A tethered satellite control method and system based on filter and energy feedback

Abstract

The application discloses a kind of filter and energy feedback based on tethered satellite control method and system, comprising: adopting dumbbell model to establish space tether dynamics model;Using space tether dynamics model design Lyapunov function candidate function;According to Lyapunov function candidate function, the actual speed of virtual speed measurement is obtained, and the control law of tethered satellite is obtained.The filter and energy feedback tethered satellite controller proposed in the application realizes the replacement of tether speed and the stable control of tethered satellite deployment process.Experiments show that the method of using filter virtual speed instead of tether speed can solve the problem that tether speed is not easy to measure, and the energy feedback controller designed can quickly and stably complete the tethered satellite deployment process, and the size of the thrust required for control meets the actual situation of engineering, and the control effect is good.Finally, the application has solid theoretical basis, simple principle and simple and feasible derivation process.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spaceflight, and relates to a tether satellite control method and system based on a filter and energy feedback. BACKGROUND

[0002] In recent years, space tether satellite systems (TSS) have been widely concerned and researched due to their great potential in actively removing space debris, creating microgravity environments, deep space exploration, spacecraft orbit transfer, etc. The system usually connects two end satellites together by a space tether as long as several hundred to several thousand kilometers. The typical mission of TSS includes three processes: tether deployment, system state maintenance and sub-satellite recovery. Smooth deployment of the tether is the key to the operation of any space tether satellite system. However, due to the Coriolis force induced by the coupling of tether swing and deployment speed, it is not easy to achieve the rapid and stable deployment of the tether to the expected length. At the same time, the control of TSS mostly adjusts only the tension in the tether to achieve system stability, which makes the system state equation an under-actuated system with single input and multiple outputs. Therefore, designing an effective control strategy to achieve stable and rapid deployment of the tether has always been one of the research hotspots of the system.

[0003] At present, the existing technology has made in-depth research and simulation verification on the deployment control of space tether satellites, and the main conclusions are as follows:

[0004] Zhou Ru et al. proposed a linear tension feedback control law in "A simple tension control strategy for variable tether length tether satellite system" according to the linear stability theory, which realized the stable deployment of TSS and effectively suppressed the swing of the tether.

[0005] Sun and Zhu designed a fractional-order tension control law in "Fractional-Order tension control law for deployment of space tether system", which found that the control law can achieve the deployment task of the tether more quickly and stably. Since the important indicators in the mission process are rapidity and stability, therefore, the optimal control strategy considering time and state constraints has been deeply researched.

[0006] Wen Hao et al. proposed a second-order differential inclusion method in "Time-optimal release control of tether satellite based on differential inclusion", which converted the continuous-time optimal control problem of tether deployment into a dynamic programming problem, and obtained the time-optimal process of tether satellite deployment.

[0007] Feng et al. studied a deployment strategy of a tethered net capture system in "Optimal release control of tethered satellite system under safe capture strategy", considering the zero relative velocity end constraint and the conditions of system state constraint and control constraint, a composite performance index is given, the problem is discretized based on Legendre pseudospectral method, and the stable deployment problem of TSS under complex constraints is solved. In addition, the control method of nonlinear feedback linearization is also widely used in the control research of TSS.

[0008] Zhong Xiaojing et al. in "Elliptical orbit tethered satellite system release anti-windup method control" designed a kind of anti-windup method feedback control to deal with the stable deployment problem of TSS on elliptical orbit, which introduced the dynamic model into the controller and improved the control effect.

[0009] The above prior art needs the motor of the winch to realize the winding and unwinding of the tether, and the accurate measurement of the speed of the tether needs the accurate measurement of the speed of the motor, but it is not easy to realize. Therefore, while designing the controller, it is necessary to consider avoiding the measurement of the speed of the tether. SUMMARY

[0010] The purpose of the present application is to solve the problems in the prior art and provide a tethered satellite control method and system based on filter and energy feedback. Due to the Coriolis force induced by the coupling of tether swing and deployment speed during the tether deployment stage of space tethered satellite, it is not easy to realize the rapid and stable deployment of the tether according to the expected length. The present application aims to use the virtual signal of the filter to replace the speed of the tether based on the energy feedback control law, solve the problem of rapid and stable deployment of space tethered satellite, and avoid the measurement of the speed of the tether.

