![Fourth World Conference on Structural Control and Monitoring, San Diego 2006
N.T.U.A.
17
Selection of poles of the controlled
structure based on earthquake signal
10 20 30 40 50 60 70 80 90
10
20
30
40
50
60
70
80
90
100
ap
Ip
average
Aigio
Athens
Elcentro
Kobe
Lomaprieta
Mex
Northridge
Northridge near
Pulse
Sanfernanto
Tabas
Virginia
p p
p
p
a a
I
a
2
1.669 86.11 12580
125
Ag(f)
f
fi
max[Ag(f)]
apmax[Ag(f)]
Ip
Ag(f)
f
fi
max[Ag(f)]
apmax[Ag(f)]
Ip
Selection of ap](https://image.slidesharecdn.com/4wcscmpresentation-230903102933-b4970c6c/85/4WCSCM_PRESENTATION-ppt-9-320.jpg)
4WCSCM_PRESENTATION.ppt
- 1. On line selection of poles of controlled structure based on frequency content of applied dynamic loading National Technical University of Athens School of Civil Engineering Metal Structures Laboratory Nikos Pnevmatikos, Charis Gantes Fourth World Conference on Structural Control and Monitoring (4WCSCM) 11-13 July, 2006 San Diego, California, U.S.A.
- 2. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 2 Contents • Control strategy based on Pole Assignment algorithm • Numerical Examples • Selection of poles based on the frequency content of the incoming dynamic load signal
- 3. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 3 Structural control PC Data manipulation Control algorithm Pole placement sensors Hybrid Actuator Active Tendons AVSD MR DAMPERS Semi-Active Control is a multidisciplinary research area
- 4. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 5 Structural control sensors Real time Fourier or Wavelet analysis ω1 ωl ωh ω2 ω3 ω ω ω ωo,1 ωo,2 ξc ωc λc ξc ωc λc Tendons Actuator AVSD MR DAMPERS Data manipulation control algorithm Pole assignment Wire or wireless sensors
- 5. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 12 Selection of poles of the controlled structure based on dynamic signal From structure to the complex plane 2 i i i i i λ =ζ ω jω 1-ζ ωi ζi=Cosφi λi ωci ζci=Cosφci λci 2 ci ci ci ci ci λ =ζ ω jω 1-ζ Re Im
- 6. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 13 e o o ξ ω t Im Re ωq 2 c c c c c λ =ζ ω jω 1-ζ e c c ξ ω t Selection of poles of the controlled structure based on dynamic signal e ci ci ξ ω t λc ωq=ωο ω q1…. ωqi ap% ωqi ω q1 λo ζοωο 2 o o ω 1-ζ 2 o o o o o λ =ζ ω jω 1-ζ ωc λc λc λc e c c ξ ω t λc From loading to the complex plane Requirement: Equivalent control force from the device
- 7. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 14 ωl ωh Im Re Selection of poles of the controlled structure based on dynamic signal ω1 0 λ c λc,1 C B A λο,3 λο,2 λo,1 Β’ C’ A’ ω1 ω2 ω3 ω2 ω3 ωs ωs ap % G F ap?, ωs or AB ?, ζc or BC ? λc,3
- 8. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 16 Selection of poles of the controlled structure based on earthquake signal p p p p a a I a 2 1.669 86.11 12580 125 Selection of ap 2 s x x+0.9641 ω x+0.01857 1.232 0.30 Selection of ωs 2 c 3385x x+4300 ζ x+1342 7625 Selection of ζc
- 9. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 17 Selection of poles of the controlled structure based on earthquake signal 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 100 ap Ip average Aigio Athens Elcentro Kobe Lomaprieta Mex Northridge Northridge near Pulse Sanfernanto Tabas Virginia p p p p a a I a 2 1.669 86.11 12580 125 Ag(f) f fi max[Ag(f)] apmax[Ag(f)] Ip Ag(f) f fi max[Ag(f)] apmax[Ag(f)] Ip Selection of ap
