This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing t...This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.展开更多
The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft.The test mass must be released to the cage center of the inertial sensor accurately and quickly.This paper...The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft.The test mass must be released to the cage center of the inertial sensor accurately and quickly.This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft.An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase.The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction.Compared with the exact numerical solution by the hp-adaptive pseudospectral method,the analytical solution is proved to be minimum-time.Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor.The capture time to stabilization is only half that of the traditional controller.展开更多
文摘This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.
基金supported by Guangdong Major Project of Basic and Applied Basic Research(grant no.2019B030302001)National Key Research and Development Program(2022YFC2204200)+1 种基金Beijing Nova Program(Z211100002121137)Beijing Natural Science Foundation(1222018).
文摘The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft.The test mass must be released to the cage center of the inertial sensor accurately and quickly.This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft.An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase.The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction.Compared with the exact numerical solution by the hp-adaptive pseudospectral method,the analytical solution is proved to be minimum-time.Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor.The capture time to stabilization is only half that of the traditional controller.
