Quasistatic optimal actuator placement with minimum worst case distortion criterion

Abstract

The problem of placing actuators optimally in truss structures for quasistatic shape control is considered. Optimal actuator placement in large truss structures is a formidable task due to the combinatorial nature of the problem. In this paper we use and compare the performances of several heuristic search techniques to determine their effectiveness in solving this design problem. The selected methods are simulated annealing, exhaustive single-point substitution, and single location iterative minimization, a sequential minimization technique presented herein. The optimality criterion is the worst case distortion after correction. This worst case value of a performance measure is obtained through a constrained min-max procedure. An ideal actuator concept is employed to determine limits on the optimal criterion value, which is then used also to evaluate the number of actuators needed for given levels of correction. The procedures just discussed are performed on representative trusses. Results show that heuristics can handle the optimization problem since the number of function calls grows linearly with the size of the problem and not in a combinatorial fashion, typical in such cases. The different algorithms exhibit similar performances ; however, exhaustive single-point substitution requires a significantly higher computational effort. The applicability of the lower limit is investigated, and in most cases there is good agreement with the optimization results.