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Actuator-Placement Considerations for the Control of Large Space Structures.

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Final rept.,

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Actuator placement for the control of distributed-parameter systems such as large flexible space structures is considered in detail. The first focus is on the degree of controllability as defined in a previous work. Its behavior and approximation is considered via simple problems for which the exact value may be computed. The upper-bound approximation is found to be periodically exact for harmonic systems and acceptable for lightly damped systems. A method is proposed for avoiding the unacceptable behavior of the approximation when a problem has nearly repeated roots. Because the upper-bound approximation in the problem of a double-integral plant diverges, a new lower-bound approximation is developed based on discretization of the continuous-time system. The approximate degree of controllability in three forms for time-optimal, energy-optimal, or fuel-optimal control policy is applied to the problem of optimal actuator placement for control of transverse oscillation of a simply supported beam. Both predictable and unanticipated optimal solutions are encountered. The concept of a degree of control spillover is then developed, motivated by the limited fidelity inherent in structural models. A composite criterion incorporating both degree of controllability and degree of control spillover is again applied to the simply-supported-beam problem. Design freedom involving number and placement of actuators is next examined for the computationally simple Independent Modal Space Control IMSC design method. Actuator placement is then of prime importance in physically realizing the optimal control laws. Methods for actuator-placement optimization are developed for use with ISMC.

Subject Categories:

  • Numerical Mathematics
  • Astronautics
  • Spacecraft Trajectories and Reentry

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