Electromagnetic docking tube model predictive control method for on-orbit refueling

Abstract

This invention discloses a Tube model predictive control method for electromagnetic docking in on-orbit refueling, comprising: S1, establishing a spacecraft orbit-electromagnetic-liquid coupled dynamic model and converting it into a discrete state-space form; S2, designing a constraint tightening method based on adaptive robust invariant sets to address disturbance terms in the dynamic model, ensuring recursive feasibility under bounded disturbance conditions; S3, constructing an energy consumption-accuracy multi-objective optimization function, and using a rolling time-domain optimization framework to achieve a dynamic trade-off between energy consumption and docking accuracy; S4, constructing a control Lyapunov function, and using robust invariant sets to ensure the stability of the algorithm under constraints, thereby obtaining the optimal controller; S5, substituting the Tube model predictive controller into the closed-loop system to achieve a stable relative position of the spacecraft, realizing coupled control. This invention can achieve precise electromagnetic docking control under conditions of system time-varying dynamics and coexistence of external and tank liquid disturbances, with low control energy consumption and wide applicability.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft on-orbit servicing, and specifically relates to an electromagnetic docking Tube model predictive control method for on-orbit refueling. Background Technology

[0002] In-orbit refueling technology for spacecraft has become a research focus in the field of space control due to its core role in extending mission duration and reducing launch costs. The realization of this technology depends on high-precision and high-safety docking control. However, traditional servicing spacecraft carrying large-capacity propellant tanks face multiple challenges: First, the sloshing and distribution changes of liquid fuel cause liquid-solid interaction forces, leading to a significant increase in the complexity of attitude-orbit coupling dynamics modeling; second, the flammable and explosive nature of propellants requires strict avoidance of mechanical collisions and thermodynamic risks during the docking process; third, traditional thruster-based docking methods have inherent defects such as plume contamination, high fuel consumption, and high impact loads, making it difficult to meet the requirements of long-term on-orbit servicing.

[0003] Because electromagnetic force exhibits a nonlinear decay characteristic with increasing distance and is strongly coupled with relative attitude, high-precision modeling is difficult. Furthermore, multiple uncertainties, such as space magnetic field interference and propellant sloshing disturbances, significantly reduce controller robustness, resulting in numerous technical bottlenecks. Traditional spacecraft electromagnetic docking control systems primarily focus on linear, steady-state systems or single disturbance compensation, or employ model-free control. These methods lack comprehensive consideration of the time-varying characteristics of elliptical orbits, multi-objective optimization requirements, and complex multi-source disturbances. Therefore, these methods have limitations in energy consumption optimization, constraint compatibility, and computational efficiency, making it difficult to meet the increasingly complex demands of on-orbit servicing missions.

[0004] Model predictive control (MDC) has demonstrated unique advantages in the control of complex systems such as vehicle fleets, drones, and spacecraft due to its rolling optimization, explicit constraint handling, and multivariable coordination capabilities. However, standard MDC is sensitive to disturbances and is difficult to apply directly to scenarios with strong uncertainties. Tube model predictive control, by introducing robust invariant sets and feedback compensation mechanisms, constrains the system state to the neighborhood of the nominal trajectory, reducing computational complexity while ensuring robustness, and has become an efficient control strategy for handling bounded uncertainties. However, general Tube model predictive control requires the controlled system to be a linear time-invariant system, and due to the time-varying nature of electromagnetic docking systems for elliptical orbit spacecraft, traditional Tube model predictive control is difficult to apply directly. Furthermore, there is currently no research on Tube model predictive control for electromagnetic docking of elliptical orbit spacecraft during on-orbit refueling. Summary of the Invention

[0005] In view of this, the technical problem to be solved by the present invention is to provide a Tube model predictive control method for electromagnetic docking in on-orbit refueling. Addressing the above-mentioned shortcomings of the prior art, the Tube model predictive control method for electromagnetic docking in on-orbit refueling provided by the present invention establishes a liquid-solid-magnetic coupling dynamic model for electromagnetic docking of an elliptical orbit spacecraft under the action of external disturbances and liquid interference forces. Furthermore, an improved Tube model predictive controller suitable for elliptical orbits is designed, compatible with the time-varying characteristics of elliptical orbit parameters. A multi-objective optimization index of energy consumption and accuracy is proposed, enabling a dynamic balance between control performance and energy consumption, resulting in higher control accuracy, lower control energy consumption, and further improved control efficiency.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a predictive control method for electromagnetic docking Tube model with a base plane for on-orbit refueling, comprising the following steps:

[0007] S1. Establish a spacecraft orbit-electromagnetic-liquid coupled dynamic model and convert it into a discrete state-space form;

[0008] S2. To address the disturbance terms in the dynamic model, a constraint tightening method based on adaptive robust invariant sets is designed to ensure the recursive feasibility under the bounded condition of disturbance.

