Decentralized static output‐feedback H_∞ controller design for buildings under seismic excitation

Abstract

SUMMARY In this work, we present a new method in designing static output‐feedback H∞ controllers suitable for vibrational control of buildings under seismic excitation. The method produces a Linear Matrix Inequality (LMI) formulation that allows obtaining static output‐feedback controllers with different information structure constraints by imposing a convenient zero–nonzero structure on the LMI variables. The application of the proposed methodology is illustrated by designing centralized and decentralized velocity‐feedback H∞ controllers to mitigate the seismic response of a five‐story building. Copyright © 2011 John Wiley & Sons, Ltd.

ptimal passive-damping design using a decentralized velocity-feedback H-Infinity approach

“…However, as pointed out in Rubió-Massegú et al (2012a), this difficulty can be conveniently circumvented by adding a small perturbation to the system matrix. Using the perturbed state matrix…”

“…Moreover, decentralized static output-feedback controllers can also be designed by imposing an appropriate zero-nonzero structure on the new LMI variables. Next, we summarize the main ideas of this design strategy; a detailed discussion can be found in Rubió-Massegú et al (2012a). Given a full row-rank output matrix C y with dimensions p × n, p ≤ n, we consider an n × (n − p) matrix Q, whose columns are a basis of Ker(C y ); and the MoorePenrose pseudo-inverse of C y , which is given by…”

“…Recently, an effective strategy to compute static output-feedback controllers was presented by Rubió-Massegú et al (2012a). This strategy is based on a simple transformation of the LMI variables that allows computing structured output-feedback control gain matrices by solving a single optimization problem with LMI constraints.…”

Computational Effectiveness of Lmi Design Strategies for Vibration Control of Large Structures

“…, f n (t)] T is a real vector of dimension n. The objective of the paper is to conduct a comparative study of the computational effectiveness of three different LMIbased controller design strategies: H ∞ , energy-to-peak and energy-to-componentwise-peak. The H ∞ approach is a well-known design methodology that uses the 2-norm to measure both the controlled-output and the disturbance-input [9][10][11][12][13][14][15]. The energy-to-peak approach is a particular case of generalized H 2 design [16] that is gaining a growing relevance in structural vibration control [17][18][19][20].…”

Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

“…to obtain decentralized or semidecentralized controllers that, for a given actuation device, make it possible to compute the corresponding control actions using neighbouring state information provided by the local sensor or by sensors located in adjacent stories [14][15][16].…”