Definition and dynamic portrait of large space structures for control system synthesis

摘要

A new definition of large space structures (LSS) is given, yielding a mathematical model of minimal order for three-axis attitude control system synthesis. Then, the dynamic portrait is introduced, allowing the structure to be designed with minimal excitation of certain vibration modes by the control variables. The theory is developed by considering space structures having a branched configuration near the centre of which are located attitude sensors and actuators collocated with an orthogonal control axis set to be orientated. It is well known that the complete set of space structures comprises two subsets, one in which rigid body dynamics may be assumed and the other, referred to as the Large Space Structures (LSS), for which one or more flexure modes, typically with very low natural frequencies, must be taken into account. This paper provides a much needed quantitaive boundary between the two subsets, given by the definition that a structure is a LSS if the inequalities, k_i > 2.47 and omega_i~2 < 2k_i, are satisfied for any i, where omega_i and k_i are, respectively, the natural frequency and excitability coefficient of the i~(th) flexure mode. The approach is based on a comparison of the flexure mode motion with the rigid-body mode motion in the phase double-plane (i~(th) modal phase-plane superposed on the rigid-body phase-plane) of a structural model in the modal state representation to which is applied a step control variable. Hence, the model derived is suitable for designing control systems employing discontinuous on-off thrusters as well as continuous actuators. The Lagrangian and Modal dynamic models of the structure are then used together to derive the dynamic portrait as a set of graphs, [omega_i] (lambda) and [k_i] (lambda), where lambda is a selected physical parameter of the spacecraft. The structure may be designed, where practicable, to correspond with minima in these graphs to simplify the control problem. The new method is demonstrated by examples.