In terms of vibrations along bidirectional earthquake forces, several problems are faced when modelling and controlling the structure of a building, such as lateral-torsional vibration, uncertainties surrounding the rigidity and the difficulty of estimating damping forces.
In this paper, we use a fuzzy logic model to identify and compensate the uncertainty which does not require an exact model of the building structure. To attenuate bidirectional vibration, a novel discrete-time sliding mode control is proposed. This sliding mode control has time-varying gain and is combined with fuzzy sliding mode control in order to reduce the chattering of the sliding mode control. We prove that the closed-loop system is uniformly stable using Lyapunov stability analysis. We compare our fuzzy sliding mode control with the traditional controllers: proportional–integral–derivative and sliding mode control. Experimental results show significant vibration attenuation with our fuzzy sliding mode control and horizontal-torsional actuators. The proposed control system is the most efficient at mitigating bidirectional and torsional vibrations.
AndersonJCNaeimF (2012) Basic Structural Dynamics. Los Angeles: Wiley.
2.
BartoszewiczA (1998) Discrete-time quasi-sliding mode control strategies. IEEE Transactions on Industrial Electronics45(4): 633–637.
3.
CaiGHuangJ (2002) Discrete-time variable structure control method for seismic-excited building structures with time delay in control. Earthquake Engineering & Structural Dynamics31(7): 1347–1359.
4.
ChangCC (1999) Mass dampers and their optimal designs for building vibration control. Engineering Structures21(5): 454–463.
5.
ChoiKMChoSWKimDOet al. (2005) Active control for seismic response reduction using modal-fuzzy approach. International Journal of Solids and Structures42(16–17): 4779–4794.
6.
ChopraAK (2011) Dynamics of Structures - Theory and Applications to Earthquake Engineering. 4th ed.Upper Saddle River, NJ: Prentice–Hall.
7.
DaiJ(2010) Fuzzy logic based control and simulation analysis for nonlinear structure. In: Second international conference on computer modeling and simulation, Sanya, China, 22–24 January 2010, pp. 447–451. Piscataway, NJ: IEEE.
8.
DasDDattaTKMadanA (2012) Semiactive fuzzy control of the seismic response of building frames with MR dampers. Earthquake Engineering and Structural Dynamics41(1): 99–118.
9.
FiscoNRAdeliH (2011) Smart structures: Part I – active and semi-active control. Scientia Iranica18(3): 275–284.
10.
GucluRYaziciH (2008) Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers. Journal of Sound and Vibration318(1–2): 36–49.
11.
HaciogluYYagizN (2011) Adaptive backstepping control with estimation for the vibration isolation of buildings. Journal of Vibration and Control18(3): 1996–2005.
12.
HochrainerMJAdamCZieglerF (2000) Application of tuned liquid column dampers for passive structural control. In: 7th international congress on sound and vibration (ICSV 7), Garmisch–Partenkirchen, Germany, 4–7 July 2000, pp. 3107–3114. Auburn, AL: Institute of Acoustics and Vibration.
13.
HornRAJohnsonCR (1985) Matrix Analysis. Melbourne: Cambridge University Press.
14.
HousnerGWBergmanLACaugheyTKet al. (1997) Structural control: Present and future. Journal of Engineering Mechanics123(9): 897–971.
IwamotoKYujiKKenzoNet al. (2002) Output feedback sliding mode control for bending and torsional vibration control of 6-story flexible structure. JSME International Journal Series C45(1): 150–158.
17.
KarimiHRLuoNZapateiroMet al. (2011) control design for building structures under seismic motion with wireless communication. International Journal of Innovative Computing Information and Control7(9): 5269–5284.
18.
LiZDengZ (2009) Improving existing “ reaching law” for better discrete control of seismically-excited building structures. Frontiers of Structural and Civil Engineering3(2): 111–116.
19.
LiZGuZDengZ (2010) Discrete-time fuzzy variable structure control for buildings with delay time in control. In: 8th world congress on intelligent control and automation (WCICA), Jinan, China, 7–9 July 2010, pp. 4963–4967. Piscataway, NJ: IEEE.
