High Precision Surface Control of Flexible Space Reflectors

Open Access
Hill, Jeffrey Ray
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
February 28, 2011
Committee Members:
  • Dr Kon Well Wang, Dissertation Advisor
  • Dr Kon Well Wang, Committee Chair
  • Christopher Rahn, Committee Chair
  • George A Lesieutre, Committee Member
  • Mary I Frecker, Committee Member
  • Gossamer
  • control
  • En Masse Elimination
  • modeling
Flexible reflectors are used for a number of applications in space, including resource monitoring, weather analysis, hazard assessment, reconnaissance, and imaging. With the rapid advances in deployable membrane and mesh antenna technologies, the feasibility of developing large, lightweight reflectors has greatly improved, though high-precision surface control is needed in order to achieve the required surface accuracy. The purpose of this research is to advance the state of the art by implementing high-precision surface control on a flexible reflector using PVDF actuators, as well as introducing methods to overcome real world problems that can develop when implementing this technology. A reflector/actuator system is modeled such that the model can be quickly modified in order to accommodate different actuator locations. Experimental results show that while the analytical reflector model is generally correct, due to idiosyncrasies in the reflector it should not be used for online control. Therefore, a methodology is proposed for online system identification for use with an online control law. Using the PVDF actuators, surface control is executed using a least squares control law, where photogrammetry is used to determine the out-of-plane displacement at designated points on the surface. When the surface cannot be fully covered with actuators, optimal placement of the available actuators must be considered. First, when focusing solely on the constraint on the number of possible actuators, optimal placement of the actuators is found using a genetic algorithm. A constraint on how many independent power supplies are available is added. A new method to determine the optimal grouping of actuators to power supplies is derived, called the En Masse Elimination (EME) method. This method can determine the global optimal solution without having to exhaustively search every possible grouping combination. A number of improvements to the EME method are given which increase the speed of the algorithm as well as enable the EME algorithm to be used online during dynamically changing error conditions. Finally, the EME method is experimentally validated using a single pinned-pinned beam. Using a beam rather than a reflector reduces the complexity of the problem while still showing the functionality of the EME algorithm. Experimental data show that the EME algorithm is able to quickly and accurately find the global optimal actuator grouping.