Minimum Control Energy of Spatial Beam with Assumed Attitude Adjustment Target

Abstract

The dynamic analysis on the ultra-large spatial structure can be simplified drastically by ignoring the flexibility and damping of the structure. However, these simplifications will result in the erroneous estimate on the dynamic behaviors of the ultra-large spatial structure. Taking the spatial beam as an example, the minimum control energy defined by the difference between the initial total energy and the final total energy in the assumed stable attitude state of the beam is investigated by the structure-preserving method proposed in our previous studies in two cases: the spatial beam considering the flexibility as well as the damping effect, and the spatial beam ignoring both the flexibility and the damping effect. In the numerical experiments, the assumed simulation interval of three months is evaluated on whether or not it is long enough for the spatial flexible damping beam to arrive at the assumed stable attitude state. And then, taking the initial attitude angle and the initial attitude angle velocity as the independent variables, respectively, the minimum control energies of the mentioned two cases are investigated in detail. From the numerical results, the following conclusions can be obtained. With the fixed initial attitude angle velocity, the minimum control energy of the spatial flexible damping beam is higher than that of the spatial rigid beam when the initial attitude angle is close to or far away from the stable attitude state. With the fixed initial attitude angle, ignoring the flexibility and the damping effect will underestimate the minimum control energy of the spatial beam.