[0011] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0012] In a first aspect, the present application provides a tethered satellite control method based on filter and energy feedback, comprising the following steps:

[0013] A dumbbell model is used to establish a space tether dynamics model;

[0014] A Lyapunov function candidate function is designed using the space tether dynamics model;

[0015] According to the Lyapunov function candidate function, the actual speed of the tether is measured by using the virtual speed, and the control law of the tethered satellite is obtained.

[0016] In a second aspect, the present application provides a tethered satellite control system based on filter and energy feedback, comprising:

[0017] A model construction module is used to establish a space tether dynamics model using a dumbbell model;

[0018] A function design module is configured to design a Lyapunov function candidate by using the spatial tether dynamics model;

[0019] A tether speed measurement module is configured to measure the actual tether speed by using the virtual speed according to the Lyapunov function candidate, and obtain the control law of the tether satellite.

[0020] In a third aspect, the present application provides a computer device, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the above method when executing the computer program.

[0021] In a fourth aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program implements the steps of the above method when executed by a processor.

[0022] Compared with the prior art, the present application has the following beneficial effects:

[0023] The present application realizes the replacement of the tether speed and the stable control of the tether satellite deployment process. Experiments show that the method of using the filter virtual speed to replace the tether speed can solve the problem that the tether speed is not easy to measure, and the energy feedback controller designed can quickly and stably complete the tether satellite deployment process, the required thrust size conforms to the engineering actual situation, and the control effect is good. Finally, the present application has a solid theoretical basis, simple principle, and simple and feasible derivation process. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0025] Figure 1 The flow chart of the method of the present application.

[0026] Figure 2 The principle diagram of the system of the present application.

[0027] Figure 3 The tether satellite (TTS) schematic diagram of the present application.

[0028] Figure 4 The error between the virtual speed η and the tether speed ξ' of the present application.

[0029] Figure 5 The in-plane swing angle θ of the present application.

[0030] Figure 6The present invention is a tether length variation curve.

[0031] Figure 7 The present invention is a tether tension variation curve. DETAILED DESCRIPTION

[0032] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some but not all of the embodiments of the present application. Generally, the components of the embodiments of the present application described and shown in the accompanying drawings can be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0034] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, therefore, once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0035] In the description of the embodiments of the present application, it should be noted that, if the terms "upper", "lower", "horizontal", "inner" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship when the product of the present application is used, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" and the like are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0036] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly inclined. For example, "horizontal" only means that its direction is relatively more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined.

[0037] It should be noted that, in the description of the embodiments of the present application, unless otherwise explicitly specified and limited, if the terms "arrange", "install", "connect", "join" appear, they should be understood in a broad sense, for example, they can be fixedly connected, or detachably connected, or integrally connected, or mechanically connected, or electrically connected, or directly connected, or indirectly connected through an intermediate medium, or the internal communication of two elements. For those skilled in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0038] The present application will be further described in detail below with reference to the accompanying drawings:

[0039] Referring to Figure 1 The embodiments of the present application disclose a tethered satellite control method based on filter and energy feedback, comprising the following steps:

[0040] S1 adopts a dumbbell model to establish a space tether dynamics model;

[0041] S2 designs a Lyapunov function candidate function by using the space tether dynamics model;

[0042] S3 obtains a control law of the tethered satellite according to the Lyapunov function candidate function and by using virtual velocity to measure actual tether speed.

[0043] In a specific embodiment of the present application, a dumbbell model is adopted to establish a space tether dynamics model, comprising:

[0044] The space tether dynamics model is obtained by Euler-Lagrange equation:

[0045]

[0046] In the formula, represents in-plane angular acceleration, represents tether speed, l represents instantaneous tether length, represents out-of-plane angular velocity, represents out-of-plane angle, represents in-plane angular velocity, Omega represents orbital angular velocity of the system mass center, and theta represents in-plane angle. represents out-of-plane angular acceleration, represents tether acceleration, T represents tension on the tether, and m represents mass of the sub-satellite.

