0
Research Papers

Robust Delay-Dependent H∞ Control for Uncertain Structural Systems With Actuator Delay

[+] Author and Article Information
Hakan Yazici

 Department of Mechanical Engineering,Yildiz Technical University, Istanbul 34349, Turkeyhyazici@yildiz.edu.tr

Rahmi Guclu

 Department of Mechanical Engineering,Yildiz Technical University, Istanbul 34349, Turkeyguclu@yildiz.edu.tr

Ibrahim B. Kucukdemiral

 Department of Control and Automation Engineering, Yildiz Technical University, Istanbul 34349, Turkeybeklan@yildiz.edu.tr

M. N. Alpaslan Parlakci

 Department of Electrical and Electronics Engineering, Istanbul Bilgi University, Istanbul 34349, Turkeyaparlakci@bilgi.edu.tr

J. Dyn. Sys., Meas., Control 134(3), 031013 (Apr 06, 2012) (15 pages) doi:10.1115/1.4005500 History: Received July 16, 2010; Revised October 10, 2011; Published April 06, 2012; Online April 06, 2012

This paper is concerned with the design of a robust, state-feedback, delay-dependent H∞ controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H∞ stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Physical model of the structural system

Grahic Jump Location
Figure 2

Time responses of Kobe earthquake excitation

Grahic Jump Location
Figure 3

Controlled and uncontrolled displacements and accelerations time responses of each storey of structure

Grahic Jump Location
Figure 4

Time history of the applied control force for controller 1

Grahic Jump Location
Figure 5

Controlled and uncontrolled frequency responses of each storey of structure

Grahic Jump Location
Figure 6

Controlled peak response of fourth storey displacements against the actuator delay for controller 1

Grahic Jump Location
Figure 7

Controlled and uncontrolled displacement and accelerations time responses of each storey of structure

Grahic Jump Location
Figure 8

Time history of the applied control force for controller 2

Grahic Jump Location
Figure 9

Controlled and uncontrolled displacements and accelerations of each storey of structure

Grahic Jump Location
Figure 10

Controlled and uncontrolled displacements and accelerations of each storey of the uncertain structure with actuator delay for Case 1

Grahic Jump Location
Figure 11

Controlled and uncontrolled displacements and accelerations of each storey of the uncertain structure with actuator delay for Case 2

Grahic Jump Location
Figure 12

Controlled and uncontrolled frequency responses of each storey of the uncertain structure having actuator delay for Case 1

Grahic Jump Location
Figure 13

Time responses of Kocaeli earthquake excitation

Grahic Jump Location
Figure 14

Controlled and uncontrolled displacements and accelerations of each storey of the uncertain structure having actuator delay against Kocaeli earthquake for Case 1

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In