Periodic time-delay sliding mode control method for nonlinear spacecraft elliptical orbit rendezvous system

Abstract

The invention discloses a periodic time-lag sliding-mode control method for a nonlinear spacecraft elliptical orbit intersection system. A nonlinear spacecraft elliptic orbit rendezvous system model subjected to external interference is simplified into a nonlinear periodic system according to reversible linear transformation. On the basis, the nonlinear periodic system is written into a strict nonlinear system matched with interference. A periodic time-lag sliding mode controller with a strict nonlinear system matched with interference is designed by using a periodic time-lag sliding mode control method, and a closed-loop system formed by the strict nonlinear system matched with interference and the controller is stable within a preset true anomaly under the action of the controller. The control design method overcomes the defects that a traditional sliding mode control method of an existing spacecraft elliptic orbit rendezvous system is prone to neglecting control constraints, singularity occurs in preset time control implementation, convergence time depends on an initial value condition, the convergence speed is low, and the traditional sliding mode control method is only suitable for a low-order or single-input system. The problem of spacecraft rendezvous in the preset time is solved.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control technology, specifically a periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system. Background Technology

[0002] Spacecraft rendezvous technology is one of the three most core technologies in the aerospace field. Together with spacecraft launch and recovery technologies, it forms the three fundamental pillars of manned spaceflight engineering. Spacecraft rendezvous is indispensable for the completion of space missions such as satellite maintenance, satellite networking, deep space interception, space station construction, and space rescue. This technology has been widely applied in aerospace engineering projects including space laboratories, space stations, remote sensing platforms, and space communication systems. Therefore, research on spacecraft rendezvous technology has significant application value.

[0003] Consider two spacecraft, one a target spacecraft and the other a tracking spacecraft. When the target spacecraft operates in an elliptical orbit, the relative motion between the two spacecraft can be described by a set of nonlinear time-varying differential equations, also known as a nonlinear spacecraft elliptical orbit rendezvous system. However, due to the dual time-varying and nonlinear characteristics of the nonlinear spacecraft elliptical orbit rendezvous system, the related control problems become extremely complex, resulting in very little research on this system. When the system is affected by external disturbances, the difficulty of studying the nonlinear spacecraft elliptical orbit rendezvous system is further exacerbated, making the research on the related control problems even more challenging.

[0004] As a powerful tool for robust nonlinear control design, sliding mode control is widely used due to its simple structure and strong disturbance resistance. Sliding mode control methods mainly include linear sliding mode control, adaptive sliding mode control, terminal sliding mode control, finite-time terminal sliding mode control, fixed-time terminal sliding mode control, and predetermined-time terminal sliding mode control. Although there is a wealth of research on sliding mode control methods, several drawbacks remain, such as neglecting control constraints, singularities in predetermined-time control due to high gain functions, convergence time dependence on initial conditions, slow convergence speed, and applicability only to low-order or single-input systems. These drawbacks limit the applicability of sliding mode control in more complex scenarios. This leads us to explore new control design methods to solve the predetermined-time control design problem of nonlinear spacecraft elliptical orbit rendezvous systems under external disturbances. Summary of the Invention

[0005] This invention proposes a periodic time-delay sliding mode control method for nonlinear spacecraft elliptical orbit rendezvous systems. This method overcomes the shortcomings of existing sliding mode control methods for elliptical orbit rendezvous systems, such as easily neglected control constraints, singularities in predetermined time control implementation, convergence time dependence on initial conditions, slow convergence speed, and applicability only to low-order or single-input systems. Based on the designed periodic time-delay sliding mode controller, this control method enables two spacecraft to complete the rendezvous mission within a predetermined time.

[0006] A periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system includes the following steps:

[0007] Step 1: Use invertible linear transformation to simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system. Based on this, further write the nonlinear periodic system into two subsystems, which are strictly nonlinear systems for matching disturbances.

[0008] Step 2: Based on the two subsystems obtained in Step 1, construct a time-delay sliding surface using the periodic time-delay sliding mode control method, and verify the convergence of the time-delay sliding surface within the predetermined true anomaly angle;

[0009] Step 3: Based on Step 1 and Step 2, design a periodic time-delay sliding mode controller using the all-drive system method. This will enable the closed-loop system, consisting of a strictly nonlinear system with matched disturbances and the periodic time-delay sliding mode controller, to stabilize within a predetermined true perihelion angle, thereby allowing the spacecraft to complete the rendezvous mission within a predetermined time.

