Frequency band-wise passive control of linear time invariant structural systems with H∞ optimization

A frequency band specific passive control strategy is presented based on H∞ optimization for multi-degree of freedom (MDOF) linear time invariant (LTI) structural systems. Effective control can be achieved if passive control devices are designed by considering frequency bands of excitation. Minimization of maximum spectral norm or worst-case gain in the excitation frequency range is taken into account for the design of passive control devices for effective performance. A multi-storey shear planer frame coupled with a tuned mass damper (TMD) system as the passive control device is considered in the numerical simulation for controlling both displacement and acceleration subjected to base excitation. The band-specific H∞ optimization problem for design of passive control devices has been transformed into GA-friendly form for the TMD system as control devices. Such a design strategy of passive control devices based on minimizing worst-case gain associated to finite frequency band is observed to provide efficient design of a TMD system with better performance than that designed based on conventional H∞ optimization associated to entire frequency range.