Pole Placement for Time Periodic Systems

摘要

The technique of pole placement was applied to a time varying periodic system. When the control matrix was of full rank, unstable real roots were predictably moved to stable locations. Specified damping was successfully applied to oscillatory roots. In the case of the control matrix having less than full rank a least squares gain was applied. This minimized the error between all desired pole locations and controlled pole locations and as a consequence, prediction of final pole location was not possible. An exact method for predictably placing poles as desired was restricted by a controllability condition. The method was applied to the restricted four-body problem and control of a satellite in a periodic orbit about the Earth-Moon Lagrangian point, L sub 3. A stabilized orbit was obtained for a model which allowed instantaneous control of both position and velocity. Stabilization was not successful in the case of control of velocity only. The least squares solution effected several modes simultaneously. The exact solution for gain was unobtainable as the controllability condition was not met. (Author)