[0010] The specific process of step one is as follows:

[0011] 2.1 Establishing a nonlinear spacecraft elliptical orbit rendezvous system:

[0012] Introducing the target spacecraft's orbital translation coordinate system The origin of this coordinate system is located at the center of mass of the target spacecraft. The axis is along the radius of the elliptical orbit. direction, The axis is along the direction of the target spacecraft's flight and perpendicular to... axis, The axis points out of the orbital plane and is parallel to the orbital plane. shaft and The axes form a right-handed coordinate system; let the relative positions of the tracking spacecraft and the target spacecraft in this moving coordinate system be . Its time The first and second derivatives are and ,and and These represent the relative velocity and relative acceleration of the two spacecraft, respectively; (Note: The original text contains some inconsistencies and unclear punctuation. A more accurate translation would require the full context.) Let be the semi-major axis of the elliptical orbit. It is the eccentricity of the elliptical orbit. It's a true near-point angle. , Let be the orbital radius of the target spacecraft. In the target spacecraft's orbital translation coordinate system, the nonlinear elliptical orbit rendezvous system affected by external disturbances is as follows:

[0013] (1),

[0014] in It tracks the distance of a spacecraft to the center of the Earth; It is the Earth's gravitational constant; It tracks the acceleration vector generated by the thrust on the spacecraft; It's external interference;

[0015] To simplify formula (1), let:

[0016] ,

[0017] Then, the nonlinear spacecraft elliptical orbit rendezvous system represented by formula (1) is:

[0018] (2),

[0019] in:

[0020] ,

[0021] ,

[0022] and

[0023] ;

[0024] 2.2 Simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system:

[0025] To simplify the rendezvous system of a nonlinear spacecraft orbiting an elliptical orbit, the true anomaly angle is selected. As a new independent variable, let [the variable be...] For function true near point angle The derivative of is used to introduce an invertible linear transformation:

[0026] (3),

[0027] in

[0028] ,

[0029] and If the matrix is ​​invertible, then the nonlinear spacecraft elliptical orbit rendezvous system is transformed into the following nonlinear periodic system:

[0030] (4),

[0031] The initial condition is: , To control the input, External interference, system matrix and The following formulas are given respectively.

[0032] (5),

[0033] and

[0034] (6),

[0035] in

[0036] ,

[0037] ;

[0038] 2.3 The nonlinear periodic system is written as two subsystems, i.e., the strictly nonlinear system form with matched disturbances:

[0039] make:

[0040] ,

[0041] Then formula (4) can be written as:

[0042] (7),

[0043] in and Defined by formula (6), and

[0044] , .

[0045] The specific process of step two is as follows:

[0046] 3.1 Definition of a periodic function and periodic matrix ;

[0047] set up Given a constant, Given an integer, if the function is nonnegative The following three conditions must be met:

[0048] (1) yes A periodic function, and for all ,have ;

[0049] (2) For all ,have And exist , making ;

[0050] (3) ,in for A continuously differentiable function of order 1, and , ;

[0051] Then it is called for function;

[0052] right Choose a constant matrix This makes the matrix pair Controllable, note:

[0053] ,

[0054] but ,definition Periodic matrix:

[0055] (8),

[0056] and

[0057] ,

[0058] in for function;

[0059] 3.2 Constructing a time-delay sliding surface:

[0060] (9).

[0061] The specific process of designing a periodic time-delay sliding mode controller in step three, which combines the all-drive system method, is as follows:

[0062] 4.1 Defining Symbolic Functions :

[0063] set up For any constant, its sign function Defined as:

[0064] ,

[0065] for dimensional vector

[0066] ,

[0067] Its sign function Defined as:

[0068] ,

[0069] for Diagonal matrix of order:

[0070] ,

[0071] Its sign function Defined as:

[0072] ;

[0073] 4.2 Assume there exists a known function:

[0074] ,

[0075] This causes external interference.

[0076] ,

[0077] satisfy

[0078] ,

[0079] Design a periodic time-delay sliding mode controller:

[0080] (10)

[0081] in

[0082] ,

[0083] and

[0084] .