- 10. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 18 3 5 7 9 11 13 15 17 19 21 23 25 25 0 1000 2000 3000 4000 5000 6000 ωi (rad/sec) Fmax ωo ωmin ωs1 ωs2 ωi 3 5 7 9 11 13 15 17 19 21 23 25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 ωi (rad/sec) Umax/U o,max ωmin ωo ωi Selection of poles of the controlled structure based on earthquake signal 2 s x x+0.9641 ω x+0.01857 1.232 0.30 Im Re ωs2 ωs1 λο ωmin Umax ζ ωi λοi Umax,i ωs1 ωs2 ωο Selection of ωs
- 11. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 19 ξ ωi λοi Im Re ωs2 ωs1 λo, ωο ωq umax/uo,max ωi ω m i n 1 x
- 12. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 1 1.1 Fmax /Fmax,i 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 1 1.1 ζi Selection of poles of the controlled structure based on earthquake signal Im Re ωs2 ωs1 λο ωmin ζ ωi λοi Umax Umax,i ωο 2 3385x x+4300 ξ x+1342 7625 ζi Selection of ζc
- 13. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 21 Flow chart of control program pole_place_mdof_on_line.mdl Load System Response Kfm Saturation Time delay Selection of poles.m • FFT • Selection of frequencies based on ap and Ιp • Design of cycles of quake and the unsafe zone in the complex plane • Placement of poles of the uncontrolled structure • Selection of poles of the controlled structure base on the rules: If pole inside the unsafe zone put them out. If pole outside of the unsafe zone leave them temporarilly If you want more reduction give artificial damping If signal too small no control • Calculate the new values of poles based on the above new position ni =α+βi. Control on line.m • M, C, K • State space formulation A, B • Ti, ωi, ξi • Define parameters: ap Ιp, x, No of parts of signal. • Define load signal • Initial conditions • For ith part of signal: • Kfm=poles(A,B, n). • Sim(pole_place_mdof_on_line) • Keep the response and force for this part of load. • Update the initial conditions with the final of the previous part. • Continue to the next part of load
- 14. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 22 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 0 5 10 15 20 25 30 35 40 45 50 Re Im A 0 5 10 15 0 0.05 0.1 0.15 0.2 0.25 Frequency, Hz Abs acceleration, m/sec 2 First part of signal 0 50 100 150 200 250 300 350 -4 -3 -2 -1 0 1 2 3 4 x 10 -3 time Displacement 0 0.5 1 1.5 2 2.5 3 3.5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Time, sec Acc. m/sec 2 Numerical examples System: Sdof: T=0.2s, ζ=0.05, n=2±31.35 Load: T=0.2s , f1=5 Hz, amplitude=0.3g , 5 parts Control algorithm: Pole place w_secure=10 rad/s, amplification factor=1.1 Controlled system damping, ζ=0.95 Β C
- 15. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 23 0 200 400 600 800 1000 1200 -8 -6 -4 -2 0 2 4 6 8 x 10 -4 time Displacement -80 -70 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 70 80 Re Im A -80 -70 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 70 80 Re Im A -80 -70 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 70 80 Re Im 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 time part of quake 0 5 10 15 20 25 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Frequency, Hz Abs acceleration m/sec 2 Numerical examples 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Time, sec Acc. m/se 2 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 time part of quake 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Frequency, Hz Abs acceleration m/sec 2 0 200 400 600 800 1000 1200 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 -3 time Displacement 0 200 400 600 800 1000 1200 -10 -5 0 5 x 10 -4 time Displacement 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 time part of quake 0 5 10 15 20 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Frequency, Hz Abs acceleration m/sec 2 Β C A Β C C
