µ-Synthesis Control Applied to Counter the Seismic Load Action on a Building Structure

Abstract

Designing controllers that face to the seismic action on structures is the main goal of the structural active control which represents a field widely studied these last decades. Recent focus is accorded to the different sources of uncertainties affecting the structures with the application of robust controllers able to maintain the performances even in critical situations as when we include variations in the model structure coefficients (mass, stiffness, damping…etc) or the effect of some practical issues as (time delay, actuator saturation and limits…etc). The present paper evaluates the performance of a controller calculated on the base of a robust control method called µ-Synthesis to consider parametric uncertainties coming from variations in the model parameters and modeling errors in the actuator dynamic while accounting for actuator limits and sensors noise. This approach is particularly chosen for its ability to simultaneously take into account the parametric and dynamic uncertainties by shaping them into a structured uncertainties model and directly incorporate the performance and robustness objectives into multivariable control design. The designed µ-controller is applied in simulation on a three floors seismic exited building where an active bracing system (ABS) is attached to the first floor to provide the control effort. A Kanai Tajimi filter attacked by a white noise is used to model the excitation source. Good simulation results, showing a significant reduction of the structure response to the seismic load so modeled, are performed using displacement feedback control. Furthermore, the resulting controller achieves closely similar performances (vibrations attenuation) for all models including nominal and perturbed plant and presents the great benefit of costing low energy control effort. As the μ-synthesis generates controllers with too high order, a balanced realization method is applied to reduce the obtained controller order and maintain the same robust performances level.
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