[0085] The specific process by which the closed-loop system consisting of the strictly nonlinear system with matched disturbances and the periodic time-delay sliding diaphragm controller reaches stability within the predetermined true anomaly angle in step three, thereby enabling the two spacecraft to complete the rendezvous mission within a predetermined time, is as follows:

[0086] 5.1 Convergence test of the time-delay sliding surface within the predetermined true anterior angle, i.e. , ;

[0087] Construct the Lyapunov function:

[0088] ,

[0089] Its against The derivative is:

[0090] (11),

[0091] in

[0092] , ,

[0093] , ,

[0094] Substituting formula (10) into formula (11) yields:

[0095] ,

[0096] For sliding surfaces:

[0097] ,

[0098] According to the Lyapunov stability theorem for finite time, we have Convergence occurs at the predetermined true anterior angle, i.e. , ,in:

[0099] ,

[0100] Depend on and The arbitrariness is known It has arbitrariness, thus verifying the convergence of the time-delay sliding surface within the predetermined true anterior angle;

[0101] 5.2 Stability test of the closed-loop system consisting of a strictly nonlinear system with matched disturbances and a periodic time-delay sliding diaphragm controller within a predetermined true anterior angle, i.e. ;

[0102] From the convergence of the time-delay sliding surface in the predetermined true anterior angle in step 5.1, it can be seen that... , ,Will Combining with formulas (7) and (10), we get:

[0103] (12),

[0104] make:

[0105] ,

[0106] Then formula (12) can be further written as:

[0107] (13)

[0108] According to finite spectrum theory:

[0109] ,Right now ;

[0110] because have

[0111] (14)

[0112] according to The periodicity indicates that:

[0113] ,

[0114] Then apply formula (14) and have to ;right All have and According to formula (14), we get , Therefore, the closed-loop system consisting of a nonlinear periodic system and a periodic time-delay sliding diaphragm controller satisfies ,according to The arbitrariness can be used to test the stability of the closed-loop system within a predetermined true anterior angle.

[0115] The most significant advantages of the periodic time-delay sliding mode control method proposed in this technical solution for nonlinear spacecraft elliptical orbit rendezvous systems under the influence of external disturbances include three aspects:

[0116] (1) The time-delay sliding mode control method was applied to the nonlinear spacecraft elliptical orbit rendezvous system for the first time to obtain nonlinear time-delay sliding mode control. Under the action of the controller, the nonlinear spacecraft elliptical orbit rendezvous system can complete the rendezvous task within a predetermined time, and the convergence time is independent of the initial conditions.

[0117] (2) Compared with existing time-determined control methods such as time-varying high-gain function method, this technical solution adopts periodic time-delay sliding mode control method to design periodic time-delay sliding mode controller. This controller can not only successfully realize spacecraft rendezvous within a predetermined time, but also has the characteristics of control non-singularity and system deadbeat.

[0118] (3) Unlike traditional system linearization methods such as Taylor expansion, this technical solution adopts the full-drive system method for nonlinear periodic systems. While retaining higher-order terms, it simplifies the nonlinear system, which can not only effectively control the nonlinear spacecraft elliptical orbit rendezvous system, but also improve the control accuracy. Attached Figure Description

[0119] Figure 1 The coordinate system for the target spacecraft's orbital movement;

[0120] Figure 2 For the designed periodic time-delay sliding surface components , and The curve of change;

[0121] Figure 3 For the components of the designed periodic time-delay sliding mode controller , and The curve of change;

[0122] Figure 4 State components of a nonlinear periodic system , and The curve of change;

[0123] Figure 5 State components of a nonlinear periodic system , and The curve of change;

[0124] Figure 6 To track spacecraft control input components , and The curve of change;

[0125] Figure 7 Relative velocity of spacecraft , and The curve of change;

[0126] Figure 8 Relative position of spacecraft , and The curve of change;

[0127] Figure 9 The relative position of the spacecraft in a three-dimensional coordinate system , and Curve showing the change in motion trajectory. Detailed Implementation

[0128] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The schematic diagrams and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0129] Example:

[0130] A periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system includes the following steps:

[0131] Step 1: Use an invertible linear transformation to simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system, and express it as a strictly nonlinear system in the form of matching disturbances. The nonlinear system is written as two subsystems.

