PID sliding film control method and system for relative orbit of micro-nano satellite based on particle swarm optimization

Abstract

The present invention relates to a micro-nano satellite relative orbit PID sliding film control method and system based on particle swarm optimization. The method includes: establishing a nonlinear relative orbital dynamics model, i.e., a dynamic equation, between a reference satellite and a maneuvering tracking satellite under interference; establishing an ideal orbit for the maneuvering tracking satellite based on various constraints of the micro-nano satellite maneuver; introducing an error between the maneuvering tracking satellite orbit and the ideal orbit, and establishing a sliding film surface using PID control; performing particle swarm optimization on the sliding film surface parameters; and when the orbital state of the disturbed micro-nano satellite is near the sliding film surface, under the action of a control function, causing the orbital state of the disturbed micro-nano satellite to reach the sliding film surface and reach a state to be tracked on the sliding film surface. Based on the fact that the sliding mode is independent of object parameters and interference, the present invention is insensitive to parameter changes and disturbances. Even if the maneuvering satellite deviates from the ideal trajectory and appears near the sliding film surface, under the action of the control function, the system reaches the sliding film surface and finally reaches a state to be tracked on the sliding film surface.

Description

Technical Field

[0001] The present invention belongs to the technical field of relative orbit maneuvering control of micro-nano satellite platforms, and specifically relates to an effective sliding film control technology and strategy, namely a micro-nano satellite relative orbit PID sliding film control method and system based on particle swarm optimization. Background Art

[0002] Micro-nano satellite systems have progressed from early technical verification to commercial applications. Future potential micro-nano satellite space missions will place even higher demands on satellites' on-orbit autonomy, flexibility, agility, and inter-satellite coordinated control. Therefore, relative orbit maneuvering, tracking, and control technologies are crucial to determining the performance of micro-nano satellites in various missions.

[0003] Existing micro-nano satellite orbit tracking and control technology uses a reference satellite and a tracking satellite to implement orbit tracking control through their dynamic equations. This approach takes into account the relative measurement constraints and controller constraints of the micro-nano satellite and utilizes an online trajectory planning method for the entire micro-nano satellite relative orbit maneuver process. Furthermore, considering non-ideal factors such as external disturbances, model uncertainty, and controller errors in relative orbit maneuver control, a combined closed-loop control scheme for high-precision relative orbit maneuvers of the micro-nano satellite is developed to achieve orbit tracking control.

[0004] Among these existing modeling methods, there is still room for improvement in the convergence of relative orbit control under harsh conditions and in the ability to effectively predict and suppress the influence of non-ideal factors. Furthermore, existing methods do not consider interference from micro-nano satellites, which can cause them to deviate from their original trajectory when encountering interference. Therefore, it is necessary to design a control method that addresses satellite interference and returns the satellite to its ideal trajectory. Based on this, the present invention addresses the issue of global tracking control of micro-nano satellite relative orbits and proposes a micro-nano satellite relative orbit tracking method and system based on PID sliding film control with a decay term. This invention achieves global control and does not affect global control even under harsh conditions and the influence of non-ideal factors, thus exhibiting strong anti-interference capabilities. Summary of the Invention

[0005] Aiming at the shortcomings of the existing micro-nano satellite relative orbit tracking control technology, the present invention proposes a micro-nano satellite relative orbit PID sliding film control tracking method and system based on particle swarm optimization.

[0006] The PID control involved in this invention is a type of proportional-integral-derivative control (PIDC) with high algorithm robustness and reliability. Its PID controller consists of a proportional unit (P), an integral unit (I), and a differential unit (D). By setting the three parameters Kp, Ki, and Kd, control of the relative orbit tracking of micro-nano satellites is achieved. The sliding film variable structure control mentioned in this invention is a nonlinear control strategy. This control strategy differs from other control strategies in that the system's "structure" is not fixed; it can be purposefully and continuously changed during the dynamic process based on the system's current state (such as the deviation and its derivatives), forcing the system to move along a predetermined "sliding mode" state trajectory. Therefore, variable structure control is often referred to as sliding mode control, or sliding mode variable structure control. Because the sliding mode is independent of the object parameters and disturbances, variable structure control has a fast response and is insensitive to parameter changes and disturbances, i.e., has excellent anti-interference performance. In order to solve the chattering problem of sliding mode variable structure control, the present invention uses the sum of the equivalent sliding membrane and the robust hyperbolic tangent switching function as the control function. When the trajectory state of the micro-nano satellite is near the sliding membrane surface, under the action of the control function, the trajectory state of the micro-nano satellite reaches the sliding membrane surface, and then finally reaches the state to be tracked on the sliding membrane surface.

