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A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD

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Abstract

This paper presents an efficient hybrid control approach through combining the idea of proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) control algorithm. The proposed LQR-PID controller, while having the advantage of the classical PID controller, is easy to implement in seismic-excited structures. Using an optimization procedure based on a cuckoo search (CS) algorithm, the LQR-PID controller is designed for a seismic- excited structure equipped with an active tuned mass damper (ATMD). Considering four earthquakes, the performance of the proposed LQR-PID controller is evaluated. Then, the results are compared with those given by a LQR controller. The simulation results indicate that the LQR-PID performs better than the LQR controller in reduction of seismic responses of the structure in the terms of displacement and acceleration of stories of the structure.

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References

  1. Datta T K. Control of Dynamic Response of Structures. Indo-US Symposium on Emerging Trends in Vibration and Noise Engineering, 1996, 18–20

    Google Scholar 

  2. Fisco N R, Adeli H. Smart structures: Part I-Active and semi-active control. Sci Iran, Trans A, 2011, 18(3): 275–284

    Article  Google Scholar 

  3. Samali B, Al-Dawod M. Performance of a five-story benchmark model using an active tuned mass damper and a fuzzy controller. Engineering Structures, 2003, 25(13): 1597–1610

    Article  Google Scholar 

  4. Samali B, Al-Dawod M, Kwok K C S, Naghdy F. Active control of cross wind response of 76-story tall building using a fuzzy controller. Journal of Engineering Mechanics, 2004, 130(4): 492–498

    Article  Google Scholar 

  5. Pourzeynali S, Lavasani H H, Modarayi A H. Active control of high rise building structures using fuzzy logic and genetic algorithms. Engineering Structures, 2007, 29(3): 346–357

    Article  Google Scholar 

  6. Huo L, Song G, Li H, Grigoriadis K. H1robust control design of active structural vibration suppression using an active mass damper. Smart Mater Strut, 2008, 17

  7. Fisco N R, Adeli H. Smart structures: Part II—Hybrid control systems and control strategies. Sci Iran, Trans A, 2011, 18(3): 285–295

    Article  Google Scholar 

  8. Guclu R, Yazici H, Vibration control of a structure with ATMD against earthquake using fuzzy logic controllers. J Sound Vib, 2008, 318(1-2): 36–49

    Article  Google Scholar 

  9. Shen Y, Homaifar A, Chen D. Vibration control of flexible structures using fuzzy logic and genetic algorithms. In: American Control Conference 2000. Chicago, IL, USA, 2000, 1: 448–452

    Google Scholar 

  10. Jung W J, Jeong W B, Hong S R, Choi S B. Vibration control of a flexible beam structure using squeeze-mode ER mount. Journal of Sound and Vibration, 2004, 273(1-2): 185–199

    Article  Google Scholar 

  11. Fung R F, Liu Y T, Wang C C. Dynamic model of an electromagnetic actuator for vibration control of a cantilever beam with a tip mass. Journal of Sound and Vibration, 2008, 288(4-5): 957–980

    Article  MathSciNet  MATH  Google Scholar 

  12. Guclu R. Fuzzy-logic control of vibrations of analytical multidegree-of-freedom structural systems. Turk J Eng Environ Sci, 2003, 27(3): 157–167

    Google Scholar 

  13. Guclu R. Sliding mode and PID control of a structural system against earthquake. Mathematical and Computer Modelling, 2006, 44(1-2): 210–217

    Article  MATH  Google Scholar 

  14. Guclu R, Yazici H. Fuzzy-logic control of a non-linear structural system against earthquake induced vibration. Journal of Vibration and Control, 2007, 13(11): 1535–1555

    Article  MATH  Google Scholar 

  15. Guclu R, Yazici H. Seismic-vibration mitigation of a nonlinear structural system with an ATMD through a fuzzy PID controller. Nonlinear Dynamics, 2009, 58(3): 553–564

    Article  MATH  Google Scholar 

  16. Aguirre N, Ikhouane F, Rodellar J. Proportional-plus-integral semi active control using magneto-rheological dampers. Journal of Sound and Vibration, 2011, 330(10): 2185–2200

    Article  Google Scholar 

  17. Etedali S, Sohrabi M R, Tavakoli S. Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers. Earthquake Engineering and Engineering Vibration, 2013, 12(1): 39–54

