Attitude Control Next let us explore the possibility of using the generally destabilizing solar torques induced by differential heating for pitch control. For this purpose, the panels are assumed to be made up of two layers of different materials with widely differing coefficients of thermal expansion. This in conjunction with rotation of the panels about their long axes enables control of the direction of their bending and hence the sign of the pitching solar torque. As before, in view of the relatively small ‘time constants’ of heating, a quasi-steady thermal analysis is undertaken in order to determine the curvature of the panels under heating. The resulting expression for can be written as On substituting this from (5) into (1) and carrying out some further algebraic simplification, the equation of pitching motion can be written as It may be noted that even though the parameter Sj is always positive, change in the sign of the parameter S2 is possible through rotation of the panels about their long axes by 7t radians. Proposed here is a ‘bang-bang’ scheme which judiciously exploits the rotations of the panels in order to attain the sign of S2 as follows: where: Figures 4-6 present some typical situations in which the proposed attitude controller attempts to achieve preferred satellite orientation. The effectiveness of this control strategy for aligning the satellite with its axis of symmetry along the local vertical is quite evident (Fig. 4). The controller continues to perform satisfactorily even in elliptical orbits. It is interesting to note that the proposed control approach is equally effective in positioning the satellite along the local horizontal configuration—normally an unstable equilibrium configuration for gravity oriented systems (Fig. 5). As expected, satellite attitude control in elliptical orbits is accompanied by larger amplitude relaxation oscillations about the equilibrium configuration. This may be attributed to the strongly non-autonomous character of the system. Fortunately, through a judicious choice of control parameters, it is normally possible to restrict the limit cycle amplitude to within acceptable limits. Finally, it is interesting to note that by suitably selecting the position control parameter, it is possible to attain an arbitrary intermediate satellite orientation (Fig. 6). Once again, the control leads to the limit cycle type of oscillatory response about the preferred orientation. This may be explained through ever present gravity gradient torque as well as the non-autonomous character of the system. Needless to say, the gravity gradient torque now becomes a liability, thus suggesting stubby rather than slender shapes as clearly desirable for satellite design.
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