A non-cooperative spacecraft dual non-fragile control method based on electromagnetic capture

Abstract

This invention discloses a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture, comprising: S1, establishing a dynamic model of the relative motion of the non-cooperative spacecraft under electromagnetic capture based on the T-H equations; S2, considering comprehensive disturbances and rewriting the dynamic model into state-space form; S3, designing a dual non-fragile observer / controller to address the coexistence of additive / multiplicative gain perturbations in the observer and controller; S4, substituting the dual non-fragile observer / controller into the state-space equations in step S2 to establish a state-space model of the closed-loop electromagnetic capture system; S5, deriving sufficient conditions for the system to be uniformly eventually bounded based on the LMI method and Lyapunov stability theorem, and solving for the observer / controller parameters in step S3. This invention fully considers the complex situation of coexistence of additive / multiplicative gain perturbations in the observer and controller, and can solve the electromagnetic capture control problem of non-cooperative spacecraft under multi-source disturbances such as external interference, elliptical orbit eccentricity, and unknown mass.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture. Background Technology

[0002] In recent years, human space technology has made rapid development and major breakthroughs, and the number of spacecraft in orbit has increased rapidly. At the same time, the arrival of the era of space games requires future spacecraft to have stronger offensive and defensive capabilities. Research on the capture problem of non-cooperative spacecraft, represented by space-failed spacecraft and hostile spacecraft, is imminent.

[0003] Traditional methods for capturing non-cooperative spacecraft mostly rely on robotic arms, nets, and harpoons. Robotic arm capture typically uses a robotic arm with an end effector, which is prone to collisions with the target. Net capture is adaptable and low-cost, effectively solving the collision problem, but its application is limited and it struggles with complex capture tasks. Harpoon capture can target targets at long distances and adapt to various shapes, but it easily generates new space debris during the capture process. Electromagnetic capture, a soft docking method, can effectively solve these problems, offering strong capture capabilities while avoiding rigid collisions. However, capture control is susceptible to gain perturbations from the observer / controller, and existing methods do not fully consider the coexistence of additive / multiplicative gain perturbations from the observer and controller, resulting in low capture accuracy and a high risk of mission failure.

[0004] In reality, there are multiple sources of disturbance such as external interference, elliptical orbit eccentricity, and unknown mass, which can easily lead to a decline in the performance of the control system or even instability. At present, there is no dual non-fragile electromagnetic capture method based on electromagnetic docking with non-cooperative spacecraft under the coexistence of additive / multiplicative gain perturbations of the observer and controller. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture. The aim is to solve the capture and control problem of non-cooperative spacecraft under complex conditions of combined disturbances including external interference, elliptical orbit eccentricity, and unknown mass, considering the coexistence of additive / multiplicative gain perturbations of the observer and controller.

[0006] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture, comprising the following steps:

[0007] S1. Establish a dynamic model of the relative motion of non-cooperative spacecraft electromagnetic capture on an elliptical orbit based on the TH equation;

[0008] S2. Considering external disturbances, orbital eccentricity, and unknown mass, we attribute them to a comprehensive disturbance and rewrite the dynamic model in state-space form.

[0009] S3. To address the coexistence of additive / multiplicative gain perturbations in the observer and controller, define the parameters of the observer and controller, and design a non-fragile observer / controller.

[0010] S4. Substitute the non-fragile observer / controller into the state-space equation in step S2 to establish the closed-loop system state-space model.

[0011] S5. Based on the LMI method and Lyapunov stability theorem, derive the sufficient conditions for the system to be uniformly eventually bounded, and solve for the observer / controller parameters in step S3.

[0012] Furthermore, the spacecraft electromagnetic capture relative motion dynamics model in step S1 is as follows:

[0013]

[0014] Where x, y, and z represent the relative positions between the two spacecraft (the capturing spacecraft and the non-cooperative spacecraft). and The relative velocity of the two spacecraft and F is the relative acceleration between the two spacecraft. eCx ,F eCy and F eCz Let d be the components of the electromagnetic force between the two spacecraft in the three-axis directions. x ,d y and d z Let m be the component of external disturbance in the three axes, m be the combined mass of the two spacecraft, and ω and Let ω represent the orbital angular velocity and angular acceleration, μ represent the gravitational parameter, and R represent the distance from the center of mass of the two spacecraft to the center of Earth.

