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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2018, Vol. 12 Issue (1) : 44-57     https://doi.org/10.1007/s11709-016-0382-6
RESEARCH ARTICLE
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
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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.

Keywords seismic control      tuned mass dampers      cuckoo search      PID controller      LQR controller     
Corresponding Author(s): Sadegh ETEDALI   
Online First Date: 07 April 2017    Issue Date: 08 March 2018
 Cite this article:   
Amir Hossein HEIDARI,Sadegh ETEDALI,Mohamad Reza JAVAHERI-TAFTI. A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD[J]. Front. Struct. Civ. Eng., 2018, 12(1): 44-57.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-016-0382-6
http://journal.hep.com.cn/fsce/EN/Y2018/V12/I1/44
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Amir Hossein HEIDARI
Sadegh ETEDALI
Mohamad Reza JAVAHERI-TAFTI
Fig.1  A block diagram of a PID controller in a feedback loop
Fig.2  Pseudo code of CS
Fig.3  The time histories of the top story displacement of the structure during El Centro
Fig.4  The time histories of the top story acceleration of the structure during El Centro
Fig.5  The time histories of the required control force during El Centro earthquake using LQR and the proposed LQR-PID controllers
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 structural responses of the structure during El Centro earthquake
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 structural responses of the structure during Kobe earthquake
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 structural responses of the structure during Northridge earthquake
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  Maximum structural responses of the structure during Hachinohe earthquake
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  Average of reductions of structural responses in comparison with the passive TMD and the maximum demand control force and mechanical power
Fig.6  The frequency responses of the controlled structure using LQR and LQR-PID controller
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