The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and...The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.展开更多
For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption th...For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption that the static equilibri- um position of the tether is a quadratic parabola, the governing differential equations of the tether motion are derived by use of the Hamihon principle. An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method. The results show that, when the static equilibrium position of the tether is assumed to be. a quadratic parabola, the tether sag effect on its vibration may be reflected; the tether sag results in the asymmetry of tether vibration amplitude ; for the reduction of the tether amplitude, the buoyant unit weight of the tether should approach to zero as far as possible during the design.展开更多
This paper presents the Hill instability analysis of Tension keg Platform （TLP） tether in deep sea. The 2-D nonlinear beanl model, which is undergoing coupled axial and transverse vibrations, is applied. The governi...This paper presents the Hill instability analysis of Tension keg Platform （TLP） tether in deep sea. The 2-D nonlinear beanl model, which is undergoing coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin＇ s method and the modes superposition principle. The Hill instability charted up to large parameters is obtained. An important parameter M is defined and can be expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various envirotnnental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure. It needs to be considered for the accurate dynamic analysis of long TI2 tether subjected to the combined platfolna surge and heave motions.展开更多
For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel ...For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.展开更多
A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fo...A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.展开更多
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital ...The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.展开更多
This paper studies the thrust regulation of the tethered space-tug in order to stabilize the target towed by a flexible tether.To compromise between model accuracy and simplicity,a rigid-flexible coupling multi-body m...This paper studies the thrust regulation of the tethered space-tug in order to stabilize the target towed by a flexible tether.To compromise between model accuracy and simplicity,a rigid-flexible coupling multi-body model is proposed as the full model of the tethered space-tug.More specifically,the tug and the towed target are assumed as rigid bodies,whereas the flexible tether is approximated as a series of hinged rods.The rods are assumed extensible but incompressible.Then the equations of motion of the multi-body system are derived based on the recursive dynamics algorithm.The attitude motion of the towed target is stabilized by regulating the thrust on the tug,whereas the tether-tension-caused perturbation to the tug's attitude motion is eliminated by the control torque on the tug.The regulated thrust is achieved by first designing an optimal control trajectory considering the simplified system model with constraints for both state variables and control input.Then the trajectory is tracked using a neural-network based terminal sliding-mode controller.The radial basis function neural network is used to estimate the unknown nonlinear difference between the simple model and the full model,while the terminal sliding mode controller ensures the rapid tracking control of the target's attitude motion.Thrust saturation and tether slackness avoidance are also considered.Finally,numerical simulations prove the effectiveness of the proposed controller using the regulated thrust.Without disturbing orbital motion much,the attitude motion of the tug and the target are well stabilized and the tether slackness is avoided.展开更多
This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel an...This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only.The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS.To enhance the robustness of the proposed controller,multiple perturbations of the orbital dynamics,modeling uncertainties,and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously,such that these perturbations are well compensated for during the control design of the EDTS.Furthermore,a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law.The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory.Finally,numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.展开更多
Spinning electrodynamic tether systems(SEDTs)have promising potential for the active removal of space debris,the construction of observation platforms,and the formation of artificial gravity.However,owing to the survi...Spinning electrodynamic tether systems(SEDTs)have promising potential for the active removal of space debris,the construction of observation platforms,and the formation of artificial gravity.However,owing to the survivability problem of long tethers,designing collision-avoidance strategies for SEDTs with space debris is an urgent issue.This study focuses on the design of collision-avoidance strategies for SEDTs with an electrodynamic force(Ampere force).The relative distance between the debris and the SEDT is first derived,and then two collision-avoidance strategies are proposed according to the two different cases.When debris collides closer to a lighter subsatellite,a stationary avoidance strategy is proposed to change the spatial position of the subsatellite by adjusting only the angular motion of the tether,which maintains the original orbit of the SEDT.When debris collides closer to a heavier main spacecraft,a comprehensive avoidance strategy is proposed to change the spatial position of the SEDT by slightly modifying the orbital height and changing the tether angular motion simultaneously.The numerical results illustrate that the proposed strategies promptly avoid potential collisions of an SEDT with space debris without significant changes in the orbital parameters of the SEDT.展开更多
This study examines the impact of electric solar wind sail(E-sail)parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model.In this model,the ...This study examines the impact of electric solar wind sail(E-sail)parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model.In this model,the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements.The attitude dynamics of the central spacecraft is described using a natural coordinate formulation.The rigid–flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers.Our research reveals the significant influences of parameters such as tether numbers,tether’s electric potential,and solar wind velocity on attitude stability.Specifically,solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft.For consistent management,the angular velocities of the spacecraft must remain at target values.Moreover,the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail,with axisymmetric E-sails proving to be more stable.展开更多
基金the National Natural Science Foundation of China(10672073)the Innovation Fund for Graduate Students,Nanjing University of Aeronautics and Astronautics
文摘The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.
