H∞-optimal mapping of actuators and sensors in flexible structures

A computationally efficient method is described to search and find optimal spatial configurations for the placement (mapping) of a finite number of actuators and sensors on a continuous flexible structure to reduce the vibrations or deformations in the structure to a minimum in the H_∞ sense. The method produces a feedback controller corresponding to the minimal H_∞ norm of the disturbance-deformation operator. The computational cost of the optimal mapping search is reduced through two techniques. First, the computationally expensive goal function based on the complete H_∞ synthesis is evaluated only for the mappings that pass a computationally inexpensive test. Next, the target norm is adjusted statistically based on the already evaluated mappings. Mapping optimization based on exhaustive search and genetic algorithms are presented and demonstrated on a 30-node finite-element model of a simply supported beam