[0009] S3. Construct a multi-objective optimization function for energy consumption and accuracy, and use a rolling time-domain optimization framework to achieve a dynamic trade-off between energy consumption and docking accuracy;

[0010] S4. Construct the control Lyapunov function, and based on the robust invariant set to guarantee the stability of the algorithm under the constraints, obtain the optimal controller;

[0011] S5. Substitute the Tube model predictive controller into the closed-loop system to achieve a stable relative position of the spacecraft and realize coupled control.

[0012] Furthermore, in step S1, the continuous state-space form of the spacecraft orbit-electromagnetic-fluid coupled dynamics model is as follows:

[0013]

[0014] In the formula, Represents system state variables. Represents system control variables. Indicates the three-axis directional control force; The variable representing the disturbance experienced by the system is denoted as , where , This represents the three-axis disturbance force, which consists of external disturbances and fluid forces. This represents the steady part of the electromagnetic docking system matrix. For the time-varying part of the separated electromagnetic docking system matrix, This is the control matrix for the electromagnetic docking system.

[0015] Furthermore, the method for calculating the electromagnetic force experienced by a spacecraft is as follows:

[0016]

[0017]

[0018] In the formula, and The combined magnetic moment of the two spacecraft is derived from the magnetic moments generated by multiple coils on the spacecraft. and The target spacecraft i The first coil and tracking spacecraft j The ampere-turns of each coil, The permeability of free space, r This represents the relative position of the spacecraft.

[0019] Furthermore, the method for calculating the disturbance variables affecting the system is as follows:

[0020]

[0021]

[0022]

[0023]

[0024] In the formula: For random bounded disturbances, Forces acting in a fluid The magnitude of the normal component of the liquid force. It is a tangential force of the liquid. Let the mass be the equivalent mass of the pulsating sphere in liquid form. Let be the position vector of the center of mass of the pulsating sphere in the spacecraft's body coordinate system. For its modulus length, Let it be its unit vector. Let be the angular velocity of the spacecraft's rotation in the inertial frame. , Let be the translational velocity of the spacecraft in the inertial frame. Let the equivalent radius of the storage tank be _____. Let be the rotational angular velocity of the pulsating sphere in this system. For liquid surface tension, The kinematic viscosity of the liquid. Let be the relative translational velocity of the pulsating ball at the contact point along the tangential direction. , Let be the translational velocity of the pulsating sphere relative to the system. Let be the radius of the pulsating sphere. When the radius of the pulsating sphere reaches its minimum value, its radial velocity component... Conversely, at this point, not only are there forces acting between the pulsating sphere and the spacecraft, but momentum will also be exchanged:

[0025]

[0026] In the formula: This represents the translational velocity of the spacecraft's center of mass immediately after the collision. This represents the collision coefficient.

[0027] Further, in step S1, the discrete state-space form of the spacecraft orbit-attitude vibration coupled dynamics model is as follows:

[0028]

[0029] In the formula, For the system in The state transition matrix at time t, .

[0030] Furthermore, in step S2, the designed constraint tightening method for the adaptive robust invariant set includes the following constraints. :

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[0032]

[0033]

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[0042] In the formula, It is a closed convex set. , It is a compact convex set containing the origin. For the terminal constraint set, and for Predict system state and input in all times. To predict the system at the current moment k To predict the time domain The resulting state sequence, To predict the system at the current moment k To predict the time domain The obtained control sequence, , To ensure the matrix It is Schur's matrix. Denotes the Pontryagin difference between two sets. Indicates the prediction system in k + i The state set allowed at time, Indicates the prediction system in k + i The allowed set of inputs at time 1. For the system A robust invariant set.

[0043] Further, in step S3, the energy consumption-accuracy multi-objective optimization function is:

[0044]

[0045] In the formula, , These are the given positive definite and positive semi-definite matrices, respectively.

