CN-121990180-A - Nonlinear spacecraft elliptical orbit intersection system period time lag sliding mode control method

CN121990180ACN 121990180 ACN121990180 ACN 121990180ACN-121990180-A

Abstract

The invention discloses a nonlinear spacecraft elliptical orbit intersection system period time-lag sliding mode control method. Aiming at a nonlinear spacecraft elliptical orbit intersection system model subjected to external interference, the model is simplified into a nonlinear periodic system according to reversible linear transformation. On this basis, the nonlinear periodic system is written as a strictly nonlinear system matching the disturbance. The cycle time-lag sliding mode controller of the strict nonlinear system with the matched interference is designed by utilizing a cycle time-lag sliding mode control method, and under the action of the controller, a closed loop system formed by the strict nonlinear system with the matched interference and the controller is stable in a preset true near point angle. The control design method of the invention overcomes the defects that the traditional sliding mode control method of the elliptical orbit intersection system of the existing spacecraft is easy to ignore, the control constraint is easy to ignore, the control implementation of the preset time is abnormal, the convergence time depends on the initial value condition, the convergence speed is low, the method is only suitable for a low-order or single-input system and the like, and solves the problem of the intersection of the spacecraft in the preset time.

Inventors

GAO XIANGYU
CHEN MENGJIE

Assignees

广西师范大学

Dates

Publication Date: 20260508
Application Date: 20260402

Claims (5)

1. A nonlinear spacecraft elliptical orbit intersection system period time lag sliding mode control method is characterized by comprising the following steps: step one, simplifying a nonlinear spacecraft elliptical orbit intersection system into a nonlinear periodic system by using reversible linear transformation, and further writing the nonlinear periodic system into two subsystems, wherein the two subsystems are strict nonlinear systems for matching interference; Step two, based on the two subsystems obtained in the step one, adopting a periodic time-lag feedback control method to construct a time-lag sliding mode surface, and checking the convergence of the sliding mode surface in a preset true near point angle; And thirdly, designing a cycle time-lag sliding mode controller according to the first step and the second step by combining a full-drive system method, so that a closed loop system formed by a strict nonlinear system matched with interference and the cycle time-lag sliding mode controller is stable in a preset real near point angle, and the task of intersecting the spacecraft in a preset time is achieved.
2. The method for controlling the periodic time-lag sliding mode of the elliptical orbit intersection system of the nonlinear spacecraft according to claim 1, wherein the specific process of the first step is as follows: 2.1, establishing a nonlinear spacecraft elliptical orbit intersection system: introducing a target spacecraft orbital motion coordinate system The origin of the coordinate system is located at the centroid of the target spacecraft, The axis being along the radius of the elliptical orbit Is provided in the direction of (a), The axis is along the direction of the target spacecraft and perpendicular to The axis of the shaft is provided with a plurality of grooves, The axis being directed out of the plane of the track and being parallel to Shaft and method for producing the same The axis forms a right-hand coordinate system, and the relative position of the tracking spacecraft and the target spacecraft under the moving coordinate system is set as Which is time-lapse The first and second derivatives of (2) are And And (2) and And Representing the relative speeds and accelerations of two spacecraft respectively Is a long half shaft of an elliptical orbit, Is the eccentricity of the elliptical orbit and, Is the true angle of the point of approach, , The orbit radius of the target spacecraft is the orbit radius of the nonlinear spacecraft elliptical orbit intersection system which is subject to external interference under the orbit movement coordinate system of the target spacecraft is as follows: (1), Wherein the method comprises the steps of Tracking the distance from the spacecraft to the sphere center of the earth; Is the gravitational constant of the earth; The method is to track an acceleration vector generated by thrust on a spacecraft; Is an external disturbance; To simplify equation (1), let: , the nonlinear spacecraft elliptical orbit intersection system represented by equation (1) is: (2), Wherein: , , And ; 2.2 Simplifying the nonlinear spacecraft elliptical orbit intersection system into a nonlinear periodic system: in order to simplify the elliptic orbit meeting system of the nonlinear spacecraft, a true near point angle is selected As a new argument, note As a function of For true near point angle Introducing a reversible linear transformation: (3), Wherein the method comprises the steps of , And is also provided with As a reversible matrix, the nonlinear spacecraft elliptical orbit intersection system is converted into the following nonlinear periodic system: (4), Wherein the initial conditions are , In order to control the input of the device, For external interference, system matrix And Respectively given by (5), And (6), Wherein the method comprises the steps of , ; 2.3 Writing the nonlinear periodic system into two subsystems, namely a strictly nonlinear system form of matched interference: And (3) making: , Then equation (4) is written as: (7), Wherein the method comprises the steps of And Is defined by equation (6) and , 。
3. The method for controlling the periodic time-lag sliding mode of the elliptical orbit intersection system of the nonlinear spacecraft according to claim 2, wherein the specific process of the second step is as follows: 3.1 definition of periodic functions And a period matrix : Is provided with For a given constant value of the number, For a given integer, if not a negative function The following three conditions are satisfied: (1) Is that Periodic function, and for all There is ; (2) For all of There is And is provided with So that ; (3) Wherein Is that The order is continuously differentiable, and , ; Then call for Is that A function; For a pair of Selecting a constant matrix So that the matrix pairs Energy control and record: , Then Definition of A period matrix: (8), And is also provided with , Wherein the method comprises the steps of Is that A function; 3.2 construction of a time-lapse slip die surface: (9)。
4. The method for controlling the periodic time-lapse sliding mode of the elliptical orbit intersection system of the nonlinear spacecraft according to claim 3, wherein the specific process of designing the periodic time-lapse sliding mode controller by combining the full-drive system method in the third step is as follows: 4.1 Defining a sign function : Is provided with Is an arbitrary constant, its sign function The definition is as follows: , For the following Dimension vector , Its sign function The definition is as follows: , For the following Order diagonal matrix: , Its sign function The definition is as follows: ; 4.2 Assume that there is a known function: , so that the external interference is caused, , Satisfy the following requirements , Design cycle time lag sliding mode controller: (10), Wherein the method comprises the steps of , And 。
5. The method for controlling the periodic time-lag sliding mode of the elliptical orbit intersection system of the nonlinear spacecraft according to claim 4, wherein in the third step, a closed loop system formed by a strict nonlinear system matched with interference and a periodic time-lag sliding film controller is stabilized within a preset true near point angle, so that the specific process of completing the intersection task of two spacecraft within preset time is realized: 5.1 Convergence test of the time-lapse slip-form surface at a predetermined true near point angle, i.e , ; Constructing a Liapunov function: , Its pair of The derivative of (2) is: (11), Wherein the method comprises the steps of , , , Substituting formula (10) into formula (11) to obtain: , For the slide face: , According to the limited-time Lyapunov stability theorem Converging within a predetermined true angle of approach, i.e , Wherein: , From the following components And Can be seen from the arbitrary nature of (2) The convergence in a preset true near point angle of the time-lag sliding mode surface is verified; 5.2 stability test of closed-loop System consisting of strictly nonlinear System matching interference and cycle time-lapse sliding-mode controller in predetermined true near Point angles, i.e ; From the convergence of the lag-slide surface at step 5.1 within a predetermined true near point angle , Will be And formula (7) and formula (10) are combined to obtain: , (12), And (3) making: , then equation (12) is further written as: (13), According to the finite spectrum theory, the method comprises the following steps: I.e. ; Due to Has the following components (14), According to The periodicity of (2) can be seen as: , And then apply equation (14) and Obtaining the product To (3) pair All have And Obtained according to formula (14) , Therefore, the closed loop system formed by the nonlinear periodic system and the period time lag synovial membrane controller meets the following requirements According to Can verify the stability of the closed loop system within a predetermined true near point angle.

