Please wait a minute...
购物车 申请加入邮件组 English
高级检索 图表检索
Frontiers of Structural and Civil Engineering

ISSN 2095-2430

ISSN 2095-2449(Online)

CN 10-1023/X

邮发代号 80-968

2019 Impact Factor: 1.68

热点文章  |  下载排行  |  浏览排行
在线投稿 免费RSS订阅
Frontiers of Structural and Civil Engineering  2018, Vol. 12 Issue (1): 44-57   https://doi.org/10.1007/s11709-016-0382-6
  本期目录
A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD
Amir Hossein HEIDARI1, Sadegh ETEDALI2(), Mohamad Reza JAVAHERI-TAFTI1
1. Department of Civil Engineering, Taft Branch, Islamic Azad University, Taft, Iran
2. Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran
 全文: PDF(1272 KB)   HTML
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.
Key words： seismic control    tuned mass dampers    cuckoo search    PID controller    LQR controller
收稿日期: 2016-06-10      出版日期: 2018-03-08
Corresponding Author(s): Sadegh ETEDALI   
 引用本文:   
. [J]. Frontiers of Structural and Civil Engineering, 2018, 12(1): 44-57.
Amir Hossein HEIDARI, Sadegh ETEDALI, Mohamad Reza JAVAHERI-TAFTI. A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD. Front. Struct. Civ. Eng., 2018, 12(1): 44-57.
 链接本文:  
https://academic.hep.com.cn/fsce/CN/10.1007/s11709-016-0382-6
https://academic.hep.com.cn/fsce/CN/Y2018/V12/I1/44
Fig.1  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
maximum relative displacements of floors (cm) maximum absolute accelerations of floors (g)
TMD ATMD TMD ATMD
floor unctrl. passive LQR LQR-PID unctrl. passive LQR LQR-PID
1 2.62 1.61 1.14 0.96 0.26 0.24 0.14 0.11
2 5.13 3.14 2.06 1.68 0.35 0.19 0.20 0.13
3 7.46 4.56 3.18 2.84 0.44 0.31 0.25 0.20
4 9.55 5.83 4.24 3.99 0.50 0.35 0.26 0.20
5 11.37 7.00 5.60 4.39 0.54 0.36 0.28 0.22
6 12.90 8.02 6.19 5.02 0.58 0.33 0.32 0.24
7 14.13 8.93 6.72 5.61 0.60 0.40 0.35 0.28
8 15.12 9.66 6.90 5.90 0.64 0.45 0.34 0.31
9 15.87 10.17 7.11 6.21 0.72 0.49 0.41 0.33
10 16.25 10.43 7.33 6.25 0.76 0.51 0.44 0.35
TMD - 31.00 47.43 68.41 - 0.52 0.97 1.21
Tab.1  
maximum relative displacements of floors (cm) maximum absolute accelerations of floors (g)
TMD ATMD TMD ATMD
floor unctrl. passive LQR LQR-PID unctrl. passive LQR LQR-PID
1 2.66 2.33 1.66 1.40 0.27 0.42 0.22 0.18
2 5.32 4.66 3.33 2.94 0.35 0.29 0.30 0.28
3 7.91 6.92 5.01 4.07 0.44 0.37 0.37 0.31
4 10.37 9.08 6.46 5.16 0.50 0.41 0.42 0.39
5 12.63 11.06 8.21 6.78 0.51 0.41 0.41 0.41
6 14.65 12.83 9.11 8.16 0.58 0.42 0.47 0.49
7 16.36 14.32 10.19 7.91 0.68 0.52 0.56 0.59
8 17.70 15.49 10.97 8.42 0.78 0.61 0.65 0.58
9 18.63 16.30 11.60 9.12 0.85 0.69 0.69 0.68
10 19.11 16.71 12.06 9.74 0.90 0.76 0.75 0.60
TMD - 41.64 89.54 111.94 - 0.80 1.77 1.82
Tab.2  
maximum relative displacements of floors (cm) maximum absolute accelerations of floors (g)
TMD ATMD TMD ATMD
floor unctrl. passive LQR LQR-PID unctrl. passive LQR LQR-PID
1 1.99 1.87 1.53 1.45 0.40 0.27 0.25 0.19
2 3.80 3.57 2.96 2.32 0.49 0.39 0.43 0.31
3 5.35 5.01 4.02 4.23 0.55 0.48 0.47 0.39
4 6.61 6.21 5.41 5.21 0.57 0.53 0.50 0.39
5 7.60 7.13 5.79 5.10 0.53 0.54 0.46 0.34
6 8.31 7.81 6.29 5.31 0.46 0.50 0.39 0.31
7 8.81 8.34 6.84 5.32 0.36 0.42 0.32 0.24
8 9.19 8.86 7.02 6.09 0.42 0.32 0.31 0.27
9 9.51 9.33 7.46 6.21 0.51 0.41 0.36 0.30
10 9.68 9.62 7.49 5.98 0.55 0.49 0.41 0.33
TMD - 28.87 44.25 54.76 - 0.53 0.91 1.45
Tab.3  
maximum relative displacements of floors (cm) maximum absolute accelerations of floors (g)
TMD ATMD TMD ATMD
floor unctrl. passive LQR LQR-PID unctrl. passive LQR LQR-PID
1 2.36 2.04 1.51 1.45 0.31 0.30 0.19 0.18
2 4.64 4.03 3.37 3.10 0.39 0.32 0.23 0.25
3 6.79 5.92 4.28 3.78 0.46 0.38 0.30 0.24
4 8.80 7.69 6.23 5.12 0.52 0.47 0.34 0.27
5 10.61 9.33 7.55 5.48 0.54 0.53 0.34 0.28