[0132] 1.1 Establish a nonlinear spacecraft elliptical orbit rendezvous system;

[0133] Introducing the target spacecraft's orbital translation coordinate system The origin of this coordinate system is located at the center of mass of the target spacecraft. The axis is along the direction of the radius R of the elliptical orbit. The axis is along the direction of the target spacecraft's flight and perpendicular to... axis, The axis points out of the orbital plane and is parallel to the orbital plane. shaft and The axes form a right-handed coordinate system; let the relative positions of the tracking spacecraft and the target spacecraft in this moving coordinate system be . , and Representing relative position to time Let the first and second derivatives be:

[0134] , ,

[0135] and

[0136] ,

[0137] The relative motion between the target spacecraft and the tracking spacecraft can be described by the following nonlinear spacecraft elliptical orbit rendezvous system:

[0138] (1),

[0139] in It is the target's orbital radius. It is the Earth's gravitational constant; It tracks the acceleration vector generated by the thrust on the spacecraft; It's external interference;

[0140] For nonlinear spacecraft elliptical orbit rendezvous systems, due to the true anomaly angle... It is time The implicit function makes direct processing of the system quite complex; in addition, the system itself is affected by external disturbances, making the control design of the nonlinear spacecraft elliptical orbit rendezvous system even more difficult.

[0141] 1.2 Simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system:

[0142] To simplify the rendezvous system of a nonlinear spacecraft in an elliptical orbit, the true anomaly angle is selected. As a new independent variable, the nonlinear spacecraft elliptical orbit rendezvous system is transformed into a nonlinear periodic system, allowing...

[0143]

[0144] in

[0145] ,

[0146] Then there is

[0147] ,

[0148] and

[0149] ,

[0150] in , It is a constant; defined as:

[0151] ,

[0152] according to

[0153] ,

[0154] but It can be used and Linear representation is:

[0155]

[0156] in

[0157] ,

[0158] ,

[0159] ,

[0160] because and achievable

[0161]

[0162] in

[0163] ,

[0164] remember

[0165] ,

[0166] Then, the nonlinear spacecraft elliptical orbit rendezvous system represented by formula (1) is:

[0167] (2),

[0168] in:

[0169] ,

[0170] ,

[0171] and

[0172] ;

[0173] Easy to calculate

[0174] (3),

[0175] in

[0176] ,

[0177] and Since it is an invertible matrix, equation (1) is transformed into the following nonlinear periodic system:

[0178] (4),

[0179] The initial condition is: , To control the input, the system matrix and The following formulas are given respectively.

[0180] (5),

[0181] and

[0182] (6),

[0183] in

[0184] ,

[0185] ;

[0186] The process of transforming a nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system employs a reversible linear transformation, which means that the nonlinear spacecraft elliptical orbit rendezvous system and the nonlinear periodic system are equivalent. Since the nonlinear periodic system is periodic, the dynamic performance of the system can be achieved by designing periodic control.

[0187] 1.3 Rewrite the nonlinear periodic system as a strictly nonlinear system with matched disturbances:

[0188] make

[0189] ,

[0190] Then formula (4) can be written as

[0191] (7),

[0192] in and Defined in equation (6), and

[0193] , ;

[0194] The above nonlinear periodic system is represented as two subsystems. These two subsystems are strictly nonlinear systems that match disturbances, which facilitates the construction of the sliding surface of the periodic sliding mode controller.

[0195] Step 2: Construct the time-delay sliding surface:

[0196] 2.1 Definition of a periodic function and periodic matrix :

[0197] set up Given a constant, Given an integer (which can be infinite), if the function is non-negative The following three conditions must be met:

[0198] (1) yes A periodic function, and for all ,have ;

[0199] (2) For all ,have And exist , making ;

[0200] (3) ,in for A continuously differentiable function of order 1, and , ,

[0201] Then it is called for function;

[0202] Based on the above definition, it is easy to construct a Function; for example, for any integer The following options can be selected: Function (considering only) ):

[0203]

[0204] in and It is a constant, and , ;

[0205] Choose an appropriate constant matrix This makes the matrix pair Controllable, memorized

[0206] ,

[0207] but ,definition Periodic matrix

[0208] (8),

[0209] and

[0210] ,

[0211] in for function;

