This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving p...This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.展开更多
The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rat...The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.展开更多
According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanica...According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanical systems by employing the spectral-collocation method to discretize the corresponding Lagrangian and kinematic constraints.The constructed framework can be transformed easily to the well-known symplectic partitioned Runge–Kutta methods and the higher order symplectic partitioned Lie Group methods by choosing same interpolation nodes and quadrature points.Two numerical experiments about the orbit propagation of Kepler two-body system and the rigid-body flow propagation of a free rigid body are conducted,respectively.The simulating results reveal that the constructed update schemes can possess simultaneously the excellent exponent convergence rates of spectral methods and the attractive long-term structure-preserving properties of geometric numerical algorithms.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11472041, 11532002)the Doctoral Fund of Ministry of Education of China (Grant 20131101110002)
文摘This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.
基金the National Natural Science Foundation of China (Nos. 11472041,11532002,11772049,and 11802320)。
文摘The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.
基金This work was supported by the National Natural Science Foundation of China(Grants 11772049,and 12132002).
文摘According to the discrete Hamilton–Pontryagin variational principle,we construct a class of variational integrators in the real vector spaces and extend to the Lie groups for the left-trivialized Lagrangian mechanical systems by employing the spectral-collocation method to discretize the corresponding Lagrangian and kinematic constraints.The constructed framework can be transformed easily to the well-known symplectic partitioned Runge–Kutta methods and the higher order symplectic partitioned Lie Group methods by choosing same interpolation nodes and quadrature points.Two numerical experiments about the orbit propagation of Kepler two-body system and the rigid-body flow propagation of a free rigid body are conducted,respectively.The simulating results reveal that the constructed update schemes can possess simultaneously the excellent exponent convergence rates of spectral methods and the attractive long-term structure-preserving properties of geometric numerical algorithms.
