Design of linear active control algorithms for non-stationary unknown forcing function

The object of the research is the design procedure of a linear control algorithm able to mitigate the effects of seismic shaking as far as possible, maintaining the running and installation costs within admissible bounds. The procedure starts from approaching the solution of the equation of motion of a SDOF structure in the norm sense, as explained in Secs. 2–3, which allows to obtain results that do not depend on the details of the forcing function. The approach is generalized to MDOF structures by modal decomposition, and it is shown that the control algorithm can be designed by independent modal control, by applying at each mode the procedure outlined for a SDOF system. Robustness of the algorithm with reference to uncertain identification of the structural properties is successfully investigated, both by theoretical tools and by numerical simulation. The whole pattern proves to be effective and poorly conditioned by the peculiar characters of the excitation.