Computational methods for the optimization of the mapping of actuators and sensors in the control of flexible structures

Abstract

In this work the problem of actuator and sensor mapping and controller design for the flexible structure control is approached as minimization of the residual deformations index (Hinfinity norm of the closed-loop disturbance - deformation path) over the set of non-destabilizing feedback controllers and over the set of possible actuator and sensor mappings. Computational load associated with this approach is reduced by restricting the search to the mapping areas where an inexpensive lower estimate of residual deformations index (derived as a part of this study) is less than the desired value of this index. Further improvement is achieved by including statistical description of the difference between the actual and the estimated performance index over the set of mappings, in order to adjust the level of the mapping acceptance/rejection in such a way that the number of rejected mappings is increased. Serial and parallel optimization procedures based on exhaustive search and genetic algorithms are discussed. These concepts and algorithms are applied to test cases of simply supported beam, the UCLA Large Space Structure, and a telescope mirror model: a hinged round plate.