[0047] In a specific embodiment of the present application, the out-of-plane angle is controlled by additional thrust to realize stable control, specifically as follows:

[0048] Let be obtained:

[0049]

[0050] Non-dimensionalizing equation (2) gives:

[0051]

[0052] where ξ represents the non-dimensional rope length, ξ' represents the non-dimensional rope speed, ξ" represents the non-dimensional rope acceleration, θ" represents the non-dimensional in-plane angular acceleration, and θ' represents the non-dimensional in-plane angular speed;

[0053] In equation (3), the non-dimensional variables are:

[0054] ξ = l / l c

[0055] u = T / (mΩ 2 l c )

[0056]

[0057] ν = Ωt

[0058] where l c represents the reference rope length, u represents the non-dimensional tension, and the "(')" denotes ν is the non-dimensional form of time t.

[0059] In one specific embodiment of the present application, a Lyapunov function candidate is designed using a spatial tethers dynamics model, including:

[0060] The Lyapunov function candidate is:

[0061]

[0062]

[0063] where V(q, q') represents the Lyapunov function and is positive definite, q represents the system state variables {θ, l} T , E represents the system energy function, k p is a positive constant, and ξ d represents the non-dimensional rope length; taking the derivative of equation (4) with respect to the non-dimensional quantity v gives:

[0064]

[0065] where V'(q, q') represents the derivative of the Lyapunov function with respect to the non-dimensional time, and E' represents the derivative of the system energy function with respect to the non-dimensional time;

[0066] Equation (6) is defined as:

[0067] -u + kp (ξ-ξ d )=-k d ξ′ (7) Thus, we get the expression for u:

[0068] u=k p (ξ-ξ d )+k d ξ′ (8)

[0069] Substituting formula (8) into formula (6), we get:

[0070] V(q,q′)=-k d ξ′ 2 ≤0 (9).

[0071] In a specific embodiment of the present invention, based on the candidate Lyapunov function, the actual rope speed is measured using the virtual speed to obtain the control law of the tethered satellite, including:

[0072] The candidate Lyapunov function is selected as:

[0073]

[0074] Where V η is the newly selected Lyapunov function, α and k η is a positive constant, η is the output of the filter;

[0075] The actual rope speed ξ′ is replaced by the virtual speed η, then:

[0076] η′=-αη+αξ′ (11)

[0077] Where η′ represents the virtual acceleration;

[0078] Taking the derivative of Equation (10) with respect to dimensionless time ν and substituting Equation (11) into it, we get:

[0079]

[0080] Where V′ η represents the derivative of the newly selected Lyapunov function with respect to dimensionless time;

[0081] So, choose the new expression of input u:

[0082] u=k η η+k p (ξ-ξ d ) (13)

[0083] Substituting formula (13) into formula (12), we get:

[0084] V′ η =-kη η 2 ≤0 (14)

[0085] The control law of formula (14) is.

[0086] As Figure 2 shown, the embodiment of the application discloses a tethered satellite control system based on a filter and energy feedback, comprising:

[0087] A model construction module is used to establish a space tether dynamics model by adopting a dumbbell model;

[0088] A function design module is used to design a Lyapunov function candidate function by using the space tether dynamics model;

[0089] A tether speed measurement module is used to obtain a control law of the tethered satellite by measuring the actual tether speed by using the virtual speed according to the Lyapunov function candidate function.

[0090] In another feasible embodiment provided by the application, the working body of the application is a space tethered satellite system composed of two space vehicles connected by a tether. The length of the tether is determined according to specific working conditions, and is generally about 10-100 kilometers. When the system is connected, the whole system can be regarded as a space tether system. The application establishes a model of the space tethered satellite system, proposes a control strategy according to the characteristics of the system, proposes a speed replacement control law for the target, and finally verifies the effectiveness of the method proposed by the application through simulation examples. The implementation of the application mainly includes the following three steps:

[0091] First step: dynamics modeling

[0092] The dumbbell model is adopted to establish the space tether dynamics model, that is, two satellites are connected by a rigid tether without considering mass, elasticity and damping. As Figure 3 shown, a main satellite with a mass of M and a sub-satellite with a mass of m are connected by a tether with a variable length l and run on a Kepler circular orbit. The geocentric inertial coordinate system Exyz is defined, the origin of which is located at the center of the earth, the Ex axis points to the vernal equinox, the Ey axis points to the orbit plane in which the system mass center runs, and the Ez axis is determined by the right-hand rule. In addition, the orbit coordinate system oxyz is defined, the origin o of which is located at the system mass center, the ox axis points to the tangent direction of the orbit in which the system mass center runs, the oy axis points to the center of the earth, and the oz axis is perpendicular to the orbit plane and the above two axes to form a right-hand coordinate system. In addition, the body coordinate system is defined, the oy o The tether is connected from the main satellite to the sub-satellite, and after rotating by θ around the oy axis and then rotating around the ox o axis, the tether is obtained. , and the face-out angle is defined as , and the face-in angle is θ.