[0007] The object of the present invention is achieved through the following technical solutions:

[0008] A PID sliding film control method for micro-nano satellite relative orbit based on particle swarm optimization is proposed. It involves particle swarm optimization of parameters of PID control sliding film surface and selection of sliding film control function, including the following specific steps:

[0009] Step 1) establishing a nonlinear relative orbital dynamics model, i.e., a dynamics equation, between the reference satellite and the maneuvering tracking satellite in the presence of interference;

[0010] Step 2) establishing the ideal orbit of the maneuverable tracking satellite based on various constraints of the micro-nano satellite maneuver;

[0011] Step 3), introduce the error between the maneuver tracking satellite orbit and the ideal orbit, and use PID control with attenuation to establish the sliding membrane surface;

[0012] Step 4), particle swarm optimization of synovial surface parameters;

[0013] Step 5) When the orbital state of the disturbed micro-nano satellite is near the sliding surface, under the action of the control function, the orbital state of the disturbed micro-nano satellite reaches the sliding surface and finally reaches the state that needs to be tracked on the sliding surface.

[0014] Preferably, in step 1), a nonlinear relative orbital dynamics model of the reference satellite and the maneuvering tracking satellite in the presence of interference is established according to Newton's law. In the inertial coordinate system, it is assumed that the absolute position vector r of the reference satellite is s , the absolute position vector of the maneuvering satellite is r t , the relative position vector of the two stars ρ = r t -r s .

[0015] Using Newton's law, we can get ρ = r t -r s The equation that follows:

[0016]

[0017] Where μ is the Earth's gravitational constant, Δf is the relative perturbation acceleration caused by the resultant perturbation force during satellite operation, f is the control force applied to the maneuvering satellite, and m is the mass of the maneuvering satellite. Transformed to the local vertical and local horizontal coordinate system of the reference satellite, the vector form of the nonlinear relative orbital dynamics model of the maneuvering satellite is:

[0018]

[0019] Where ω is the reference star orbital angular velocity, and its value is equal to the rate of change of the true anomaly ν. ​​Then the state quantity is written in the following component form:

[0020]

[0021] Ignoring high-order small quantities, assume The nonlinear relative orbital dynamics model is obtained:

[0022]

[0023]

[0024]

[0025] The reference orbit is a circular orbit, the perturbation force is ignored, and the state variables are written as The acceleration vector formed by the three directions is a=[a x ,a y ,a z ], which is the sum of the relative perturbation acceleration caused by the resultant perturbation force and the acceleration caused by the force applied to the maneuvering satellite. At the same time, considering the satellite in the absence of interference, the state equation describing the relative motion can be written as:

[0026]

[0027] in,

[0028]

[0029] Where n is the angular velocity of the reference satellite.

[0030] Define normalized coordinate variables:

[0031]

[0032] Define the state variable as The acceleration vector formed by the three directions is The above equation becomes:

[0033]

[0034]

[0035] When the interference term is taken into account, the above equation becomes:

[0036]

[0037] d is a bounded interference term and u is a control term.

[0038] Preferably, in step 2), the ideal orbit of the maneuverable tracking satellite is established according to various constraints of the micro-nano satellite maneuver, that is, the relative motion trajectory is planned and designed to obtain the ideal trajectory.

[0039] The main goal of relative orbit maneuver trajectory planning in this step is to comprehensively consider all constraints of the micro-nano satellite maneuver and obtain an optimal path that meets the maneuver's starting and ending conditions. Optimality in the constraints for longer-range maneuvers refers to optimizing fuel consumption, that is, minimizing the velocity increment consumed by the transfer, and the trajectory should be planned by fully utilizing the characteristics of orbital dynamics. Trajectory optimality for shorter-range maneuvers requires ensuring terminal accuracy and matching control modes while also considering fuel consumption, while also balancing trajectory safety.

[0040] The long-distance stage of the mobile star starts from the origin and the target end point is x N In order to make the entire maneuver trajectory converge within the primary star's horizon angle α, first perform a straight path maneuver to reach point x0, then start from x0 and perform N radial impulse transfers to reach x N The trajectory angle of each time converges within α.

[0041] The orbital angular rate of the maneuvering satellite is n, the orbital period is T, and the maneuvering time of the straight path maneuvering segment is t0. The total velocity increment required for the maneuvering process is V total and the total time t total for:

[0042]

[0043]

[0044] The planning performance index pursues the optimal fuel under the planning constraints. The planning model is:

[0045]

[0046]

[0047]

[0048] Among them, t lim is the upper bound of the total transfer time constraint.

[0049] The trajectory planning requirements for the two maneuvering processes in the mid-range phase are essentially the same. Both require given initial and terminal conditions, as well as given constraints such as maneuvering duration and boundaries, to achieve the optimal fuel consumption trajectory from the starting point to the end point.