[0212] 2.2 Constructing a time-delay sliding surface:

[0213] (9);

[0214] Step 3: Design a periodic time-delay sliding mode controller:

[0215] 3.1 Define symbolic functions :

[0216] set up For any constant, its sign function Defined as

[0217] ,

[0218] for dimensional vector

[0219] ,

[0220] Its sign function Defined as

[0221] ,

[0222] for Diagonal matrix of order

[0223] ,

[0224] Its sign function Defined as

[0225] ,

[0226] 3.2 Given external disturbances Boundedness assumption:

[0227] Assume there exists a known function

[0228] ,

[0229] External interference

[0230] ,

[0231] satisfy

[0232] ;

[0233] 3.3 Design of a periodic time-delay sliding mode controller:

[0234] (10)

[0235] in

[0236] ,

[0237] and

[0238] ;

[0239] 3.4 Convergence test of the time-delay sliding surface within the predetermined true anterior angle, i.e. , ;

[0240] Constructing Lyapunov functions

[0241] ,

[0242] Its against The derivative is

[0243] (11),

[0244] in

[0245] , ,

[0246] ;

[0247] Substituting formula (10) into formula (11) yields

[0248] ,

[0249] According to Lyapunov's stability theorem for finite-time conditions, the sliding surface can be obtained... It is convergent, that is... , ,in

[0250] ,

[0251] Depend on and The arbitrariness is known It has arbitrariness, thus verifying the convergence of the time-delay sliding surface within the predetermined true anterior angle;

[0252] 3.5 Stability test of a closed-loop system consisting of a strictly nonlinear system with matched disturbances and a periodic time-delay sliding diaphragm controller within a predetermined true anterior angle, i.e. ;

[0253] From the convergence of the time-delay sliding surface, we can know

[0254] , ,

[0255] This means

[0256] (12),

[0257] remember

[0258] ,

[0259] Then formula (12) can be further written as

[0260] (13)

[0261] According to finite spectrum theory, we can obtain

[0262] ,

[0263] Right now ;

[0264] because ,have

[0265] (14)

[0266] And from

[0267] ,

[0268] and

[0269] ,

[0270] but ;right All have and From formula (14), we can obtain , Thus, the closed-loop system satisfies... ;according to The arbitrariness of the value can be used to test the stability of the closed-loop system within a predetermined true anterior angle.

[0271] To verify the effectiveness of the proposed method, a simulation verification will be performed on a nonlinear spacecraft elliptical orbit rendezvous system.

[0272] Assume the target spacecraft and the tracking spacecraft are in axis, shaft and The relative position and relative velocity on the axis are respectively and The control input is The orbital parameters of the target spacecraft are shown in Table 1 below:

[0273] Table 1 Orbital parameters of the target spacecraft

[0274]

[0275] The system initialization parameters are set as follows: Let the initial time be... The relative position and relative velocity are respectively

[0276] ,

[0277] and

[0278] ,

[0279] That is, spacecraft in such Figure 1 The relative positions in the shown moving coordinate system are -45000m, 65000m, and 45000m, with relative velocities of -20m / s, 50m / s, and -10m / s, respectively. Due to time... Angle with true nearest point The relationship can be expressed by the following Kepler equation:

[0280] ,

[0281] when When this is the case, it is easy to calculate the initial value of the true anterior angle. The initial state of the nonlinear periodic system can be obtained by using an invertible linear transformation:

[0282] ,

[0283] Select constant matrix

[0284] ,

[0285] The form is defined in a specific implementation, and its parameters are selected as follows:

[0286] ,

[0287] External interference Selected as

[0288] ,

[0289] Its upper bound is selected as

[0290] ,

[0291] Control delay The controller parameters can be selected as follows:

[0292] ;

[0293] exist In the - domain, based on the designed time-delay sliding surface, the component images of the time-delay sliding surface are as follows: Figure 2 As shown, by Figure 2 It can be seen that the time-delay sliding surface is It converges to zero, that is... , This further verifies the convergence of the time-delay sliding surface within the predetermined true anterior angle. Based on the periodic time-delay sliding mode control method proposed in this example, the designed periodic time-delay sliding mode controller... Changes in the image, such as Figure 3 As shown. Under the action of this controller, the state change graph of the nonlinear periodic system is as follows. Figure 4-5 As shown, from Figure 4-5 It can be seen that the closed-loop system state is It converges to zero, that is... , This verifies the stability of the closed-loop system, consisting of a nonlinear periodic system and a controller, within a predetermined true anomaly angle.

