Quasi-Static Shape Control of Flexible Space Structures by Using Heaters

Abstract

L ARGE flexible structures composited of thin-walled beams, such as antennae, solar arrays, etc., are extensively used in space applications. These structures may undergo thermally-induced deformations or even vibrations due to the change of orbital heating [1]. To suppress these adverse responses one may use passive control methods to obtain a good design [2]. However, active methods are still needed to achieve precise control in transient manner. Many popular active shape control methods usually use piezoelectric actuators [3]. In this way, cautions should be paid on the interface debounding failure, because the control force is transferred by the tight bounding between the actuator and the structure. Because the thermally-induced response is principally due to the change of thermal environment it could be reliably and economically suppressed if one can control the temperature distribution of the structure. In this manner, the control force induced by thermal expansion strains is generated naturallywithin the structure instead of being transferred through the shear force. Thus, the interface debounding is unlikely to happen. Haftka and Adelman [4] were probably the first to have the idea of shape control by imposing prescribed temperatures on the control elements. They pointed out that the corresponding thermal stresses are self-equilibrating and smaller than those associated with applied forces. Therefore, one need not worry about small inaccuracies in equilibrating control forces, which lead to the drift in position or orientation. In addition, the solar energy could be a natural source of heating. Similar to the idea in [4] thermal bending moments have been applied to control the vibration of cantilevers, ignoring the longitudinal heat conduction and radiation boundary condition [5,6]. Irschik and Ziegler [7] and Irschik and Pichler [8] gave theoretical models of both the static and dynamic shape control by imposing thermal strains. However, the practical realization of the required thermal strains is still unresolved [9]. In present Note, we investigate the practical implementation of quasi-static shape control for thin-walled structures by using heaters. For this purpose, a nonlinear optimization problem is formulated to determine the required control heat fluxes. Because radiation is considered for this transient problem the Fourier finite element [10] is adopted to reduce the computational cost. Besides, an efficient optimization heuristic is constructed to find the good placement of heaters that minimizes the total control energy.