[0015] Furthermore, the state-space equation in step S2 is in the form of:

[0016]

[0017] Among them, state variables Control input u(t) = [F eCx F eCy F eCz ] Τ w(t) represents the combined disturbance, and the state matrix A and input matrix B are:

[0018]

[0019] Where a is the semi-major axis of the track, and m0 is the effective mass.

[0020] Furthermore, the non-fragile observers / controllers in step S3 are respectively:

[0021]

[0022]

[0023] Where z(t) is the internal state vector of the nonfragile observer. Let be the first derivative of z(t), L and ΔL be the observer gain matrix and parameter uncertainty matrix, and K and ΔK be the controller gain matrix and parameter uncertainty matrix, respectively. This is an estimate of the overall disturbance.

[0024] Furthermore, the closed-loop system state-space model in step S4 is as follows:

[0025]

[0026] in, The first derivative of , where I is the identity matrix;

[0027] The sufficient condition for the system to be uniformly eventually bounded in step S5 is:

[0028] If there exist symmetric positive definite matrices V1, V2, and matrices W, H, and positive real numbers ξ1, ξ2, ε, satisfying LMI:

[0029]

[0030] in,

[0031] Θ 11 =V1A Τ +W Τ B Τ +AV1+BW+ξ2V1

[0032] Θ 22 =-H Τ -H+εξ1I+ξ2V2

[0033] The closed-loop system is then uniformly bounded, and the controller gain matrix K = WV1. -1 The observer gain matrix L = H(BV²) * (BV2) * This represents the pseudoinverse of BV2.

[0034] The beneficial effects of this invention are as follows:

[0035] Compared with the prior art, the beneficial effects of the present invention are that it takes into account external interference, elliptical orbit eccentricity and unknown mass of the target non-cooperative spacecraft, and can quickly and accurately capture non-cooperative targets under the condition of coexistence of additive / multiplicative gain perturbations of the observer and controller. The designed non-fragile electromagnetic capture method meets the mission requirements, can effectively avoid plume contamination and has continuous, reversible and synchronous controllability. Attached Figure Description

[0036] Figure 1 The present invention provides a flowchart of a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture. Detailed Implementation

[0037] Combination Figure 1 This embodiment describes a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture, comprising the following steps:

[0038] S1. Establish a dynamic model of the relative motion of non-cooperative spacecraft electromagnetic capture on an elliptical orbit based on the TH equation;

[0039] S2. Considering external disturbances, orbital eccentricity, and unknown mass, we attribute them to a comprehensive disturbance and rewrite the dynamic model in state-space form.

[0040] S3. To address the coexistence of additive / multiplicative gain perturbations in the observer and controller, define the parameters of the observer and controller, and design a non-fragile observer / controller.

[0041] S4. Substitute the non-fragile observer / controller into the state-space equation in step S2 to establish the closed-loop system state-space model.

[0042] S5. Based on the LMI method and Lyapunov stability theorem, derive the sufficient conditions for the system to be uniformly eventually bounded, and solve for the observer / controller parameters in step S3.

[0043] In step S1, a dynamic model of the relative motion of a non-cooperative spacecraft electromagnetic capture on an elliptical orbit is established based on the TH equation; the specific process is as follows:

[0044] Define the CM orbital coordinate system, where "CM" is the origin of the coordinate system and also the center of mass of the spacecraft's electromagnetic capture system. The z-axis points to the Earth's center, the y-axis is perpendicular to the orbital plane and coincides with the negative direction of the orbital angular velocity, and the x-axis follows the right-hand rule.

[0045] The relative motion dynamics model of the spacecraft's electromagnetic capture in the CM orbital coordinate system is as follows:

[0046]

[0047] Where x, y, and z represent the relative positions between the two spacecraft (the capturing spacecraft and the non-cooperative spacecraft). and The relative velocity of the two spacecraft and F is the relative acceleration between the two spacecraft. eCx ,F eCy and F eCz Let d be the components of the electromagnetic force between the two spacecraft in the three-axis directions. x ,d y and d z Let m be the component of external disturbance in the three axes, m be the combined mass of the two spacecraft, and ω and Let ω represent the orbital angular velocity and angular acceleration, μ represent the gravitational parameter, and R represent the distance from the center of mass of the two spacecraft to the center of Earth.

