A Predetermined Error Trajectory Control Method for Non-cooperative Target Rendezvous System

Abstract

The present invention discloses a method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system with external interference, actuator failure and modeling uncertainty. Compared with the existing tracking control method, this method takes into account the performance of the tracking error and simplifies the design steps of the controller. The method of the present invention includes: establishing a second-order full-drive system model of a non-cooperative target rendezvous system, designing a sliding mode controller, designing a disturbance observer, designing an intermediate control variable, and analyzing the stability of a closed-loop system. Based on the disturbance observer, the full-drive system method, and the sliding mode control theory, the present invention designs a predetermined error trajectory controller in consideration of actuator failures and the system having external interference and modeling uncertainty, thereby realizing the tracking of the desired state trajectory, and the tracking error meets the specified performance.

Description

Technical Field

[0001] The invention belongs to the field of aerospace control technology, relates to the control of a non-cooperative target rendezvous system, and specifically relates to a predetermined error trajectory control method for a non-cooperative target rendezvous system. Background Art

[0002] In-orbit space service missions, such as space debris removal, capturing tumbling spacecraft, and tracking enemy spacecraft, are all very typical non-cooperative targets. To complete these tasks, the spacecraft needs to autonomously rendezvous with the non-cooperative target and track it. Therefore, the study of the control of the non-cooperative target rendezvous system has very important theoretical significance and application value.

[0003] At present, many non-cooperative target rendezvous control problems are solved by state space methods. The mainstream method is to linearize the nonlinear terms of the system, but this will lead to inaccurate control models and affect the control accuracy of the system. At the same time, due to measurement errors and fuel consumption, the actual mass of the spacecraft cannot be accurately determined, so there may be modeling uncertainties in the non-cooperative target rendezvous system. In the control and analysis of the system, ignoring these problems will affect the performance of the system and even cause system instability. In addition to external interference and actuator failure, in the process of serving spacecraft to perform some space missions, the controller needs to ensure that the trajectory tracking error meets certain performance. For this reason, it is necessary to develop a new control method to improve the control accuracy and consider the performance of the trajectory tracking error. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention proposes a predetermined error trajectory control method for a non-cooperative target rendezvous system. Based on the disturbance observer, the full drive system method and the sliding mode control theory, actuator failure, external interference and modeling uncertainty are taken into consideration, and a predetermined error estimation controller based on the full drive system (FAS) method and sliding mode control is designed to achieve effective tracking control of the non-cooperative target rendezvous system.

[0005] A method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system specifically comprises the following steps:

[0006] Step 1: Establish a second-order all-wheel drive system model for a non-cooperative target rendezvous system

[0007] Establish an inertial coordinate system O with the center of the earth as the origin I -X I Y I Z I , establish the inertial coordinate system O with the center of mass of the chasing spacecraft as the origin i -X i Y i Z i, establish the line of sight coordinate system O with the center of mass of the chasing spacecraft as the origin and the direction pointing to the center of mass of the target spacecraft as the positive direction of the X-axis ls -X ls Y ls Z ls According to the principles of aerospace dynamics, the following relative orbit model of spacecraft with external disturbance facing non-cooperative targets is established:

[0008]

[0009]

[0010] in, To calculate the relative distance between the chasing spacecraft and the target spacecraft, and They represent the inclination and azimuth of the line of sight coordinate system relative to the inertial coordinate system, is the gravitational constant, is the distance vector from the center of the Earth to the chasing spacecraft, represent the thrust of the chasing spacecraft at X ls Axis, Y ls Axis and Z ls The acceleration provided in the axis direction, For unknown interference, . , denote the first and second derivatives respectively, represents the 2-norm.

[0011] The above spacecraft relative orbit model is written as the following second-order full drive system:

[0012]

[0013] in, .

[0014] Assuming that the actuator of the spacecraft has gain fault and bias fault during operation, and the actual mass of the spacecraft cannot be accurately determined due to measurement error and consumption, the disturbance quantity is introduced into the second-order full drive system. :

[0015]

[0016]

[0017] in, , and are the nominal mass and actual mass of the spacecraft, Represents the identity matrix of dimension 3. , is the gain fault matrix, diag{} represents the set of diagonal elements, , is the deviation fault vector, are all constants.

[0018] Step 2: Sliding mode controller design based on full drive system approach

[0019] The following controller u is designed using the FAS method:

[0020]

[0021] in is the intermediate control variable to be designed. Apply this controller to the disturbance introduced in step 1 In the second-order all-wheel drive system:

[0022]

[0023] in , Represents the inverse matrix.

[0024] Step 3: Disturbance Observer Design

[0025] Calculate the tracking error e:

[0026]

[0027] in, is the expected trajectory vector.