- 16. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 24 0 5 10 15 20 25 30 0 0.005 0.01 0.015 0.02 0.025 Frequency, Hz Abs acceleration m/sec 2 0 50 100 150 200 250 300 350 400 450 500 -8 -6 -4 -2 0 2 4 x 10 -5 Time steps Displacement (m) 0 50 100 150 200 250 300 350 400 450 500 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 -3 Time steps Displacement (m) 0 50 100 150 200 250 300 350 400 450 500 -3 -2 -1 0 1 2 3 x 10 -4 Time steps Displacement (m) 0 1000 2000 3000 4000 5000 6000 7000 8000 -4 -3 -2 -1 0 1 2 3 Time steps Acc. (m/sec 2 ) 0 5 10 15 20 25 30 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 Frequency, Hz Abs acceleration m/sec 2 0 5 10 15 20 25 30 0 0.005 0.01 0.015 0.02 0.025 Frequency, Hz Abs acceleration m/sec 2 -70 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 70 Re Im A C -35 -30 -25 -20 -15 -10 -5 0 0 5 10 15 20 25 30 35 Re Im A -45 -40 -35 -30 -25 -20 -15 -10 -5 0 0 5 10 15 20 25 30 35 40 45 Re Im A C B C
- 17. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 25 0 500 1000 1500 2000 2500 3000 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 time Displacement 0 500 1000 1500 2000 2500 3000 -25 -20 -15 -10 -5 0 5 10 15 20 25 time Acceleration 0 500 1000 1500 2000 2500 3000 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 Time steps Displacement (m) 0 500 1000 1500 2000 2500 3000 -25 -20 -15 -10 -5 0 5 10 15 20 25 Time steps Acceleration (m/sec 2 0 1000 2000 3000 4000 5000 6000 7000 8000 -6 -4 -2 0 2 4 6 x 10 -3 Time steps Displacement (m) Numerical examples Sinusoidal u1 F mm m/sec2 kN Controlled 1.00 3.08 1002 Uncontrolled 23.90 23.81 Two Sinusoidal u1 F mm m/sec2 kN Controlled 1.10 5.04 1079 Uncontrolled 23.80 25.06 Athens 99 quake u1 F mm m/sec2 kN Controlled 1.30 3.63 787 Uncontrolled 5.70 7.41 1 u 1 u 1 u 0 1000 2000 3000 4000 5000 6000 7000 8000 -6 -4 -2 0 2 4 6 8 Time steps Acceleration (m/sec 2 )
- 18. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 26 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 Re Im -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 Re -70 -60 -50 -40 -30 -20 -10 0 0 10 20 30 40 50 60 70 Re Im Numerical examples System: 3 dof: mi= 50 t, ki=39000 kN/m Load: Athens 99, PGA=0.3g 16 parts 80% of max amplitude freq Control algorithm: Pole place w_secure=25 rad/s, Controlled and no controlled, system damping, ζi={0.90, 0.95,0.97} 0 1000 2000 3000 4000 5000 6000 7000 8000 -4 -3 -2 -1 0 1 2 3 4 Time steps Acc. (m/sec 2 )
- 19. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 27 Numerical examples 1 u 2 u 3 u u1 u2 u3 F1 F2 F3 mm m/sec2 kN Controlled 0.70 0.90 0.8 3.30 3.48 3.39 152 162 170 Uncontrolled 22.50 26.20 31.90 6.72 7.89 10.33 0 1000 2000 3000 4000 5000 6000 7000 8000 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 Time steps Displacement 3rd (m) 0 1000 2000 3000 4000 5000 6000 7000 8000 -8 -6 -4 -2 0 2 4 6 8 10 12 Time steps Acceleration 3rd (m/sec 2 ) 0 1000 2000 3000 4000 5000 6000 7000 8000 -200 -150 -100 -50 0 50 100 150 200 Time steps Force (kN)
- 20. Fourth World Conference on Structural Control and Monitoring, San Diego 2006 N.T.U.A. 28 Conclusions • On line procedure of selection of poles of the controlled structure were proposed. • The procedure is based on the frequency content from the specific incoming dynamic signal and the control face wide range of the applied signals. • The numerical examples shows reduction to both the displacement and the acceleration with adequate control force. • Pole Assignment algorithm adequate for active or semi- active control were used.