[0046] Furthermore, in step S4, the control Lyapunov function is expressed as:

[0047]

[0048] In the formula, d Representation of canonical space ( , Distance and norm in ) Defined as ;

[0049] Furthermore, in step S4, the designed optimal controller is expressed as:

[0050]

[0051] In the formula, For the energy consumption-accuracy multi-objective optimization function under constraints The first element of the optimal control sequence obtained by solving the problem. The beneficial effects of this invention are:

[0052] (1) This invention proposes a Tube model predictive control method for electromagnetic docking in on-orbit refueling, which is applicable to electromagnetic docking control of elliptical orbit spacecraft considering external disturbances and liquid interference. It can achieve a dynamic balance between control performance and energy consumption, and has low control energy consumption and high precision.

[0053] (2) The present invention has a wide range of applications. It can be applied not only to electromagnetic docking control for on-orbit refueling of spacecraft, but also to electromagnetic docking control for on-orbit construction and assembly of future ultra-large space infrastructure. Attached Figure Description

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0055] Figure 1 Flowchart of the predictive control method for electromagnetic docking using a Tube model for on-orbit refueling.

[0056] Figure 2 This is a curve showing the relative position change of the spacecraft. x , y and z This indicates the change in the relative position of the three axes, where m represents the relative position in meters.

[0057] Figure 3 The curve showing the relative velocity change of the spacecraft. v x , v y and v z It represents the change in relative velocity across the three axes. m / s indicates that the unit of relative velocity is meters per second.

[0058] Figure 4 The curve showing the change in the required electromagnetic force. u x , u y and u z It represents the change in triaxial electromagnetic force, where N represents the unit of electromagnetic force, which is Newton.

[0059] Figure 5 To track the magnetic moment required by the spacecraft, μ x , μ x and μ x Am represents the amount of change in the three-axis magnetic moment of a spacecraft. 2 The unit for magnetic moment is ampere-square meters. Detailed Implementation

[0060] The specific embodiments of the present invention will now be described in conjunction with the accompanying drawings to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0061] This invention provides a Tube model predictive control method for electromagnetic docking in on-orbit refueling, comprising the following steps:

[0062] S1. Establish a spacecraft orbit-electromagnetic-liquid coupled dynamic model and convert it into a discrete state-space form;

[0063] S2. To address the disturbance terms in the spacecraft orbit-electromagnetic-fluid coupled dynamics model, a constraint tightening method based on adaptive robust invariant sets is designed. By adjusting the contraction strategy, the method is compatible with the time-varying characteristics of the system, ensuring recursive feasibility under bounded disturbance conditions.

[0064] S3. Construct a multi-objective optimization function for energy consumption and accuracy, and use a rolling time-domain optimization framework to achieve a dynamic trade-off between energy consumption and docking accuracy;

[0065] S4. Construct the control Lyapunov function, and based on the robust invariant set to guarantee the stability of the algorithm under the constraints, obtain the optimal controller;

[0066] S5. Substitute the Tube model predictive controller into the closed-loop system to achieve a stable relative position of the spacecraft and realize coupled control.

[0067] In step S1 of this embodiment of the invention, the continuous state-space form of the spacecraft orbit-electromagnetic-liquid coupled dynamics model is as follows:

[0068]

[0069] In the formula, Represents system state variables. Represents system control variables. Indicates the three-axis directional control force; The variable representing the disturbance experienced by the system is denoted as , where , This represents the three-axis disturbance force, which consists of external disturbances and fluid forces. This represents the steady part of the electromagnetic docking system matrix. For the time-varying part of the separated electromagnetic docking system matrix, This is the control matrix for the electromagnetic docking system.

[0070] Specifically, the method for calculating the electromagnetic force experienced by a spacecraft is as follows:

[0071]

[0072]

[0073] In the formula, and The combined magnetic moment of the two spacecraft is derived from the magnetic moments generated by multiple coils on the spacecraft. and The target spacecraft i The first coil and tracking spacecraft j The ampere-turns of each coil, The permeability of free space, r This represents the relative position of the spacecraft.