[0048] In step S2, external disturbances, orbital eccentricity, and unknown mass are considered, and they are reduced to a comprehensive disturbance. The dynamic model is then rewritten in state-space form. The specific process is as follows:

[0049] The relative motion dynamics model of the spacecraft electromagnetic capture in S2 is transformed into the following form:

[0050]

[0051] Among them, state variables Control input u(t) = [F eCx F eCy F eCz ] Τ External disturbance w0(t)=[d x d y d z ] Τ State matrix A and input matrix B:

[0052]

[0053] The unknown and uncertain inertial parameter information is placed into the following matrix:

[0054]

[0055]

[0056] Where a is the semi-major axis of the track, and m0 is the effective mass;

[0057] Then, combining the external disturbance with the aforementioned inertial parameter uncertainty to form the comprehensive disturbance w(t), we obtain:

[0058] w(t) = B Τ (BB Τ )* (ΔAη(t)+ΔBu(t)+(B+ΔB)w0(t))

[0059] Among them, (BB) Τ ) * It means BB Τ The pseudo-inverse, combining the disturbance w(t) including external disturbances, elliptical orbit eccentricity, and unknown mass, yields the state-space equation:

[0060]

[0061] In step S3, to address the coexistence problem of additive / multiplicative gain perturbations in the observer and controller, the parameters of the observer and controller are defined, and a non-fragile observer / controller is designed. The specific process is as follows:

[0062] Introduce auxiliary variables:

[0063]

[0064] Where z(t) is the internal state vector of the nonfragile observer. For the estimation of the overall perturbation, L and ΔL are the observer gain matrix and parameter uncertainty matrix, respectively. Considering both the observer additive and multiplicative gain perturbations, the mathematical expression for ΔL is:

[0065] ΔL=σ1M1F1(t)N1+(1-σ1)M2F2(t)N2Lσ1∈(0,1)

[0066] Where σ1 is a constant, M1, M2, N1 and N2 are constant matrices reflecting the uncertainty structure, and F1(t) and F2(t) satisfy ||F1(t)||≤1, ||F2(t)||≤1;

[0067] Design a non-fragile disturbance observer:

[0068]

[0069] Based on the above non-fragile disturbance observer, design a non-fragile controller:

[0070]

[0071] Where K and ΔK are the controller gain matrix and parameter uncertainty matrix, respectively. Considering both additive and multiplicative gain perturbations of the controller, the mathematical expression for ΔK is:

[0072] ΔK=σ2M3F3(t)N3+(1-σ2)M4F4(t)N4Kσ2∈(0,1)

[0073] Where σ2 is a constant, M3, M4, N3 and N4 are constant matrices reflecting the uncertainty structure, and F3(t) and F4(t) are Lebesgue measurable matrix functions that satisfy ||F3(t)||≤1 and ||F4(t)||≤1.

[0074] In step S4, the non-fragile observer / controller is substituted into the state-space equations of step S2 to establish a closed-loop system state-space model. The specific process is as follows:

[0075] Substitute the nonfragile observer / controller from step S3 into... and

[0076]

[0077]

[0078] The state-space model of the closed-loop system is obtained as follows:

[0079]

[0080] in, for The first derivative of , where I is the identity matrix.

[0081] In step S5, sufficient conditions for the system to be uniformly eventually bounded are derived based on the LMI method and Lyapunov stability theorem, and the observer / controller parameters in step S3 are solved. The specific process is as follows:

[0082] Define Lyapunov functions:

[0083]

[0084] Where P1 and P2 are defined symmetric positive definite matrices, the derivative of the above equation is simplified by the mean inequality lemma and the uniform final bounded definition, yielding:

[0085]

[0086] Where ξ1 and ξ2 are any positive constants introduced when using the AM-GM inequality lemma and the uniform final bounded definition;

[0087] Multiply both sides of the above expression Substituting ΔL and ΔK, let X1 = P1 -1 X2 = P2 -1 Furthermore, by simplifying using the arithmetic mean-geometric mean inequality lemma, we obtain:

