A mixed H2/H∞ output-feedback control design methodology for vibration reduction of base-isolated building structures modelled in the form of second-order linear systems is presented. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities. A controller that guarantees asymptotic stability and a mixed H2/H∞ performance for the closed-loop system of the structure is developed, based on a Lyapunov function. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.
SpencerB.SainM.‘Controlling buildings: A new frontier in feedback.’IEEE Control Syst. Mag.17 (1997): 19–35
3.
DykeS.SpencerB.SainM.CarlsonJ.‘An experimental study of MR dampers for seismic protection.’Smart Mater. Struct.7 (1998): 693–703
4.
SpencerB.SongT.‘New applications and development of active, semi-active and hybrid control techniques for seismic and non-seismic vibration in the USA.’ In Proceedings of the International Post-SMIRT Conference Seminar onSeismic isolation, passive energy dissipation and active control of vibration of structures, Cheju, Korea, 1999.
5.
DuH.SzeKam Y.LamJ.‘Semi-active H∞ control of vehicle suspension with magneto-rheological dampers.’J. Sound Vib.283 (2005): 981–996
6.
KarimiH. R.ZapateiroM.LuoN.‘Wavelet-based parameter identification of a nonlinear magnetorheological damper.’Int. J. Wave., Multires. Image Process.7 (2) (2009): 183–198
7.
AlvinK. F.ParkK. C.‘Second-order structural identification procedure via state-space-based system identification.’AIAA J.32 (2) (1994): 397–406
8.
FriswellM. I.‘Extracting second-order systems from state-space representations.’AIAA J.37 (1) (1999): 132–135
9.
GarrardW. L.WalkerJ. A.‘Stability of a class of coupled systems.’IEEE Trans. Autom. Control12 (6) (1967): 786–787
10.
HenrionD.SebekM.KuceraV.‘Robust pole placement for second-order systems: an LMI approach.’ October 2002, available from http://citeseer.ist.psu.edu/623785.html.
11.
DattaB. N.RinconF.‘Feedback stabilization of a second-order system: A nonmodal approach.’Linear Algebr. Appl.188 (1993): 138–161
12.
DuanG. R.‘Parametric eigenstructure assignment in second-order descriptor linear systems.’IEEE Trans. Autom. Control49 (10) (2004): 1789–1795
13.
KarimiH. R.‘Optimal vibration control of vehicle engine-body system using Haar functions.’Int. J. Control, Autom. Syst.4 (6) (2006): 714–724
14.
LuoN.RodellarJ.de la SenM.VehiJ.‘Output feedback sliding mode control of base isolated structures.’J. Franklin Inst.337 (2000): 555–577
15.
YangJ. N.LinS.JabbariF.‘H2 based control strategies for civil engineering structures.’J. Struct. Control10 (2003): 205–230
16.
YangJ. N.LinS.JabbariF.‘H∞ based control strategies for civil engineering structures.’Struct. Control Health Monit.11 (2004): 223–237
17.
KarimiH. R.ZapateiroM.LuoN.‘A linear matrix inequality approach to H∞ control of vehicle engine-body vibration systems with a time-varying actuator delay.’Proc. IMechE, Part I: J. Systems and Control Engineering222 (I8) (2008): 883-899 DOI: 10.1243/09596518JSCE620.
18.
KarimiH. R.GaoH.‘LMI-based delay-dependent mixed H2/H∞ control of second-order neutral systems with time-varying state and input delays.’ISA Trans.47 (3) (2008): 311–324
19.
ChenY.ZhuC.‘Active vibration control based on linear matrix inequality for rotor system under seismic excitation.’J. Sound Vib.314 (2008): 53–69
20.
HongS.ParkC. H.ParkH. C.‘Vibration control of beams using multiobjective state-feedback control.’Smart Mater. Struct.15 (2006): 157–163
21.
GaoH.LamJ.WangC.‘Multi-objective control of vehicle active suspension systems via load-dependent controllers.’J. Sound Vibr.290 (2006): 654–675
22.
WangZ.ZengH.HoD. W. C.UnbehauenH.‘Multiobjective control of a four-link flexible manipulator: A robust H∞ approach.’IEEE Trans. Control Syst. Technol.10 (6) (2002): 866–875
23.
WangZ.‘Robust H∞ state feedback control with regional pole constraints: an algebraic Riccati equation approach.’Trans. ASME: J. Dyn. Syst., Meas. Control120 (2) (1998): 289–292
24.
WangZ.TangG.ChenX.‘Robust controller design for uncertain linear systems with circular pole constraints.’Int. J. Control65 (6) (1996): 1045–1054
25.
ZapateiroM.LuoN.KarimiH. R.‘Semiactive control of a base isolated building using magnetorheological dampers.’Int. J. Model., Identif. Control7 (1) (2009): 41–48
26.
DykeS.SpencerB.SainM.CarlsonJ.‘Modeling and control of magnetorheological dampers for seismic response reduction.’Smart Mater. Struct.5 (1996): 565–575
27.
JansenL.DykeS.‘Semiactive control strategies for MR dampers: Comparative study.’J. Engng Mech.126 (2000): 795–803
28.
YangG.Large-scale magnetorheological fluid damper for vibration mitigation: modeling, testing and control PhD Thesis, University of Notre Dame, 2001.
29.