[0050] Preferably, in step 3), the error between the tracking satellite orbit and the ideal orbit is introduced, and a sliding film surface is established using PID control, and the sum of an equivalent sliding film function and a robust hyperbolic tangent switching function is selected as the control function.

[0051] Under the interference, the maneuver tracking satellite orbit and the ideal orbit are introduced The error of the ideal orbit is:

[0052] e1=ξ-ξ d ,e2=η-η d ,

[0053] The synovial surfaces usually controlled by the synovium are:

[0054]

[0055] n is the order of the synovial membrane. Considering the globality of the control, the present invention adopts the PID control synovial membrane surface with attenuation.

[0056]

[0057] k pj ,k ij ,k dj are PID parameters.

[0058] The present invention adopts equivalent sliding film control, and its control function consists of two parts:

[0059] u j =u jeq +u jsw

[0060] u jeq Depend on We get:

[0061]

[0062]

[0063]

[0064] Among them, λ>0,p>0 considers the globality and vibration resistance of the control, u jsw To have boundaries Hyperbolic tangent switching function: Considering the vibration resistance of the control, u jsw To have boundaries Hyperbolic tangent switching function of :

[0065]

[0066] Among them, λ j >0, Considering the boundedness of d, assume that the maximum value of d is d m , minimum value d l ,λ j =(d m +d l ) / 2,κ j =(d m -d l ) / 2. Choose appropriate parameters for the Lyapunov energy function:

[0067]

[0068] Make Thus achieving synovial control.

[0069] Preferably, in the simulation, the upper limit of the interference d is 0.03 and the lower limit is 0.001.

[0070] Preferably, in step 4), the particle swarm optimization algorithm is used to optimize the synovial surface parameters.

[0071] The fitness function is selected as the derivative of the Lyapunov energy function, which is:

[0072]

[0073] The condition is Particle k pj ,k ij ,k dj The dimension is 3. In the particle swarm algorithm, the velocity and position of the particles are updated after each iteration as follows:

[0074] v k+1=w·v k +c1×r1×(Pbest k -p k )+c2×r2×(Gbest-p k )

[0075] p k+1 =p k +v k+1

[0076]

[0077] Among them, v k 、p k are the velocity and position of the particle at the kth iteration, v k+1 、p k+1 are the velocity and position of the particle at the k+1th iteration, w max 、w min , iteration are the maximum and minimum inertia weights respectively, iteration is the total number of iterations, w is the inertia weight, c1, c2 represent the acceleration factors of individuals and groups, r1, r2. are random numbers between (0, 1), Pbest k ,Gbest is the individual and group positions optimized according to the ,fitness function in each iteration. When the conditions are met or the maximum ,number of iterations is reached, the optimal individual position value is used as the PID ,control parameter.

[0078] Preferably, in step 5), when the state of the system is near the synovial surface, under the action of the control function, the system reaches the synovial surface and then finally reaches the state to be tracked on the synovial surface.

[0079] The process is as follows: according to the minimum energy rule, the ideal trajectory of the maneuvering satellite is optimized as the instruction of the ideal trajectory; the main program of the sliding membrane control is constructed using Simulink in MATLAB to generate a file with the suffix mdl; based on the orbit equation of the maneuvering satellite containing interference, the controlled object function is edited to generate a file with the suffix m; the particle swarm optimization program is edited to obtain the PID sliding membrane control parameters; the controller function is edited (specifically, it can be input through the corresponding module in Simulink in MATLAB); finally, the results are obtained, which shows that the control scheme can realize that the maneuvering satellite can finally reach the state that needs to be tracked.

[0080] The present invention also discloses a micro-nano satellite relative orbit PID sliding membrane control system based on particle swarm optimization, which includes a maneuvering satellite relative orbit dynamics model establishment module, a maneuvering satellite ideal orbit planning module, a PID control sliding membrane surface establishment module, a sliding membrane surface parameter optimization module, and a tracking state realization module. The specific descriptions of each module are as follows:

[0081] Maneuvering satellite relative orbit dynamics model establishment module: Based on Newtonian dynamics theory, a nonlinear relative orbit dynamics model, i.e., dynamic equation, is established between the reference satellite and the maneuvering tracking satellite under interference.

[0082] Maneuvering Satellite Ideal Orbit Planning Module: This module optimizes the ideal orbit of the maneuvering satellite based on constraints such as the minimum fuel consumption for micro-nano satellite maneuvers. This module plans and designs the relative motion trajectory to obtain the ideal trajectory.

[0083] PID control sliding membrane surface establishment module: This module introduces the error between the tracking satellite orbit and the ideal orbit to establish the PID control sliding membrane surface. The sum of the equivalent sliding membrane function and the robust hyperbolic tangent switching function is selected as the control function.

