the step three:

and substituting the closed-loop system state space equation in the step four.

7. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 6, characterized in that: under the condition of control input saturation, the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly spacecraft are controlled to be quickly stable, and certain precision is ensured; the specific process is as follows:

due to physical and safety constraints, there are constraints on the actuators and saturation of control inputs, which negatively impacts the stability and performance of the attitude control system designed for "ideal" situations. For a positive scalar λ:

||u||<λ

the two-norm saturation value representing the control input is λ. And adding a saturation amplitude limit to the controller obtained in the step five, namely the actual control torque can be described as:

sat(u_i＝1,2,3(t))＝sign(u_i(t))min{|u_i(t)|,u_mi}

wherein u is_miIs the upper limit of the control torque provided by the actuator.

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