In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid sing...In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.展开更多
The stability and singularity problem of agile small satellite （ASS） with actuator failure is discussed in this paper. Firstly, the three-axis stabilized controller of an ASS is designed, where micro control moment ...The stability and singularity problem of agile small satellite （ASS） with actuator failure is discussed in this paper. Firstly, the three-axis stabilized controller of an ASS is designed, where micro control moment gyros （MCMG＇s） in pyramid configuration （PC） is used as the actuator. By using the same controller and steering law, the control results before and after one gyro fails are compared by simulation. The variation of singular momentum envelope before and after one gyro fails is also compared. The simulation results show that the failure intensively decreases the capacity of output torque, which leads to the emergence of more singular points and the rapid saturation of MCMG＇s. Finally, the parameters of system controller are changed to compare the control effect.展开更多
This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular ...This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.展开更多
Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gim...Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gimbal control moment gyros （SGCMGs） as the actuator for the attitude control system.The expression of output-torque error is given at the point of singularity,proving the incompatible relationship between the gimbal rate and the output-torque error.The method of establishing a balance between the gimbal rate and the output-torque error is discussed,and a new steering law is designed.Simulation results show that the proposed steering law can effectively drive SGCMGs to escape away from singularities.展开更多
Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dy...Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.展开更多
The attitude control problem of a spacecraft underactuated by two single-gimbal control moment gyros （SGCMGs） is investigated. Small-time local controllability （STLC） of the attitude dynamics of the spacecraft-SGC...The attitude control problem of a spacecraft underactuated by two single-gimbal control moment gyros （SGCMGs） is investigated. Small-time local controllability （STLC） of the attitude dynamics of the spacecraft-SGCMGs system is analyzed via nonlinear controllability theory. The conditions that guarantee STLC of the spacecraft attitude by two non-coaxial SGCMGs are obtained with the momentum of the SGCMGs as inputs, implying that the spacecraft attitude is STLC when the total angular momentum of the whole system is zero. Moreover, our results indi- cate that under the zero-momentum restriction, full attitude stabilization is possible for a spacecraft using two non-coaxial SGCMGs. For the case of two coaxial SGCMGs, the STLC property of the spacecraft cannot be determined. In this case, an improvement to the previous full attitude stabilizing control law, which requires zero-momentum presumption, is proposed to account for the singu- larity of SGCMGs and enhance the steady state performance. Numerical simulation results demonstrate the effectiveness and advantages of the new control law.展开更多
A new variable speed control moment gyro(VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command to...A new variable speed control moment gyro(VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command torque: control momentum gyro(CMG)/reaction wheel(RW) hybrid mode for the large torque case and RW single mode for the small. When working in the CMG/RW hybrid mode, the steering law deals with the gimbal dead-zone nonlinearity through compensation by RW sub-mode. This is in contrast to the conventional CMG singularity avoidance and wheel speed equalization, as well as the proof of definitely hyperbolic singular property of the CMG sub-mode. When working in the RW single mode, the motion of gimbals will be locked. Both the transition from CMG/RW hybrid mode to RW single mode and the reverse are studied. During the transition, wheel speed equalization and singularity avoidance of both the CMG and RW submodes are considered. A steering law for the RWs with locked gimbals is presented. It is shown by simulations that the VSCMGs with this new steering law could reach a better torque precision than the normal CMGs in the case of both large and small torques.展开更多
Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in usi...Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.展开更多
An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration ...An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration （FPC） whose two adjacent gyros are in failure state is reconfigured as a degraded system with DPC. Then, the singular angular momentum hypersurfaces of the original and the degraded systems are plotted via the singular angular momentum equa- tion of SGCMGs. Based on singular surfaces, the differences between FPC and DPC in singularity and momentum envelope are obtained directly, which provide an important reference for steering law design of DPC. Finally, an IC steering law is designed and applied to DPC. The simulation results demonstrate that the IC steering law has advantages in simplicity of calculation, avoidance of singularity and exactness of output torque, which endow the degraded system with fine controllability in a restricted workspace.展开更多
In the no-boundary Universe of Hartle and Hawking, the path integral for the quantum state of the Universe must be summed only over nonsingular histories. If the quantum corrections to the Hamilton-Jacobi equation in ...In the no-boundary Universe of Hartle and Hawking, the path integral for the quantum state of the Universe must be summed only over nonsingular histories. If the quantum corrections to the Hamilton-Jacobi equation in the interpretation of the wave packet is taken into account, then all classical trajectories should be nonsingular. The quantum behaviour of the classical singularity in the S1 × Sm model (m≥2) is also clarified. It is argued that the Universe should evolve from the zero momentum state, instead from a zero volume state, to a 3-geometry state.展开更多
The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism o...The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.展开更多
基金funded under the National Natural Science Foundation of China(No.61873312)。
文摘In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.
基金the National Natural Science Foundation of China (10502006)Excellent Young Scholars Research Fund of Beijing Institute of Technology (2007YS0202)
文摘The stability and singularity problem of agile small satellite （ASS） with actuator failure is discussed in this paper. Firstly, the three-axis stabilized controller of an ASS is designed, where micro control moment gyros （MCMG＇s） in pyramid configuration （PC） is used as the actuator. By using the same controller and steering law, the control results before and after one gyro fails are compared by simulation. The variation of singular momentum envelope before and after one gyro fails is also compared. The simulation results show that the failure intensively decreases the capacity of output torque, which leads to the emergence of more singular points and the rapid saturation of MCMG＇s. Finally, the parameters of system controller are changed to compare the control effect.