[0084] Synovial surface parameter optimization module: selects the fitness function and uses the particle swarm optimization algorithm to optimize the PID control parameters to achieve synovial control.

[0085] Tracking state realization module: When the orbital state of the disturbed micro-nano satellite is near the sliding surface, under the action of the control function, the orbital state of the disturbed micro-nano satellite reaches the sliding surface and reaches the state that needs to be tracked on the sliding surface.

[0086] Each processing stage involved in the above modules can be implemented by programming and the feasibility of the control method can be proved.

[0087] Compared with the prior art, the present invention has the following beneficial effects:

[0088] The present invention proposes a PID sliding film control method and system for micro-nanosatellite relative orbits based on particle swarm optimization. Its innovation lies in the fact that the sliding film variable structure control described in the present invention is a nonlinear control strategy. This control strategy differs from other control strategies in that the "structure" of the micro-nanosatellite's orbital state is not fixed but can be purposefully and continuously changed during the dynamic process based on the current state of the micro-nanosatellite's orbit (such as the deviation and its derivatives), forcing the micro-nanosatellite to move along a predetermined "sliding mode" state trajectory. Existing satellite orbit control primarily optimizes the ideal orbit of a maneuvering satellite based on constraints such as minimizing fuel consumption during maneuvering, essentially planning and designing the relative motion trajectory. In reality, maneuvering satellites may encounter various interferences that can cause them to deviate from their original trajectory. However, the present invention, based on the fact that the sliding mode is independent of object parameters and interference, is insensitive to parameter changes and disturbances. Although the maneuvering satellite deviates from the ideal trajectory and appears near the sliding film surface, under the action of the control function, the micro-nanosatellite's orbital state reaches the sliding film surface and then ultimately reaches the desired tracking state on the sliding film surface. This is the main innovation of the present invention. In addition, in order to solve the chattering problem of sliding mode variable structure control, the present invention uses the sum of an equivalent sliding film and a robust hyperbolic tangent switching function as a control function to control the state of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 This is a data simulation architecture diagram involved in a micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization in an embodiment of the present invention.

[0090] Figure 2 Optimize PID control for particle swarm p k i k d Parameter evolution diagram.

[0091] Figure 3 The figure shows the error diagram between the simulated controlled trajectory data and the ideal data. e1 represents the error along the ξ axis, e2 represents the error along the η axis, and e3 represents the error along the ζ axis. The results show that it can track well.

[0092] Figure 4 This is a flow chart of a PID sliding film control method for relative orbits of micro-nano satellites based on particle swarm optimization according to an embodiment of the present invention.

[0093] Figure 5 This is a block diagram of a micro-nano satellite relative orbit PID sliding film control system based on particle swarm optimization according to an embodiment of the present invention. DETAILED DESCRIPTION

[0094] To more clearly illustrate the embodiments of the present invention, specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings and other embodiments can be obtained based on these drawings without inventive efforts.

[0095] like Figure 1-5 As shown, a preferred embodiment of the present invention relates to a PID sliding mode control method for relative orbits of micro-nano satellites based on particle swarm optimization. When a maneuvering satellite encounters interference, it may deviate from its original trajectory. This invention utilizes sliding mode control to address this situation. Even if the maneuvering satellite deviates from its ideal trajectory but appears near the sliding mode surface, the control function is used to bring the micro-nano satellite's orbital state to the sliding mode surface, ultimately reaching the desired tracking state.

[0096] The sliding-mode variable structure control described in this embodiment is a nonlinear control strategy. This control strategy differs from other control strategies in that the "structure" of the micro-nano satellite's orbital state is not fixed. Instead, it can be dynamically and purposefully changed based on the micro-nano satellite's current orbital state (such as deviation and its derivatives), forcing the micro-nano satellite to follow a predetermined "sliding mode" state trajectory. This is known as sliding-mode variable structure control. Because the sliding mode is independent of the object parameters and disturbances, it is insensitive to parameter changes and disturbances, resulting in excellent anti-interference performance. To address the chattering problem of sliding-mode variable structure control, this embodiment utilizes the sum of an equivalent sliding membrane and a robust hyperbolic tangent switching function as the control function. When the system state is near the sliding-mode surface, the control function causes the micro-nano satellite's orbital state to reach the sliding-mode surface and then ultimately reach the desired tracking state within the sliding-mode surface.

[0097] The following describes in detail the process and principle of a PID sliding film control method for relative orbits of micro-nano satellites based on particle swarm optimization in this embodiment.

[0098] 1) Establish a relative orbital dynamics model of the maneuvering satellite.

