Singularly perturbed feedback linearization with linear attitude deviation dynamics realization |
| |
Authors: | Abdulrahman H Bajodah |
| |
Institution: | (1) Aeronautical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia |
| |
Abstract: | A new approach for feedback linearization of attitude dynamics for rigid gas jet-actuated spacecraft control is introduced.
The approach is aimed at providing global feedback linearization of the spacecraft dynamics while realizing a prescribed linear
attitude deviation dynamics. The methodology is based on nonuniqueness representation of underdetermined linear algebraic
equations solution via nullspace parametrization using generalized inversion. The procedure is to prespecify a stable second-order
linear time-invariant differential equation in a norm measure of the spacecraft attitude variables deviations from their desired
values. The evaluation of this equation along the trajectories defined by the spacecraft equations of motion yields a linear
relation in the control variables. These control variables can be solved by utilizing the Moore–Penrose generalized inverse
of the involved controls coefficient row vector. The resulting control law consists of auxiliary and particular parts, residing in the nullspace of the controls
coefficient and the range space of its generalized inverse, respectively. The free null-control vector in the auxiliary part is projected onto the controls coefficient nullspace by a nullprojection matrix, and is designed to
yield exponentially stable spacecraft internal dynamics, and singularly perturbed feedback linearization of the spacecraft attitude dynamics. The feedback control design utilizes the concept of damped generalized inverse to limit the growth of the Moore–Penrose generalized inverse, in addition to the concepts of singularly perturbed controls coefficient nullprojection and damped controls coefficient nullprojection to disencumber the nullprojection matrix from its rank deficiency, and to enhance the closed loop control system performance.
The methodology yields desired linear attitude deviation dynamics realization with globally uniformly ultimately bounded trajectory
tracking errors, and reveals a tradeoff between trajectory tracking accuracy and damped generalized inverse stability. The
paper bridges a gap between the nonlinear control problem applied to spacecraft dynamics and some of the basic generalized
inversion-related analytical dynamics principles. |
| |
Keywords: | Spacecraft attitude control Singularly perturbed feedback linearization Linear attitude deviation dynamics realization Control authority redundancy Nullspace parametrization Controls coefficient Moore– Penrose generalized inverse Damped generalized inverse Singularly perturbed nullprojection Damped nullprojection Null-control vector |
本文献已被 SpringerLink 等数据库收录! |
|