[0088]

[0089] Where ε is any positive constant introduced when using the AM-GM inequality lemma;

[0090] Multiplying both sides of the above equation by ε, and then applying Schur's complement lemma, we get:

[0091]

[0092] in,

[0093] Θ 11 =V1A Τ +W Τ B Τ +AV1+BW+ξ2V1,Θ 22 =-H Τ -H+εξ1I+ξ2V2

[0094] V1=εX1, V2=εX2, W=KV1, H=LBV2

[0095] The closed-loop system is then uniformly bounded, and the controller gain matrix K = WV1. -1 The observer gain matrix L = H(BV²) * (BV2) * This represents the pseudoinverse of BV2.

[0096] The following numerical simulation verifies a dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture, as described in this embodiment:

[0097] Semi-major axis of the track: a = 10000 km

[0098] Effective mass: m0 = 20 kg

[0099] Gravitational parameter: μ=3.986×10 5 km 3 / s 2

[0100] The constant matrix reflecting the uncertain structure:

[0101] M1=M2=M3=M4=[0.010.010.01] Τ N1=N3=[0.010.010.010.010.010.01]

[0102] N2 = N4 = [0.01 0.01 0.01]

[0103] Constants greater than zero: σ1 = 0.2, σ2 = 0.8, ε = 0.02, ξ1 = 2 × 10 3 ξ2=2×10 11

[0104] Using the YAMIP toolbox to solve the inequalities in step S5, the observer gain matrix and controller gain matrix are obtained as follows:

[0105]

[0106]

[0107] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A dual non-fragile control method for non-cooperative spacecraft based on electromagnetic capture, characterized in that, The method includes the following steps: S1. Establish a dynamic model of the relative motion of non-cooperative spacecraft electromagnetic capture on an elliptical orbit based on the TH equation; S2. Considering external disturbances, orbital eccentricity, and unknown mass, we attribute them to a comprehensive disturbance and rewrite the dynamic model in state-space form. S3. To address the coexistence of additive and multiplicative gain perturbations in the observer and controller, define the parameters of the observer and controller, and design a non-fragile observer and controller. S4. Substitute the non-fragile observer and controller into the state-space equation in step S2 to establish the state-space model of the closed-loop system. S5. Based on the LMI method and Lyapunov stability theorem, derive the sufficient conditions for the system to be uniformly eventually bounded, and solve for the observer and controller parameters in step S3. The relative motion dynamics model of the spacecraft electromagnetic capture in step S1 is as follows: in, and To capture the relative positions between the spacecraft and non-cooperative spacecraft, and The relative velocity of the two spacecraft and The relative acceleration between the two spacecraft. and The components of the electromagnetic force between the two spacecraft in the three-axis directions. and The components of external disturbances in the three-axis directions. For the combined mass of the two spacecraft, and For orbital angular velocity and angular acceleration, For gravitational parameters, This represents the distance from the center of mass of the two spacecraft to the center of the Earth. The state-space equation in step S2 is in the form of: Among them, state variables Control input , To synthesize the disturbance, the state matrix and input matrix : in, For the semi-major axis of the track, For effective quality; The non-fragile observer and controller in step S3 are respectively: in, Let be the internal state vector of the non-fragile observer. yes The first derivative, For the estimation of comprehensive disturbances; and Here are the observer gain matrix and parameter uncertainty matrix. The mathematical expression is in, It is a constant. , , and It is a constant matrix that reflects the uncertain structure. and satisfy , ; and For the controller gain matrix and parameter uncertainty matrix, The mathematical expression is: in, It is a constant. , , and It is a constant matrix that reflects the uncertain structure. and Let be a Lebesgue measurable matrix function that satisfies , ; The closed-loop system state-space model in step S4 is as follows: in, , for The first derivative, It is the identity matrix; The sufficient condition for the system to be uniformly eventually bounded in step S5 is: If a symmetric positive definite matrix exists , and matrix , and positive real numbers , , To meet LMI requirements: in, The closed-loop system is then uniformly and eventually bounded, and the controller gain matrix... Observer gain matrix , express The false rebellion.

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