[0099] According to Newton's law, a nonlinear relative orbital dynamics model of the reference satellite and the maneuvering tracking satellite under interference is established. In the inertial coordinate system, it is assumed that the absolute position vector of the reference satellite is rs and the absolute position vector of the maneuvering satellite is rt. The relative position vector of the two satellites is ρ = r t -r s .

[0100] Using Newton's law, we can get ρ = r t -r s The equation that follows:

[0101]

[0102] Where μ is the Earth's gravitational constant, Δf is the relative perturbation acceleration caused by the resultant perturbation force during satellite operation, f is the control force applied to the maneuvering satellite, and m is the mass of the maneuvering satellite. Transformed to the local vertical and local horizontal coordinate system of the reference satellite, the vector form of the nonlinear relative orbital dynamics model of the maneuvering satellite is:

[0103]

[0104] Where ω is the reference star orbital angular velocity, and its value is equal to the rate of change of the true anomaly ν. ​​Then the state quantity is written in the following component form:

[0105]

[0106] Ignoring high-order small quantities, assume The nonlinear relative orbital dynamics model is obtained:

[0107]

[0108]

[0109]

[0110] The reference orbit is a circular orbit, the perturbation force is ignored, and the state variables are written as The acceleration vector formed by the three directions is a=[a x ,a y ,a z ], which is the sum of the relative perturbation acceleration caused by the resultant perturbation force and the acceleration caused by the force applied to the maneuvering satellite. At the same time, considering the satellite in the absence of interference, the state equation describing the relative motion can be written as:

[0111]

[0112] in,

[0113]

[0114] Where n is the angular velocity of the reference satellite.

[0115] Define normalized coordinate variables:

[0116]

[0117] Define the state variable as The acceleration vector formed by the three directions is The above equation becomes:

[0118]

[0119]

[0120] When the interference term is taken into account, the above equation becomes:

[0121]

[0122] d is a bounded interference term and u is a control term.

[0123] 2) Planning of the ideal orbit of the maneuvering satellite

[0124] According to the various constraints of micro-nano satellite maneuvers, the ideal orbit of the maneuverable tracking satellite is established, that is, the relative motion trajectory is planned and designed to obtain the ideal trajectory.

[0125] The main goal of trajectory planning for relative orbital maneuvers is to comprehensively consider all constraints of micro-nano satellite maneuvers and determine the optimal path that satisfies both the initial and final requirements. Optimality in maneuvering over longer distances refers to optimizing fuel consumption, i.e., minimizing the velocity increment consumed by the transfer, and the trajectory should be planned by fully utilizing the characteristics of orbital dynamics. Trajectory optimization for closer distances, on the other hand, requires ensuring terminal accuracy and matching control modes while also considering fuel consumption, while also balancing trajectory safety.

[0126] The long-distance stage of the mobile star starts from the origin and the target end point is x N In order to make the entire maneuver trajectory converge within the primary star's horizon angle α, first perform a straight path maneuver to reach point x0, then start from x0 and perform N radial impulse transfers to reach x N The trajectory angle of each time converges within α.

[0127] The orbital angular rate of the maneuvering satellite is n, the orbital period is T, and the maneuvering time of the straight path maneuvering segment is t0. The total velocity increment required for the maneuvering process is V total and the total time t total for:

[0128]

[0129]

[0130] The performance index of planning pursues the optimal fuel under planning constraints. The planning model is

[0131]

[0132]

[0133]

[0134] Among them, t lim is the upper bound of the total transfer time constraint.

[0135] The trajectory planning requirements for the two maneuvering processes in the mid-range phase are essentially the same. Both require given initial and terminal conditions, as well as given constraints such as maneuvering duration and boundaries, to achieve the optimal fuel consumption trajectory from the starting point to the end point.

[0136] 3) Establish PID control sliding surface

[0137] The error between the tracking satellite orbit and the ideal orbit is introduced, and the sliding film surface is established using PID control. The sum of the equivalent sliding film function and the robust hyperbolic tangent switching function is selected as the control function.

[0138] Under the interference, the maneuver tracking satellite orbit and the ideal orbit are introduced The error of the ideal orbit is:

[0139] e1=ξ-ξ d ,e2=η-η d ,

[0140] The synovial surfaces usually controlled by the synovium are:

[0141]

[0142] n is the order of the synovial membrane. Considering the globality of the control, the present invention adopts the PID control synovial membrane surface with attenuation.

[0143]

[0144] k pj ,k ij ,k dj are PID parameters.

[0145] The present invention adopts equivalent sliding film control, and its control function consists of two parts:

[0146] u j =u jeq +u jsw

[0147] u jeq Depend on We get:

[0148]

[0149]

[0150]

[0151] Among them, λ>0,p>0 considers the globality and vibration resistance of the control, u jsw To have boundaries Hyperbolic tangent switching function: Considering the vibration resistance of the control, u jsw To have boundaries Hyperbolic tangent switching function of :

[0152]

[0153] Among them, λ j >0, Considering the boundedness of d, assume that the maximum value of d is d m , minimum value d l ,λ j =(d m +d l ) / 2,κj =(d m -d l ) / 2. Choose appropriate parameters for the Lyapunov energy function:

[0154]

[0155] Make Thus achieving synovial control.