Description

Nonlinear spacecraft elliptical orbit intersection system period time lag sliding mode control method Technical Field The invention belongs to the technical field of spacecraft control, and particularly relates to a period time-lag sliding mode control method for a nonlinear spacecraft elliptical orbit intersection system. Background The spacecraft intersection technology is one of the three most core technologies in the aerospace field. The method forms three bases of manned space engineering together with a spacecraft launching technology and a recovery technology. The spacecraft intersection is an indispensable condition for completing the spaceflight tasks such as satellite maintenance, satellite networking, deep space interception, space station construction, space rescue and the like, and the technology is widely applied to spaceflight engineering such as space laboratories, space stations, remote sensing platforms, space communication systems and the like. Therefore, the research on the spacecraft intersection technology has important application value. Consider two spacecraft, one of which is a target spacecraft and the other is a tracking spacecraft. When the target spacecraft is operating in an elliptical orbit, the relative motion between the two spacecraft may be described by a system of nonlinear time-varying differential equations, which may also be referred to as a nonlinear spacecraft elliptical orbit intersection system. However, the nonlinear spacecraft elliptical orbit intersection system has the dual characteristics of time-varying property and nonlinearity, so that the control problem related to the nonlinear spacecraft elliptical orbit intersection system is extremely complex, and the system is rarely researched. This makes it more difficult to study nonlinear spacecraft elliptical orbit intersection systems when the system is affected by external disturbances, making it more challenging to study control problems associated therewith. As a powerful tool for robust nonlinear control design, sliding mode control is widely used due to its advantages such as simple structure and robust against disturbance. The sliding mode control method mainly comprises linear sliding mode control, self-adaptive sliding mode control, terminal sliding mode control, limited time terminal sliding mode control, fixed time terminal sliding mode control and preset time terminal sliding mode control. Although there have been a great deal of research efforts on sliding mode control methods, there are several drawbacks, such as ignoring control constraints, high gain functions leading to the occurrence of singularities in the implementation of the predetermined time control, slow convergence time dependent initial conditions, and applicability to low-order or single-input systems only. These drawbacks limit the applicability of slipform control in more complex scenarios. This allows us to explore new control design methods to solve the problem of the design of the control of the nonlinear spacecraft elliptical orbit intersection system at a predetermined time under the influence of external disturbances. Disclosure of Invention The invention provides a periodic time-lag sliding mode control method for a nonlinear spacecraft elliptical orbit intersection system, so as to overcome the defects that the traditional sliding mode control method of the conventional spacecraft elliptical orbit intersection system is easy to ignore control constraint, the realization of singularity and convergence time dependence initial value condition of preset time control, low convergence speed, suitability for a low-order or single-input system and the like. The control method is based on a designed periodic time-lag sliding mode controller, so that two spacecrafts can finish the meeting task within a preset time. The nonlinear spacecraft elliptical orbit intersection system period time-lag sliding mode control method comprises the following steps: step one, simplifying a nonlinear spacecraft elliptical orbit intersection system into a nonlinear periodic system by using reversible linear transformation, and further writing the nonlinear periodic system into two subsystems which are strict nonlinear system forms of matching interference on the basis of the nonlinear periodic system; step two, based on the two subsystems obtained in the step one, constructing a time-lag sliding mode surface by adopting a periodic time-lag sliding mode control method, and checking the convergence of the time-lag sliding mode surface in a preset true near point angle; And thirdly, designing a periodic time-lag sliding mode controller according to the first step and the second step by combining a full-drive system method, so that a closed loop system formed by a strict nonlinear system matched with interference and the periodic time-lag sliding mode controller is stable in a preset real near point angle, and the task of meeting the spacecraft in preset tim