    Article  Google Scholar 

  18. Etedali S, Sohrabi M R, Tavakoli S. An independent robust modal PID control approach for seismic control of buildings. J Civil Eng Urban, 2013, 3(5): 270–291

    Google Scholar 

  19. Subasri R, Natarajan A M, Sundaram S, Jianliang W. Neural aided discrete PID active controller for non-linear hysteretic base-isolation building. In: Proceedings of the 9th Asian Control Conference (ASCC). 2013, 1–8

    Google Scholar 

  20. Nigdeli S M. Effect of feedback on PID controlled active structures under earthquake excitations. Earthquakes and Structures, 2014, 6(2): 217–235

    Article  Google Scholar 

  21. Yu W, Suresh T, Li X. Stable PID vibration control of building structures. In: Proceedings of the 19thWorld Congress-International Federation of Automatic Control, South Africa, 2014; 19(1): 4760–4765

    Google Scholar 

  22. Etedali S, Tavakoli S, Sohrabi M R. Design of a decoupled PID controller via MOCS for seismic control of smart structures. Earthquakes and Structures, 2016, 10(5): 1067–1087

    Article  Google Scholar 

  23. Djajakesukma S L, Samali B, Nguyen H. Study of a semiactive stiffness damper under various earthquake inputs. Earthquake Engineering & Structural Dynamics, 2003, 31(10): 1757–1776

    Article  Google Scholar 

  24. Ma T W, Yang T Y. Adaptive feedback–feedforward control of building structures. Journal of Engineering Mechanics, 2004, 130(7): 786–793

    Article  Google Scholar 

  25. Yang J N, Agrawal A K, Samali B, Wu J. Benchmark problem for response control of wind-excited tall buildings. Journal of Engineering Mechanics, 2004, 130(4): 437–446

    Article  Google Scholar 

  26. Mei G, Kareem A, Kantor J C. Model predictive control of wind excited building: benchmark study. Journal of Engineering Mechanics, 2004, 130(4): 459–465

    Article  Google Scholar 

  27. Alavinasab A, Moharrami H, Khajepour A. Active control of structures using energy-based LQR method. Comput-Aided Civ Inf, 2006, 21(8): 605–611

    Article  Google Scholar 

  28. Aldemir U. A simple active control algorithm for earthquake excited structures. Comput-Aided Civ Inf, 2010, 25(3): 218–225

    Article  Google Scholar 

  29. Rajabioun R. Cuckoo optimization algorithm. Applied Soft Computing, 2011, 11(8): 5508–5518

    Article  Google Scholar 

  30. Gandomi A H, Talatahari S, Yang X S, Deb S. Design optimization of truss structures using cuckoo search algorithm. Struct Des Tall Spec, 2013, 22(17): 1330–1349

    Article  Google Scholar 

  31. Civicioglu P, Besdok E A. Conception comparison of the cuckoo search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artificial Intelligence Review, 2013, 39(4): 315–346

    Article  Google Scholar 

  32. Yang X S, Deb S. Cuckoo search: recent advances and applications. Neural Computing & Applications, 2014, 24(1): 169–174

    Article  Google Scholar 

  33. Yang X S, Deb S. Cuckoo search via Lévy flights. The World Congress on Nature & Biologically Inspired Computing (NaBIC), 2009, 210–214

    Google Scholar 

  34. Nagarajaiah S, Narasimhan S. Smart base-isolated benchmark building part II: phase I, sample controllers for linear and friction isolation. J Struct Control Hlth, 2006, 13(2-3): 589–604

    Article  Google Scholar 

  35. MATLAB. The Math Works. Inc, Natick, MA, 2000

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Taft Branch, Islamic Azad University, Taft, Iran

    Amir Hossein Heidari & Mohamad Reza Javaheri-Tafti

  2. Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran

    Sadegh Etedali

Authors
  1. Amir Hossein Heidari
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  2. Sadegh Etedali
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  3. Mohamad Reza Javaheri-Tafti
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Correspondence to Sadegh Etedali.

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Heidari, A.H., Etedali, S. & Javaheri-Tafti, M.R. A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD. Front. Struct. Civ. Eng. 12, 44–57 (2018). https://doi.org/10.1007/s11709-016-0382-6

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  • DOI: https://doi.org/10.1007/s11709-016-0382-6

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