[0156] 4) Optimize synovial surface parameters

[0157] The particle swarm optimization algorithm is used to optimize the synovial surface parameters.

[0158] The fitness function is selected as the derivative of the Lyapunov energy function, which is:

[0159]

[0160] The condition is Particle k pj ,k ij ,k dj The dimension is 3. In the particle swarm algorithm, the velocity and position of the particles are updated after each iteration as follows:

[0161] v k+1 =w·v k +c1×r1×(Pbest k -p k )+c2×r2×(Gbest-p k )

[0162] p k+1 =p k +v k+1

[0163]

[0164] Among them, v k 、p k are the velocity and position of the particle at the kth iteration, v k+1 、p k+1 are the velocity and position of the particle at the k+1th iteration, w max 、w min , iteration are the maximum and minimum inertia weights respectively, iteration is the total number of iterations, w is the inertia weight, c1, c2 represent the acceleration factors of individuals and groups, r1, r2. are random numbers between (0, 1), Pbest k,Gbest is the individual and group positions optimized according to the ,fitness function in each iteration. When the conditions are met or the maximum ,number of iterations is reached, the optimal individual position value is used as the PID ,control parameter.

[0165] 5) When the orbital state of the micro-nano satellite is near the synovial surface, under the action of the control function, the orbital state of the micro-nano satellite reaches the synovial surface, and then finally reaches the state that needs to be tracked on the synovial surface.

[0166] The process is as follows: according to the minimum energy rule, the ideal trajectory of the maneuvering satellite is optimized as the instruction of the ideal trajectory; the main program of the sliding membrane control is constructed using Simulink in MATLAB to generate a file with the suffix mdl; based on the orbit equation of the maneuvering satellite containing interference, the controlled object function is edited to generate a file with the suffix m; the particle swarm optimization program is edited to obtain the PID sliding membrane control parameters; the controller function is edited; and finally, the results are obtained, which show that the control scheme can realize that the maneuvering satellite can finally reach the state that needs to be tracked.

[0167] In summary, the process of realizing the PID sliding film control method for the relative orbit of micro-nano satellite is briefly summarized as follows:

[0168] 1. Establish a nonlinear relative orbital dynamics model, i.e., a dynamics equation, between the reference satellite and the maneuvering tracking satellite in the presence of interference: Based on Newtonian dynamics theory, establish a nonlinear relative orbital dynamics model, i.e., a dynamics equation, between the reference satellite and the maneuvering tracking satellite in the presence of interference;

[0169] 2. Establish the ideal orbit of the maneuverable tracking satellite based on the various constraints of the micro-nano satellite maneuver: Optimize the ideal orbit of the maneuverable satellite based on the constraints of the micro-nano satellite maneuver such as the minimum fuel consumption, that is, plan and design the relative motion trajectory to obtain the ideal trajectory;

[0170] 3. Introducing the error between the maneuvering tracking satellite orbit and the ideal orbit, and using PID control with attenuation to establish a sliding film surface: Introducing the error between the tracking satellite orbit and the ideal orbit, and establishing a PID control sliding film surface. The sum of the equivalent sliding film function and the robust hyperbolic tangent switching function is selected as the control function;

[0171] 4. Optimization of synovial surface parameters: Select the fitness function and use the particle swarm optimization algorithm to optimize the PID control parameters to achieve synovial control;

[0172] 5. When the orbital state of the micro-nano satellite is near the sliding membrane surface, under the action of the control function, the orbit of the micro-nano satellite reaches the sliding membrane surface, and then finally reaches the state that needs to be tracked on the sliding membrane surface: according to the minimum energy rule, the ideal trajectory of the maneuvering satellite is optimized as the instruction of the ideal trajectory; the main program of the sliding membrane control is constructed using Simulink in MATLAB to generate a file with the suffix mdl; based on the orbital equation of the maneuvering satellite containing interference, the controlled object function is edited to generate a file with the suffix m; the particle swarm optimization program is edited to obtain the PID sliding membrane control parameters; the controller function is edited; and finally, the results are obtained, indicating that the control scheme can enable the maneuvering satellite to finally reach the state that needs to be tracked.

[0173] like Figure 3 As shown in Figure 1, it is the error diagram between the simulated controlled trajectory data and the ideal data. e1 represents the error along the ξ axis, e2 represents the error along the η axis, and e3 represents the error along the ζ axis. The results show that it can track well.

