H ₂ norm based parameter optimization of multiple tuned mass dampers for resonance suppression

Flexible dynamic behavior of ultra-precision motion stage significantly deteriorates control performance. To tackle this problem, this paper presents an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">H</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> norm based parameter optimization of multiple Tuned Mass Dampers (TMDs) for resonance suppression applied on linear flexible structures, assuming all parameters of multiple TMDs are independent, and considering locations of TMDs as variables. Linear flexible structures with multiple TMDs are modeled as a closed-loop control system through modeling in steps. Genetic algorithm is implemented employing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="script">H</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> norm as the optimization criterion. The effectiveness of the optimization is numerically verified on a free-free thin plate. The effects of uncertainties in TMDs parameters, linear flexible structure parameters, and TMDs failure on the vibration suppression effect are studied. The proposed modeling and optimization methods are promising for application to various flexible structures with provided modal frequencies and mode shape matrix.