Robust control of smart structures with natural frequency uncertainties

The research described in this dissertation integrates robust control design methodologies with flexible smart structures for achieving desired performance in the presence of uncertainties. Control of smart structures presents a number of difficult problems which arise due to structural parameter variations, limited actuation force, and restricted control bandwidth. The uncertainties associated with natural frequencies of smart structures are important because of their influence on the performance of the structures.; First, the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) controller design method was used for designing controllers for smart structures. These observer-based controllers saturated the system actuators before good loop transfer recovery was achieved. Therefore, a controller design which was not observer based, called modified LQG/LTR, was utilized for obtaining adequate loop transfer recovery with reduced control effort. This modified LQG/LTR controller was implemented to improve the damping of a cantilever beam and three-mass test article. On both test articles, the modified LQG/LTR controllers experimentally provided good closed loop performance and robustness properties in the presence of sensor noise and natural frequency variations.; As the bounds on the natural frequency uncertainties increased, the sensitivity of the modified LQG/LTR controller to the natural frequency uncertainties also increased. To overcome this problem, a new algorithm called optimal H{dollar}sbinfty{dollar}/natural frequency (NF) was developed by directly incorporating the natural frequency uncertainty bounds into the design process. The H{dollar}sbinfty{dollar}/NF algorithm was simulated for single and multi-degrees of freedom structural systems. This controller was also implemented to improve the damping of a cantilever beam test article.; The desired closed-loop performance and available actuation force are not considered in H{dollar}sbinfty{dollar}/NF algorithm. In order to accommodate these factors in the design process, the H{dollar}sbinfty{dollar}/NF algorithm was coupled with a mixed H{dollar}sb2{dollar}/H{dollar}sbinfty{dollar} algorithm to produce a new algorithm called H{dollar}sb2{dollar}/H{dollar}sbinfty{dollar}/NF algorithm. The H{dollar}sb2{dollar}/H{dollar}sbinfty{dollar}/NF algorithm has a provision to limit the available control effort as well as to alter the closed-loop performance. The closed-loop performance and robustness proprieties of the H{dollar}sb2{dollar}/H{dollar}sbinfty{dollar}/NF algorithm are verified by simulation studies. In addition, the performance and robustness properties were experimentally verified on a cantilever beam test article.; In summary, various robust controllers have been designed for smart structure test articles. The performance and robustness of these controllers have been verified experimentally.