[0093] The spatial tether dynamics model can be obtained by Euler-Lagrange equation:

[0094]

[0095] In formula (1), l represents instantaneous rope length, Ω represents orbit angular velocity of system mass center, and T represents tension on the tether.

[0096] The present application only considers in-plane swing angle of the system and pay-in / pay-out control of the tether, and motion control on out-of-plane swing angle of the system can be realized by additional thrust to achieve stable control in actual application. Therefore, let The following can be obtained:

[0097]

[0098] For convenience of simulation calculation, dimensionless processing is performed on formula (2) to obtain:

[0099]

[0100] In formula (3), dimensionless variables are as follows:

[0101] ξ=l / l c , u=T / (mΩ 2 l c ), ν=Ωt

[0102] In addition, in formula (3), '(' represents l c , and v is dimensionless form of time t.

[0103] Second step: design controller according to system characteristics

[0104] In the design of control law, it is always desired to minimize the total energy E of the system and make the length of the tether ξ reach the desired value ξ d , so the Lyapunov function candidate function is designed as:

[0105]

[0106]

[0107] In formula (4), k p is a normal number, and the function V(q, q') is positive. Derivation of formula (4) on dimensionless quantity v is as follows:

[0108]

[0109] Define equation (6) as:

[0110] -u+k p (ξ-ξd ) = -k d ξ' (7) Thus, the expression of u is obtained:

[0111] u = k p (ξ - ξ d ) + k d ξ' (8)

[0112] Substitute equation (8) into equation (6), we can get:

[0113] V(q, q') = -k d ξ' 2 ≤ 0 (9)

[0114] Third step: design the rate substitution control law for the target

[0115] From the analysis of control law (8), it is known that the realization of the control target needs to measure the rope length ξ and the rope speed ξ'. However, the winding and unwinding of the rope needs the motor of the winch to realize, so the accurate measurement of the rope speed needs the accurate measurement of the rotating speed of the motor, which is not easy to realize, even if it is realized, it needs huge cost. Next, the present application attempts to realize the feedback of the rope speed with a filter. The Lyapunov function candidate function is selected as:

[0116]

[0117] In equation (10), η(t) is the output of the filter, and α, k η are normal numbers. In order to replace the actual rope speed ξ' with the virtual speed η, define:

[0118] η' = -αη + αξ' (11)

[0119] Derive equation (10) with respect to the dimensionless time v, and substitute equation (11) into it, we get:

[0120]

[0121] Thus, the expression of the new input u is selected as:

[0122] u = k η η + k p (ξ - ξ d ) (13)

[0123] Substitute equation (13) into equation (12), we can get:

[0124] V' η = -k η η 2 ≤ 0 (14)

[0125] Equation (14) is the designed control law.

[0126] In order to verify whether the filter virtual speed η is close to the actual rope speed ξ', the orbit height of the primary star is selected as 220km, and the orbit angular velocity is selected as 1.1804*10 -3 rad / s. The initial value of the state variable is taken as: x(t=0)=(θ, θ', ξ, ξ', η) T | t＝0 =(0, 0, 0.01, 0, 0) T The input u is set to zero. Three different α values are selected for comparison and verification, α=10, α=50, and α=100. The error between the filter virtual speed η and the actual rope speed ξ' is verified.

[0127] On the basis of the above parameters, in order to verify that the controller designed in the application can quickly and stably deploy the tether, the initial value x(t=0) is selected, the dimensionless rope length ξ d is expected to stretch from the initial 0.01 to 1, that is, l c =100km. The controller parameters of the energy feedback controller are selected as: k p =5, k η =3.95.

[0128] Experiments prove that the application can realize the replacement of the virtual signal of the filter for the rope speed and can complete the fast and stable deployment control of the space tether satellite.