[0294] Based on the state of the nonlinear periodic system and the designed periodic time-delay sliding mode controller, the control input of the nonlinear spacecraft elliptical orbit rendezvous system in the time domain can be obtained using the Kepler equation and invertible linear transformation. Figure 6 As shown. Under this control input, the changes in the spacecraft's relative velocity and relative position are shown in the graphs. Figure 7 and Figure 8 As shown, from Figure 7 and Figure 8 It can be seen that the relative position and relative velocity of the spacecraft converge to zero within the predetermined time, indicating that the spacecraft can complete the rendezvous mission within the predetermined time under the obtained control input. To further verify the rendezvous between the target spacecraft and the tracking spacecraft within the predetermined time, the motion change image of the relative position of the spacecraft in three-dimensional space is shown below. Figure 9 ,from Figure 9 It can be seen that the relative positions of the spacecraft converge to zero within the predetermined time, which further demonstrates that the spacecraft can complete the rendezvous mission within the predetermined time. Therefore, for a nonlinear spacecraft elliptical orbit rendezvous system subject to external disturbances, under the action of the obtained periodic time-delay sliding mode controller, the spacecraft can achieve stability within the predetermined time, and the convergence time is independent of the initial state of the system.

[0295] It is worth noting that although the periodic time-delay sliding mode controller obtained in this example is periodic, its upper control bound is determined by the predetermined rendezvous time of the spacecraft. Generally, the shorter the predetermined rendezvous time, the larger the upper control bound of the periodic time-delay sliding mode controller; conversely, the longer the predetermined rendezvous time, the smaller the upper control bound. Setting the predetermined rendezvous time and the upper control bound of the periodic time-delay sliding mode controller requires a trade-off between the length of the predetermined rendezvous time and the magnitude of the control by the periodic time-delay sliding mode controller, based on the actual requirements of the spacecraft rendezvous. Specifically, this can be achieved by adjusting the gain delay of the periodic time-delay sliding mode controller. accomplish.

[0296] The above describes the excellent optimization effect shown by one embodiment of the present invention. Obviously, the present invention is not limited to the above embodiment. Various modifications can be made to it without departing from the basic spirit of the present invention and without exceeding the scope of the substantive content of the present invention.

Claims

1. A periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system, characterized in that, Includes the following steps: Step 1: Use invertible linear transformation to simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system. Further, write the nonlinear periodic system into two subsystems, which are strictly nonlinear systems for matching disturbances. Step 2: Based on the two subsystems obtained in Step 1, construct a time-delay sliding surface using a periodic time-delay feedback control method, and verify the convergence of the sliding surface within a predetermined true anomaly angle. Step 3: Based on Step 1 and Step 2, design a periodic time-delay sliding mode controller using the all-drive system method. This will enable the closed-loop system, consisting of a strictly nonlinear system with matched disturbances and a periodic time-delay sliding mode controller, to stabilize within a predetermined true anomaly angle, thereby achieving the rendezvous mission of the spacecraft within a predetermined time.