[0074] Specifically, the method for calculating the disturbance variables affecting the system is as follows:

[0075]

[0076]

[0077]

[0078]

[0079] In the formula: For random bounded disturbances, Forces acting in a fluid The magnitude of the normal component of the liquid force. It is a tangential force of the liquid. Let the mass be the equivalent mass of the pulsating sphere in liquid form. Let be the position vector of the center of mass of the pulsating sphere in the spacecraft's body coordinate system. For its modulus length, Let it be its unit vector. Let be the angular velocity of the spacecraft's rotation in the inertial frame. , Let be the translational velocity of the spacecraft in the inertial frame. Let the equivalent radius of the storage tank be _____. Let be the rotational angular velocity of the pulsating sphere in this system. For liquid surface tension, The coefficient of kinematic viscosity of the liquid; Let be the relative translational velocity of the pulsating ball at the contact point along the tangential direction. , Let be the translational velocity of the pulsating sphere relative to the system. Let be the radius of the pulsating sphere. When the radius of the pulsating sphere reaches its minimum value, its radial velocity component... Conversely, at this point, not only are there forces acting between the pulsating sphere and the spacecraft, but momentum will also be exchanged:

[0080]

[0081] In the formula: This represents the translational velocity of the spacecraft's center of mass immediately after the collision. This represents the collision coefficient.

[0082] Furthermore, by employing the zero-order preservation method, the continuous state-space form of the orbit-electromagnetic-fluid coupled dynamics model is transformed into a discrete state-space form:

[0083]

[0084] In the formula, For the system in The state transition matrix at time t, .

[0085] In step S2 of this embodiment of the invention, considering the time-varying nature of the system caused by the elliptical orbit, an adaptive robust invariant set constraint tightening method is designed; specifically, the introduced constraints... include:

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[0097] In the formula, It is a closed convex set. , It is a compact convex set containing the origin. For the terminal constraint set, and for Predict system state and input in all times. To predict the system at the current moment k To predict the time domain The resulting state sequence, To predict the system at the current moment k To predict the time domain The obtained control sequence, , To ensure the matrix It is Schur's matrix. Denotes the Pontryagin difference between two sets. Indicates the prediction system in k + i The state set allowed at time, Indicates the prediction system in k + i The allowed set of inputs at time 1. For the system A robust invariant set.

[0098] Based on the above constraints, by adjusting the contraction strategy to be compatible with the time-varying characteristics of the elliptical orbital angular velocity, the recursive feasibility under the bounded perturbation condition can be guaranteed.

[0099] In step S3 of this embodiment of the invention, in order to achieve a dynamic trade-off between energy consumption and docking accuracy, the following energy consumption-accuracy multi-objective optimization function is designed:

[0100]

[0101] In the formula, , These are the given positive definite and positive semi-definite matrices, respectively.

[0102] In step S4 of this embodiment of the invention, the designed control Lyapunov function is expressed as follows:

[0103]

[0104] In the formula, d Representation of canonical space ( , Distance and norm in ) Defined as .

[0105] Based on the designed control Lyapunov function, the designed robust inverse optimal controller is expressed as follows:

[0106]

[0107] In the formula, This represents the first element of the control sequence of the prediction system.

[0108] In step S5 of this embodiment of the invention, the Tube model predictive controller is substituted into the spacecraft closed-loop dynamics system to make the relative position and velocity of the spacecraft reach a stable state, which can effectively realize the electromagnetic docking control of the spacecraft.

[0109] The specific working process of this embodiment is as follows:

[0110] Step 1: Given the semi-major axis of the orbit where the center of mass of the spacecraft's electromagnetic docking system is located. a eccentricity e and the mass of the two spacecraft , Set the prediction time domain N Sampling time T Set the initial state and the initial true anterior angle Set time ;

[0111] Step 2: Solve the optimization problem

[0112]

[0113] Obtain the current optimal control input ;

[0114] Step 3: Update spacecraft status and the current true nearest angle If the two spacecraft successfully dock, the algorithm terminates; otherwise, it updates. for Return to step 2 and repeat the process.

[0115] Ultimately, the optimal control inputs at each moment are obtained, enabling high-precision control of spacecraft electromagnetic docking under external disturbances and liquid forces.

[0116] In a specific example of the present invention, the control result obtained based on the above method is as follows: Figure 2-5 As shown, Figure 2 This represents a curve showing the relative position change of the spacecraft. Figure 3 This represents the curve showing the change in the relative velocity of the spacecraft. Figure 4 This represents the curve showing the change in the required electromagnetic force. Figure 5 The curve representing the change in magnetic moment required to track the spacecraft demonstrates that the control method has good control performance.

[0117] It should be noted that the method of the present invention has a wide range of applications, not only applicable to electromagnetic docking control for on-orbit refueling of spacecraft, but also to electromagnetic docking control for on-orbit construction and assembly of future ultra-large space infrastructure.

