H2 norm based active multiple tuned mass dampers optimization for resonance suppression with robust stability constraint

Flexible modes with low damping limit the improvement of performance in nanometer precision motion stages. Tuned mass dampers (TMDs) are an effective devices to increase damping. However, active control strategies considering both the TMDs parameter optimization and system robustness have not been sufficiently explored. This paper proposes an active multi-TMD system optimization method for resonance suppression applied to a flexible structure. In the multi-TMD system, the mass, damping coefficient, stiffness, and location of each TMD are all regarded as independent design variables. The flexible structure coupled with the multi-TMD system is modeled as a general Linear Fractional Transformation (LFT) framework considering both parameter uncertainties and multiplicative uncertainties in the two subsystems. Optimal parameters of the multi-TMD system and an optimal $H_2$ controller are obtained simultaneously using genetic algorithm. With the structured singular value upper bound constraint, robust stability against uncertainties is guaranteed. Numerical studies on a thin plate demonstrate the superiority of the proposed method in both nominal and uncertain systems. Among 5000 samples, the proposed method achieves more than 82% $H_2$ norm attenuation even in the worst case.