[0129] The computer device provided by the embodiment of the application. The computer device of the embodiment comprises a processor, a memory, and a computer program stored in the memory and executable on the processor. The processor implements the steps in each of the method embodiments when executing the computer program. Alternatively, the processor implements the functions of each module / unit in each of the device embodiments when executing the computer program.

[0130] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the application.

[0131] The computer device can be a desktop computer, a notebook computer, a palm computer, a cloud server, and other computing devices. The computer device can include, but is not limited to, a processor and a memory.

[0132] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic, discrete hardware components, etc.

[0133] The memory can be used to store the computer program and / or modules, and the processor realizes various functions of the computer device by running or executing the computer program and / or modules stored in the memory, and calling the data stored in the memory.

[0134] The modules / units integrated in the computer device, if realized in the form of software function units and sold or used as independent products, can be stored in a computer readable storage medium. Based on such understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by a computer program instructing related hardware, and the computer program can be stored in a computer readable storage medium. The computer program can realize the steps of the above-mentioned various method embodiments when executed by a processor. The computer program includes computer program code, which can be in the form of source code, object code, executable file or some intermediate form. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the computer readable medium can include or exclude contents according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.

[0135] The above only describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A tethered satellite control method based on filter and energy feedback, characterized in that: The following steps are involved: The dumbbell model is used to establish the spatial tether dynamics model; The dumbbell model is used to establish a spatial tether dynamics model, including: The space tether dynamics model is obtained through the Euler-Lagrange equation: Where, represents the in-plane angular acceleration, is the tether velocity, represents the instantaneous rope length, represents the out-of-plane angular velocity, represents the outside angle of the plane, represents the in-plane angular velocity, represents the orbital angular velocity of the system's center of mass, represents the interior angle, represents the out-of-plane angular acceleration, is the tether acceleration, represents the tension on the tether; represents the mass of the sub-star; Design candidate Lyapunov functions using the space tether dynamics model; According to the candidate Lyapunov function, the actual tether velocity is measured using the virtual velocity and the control law of the tethered satellite is obtained.

2. The tethered satellite control method based on filter and energy feedback according to claim 1, characterized in that: The external angle of the plane The motion control can achieve stable control by adding thrust, as follows: make get: By dimensionless processing formula (2), we can get: Where, represents the dimensionless length of the tether, represents the dimensionless rope speed, represents the dimensionless tether acceleration, represents the dimensionless in-plane angular acceleration, represents the dimensionless in-plane angular velocity; In formula (3), the dimensionless variable is: Where, represents the reference rope length, represents dimensionless tension, " "represent , For time dimensionless form of .

3. The tethered satellite control method based on filter and energy feedback according to claim 1 or 2, characterized in that: The design of a candidate Lyapunov function using a space tether dynamics model includes: The candidate Lyapunov function is: Where, represents the Lyapunov function and is positive definite, Represents system state variables , represents the system energy function, is a positive constant, represents the dimensionless rope length; Equation (4) for the dimensionless quantity Taking the derivative, we get: Where, represents the derivative of the Lyapunov function with respect to dimensionless time, represents the derivative of the system energy function with respect to dimensionless time; Define equation (6): So, we get The expression: Substituting formula (8) into formula (6), we get: 。 4. The tethered satellite control method based on filter and energy feedback according to claim 3, characterized in that: The control law of the tethered satellite is obtained by measuring the actual tethered speed using the virtual speed according to the candidate Lyapunov function, including: The candidate Lyapunov function is selected as: Where, is the newly selected Lyapunov function, and is a positive constant, is the output of the filter; The actual rope speed Virtual speed for measurement Instead, then: Where, Indicates virtual acceleration; Formula (10) for dimensionless time Take the derivative and substitute formula (11) into it to get: Where, represents the derivative of the newly selected Lyapunov function with respect to dimensionless time; So, select the new input The expression: Substituting formula (13) into formula (12), we get: Formula (14) is the control law.

5. A tethered satellite control system based on filters and energy feedback for implementing the method of claim 1, characterized in that: include: Model building module, used to build a spatial tether dynamics model using a dumbbell model; Function design module, used to design candidate Lyapunov functions using the space tether dynamics model; The rope speed measurement module is used to measure the actual rope speed using the virtual speed according to the candidate Lyapunov function to obtain the control law of the tethered satellite.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 4 are implemented.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

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