[0118] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0119] 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. An electromagnetic docking Tube model predictive control method for on-orbit refueling, characterized in that, Includes the following steps: S1. Establish a spacecraft orbit-electromagnetic-liquid coupled dynamic model and convert it into a discrete state-space form; S2. To address the disturbance terms in the dynamic model, a constraint tightening method based on adaptive robust invariant sets is designed to ensure the recursive feasibility under the bounded condition of disturbance. S3. Construct a multi-objective optimization function for energy consumption and accuracy, and use a rolling time-domain optimization framework to achieve a dynamic trade-off between energy consumption and docking accuracy; S4. Construct the control Lyapunov function, and based on the robust invariant set to guarantee the stability of the algorithm under the constraints, obtain the optimal controller; S5. Substitute the Tube model predictive controller into the closed-loop system to achieve a stable relative position of the spacecraft and realize coupled control. The constraint tightening method of the designed adaptive robust invariant set in the step S2 includes the following constraints : In the formula, It is a closed convex set. , It is a compact convex set containing the origin. For the terminal constraint set, and for k Predict system state and input in all times. To predict the system at the current moment k To predict the time domain N The resulting state sequence, To predict the system at the current moment k To predict the time domain N The obtained control sequence, , To ensure the matrix It is Schur's matrix. Denotes the Pontryagin difference between two sets. Indicates the prediction system in k + i The state set allowed at time, Indicates the prediction system in k + i The allowed set of inputs at time 1. For the system A robust invariant set; In step S3, the energy consumption-accuracy multi-objective optimization function is: wherein , are given positive definite and positive semi-definite matrices, respectively. In step S4, the Lyapunov function is: wherein d denotes the distance in the normed space (Rn, || · ||) , ), the norm is defined as ; In step S4, the designed optimal controller is represented as follows: In the formula, The energy consumption-precision multi-objective optimization function is The first element of the optimal control sequence obtained by solving the following equation.

2. The electromagnetic docking Tube model predictive control method for on-orbit refueling as described in claim 1, characterized in that, In step S1, the continuous state-space form of the spacecraft orbit-electromagnetic-liquid coupled dynamics model is as follows: In the formula, Represents system state variables. Represents system control variables. , , Indicates the three-axis directional control force; The variable representing the disturbance experienced by the system is denoted as , where , , , This represents the three-axis disturbance force, which consists of external disturbances and fluid forces. This represents the steady part of the electromagnetic docking system matrix. For the time-varying part of the separated electromagnetic docking system matrix, This is the control matrix for the electromagnetic docking system.

3. The electromagnetic docking Tube model predictive control method for on-orbit refueling of claim 2, wherein, The method for calculating the electromagnetic force acting on a spacecraft is as follows: In the formula, , and The combined magnetic moment of the two spacecraft is derived from the magnetic moments generated by multiple coils on the spacecraft. and The target spacecraft i The first coil and tracking spacecraft j The ampere-turns of each coil, The permeability of free space, r This represents the relative position of the spacecraft.

4. The electromagnetic docking Tube model predictive control method for on-orbit refueling of claim 2, wherein, The method for calculating the disturbance variables affecting the system is as follows: In the formula: For random bounded disturbances, Forces acting in a fluid The magnitude of the normal component of the liquid force. It is a tangential force of the liquid. Let the mass be the equivalent mass of the pulsating sphere in liquid form. Let be the position vector of the center of mass of the pulsating sphere in the spacecraft's body coordinate system. For its modulus length, Let it be its unit vector. Let be the angular velocity of the spacecraft's rotation in the inertial frame. , Let be the translational velocity of the spacecraft in the inertial frame. Let the equivalent radius of the storage tank be _____. Let be the rotational angular velocity of the pulsating sphere in this system. For liquid surface tension, The kinematic viscosity of the liquid. Let be the relative translational velocity of the pulsating ball at the contact point along the tangential direction. , Let be the translational velocity of the pulsating sphere relative to the system. The radius of the pulsating sphere is the radial velocity component when the radius of the pulsating sphere reaches its minimum value. Conversely, at this point, not only are there forces acting between the pulsating sphere and the spacecraft, but momentum will also be exchanged: wherein: represents the translational velocity of the spacecraft's center of mass at the instant of impact; is the impact coefficient.

5. The electromagnetic docking Tube model predictive control method for on-orbit refueling of claim 2, wherein, In step S1, the discrete state-space form is represented as follows: In the formula, For the system in The state transition matrix at time t, .

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