Multi-Overlapping Decentralized Control Approach To Structural Vibration Systems

Structural Vibration Control (SVC) of buildings and civil structures is one of the best examples of large-scale and complex control systems, the system not only has the characteristics of interconnected systems, but also subsystems overlap under information structure constraints.In this work, A multi-overlapping decentralized control scheme is presented and applied to the design of overlapping controllers in the context of SVC of tall buildings under seismic excitation. It is a demonstration of how a new concept of the permuted inclusion principle with multi-overlapping decomposition, coordination and contraction can be efficiently applied to a system with complex information structure constraints.A multi-overlapping decomposition based on the inclusion principle is developed in order to decompose the system into a group of pair-wise subsystems (areas) under the information structure constraints. In the expanded space, these pair-wise subsystems appear as disjoint. Then, the decentralized controllers designed, by standard linear quadratic regulator (LQR) control laws are implemented in each pair-wise subsystem. Finally, the overlapping decentralized controller is obtained by coordinating and contracting the pair-wise decentralized controllers from the expanded space to the original space, preserving the inclusion conditions.Simplified dynamical models for the vibrational response of a six-story building are presented. The present work has to discuss the more general and practically interesting problem of designing multi-overlapping controllers, paying special attention to the longitudinal multi-overlapping case. When applied to SVC of six-story building model under seismic excitation, the proposed methodology not only guarantees SVC qualities, but also increases the system reliability with respect to a wide variety of structured perturbations. The simulation results show that the multi-overlapping controllers achieve levels of performance similar to those obtained by their centralized counterparts. In the future, the overlapping decentralized control may be applied to systems with more complex information structures, e.g. to systems connected to additional subsystems in various ways.