文摘This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.
基金supported by the National Natural Science Foundation of China (10872029)the Excellent Young Scholars Research Fund of the Beijing Institute of Technology (2007YS0202)
文摘Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gimbal control moment gyros （SGCMGs） as the actuator for the attitude control system.The expression of output-torque error is given at the point of singularity,proving the incompatible relationship between the gimbal rate and the output-torque error.The method of establishing a balance between the gimbal rate and the output-torque error is discussed,and a new steering law is designed.Simulation results show that the proposed steering law can effectively drive SGCMGs to escape away from singularities.
文摘Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.
基金supported by the National Natural Science Foundation of China (No.10902003)
文摘The attitude control problem of a spacecraft underactuated by two single-gimbal control moment gyros （SGCMGs） is investigated. Small-time local controllability （STLC） of the attitude dynamics of the spacecraft-SGCMGs system is analyzed via nonlinear controllability theory. The conditions that guarantee STLC of the spacecraft attitude by two non-coaxial SGCMGs are obtained with the momentum of the SGCMGs as inputs, implying that the spacecraft attitude is STLC when the total angular momentum of the whole system is zero. Moreover, our results indi- cate that under the zero-momentum restriction, full attitude stabilization is possible for a spacecraft using two non-coaxial SGCMGs. For the case of two coaxial SGCMGs, the STLC property of the spacecraft cannot be determined. In this case, an improvement to the previous full attitude stabilizing control law, which requires zero-momentum presumption, is proposed to account for the singu- larity of SGCMGs and enhance the steady state performance. Numerical simulation results demonstrate the effectiveness and advantages of the new control law.
基金supported by the National Natural Science Foundation of China (No. 11272027)
文摘A new variable speed control moment gyro(VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command torque: control momentum gyro(CMG)/reaction wheel(RW) hybrid mode for the large torque case and RW single mode for the small. When working in the CMG/RW hybrid mode, the steering law deals with the gimbal dead-zone nonlinearity through compensation by RW sub-mode. This is in contrast to the conventional CMG singularity avoidance and wheel speed equalization, as well as the proof of definitely hyperbolic singular property of the CMG sub-mode. When working in the RW single mode, the motion of gimbals will be locked. Both the transition from CMG/RW hybrid mode to RW single mode and the reverse are studied. During the transition, wheel speed equalization and singularity avoidance of both the CMG and RW submodes are considered. A steering law for the RWs with locked gimbals is presented. It is shown by simulations that the VSCMGs with this new steering law could reach a better torque precision than the normal CMGs in the case of both large and small torques.
基金support from the National Natural Science Foundation of China (No. 61403197)the National Key Research and Development Plan of China (No. 2016YFB0500901)
文摘Control Moment Gyroscope（CMG） is an effective candidate for agile satellites and large spacecraft attitude control because of its powerful torque amplification capability. The most serious situation, however, in using CMG is the inherent geometric singularity problem, where there＇s no torque output along a particular direction. Space expansion method has been proposed in this work for the singularity analysis. Based on inverse mapping transformation, an expanded Jacobian matrix which is a full rank square matrix is obtained. The singular angle sets of the 3-parallel cluster and pyramid cluster are distinguished using space expansion method. An effective hybrid steering strategy, able to deal with the elliptic singularity, is further proposed. Simulation results demonstrate the excellent performance of the proposed steering logic compared to the generalized singular robust logic and pseudo inverse logic in terms of energy consumption and torque error.
基金supported by the National Natural Science Foundation of China (10372011)
文摘An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration （FPC） whose two adjacent gyros are in failure state is reconfigured as a degraded system with DPC. Then, the singular angular momentum hypersurfaces of the original and the degraded systems are plotted via the singular angular momentum equa- tion of SGCMGs. Based on singular surfaces, the differences between FPC and DPC in singularity and momentum envelope are obtained directly, which provide an important reference for steering law design of DPC. Finally, an IC steering law is designed and applied to DPC. The simulation results demonstrate that the IC steering law has advantages in simplicity of calculation, avoidance of singularity and exactness of output torque, which endow the degraded system with fine controllability in a restricted workspace.
文摘In the no-boundary Universe of Hartle and Hawking, the path integral for the quantum state of the Universe must be summed only over nonsingular histories. If the quantum corrections to the Hamilton-Jacobi equation in the interpretation of the wave packet is taken into account, then all classical trajectories should be nonsingular. The quantum behaviour of the classical singularity in the S1 × Sm model (m≥2) is also clarified. It is argued that the Universe should evolve from the zero momentum state, instead from a zero volume state, to a 3-geometry state.
基金the National Natural Science Foundation of China(No.10502006)the ExcellentScholars Fund of Beijing(No.20071D1600300398)the Excellent Young Scholars Research Fundof Beijing Institute of Technology(No.2007YS0202)
文摘The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.