20.
LinJLTsaiKC (2008) Seismic analysis of two-way asymmetric building systems under bi-directional seismic ground motions. Earthquake Engineering & Structural Dynamics37(2): 305–328.
21.
LuXZhaoB (2001) Discrete-time variable structure control of seismically excited building structures. Earthquake Engineering & Structural Dynamics30(6): 853–863.
22.
MadanA (2005) Vibration control of building structures using self-organizing and self-learning neural networks. Journal of Sound and Vibration287(4–5): 759–784.
23.
MariaGSelvaganesanNAjith KumarBet al. (2016) Dynamic analysis and sliding mode vibration control for a two storeyed flexible building structure. In: International conference on control communication & computing India (ICCC), Trivandrum, India, 4–7 July 2000, pp. 24–29. Auburn, AL: Institute of Acoustics and Vibration.
24.
NguyenTHKwokNMHaQPet al. (2006) Adaptive sliding mode control for civil structures using magnetorheological dampers. In: International symposium on automation and robotics in construction, Tokyo, Japan, 3–5 October 2006, pp. 24–29. Waterloo, Canada: IAARC.
25.
NigdeliSBodurogluM (2013) Active tendon control of torsionally irregular structures under near-fault ground motion excitation. Computer-Aided Civil and Infrastructure Engineering28(9): 718–736.
26.
OzerHOHaciogluYYagizN (2016) Suppression of structural vibrations using PDPI + PI type fuzzy logic controlled active dynamic absorber. Journal of the Brazilian Society of Mechanical Sciences and Engineering38(7): 2105–2115.
27.
ParkKSKohHMOkSY (2002) Active control of earthquake excited structures using fuzzy supervisory technique. Advances in Engineering Software33(11–12): 761–768.
28.
ReiglesDGSymansMD (2006) Supervisory fuzzy control of a base-isolated benchmark building utilizing a neuro-fuzzy model of controllable fluid viscous dampers. Structural Control and Health Monitoring13(2–3): 724–747.
29.
RoldanCCampaFJAltuzarraOet al. (2014) Automatic identification of the inertia and friction of an electromechanical actuator. New Advances in Mechanisms, Transmissions and Applications17: 409–416.
30.
SarpturkSZIstefanopolosYKaynakO (1987) On the stability of discrete-time sliding mode control systems. IEEE Transactions on Automatic Control32(10): 930–932.
31.
SheehanA (1996) Smart materials in construction. In: 3rd international conference on intelligent materials and 3rd European conference on smart structures and materials, Lyon, France, 3–5 June 1996, pp. 1–10. Bellingham, WA: SPIE.
32.
SoleymaniMAbolmasoumiAHBahramiHet al. (2018) Modified sliding mode control of a seismic active mass damper system considering model uncertainties and input time delay. Journal of Vibration and Control24(6): 1051–1064.
33.
SongGSethiVLiHN (2006) Vibration control of civil structures using piezoceramic smart materials: A review. Engineering Structures28(11): 1513–1524.
34.
ThenozhiSYuW (2013) Advances in modeling and vibration control of building structures. Annual Reviews in Control37(2): 346–364.
35.
ThenozhiSYuW (2014) Stability analysis of active vibration control of building structures using PD/PID control. Engineering Structures81(7): 208–218.
36.
UtkinVI (1992) Sliding Modes in Control and Optimization. Berlin: Springer–Verlag.
37.
WangLX (1994) Adaptive Fuzzy Systems and Control. Upper Saddle River: Prentice–Hall.
38.
YanikAPinelliJGutierrezH (2013) Control of a three-dimensional structure with magneto-rheological dampers. In: 11th international conference on vibration problems, Lisbon, Portugal, 9–12 September 2013, pp. 1–9. London: Macmillan Publishers Limited.
39.
YinSGaoHQiuJet al. (2017a) Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults. Automatica76: 282–292.
40.
YinSYangHKaynakO (2017b) Sliding mode observer-based FTC for Markovian jump systems with actuator and sensor faults. IEEE Transactions on Automatic Control62(7): 3551–3558.