[0174] like Figure 5 As shown, the present invention also discloses an embodiment of a micro-nano satellite relative orbit PID sliding membrane control system based on particle swarm optimization. The embodiment includes a maneuvering satellite relative orbit dynamics modeling establishment module, a maneuvering satellite ideal orbit planning module, a PID control sliding membrane surface modeling establishment module, a sliding membrane surface parameter particle swarm optimization module, and a tracking state realization module. Each module is described in detail as follows:

[0175] Maneuvering satellite relative orbit dynamics modeling module: Based on Newtonian dynamics theory, a nonlinear relative orbit dynamics model, i.e., a dynamic equation, is established between the reference satellite and the maneuvering tracking satellite under interference.

[0176] Maneuvering Satellite Ideal Orbit Planning Module: This module optimizes the ideal orbit of the maneuvering satellite based on constraints such as the minimum fuel consumption for micro-nano satellite maneuvers. This module plans and designs the relative motion trajectory to obtain the ideal trajectory.

[0177] PID control sliding membrane surface modeling module: This module introduces the error between the tracking satellite orbit and the ideal orbit to establish the PID control sliding membrane surface. The sum of the equivalent sliding membrane function and the robust hyperbolic tangent switching function is selected as the control function.

[0178] Synovial surface parameter particle swarm optimization module: select the fitness function and use the particle swarm optimization algorithm to optimize the PID control parameters to achieve synoviocyte control.

[0179] Tracking state realization module: When the disturbed micro-nano satellite orbital state is near the sliding membrane surface, under the action of the control function, the disturbed micro-nano satellite orbital state reaches the sliding membrane surface and reaches the state that needs to be tracked on the sliding membrane surface.

[0180] In addition, each stage can be verified through programming to implement and prove the feasibility of the control technology solution of this embodiment.

[0181] For other contents of this embodiment, reference can be made to the above-mentioned embodiment of a micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization.

[0182] The present invention is based on the fact that the sliding mode is independent of the object parameters and interference, and is insensitive to parameter changes and disturbances. Although the maneuvering satellite deviates from the ideal trajectory and appears near the sliding surface, under the action of the control function, the orbit of the micro-nano satellite reaches the sliding surface, and then finally reaches the state that needs to be tracked on the sliding surface.

[0183] The preferred embodiments and principles of the present invention are described in detail above. For those skilled in the art, there may be changes in the specific implementation methods based on the ideas provided by the present invention, and these changes should also be considered as the scope of protection of the present invention.

Claims

1. A micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization, characterized in that: Proceed as follows: Step 1) establishing a nonlinear relative orbital dynamics model, i.e., a dynamics equation, between the reference satellite and the maneuvering tracking satellite in the presence of interference; Step 2) establishing an ideal orbit for the maneuvering tracking satellite based on the constraints of the micro-nano satellite maneuvering; Step 3), introduce the error between the maneuver tracking satellite orbit and the ideal orbit, and use PID control to establish the sliding membrane surface; Step 4), particle swarm optimization of synovial surface parameters; Step 5), when the orbital state of the disturbed micro-nano satellite is near the sliding membrane surface, under the action of the control function, the orbital state of the disturbed micro-nano satellite reaches the sliding membrane surface and reaches the state that needs to be tracked on the sliding membrane surface; In step 4), the particle swarm optimization algorithm is used to optimize the parameters of the synovial surface, as follows: The fitness function is selected as the derivative of the Lyapunov energy function, which is: The condition is Particle k pj ,k ij ,k dj The dimension is 3. In the particle swarm algorithm, the velocity and position of the particles are updated after each iteration as follows: v k+1 =w·v k +c1×r1×(Pbest k -p k )+c2×r2×(Gbest-p k ) p k+1 =p k +v k+1 Among them, v k 、p k are the velocity and position of the particle at the kth iteration, v k+1 、p k+1 are the velocity and position of the particle at the k+1th iteration, w max 、w min , iteration are the maximum and minimum inertia weights respectively, iteration is the total number of iterations, w is the inertia weight, c1, c2 represent the acceleration factors of individuals and groups, r1, r2. are random numbers between (0, 1), Pbest k ,Gbest is the individual and group positions optimized according to the ,fitness function in each iteration. When the conditions are met or the maximum ,number of iterations is reached, the optimal individual position value is used as the PID ,control parameter.