[0028] Select a specified performance function , which satisfies that for any t>0 is a positive or negative number and , t represents time; design a sliding mode function S=[s1s2s3] T , the i-th synovial variable s i Defined as:

[0029]

[0030] in Tracking error No. elements, To specify performance functions No. elements. Let the sliding mode variable be differentiated with respect to time t:

[0031]

[0032] in, They are No. elements.

[0033] Design the following disturbance observer:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] in They are S, F, The estimated value of , Respectively , No. elements. and are adjustable positive constants and positive definite matrices, respectively. . Represents a symbolic function.

[0040] Step 4: Design of intermediate control variables

[0041] Under the condition of satisfying system stability, design the intermediate control variables :

[0042]

[0043] in is a constant greater than 0, express No. elements.

[0044] The present invention has the following beneficial effects:

[0045] Aiming at the problem that the existing tracking control method of non-cooperative target rendezvous system does not consider the tracking error performance, a predetermined error trajectory control method based on the full drive system method and sliding mode control theory is proposed. The relative orbit model of the spacecraft facing the non-cooperative target is converted into a second-order full drive system form through the full drive system method, and on this basis, a sliding mode controller is designed using the full drive system method and the sliding mode control method, so that the state of the system can track the desired state trajectory and the tracking error meets the predetermined performance. Using the method of the present invention, effective tracking control of the non-cooperative target rendezvous system with external disturbance can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a schematic diagram of the non-cooperative target rendezvous system;

[0047] Figure 2 This is the tracking error result in the embodiment. DETAILED DESCRIPTION

[0048] The present invention will be further explained below with reference to the accompanying drawings;

[0049] A method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system specifically comprises the following steps:

[0050] Step 1: Establish a second-order all-wheel drive system model for a non-cooperative target rendezvous system

[0051] like Figure 1 As shown, an inertial coordinate system O is established with the center of the earth as the origin. I -X I Y I Z I , establish the inertial coordinate system O with the center of mass of the chasing spacecraft as the origin i -X i Y i Z i , establish the line of sight coordinate system O with the center of mass of the chasing spacecraft as the origin and the direction pointing to the center of mass of the target spacecraft as the positive direction of the X-axis ls -X ls Y ls Z ls , for the pursuit spacecraft and the target spacecraft in the non-cooperative target rendezvous system, the following relative orbit model of spacecraft facing the non-cooperative target with external disturbance is established:

[0052]

[0053]

[0054] in, To calculate the relative distance between the chasing spacecraft and the target spacecraft, and They represent the inclination and azimuth of the line of sight coordinate system relative to the inertial coordinate system, is the gravitational constant, is the distance vector from the center of the Earth to the chasing spacecraft, represent the thrust of the chasing spacecraft at X ls Axis, Y ls Axis and Z ls The acceleration provided in the axis direction, For unknown interference, . , denote the first and second derivatives respectively, represents the 2-norm.

[0055] The above spacecraft relative orbit model is written as the following second-order full drive system:

[0056]

[0057] in, .

[0058] Assuming that the actuator of the spacecraft has gain fault and bias fault during operation, and the actual mass of the spacecraft cannot be accurately determined due to measurement error and consumption, the disturbance quantity is introduced into the second-order full drive system. :

[0059]

[0060]

[0061] in, , and are the nominal mass and actual mass of the spacecraft, Represents the identity matrix of dimension 3. , is the gain fault matrix, diag{} represents the set of diagonal elements, , is the deviation fault vector, are all constants.

[0062] Step 2: Sliding mode controller design based on full drive system approach

[0063] The following controller u is designed using the FAS method:

[0064]

[0065] in is the intermediate control variable to be designed. Apply this controller to the disturbance introduced in step 1 In the second-order all-wheel drive system:

[0066]

[0067] in , Represents the inverse matrix.

[0068] Step 3: Disturbance Observer Design

[0069] Calculate the tracking error e:

[0070]

[0071] in, is the expected trajectory vector.

[0072] Select a specified performance function , which satisfies that for any t>0 is a positive or negative number and , t represents time; design a sliding mode function S=[s1s2s3] T , the i-th synovial variable s i Defined as:

[0073]

[0074] in Tracking error No. elements, To specify performance functions No. elements. Let the sliding mode variable be differentiated with respect to time t:

[0075]

[0076] in, They are No. elements.

[0077] Design the following disturbance observer:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] in They are S, F, The estimated value of , Respectively , No. elements. and are adjustable positive constants and positive definite matrices respectively. Represents a symbolic function.

[0084] Step 4: Design of intermediate control variables

[0085] Under the premise of ensuring system stability, design intermediate control variables :

[0086]

[0087] in is a constant greater than 0, express No. elements.