2. The periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system according to claim 1, characterized in that, The specific process of step one is as follows: 2.1 Establishing a nonlinear spacecraft elliptical orbit rendezvous system: Introducing the target spacecraft's orbital translation coordinate system The origin of this coordinate system is located at the center of mass of the target spacecraft. The axis is along the radius of the elliptical orbit. direction, The axis is along the direction of the target spacecraft's flight and perpendicular to... axis, The axis points out of the orbital plane and is parallel to the orbital plane. shaft and The axes form a right-handed coordinate system; let the relative positions of the tracking spacecraft and the target spacecraft in this moving coordinate system be . Its time The first and second derivatives are and ,and and These represent the relative velocity and relative acceleration of the two spacecraft, respectively; (Note: The original text contains some inconsistencies and unclear punctuation. A more accurate translation would require the full context.) Let be the semi-major axis of the elliptical orbit. It is the eccentricity of the elliptical orbit. It's a true near-point angle. , Let be the orbital radius of the target spacecraft. In the target spacecraft's orbital translation coordinate system, the nonlinear elliptical orbit rendezvous system affected by external disturbances is as follows: （1）， in It tracks the distance of a spacecraft to the center of the Earth; It is the Earth's gravitational constant; It tracks the acceleration vector generated by the thrust on the spacecraft; It's external interference; To simplify formula (1), let: ， Then, the nonlinear spacecraft elliptical orbit rendezvous system represented by formula (1) is: （2）， in: ， ， and ； 2.2 Simplify the nonlinear spacecraft elliptical orbit rendezvous system into a nonlinear periodic system: To simplify the rendezvous system of a nonlinear spacecraft orbiting an elliptical orbit, the true anomaly angle is selected. As a new independent variable, let [the variable be...] For function true near point angle The derivative of is used to introduce an invertible linear transformation: （3）， in ， and If the matrix is ​​invertible, then the nonlinear spacecraft elliptical orbit rendezvous system is transformed into the following nonlinear periodic system: （4）， The initial condition is: , To control the input, External interference, system matrix and The following formulas are given respectively. （5）， and （6）， in ， ； 2.3 The nonlinear periodic system is written as two subsystems, i.e., the strictly nonlinear system form with matched disturbances: make: ， Then formula (4) can be written as: （7）， in and Defined by formula (6), and ， 。 3. The periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system according to claim 2, characterized in that, The specific process of step two is as follows: 3.1 Definition of a periodic function and periodic matrix : set up Given a constant, Given an integer, if the function is nonnegative The following three conditions must be met: (1) yes A periodic function, and for all ,have ; (2) For all ,have And exist , making ; (3) ,in for A continuously differentiable function of order 1, and , ; Then it is called for function; right Choose a constant matrix This makes the matrix pair Controllable, note: ， but ,definition Periodic matrix: （8）， and ， in for function; 3.2 Constructing a time-delay sliding surface: （9）。 4. The periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system according to claim 3, characterized in that, The specific process of designing a periodic time-delay sliding mode controller in step three, which combines the all-drive system method, is as follows: 4.1 Defining Symbolic Functions : set up For any constant, its sign function Defined as: ， for dimensional vector ， Its sign function Defined as: ， for Diagonal matrix of order: ， Its sign function Defined as: ； 4.2 Assume there exists a known function: ， This causes external interference. ， satisfy ， Design a periodic time-delay sliding mode controller: （10）， in ， and 。 5. The periodic time-delay sliding mode control method for a nonlinear spacecraft elliptical orbit rendezvous system according to claim 4, characterized in that, The specific process by which the closed-loop system consisting of the strictly nonlinear system with matched disturbances and the periodic time-delay sliding diaphragm controller reaches stability within the predetermined true anomaly angle in step three, thereby enabling the two spacecraft to complete the rendezvous mission within a predetermined time, is as follows: 5.1 Convergence test of the time-delay sliding surface within the predetermined true anterior angle, i.e. , ; Construct the Lyapunov function: ， Its against The derivative is: （11）， in ， ， ， Substituting formula (10) into formula (11) yields: ， For sliding surfaces: ， According to the Lyapunov stability theorem for finite time, we have It converges within the predetermined true anterior angle, i.e. , ,in: ， Depend on and The arbitrariness is known It has arbitrariness, thus verifying the convergence of the time-delay sliding surface within the predetermined true anterior angle; 5.2 Stability test of the closed-loop system consisting of a strictly nonlinear system with matched disturbances and a periodic time-delay sliding mode controller within a predetermined true anomaly angle, i.e. ; From the convergence of the time-delay sliding surface in the predetermined true anterior angle in step 5.1, it can be seen that... , ,Will Combining with formulas (7) and (10), we get: ， （12）， make: ， Then formula (12) can be further written as: （13）， According to finite spectrum theory: , Right now ; because have （14）， according to The periodicity indicates that: ， Then apply formula (14) and have to ;right All have and According to formula (14), we get , Therefore, the closed-loop system consisting of a nonlinear periodic system and a periodic time-delay sliding diaphragm controller satisfies ,according to The arbitrariness can be used to test the stability of the closed-loop system within a predetermined true anterior angle.

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