2. According to the particle swarm optimization-based micro-nano satellite relative orbit PID sliding film control method of claim 1, it is characterized in that: Step 1) is as follows: In the inertial coordinate system, assume that the absolute position vector r of the reference satellite is s , the absolute position vector of the maneuvering satellite is r t , the relative position vector of the two stars ρ = r t -r s ; Using Newton's law, we can get ρ = r t -r s The equation that follows: Where μ is the Earth's gravitational constant, Δf is the relative perturbation acceleration caused by the resultant perturbation force during satellite operation, f is the control force applied to the maneuvering satellite, and m is the mass of the maneuvering satellite. Transformed into the local vertical and local horizontal coordinate system of the reference satellite, the vector form of the nonlinear relative orbital dynamics model of the maneuvering satellite is: Where ω is the reference star orbital angular velocity, which is equal to the rate of change of the true anomaly ν. ​​The state quantity is written in the following component form: Ignoring high-order small quantities, assume The nonlinear relative orbital dynamics model is obtained: The reference orbit is a circular orbit, the perturbation force is ignored, and the state variables are written as The acceleration vector formed by the three directions is a=[a x ,a y ,a z ], which is the sum of the relative perturbation acceleration caused by the resultant perturbation force and the acceleration caused by the force applied to the maneuvering satellite; considering the satellite in the absence of interference, the state equation describing the relative motion is written as: in, Where n is the reference satellite angular velocity; Define normalized coordinate variables: Define the state variable as The acceleration vector formed by the three directions is The above equation becomes: When the interference term is taken into account, the above equation becomes: d is a bounded interference term and u is a control term.

3. The micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization according to claim 2 is characterized in that: Step 2) is as follows: The long-distance stage of the mobile star starts from the origin and the target end point is x N , a total of N+1 segments are experienced; in order to make the entire maneuvering trajectory converge within the primary star horizon angle α, first perform a straight path maneuver to reach point x0, and then start from x0 and perform N radial impulse transfers to reach x N The trajectory horizon angle converges within α each time; The orbital angular rate of the maneuvering satellite is n, the orbital period is T, and the maneuvering time of the straight path maneuvering segment is t0. The total velocity increment required for the maneuvering process is V total and the total time t total for: The planning performance index pursues the optimal fuel under the planning constraints. The planning model is: In the above formula, t lim is the upper bound of the total transfer time constraint.

4. The micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization according to claim 3 is characterized in that: Step 3) is as follows: Under the interference, introduce the maneuver tracking satellite orbit and the ideal orbit The error of the ideal orbit is: e1=ξ-ξ d ,e2=η-η d , The synovial surfaces of synovial control are: n is the order of the synovial membrane. Considering the globality of the control, the PID control synovial membrane surface with attenuation is taken. k pj ,k ij ,k dj is the PID parameter; Equivalent sliding film control is adopted, and its control function consists of two parts: in j =in jeq +in jsw u jeq Depend on We get: Among them, λ>0,p>0 Considering the globality and vibration resistance of the control, considering the vibration resistance of the control, u jsw To have boundaries Hyperbolic tangent switching function of : Among them, λ j >0, Considering the boundedness of d, assume that the maximum value of d is d m , minimum value d l ,λ j =(d m +d l ) / 2,κ j =(d m -d l ) / 2; choose appropriate parameters, for Lyapunov energy function: Make Thus achieving synovial control.

5. A micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization according to any one of claims 2 to 4, characterized in that: The upper limit of interference d is 0.03 and the lower limit is 0.

001.

6. A micro-nano satellite relative orbit PID sliding film control method based on particle swarm optimization according to any one of claims 1 to 4, characterized in that: Step 5) is as follows: according to the minimum energy rule, the ideal trajectory of the maneuvering star is optimized as the instruction of the ideal trajectory; the main program of the synovial control is constructed and the file with the suffix mdl is generated; Based on the orbit equation of the maneuvering star with interference, edit the controlled object function and generate a file with the suffix m; Edit the particle swarm optimization program to obtain PID sliding film control parameters; edit the controller function; The result is obtained, and the maneuvering satellite reaches the state that needs to be tracked.

7. A micro-nano satellite relative orbit PID sliding film control system based on particle swarm optimization, used to execute the method according to claim 1, characterized in that: Includes the following modules: Maneuvering satellite relative orbit dynamics model establishment module: establishes the nonlinear relative orbit dynamics model, i.e., the dynamic equation, between the reference satellite and the maneuvering tracking satellite under interference; Maneuvering satellite ideal orbit planning module: establishes the ideal orbit of the maneuvering tracking satellite based on various constraints of the micro-nano satellite maneuver; PID control sliding membrane surface establishment module: introduces the error between the tracking satellite orbit and the ideal orbit to establish the PID control sliding membrane surface; Synovial surface parameter optimization module: particle swarm optimization of synovial surface parameters; Tracking state realization module: When the disturbed micro-nano satellite orbital state is near the sliding membrane surface, under the action of the control function, the disturbed micro-nano satellite orbital state reaches the sliding membrane surface and reaches the state that needs to be tracked on the sliding membrane surface.

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