WangX.GordaninejadF.‘Lyapunov-based control of a bridge using magnetorheological fluid dampers.’J. Intell. Mater. Syst. Struct.13 (2002): 415–419
30.
ParkC.JeonD.‘Semiactive vibration control of a smart seat with an MR fluid damper considering its time delay.’J. Intell. Mater. Syst. Struct.13 (2002): 521–524
31.
LuoN.VillamizarR.VehiJ.RodellarJ.ManosaV.‘Sliding mode control of structures with uncertain coupled subsystems and actuator dynamics.’ In Proceedings of theEuropean control conference, Cambridge, UK, 1-4 September 2003.
32.
NagarajaiahS.NarasimhanS.AgrawalA.TangP.‘Semiactive Lyapunov controller for phase II seismic isolated bridge benchmark.’ Structures Congress 2006, St. Louis, Missouri, USA, 2006.
33.
McClamrochN.GavinH.OrtizD.HansonR.‘Electrorheological dampers and semi-active structural control.’ In Proceedings of the 33rd Conference onDecision and control, Florida, USA, 14-16 December 1994, vol. 1, pp. 97–102.
34.
McClamrochN.GavinH.‘Closed loop structural control using electrorheological dampers.’ In Proceedings of theAmerican control conference, Seattle, Washington, 1995, pp. 4173–4177.
35.
VillamizarR.LuoN.VehiJ.RodellarJ.‘Semiactive sliding mode control of uncertain base isolated structures with actuator dynamics.’ In Proceedings of the AMAS/ECCOMAS/STC Workshop on Smart Materials and Structures (ECCOMAS-SMART), Jadwisin, Poland, 2-5 September 2003, pp. 224–231.
36.
MoonS.BergmanL.VoulgarisP.‘Sliding mode control of cable-stayed bridge subjected to seismic excitation.’J. Engng Mech.129 (2003): 71–78
37.
LuoN.VillamizarR.VehiJ. ‘Backstepping control of nonlinear building structures with hysteretic and frictional dynamics.’ European Control Conference, Kos, Greece, 2007.
38.
ZapateiroM.VillamizarR.LuoN.‘Semiactive seismic vibration control of structures equipped with magnetorheological dampers.’Int. J. Fact. Autom., Robot. Soft Comput. (1) (2008): 77–84
39.
KimH.RoschkeP.‘Fuzzy control of base-isolation system using multiobjective genetic algorithm.’Comput.-Aid. Civil Infrastruct. Engng21 (2006): 436–446
40.
SchurterK.RoschkeP.‘Neuro-fuzzy control of structures using acceleration feedback.’Smart Mater. Struct.10 (2001): 770–779
41.
ZapateiroM.LuoN.KarimiH. R.VehíJ.‘Vibration control of a class of semiactive suspension system using neural network and backstepping techniques.’Mech. Syst. Signal Process.23 (6) (2009): 1946–1953
42.
ShieldC. K.FrenchC. W.TimmJ.‘Development and implementation of the effective force testing method for seismic simulation of large-scale structures.’Philos. Trans. R. Soc.359 (2001): 1911–1929
43.
MosquedaG.StojadinovicB.MahinS., Implementation and accuracy of continuous hybrid simulation with geographically distributed substructures, technical report, Earthquake Engineering Research Center, University of California, Berkeley, 2005.
44.
JungR. Y.ShingP. B.‘Performance evaluation of a real-time pseudodynamic test system.’Eartha. Engng Struct. Dyn.35 (2006): 789–810
45.
CarrionJ.SpencerB., Model-based strategies for real-time hybrid testing, technical report, University of Illinois at Urbana-Champaign, 2007.
46.
WangZ.YangF.HoD. W. C.LiuX.‘Robust H∞ control for networked systems with random packet losses.’IEEE Trans. Syst. Man Cybern., Part B: Cybern.37 (4) (2007): 916–924
47.
LimebeerD. J. N.AndersonB. D. O.HendelB.‘A Nash game approach to mixed H2/H∞ control.’IEEE Trans. Automat. Control39 (1994): 69–82
48.
LinW.‘MixedH2/H∞ control of nonlinear systems.’ In Proceedings of the 34th Conference on Decision and control, New Orleans, USA, 13-15 December 1995, pp. 333–338.
49.
ChenX.ZhouK.‘Multiobjective H2/H∞ control design.’SIAM J. Control Optim.40 (2001): 628–660
50.
ChenB. S.ZhangW.‘Stochastic H2/H∞ control with state-dependent noise.’IEEE Trans. Autom. Control49 (1) (2004): 45–57
51.
ZhangW.ZhangH.ChenB. S.‘Stochastic H2/H∞ control with (x,u,v)-dependent noise: finite horizon case.’Automatica42 (11) (2006): 1891–1898
52.
ZhangW.HuangY.ZhangH.‘Stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noise.’Automatica43 (3) (2007): 513–521
53.
DahlehM. A.PearsonJ. B.‘L1-optimal feedback controllers for MIMO discrete-time systems.’IEEE Trans. Autom. Control32 (1987): 314–322
54.
GahinetP.NemirovskyA.LaubA. J.ChilaliM.LMI control toolbox: for use with Matlab, (The MATH Works, Inc. Natik, Massachusetts1995)
55.
HoD. W. C.LuG.‘Robust stabilization for a class of discrete-time nonlinear systems via output feedback: The unified LMI approach.’Int. J. Control76 (2) (2003): 105–115