基金supported by the Program for New Century Excellent Talents in University of China(Grant No.NCET-06-0270)the National Natural Science Foundation of China (Grant No.50578032)
文摘For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption that the static equilibri- um position of the tether is a quadratic parabola, the governing differential equations of the tether motion are derived by use of the Hamihon principle. An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method. The results show that, when the static equilibrium position of the tether is assumed to be. a quadratic parabola, the tether sag effect on its vibration may be reflected; the tether sag results in the asymmetry of tether vibration amplitude ; for the reduction of the tether amplitude, the buoyant unit weight of the tether should approach to zero as far as possible during the design.
基金supported by the National High Technology Researchand Development Program of China(863 Program,Grant No.2006AA09Z350)the National Natural Science Foundation of China(Grant No.10702073)the Knowledge Innovation Program of Chinese Academy of Sciences(Grant No.KJCX2-YW-L02)
文摘This paper presents the Hill instability analysis of Tension keg Platform （TLP） tether in deep sea. The 2-D nonlinear beanl model, which is undergoing coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin＇ s method and the modes superposition principle. The Hill instability charted up to large parameters is obtained. An important parameter M is defined and can be expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various envirotnnental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure. It needs to be considered for the accurate dynamic analysis of long TI2 tether subjected to the combined platfolna surge and heave motions.
基金supported by the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (Grant No. BS2010HZ005)
文摘For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.
基金supported by the National Natural Science Foundation of China (Grant No. 51108224)the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province (Grant No. BS2010HZ005)
文摘A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.
基金supported by the National Natural Science Foundation of China(Nos.11002068 and11202094)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(No.0113Y01)the Priority Academic Program of Jiangsu Higher Education Institutions
文摘The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.
基金The authors acknowledge the support of the National Natural Science Foundation of China(Grant No.11402009).
文摘This paper studies the thrust regulation of the tethered space-tug in order to stabilize the target towed by a flexible tether.To compromise between model accuracy and simplicity,a rigid-flexible coupling multi-body model is proposed as the full model of the tethered space-tug.More specifically,the tug and the towed target are assumed as rigid bodies,whereas the flexible tether is approximated as a series of hinged rods.The rods are assumed extensible but incompressible.Then the equations of motion of the multi-body system are derived based on the recursive dynamics algorithm.The attitude motion of the towed target is stabilized by regulating the thrust on the tug,whereas the tether-tension-caused perturbation to the tug's attitude motion is eliminated by the control torque on the tug.The regulated thrust is achieved by first designing an optimal control trajectory considering the simplified system model with constraints for both state variables and control input.Then the trajectory is tracked using a neural-network based terminal sliding-mode controller.The radial basis function neural network is used to estimate the unknown nonlinear difference between the simple model and the full model,while the terminal sliding mode controller ensures the rapid tracking control of the target's attitude motion.Thrust saturation and tether slackness avoidance are also considered.Finally,numerical simulations prove the effectiveness of the proposed controller using the regulated thrust.Without disturbing orbital motion much,the attitude motion of the tug and the target are well stabilized and the tether slackness is avoided.
基金supported by the National Natural Science Foundation of China under Grant Nos.11902145 and 12232011China Postdoctoral Science Foundation under Grant No.2021M691574Fundamental Research Funds for the Central Universities under Grant No.NS2022002.
文摘This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only.The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS.To enhance the robustness of the proposed controller,multiple perturbations of the orbital dynamics,modeling uncertainties,and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously,such that these perturbations are well compensated for during the control design of the EDTS.Furthermore,a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law.The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory.Finally,numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.
基金the support of the National Natural Science Foundation of China(Grant No.62273277)the Key Research and Development Program of Shaanxi(Grant No.2023-GHZD-32)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.D5000220031)Russian Foundation for basic research assistance(Grant No.21-51-53002).
文摘Spinning electrodynamic tether systems(SEDTs)have promising potential for the active removal of space debris,the construction of observation platforms,and the formation of artificial gravity.However,owing to the survivability problem of long tethers,designing collision-avoidance strategies for SEDTs with space debris is an urgent issue.This study focuses on the design of collision-avoidance strategies for SEDTs with an electrodynamic force(Ampere force).The relative distance between the debris and the SEDT is first derived,and then two collision-avoidance strategies are proposed according to the two different cases.When debris collides closer to a lighter subsatellite,a stationary avoidance strategy is proposed to change the spatial position of the subsatellite by adjusting only the angular motion of the tether,which maintains the original orbit of the SEDT.When debris collides closer to a heavier main spacecraft,a comprehensive avoidance strategy is proposed to change the spatial position of the SEDT by slightly modifying the orbital height and changing the tether angular motion simultaneously.The numerical results illustrate that the proposed strategies promptly avoid potential collisions of an SEDT with space debris without significant changes in the orbital parameters of the SEDT.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.XJSJ23128)Discovery Grant(Grant No.RGPIN2018-05991)from the Natural Sciences and Engineering Research Council of Canada.
文摘This study examines the impact of electric solar wind sail(E-sail)parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model.In this model,the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements.The attitude dynamics of the central spacecraft is described using a natural coordinate formulation.The rigid–flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers.Our research reveals the significant influences of parameters such as tether numbers,tether’s electric potential,and solar wind velocity on attitude stability.Specifically,solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft.For consistent management,the angular velocities of the spacecraft must remain at target values.Moreover,the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail,with axisymmetric E-sails proving to be more stable.