[0088] First, a simulation experiment is conducted to demonstrate the effectiveness of this method. The simulation parameters are selected as follows:

[0089] , ,

[0090] , , , ,

[0091] , , ,

[0092] , ,

[0093] , ,

[0094] The change of tracking error is as follows Figure 2As shown, it can be seen that as time goes by, the tracking error tends to 0 and reaches 0 after a certain period of time, indicating that the chasing spacecraft can successfully track the target spacecraft, and the tracking error coincides with the predetermined tracking error trajectory, indicating that the error trajectory of the spacecraft tracking control is consistent with the predetermined tracking error trajectory, and its performance can be controlled to meet certain conditions.

[0095] The stability of the closed-loop system is analyzed theoretically as follows:

[0096] Disturbance Observer Error Variable It can converge to 0 in a finite time. Therefore, the disturbance observer error can be derived is bounded and satisfies:

[0097]

[0098] in is a normal number.

[0099] Select the following Lyapunov function:

[0100]

[0101] Taking the derivative with respect to time t, we get:

[0102]

[0103] If the control parameters satisfy:

[0104]

[0105] It can be solved as:

[0106]

[0107] If the initial state of the error trajectory satisfies:

[0108]

[0109] Available right All of them are established, so we can infer right Therefore, the error trajectory Will follow the specified error trajectory Tends to 0.

Claims

1. A method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system, characterized in that: The specific steps include: Step 1: Establish an inertial coordinate system O with the center of the earth as the origin I -X I Y I Z I , establish the inertial coordinate system O with the center of mass of the chasing spacecraft as the origin i -X i Y i Z i , establish the line of sight coordinate system O with the center of mass of the chasing spacecraft as the origin and the direction pointing to the center of mass of the target spacecraft as the positive direction of the X-axis ls -X ls Y ls Z ls According to the principles of aerospace dynamics, the following relative orbit model of spacecraft with external disturbance facing non-cooperative targets is established: Where ρ is the relative distance between the pursuit spacecraft and the target spacecraft, ε and β represent the inclination and azimuth of the line of sight coordinate system relative to the inertial coordinate system, μ is the gravitational constant, and R ch =[R x R y R z ] T is the distance vector from the center of the Earth to the chasing spacecraft, a x 、a y 、a z represent the thrust of the chasing spacecraft at X ls Axis, Y ls Axis and Z ls The acceleration provided in the axis direction, d i is unknown interference, i=1,2,3; represent the first derivative and the second derivative respectively, || || represents the 2-norm; The above spacecraft relative orbit model is written as a second-order all-drive system, and the disturbance f is introduced to establish the second-order all-drive system model of the non-cooperative target rendezvous system: in, The disturbance f is: f=(Bu f -u)+d=(Bl-I3)u+Ba d +d in, m0 and m are the nominal mass and actual mass of the spacecraft respectively, I3 represents the unit matrix with dimension 3; u f =lu+a d , is the gain fault matrix, is the deviation fault vector, d is the unknown disturbance, and u is the control input; Step 2: Design the sliding mode controller u based on the full drive system method: Where v is the intermediate control variable to be designed; the controller is applied to the second-order full-drive system with the disturbance f introduced in step 1 to obtain: Where F = G -1 (q)f, represents the inverse matrix; Step 3: Calculate the tracking error of the chasing spacecraft to the target spacecraft and design a disturbance observer; Step 4: Design the intermediate control variable v under the condition of satisfying the system stability.

2. The method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system according to claim 1, characterized in that: Gain fault matrix l = diag{l1,l2,l3}, deviation fault vector a d =[a d1 a d2 a d3 ] T , where diag{} represents the set of diagonal elements, 0≤l i ≤1, a d1 ,a d2 ,a d3 They are all constants, i=1,2,3.

3. The method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system according to claim 1, characterized in that: The tracking error e=qq d ,q d is the expected trajectory vector; Select a specified performance function It satisfies that for any t>0, e d is a positive or negative number and t represents time; design a sliding mode function S = [s1 s2 s3] T , the i-th synovial variable s i Defined as: where e i is the i-th element of the tracking error e, e di To specify the performance function e d The i-th element of ; let the sliding mode variable be differentiated with respect to time t: Among them, v i 、F i ,q di are v, F, q respectively d The i-th element of -1 (q)f.

4. The method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system according to claim 3, characterized in that: Based on the tracking error and the sliding mode function, the following disturbance observer is designed: Where z0, z1, and z2 are S, F, The estimated value of α 0i 、z 0i denote the i-th element of α0 and z0 respectively; η j and L are adjustable positive constant and positive definite matrix respectively, j = 0, 1, 2; sign(·) represents the sign function.

5. The method for controlling a predetermined error trajectory of a non-cooperative target rendezvous system according to claim 4, characterized in that: Design of intermediate control variables Where k1 and k2 are constants greater than 0, z 1i Represents the i-th element of z1.

6. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 5.

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