6 12.20 10.84 8.75 6.18 0.52 0.55 0.32 0.26
7 13.54 12.21 8.64 6.52 0.58 0.53 0.36 0.29
8 14.59 13.35 9.78 7.91 0.68 0.51 0.44 0.39
9 15.30 14.16 10.04 9.12 0.80 0.64 0.49 0.42
10 15.67 14.60 11.13 8.29 0.87 0.76 0.52 0.44
TMD - 35.04 69.65 82.44 - 0.82 1.43 1.52
Tab.4  
earthquake average reduction in relative displacements of floors (%) average reduction in absolute
accelerations of floors (%)		 maximum demand
control force (kN)		 maximum demand
mechanical power (kW)
LQR LQR-PID LQR LQR-PID LQR LQR-PID LQR LQR-PID
El Centro 27.71 38.60 17.37 35.54 1172 1232 781 821
Hachinohe 28.32 41.24 1.69 7.90 1204 1298 803 865
Kobe 18.71 28.84 9.72 28.83 1522 1685 1015 1123
Northridge 23.62 37.20 29.20 38.65 816 844 544 563
total average 24.59 36.47 14.50 27.73 1179 1265 786 843
Tab.5  
Fig.6  
1 Datta T K. Control of Dynamic Response of Structures. Indo-US Symposium on Emerging Trends in Vibration and Noise Engineering, 1996, 18–20
2 Fisco N R, Adeli  H. Smart structures: Part I-Active and semi-active control. Sci Iran, Trans A, 2011, 18(3): 275–284
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
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
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
6 Huo L, Song  G, Li H,  Grigoriadis K. H∞robust 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
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
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
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
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
12 Guclu R. Fuzzy-logic control of vibrations of analytical multi-degree-of-freedom structural systems. Turk J Eng Environ Sci, 2003, 27(3): 157–167
13 Guclu R. Sliding mode and PID control of a structural system against earthquake. Mathematical and Computer Modelling, 2006, 44(1-2): 210–217
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
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
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
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
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
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
20 Nigdeli S M. Effect of feedback on PID controlled active structures under earthquake excitations. Earthquakes and Structures, 2014, 6(2): 217–235
21 Yu W, Suresh  T, Li X. Stable PID vibration control of building structures. In: Proceedings of the 19th World Congress-International Federation of Automatic Control, South Africa, 2014; 19(1): 4760–4765
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
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
24 Ma T W, Yang  T Y. Adaptive feedback–feedforward control of building structures. Journal of Engineering Mechanics, 2004, 130(7): 786–793
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
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
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
28 Aldemir U. A simple active control algorithm for earthquake excited structures. Comput-Aided Civ Inf, 2010, 25(3): 218–225
29 Rajabioun R. Cuckoo optimization algorithm. Applied Soft Computing, 2011, 11(8): 5508–5518
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
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
32 Yang X S, Deb  S. Cuckoo search: recent advances and applications. Neural Computing & Applications, 2014, 24(1): 169–174
33 Yang X S, Deb  S. Cuckoo search via Lévy flights. The World Congress on Nature & Biologically Inspired Computing (NaBIC), 2009, 210–214
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
35 MATLAB. The Math Works. Inc, Natick, MA, 2000
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed