Computational effectiveness of LMI design strategies for vibration control of large structures

Distributed control systems for vibration control of large structures involve a large number of actuation devices and sensors that work coordinately to produce the desired control actions. Design strategies based on linear matrix inequality (LMI) formulations allow obtaining controllers for these complex control problems, which are characterized by large dimensionality, high computational cost and severe information constraints. In this paper, we conduct a comparative study of the computational effectiveness of three different LMI-based controller design strategies: H-infinity, energy-to-peak and energy-to-componentwise-peak. The H-infinity approach is a well-known design methodology and has been widely used in the literature. The energy-to-peak approach is a particular case of generalized H2 design that is gaining a growing relevance in structural vibration control. Finally, the energy-to-componentwise-peak approach is a less common case of generalized H2 design that produces promising results among the three considered approaches. These controller design strategies are applied to synthesize active state-feedback controllers for the seismic protection of a five-story building and a twenty-story building both equipped with complete systems of interstory actuation devices. To evaluate the computational effectiveness of the proposed LMI design methodologies, the corresponding computation times are compared and a suitable set of numerical simulations is carried out to assess the performance of the obtained controllers. As positive results, two main facts can be highlighted: the computational effectiveness of the energy-to-peak control design strategy and the particularly well-balanced behavior exhibited by the energy-to-componentwise-peak controllers. On the negative side, it has to be mentioned the computational inefficiency of the considered LMI design methodologies to properly deal with very-large-scale control problems.