Earthquake engineering and structural control University of West Attica, Faculty of Engineering, Department of Civil Engineering Athens, Greece Erasmus + International mobility program 9-13 July, 2018 Odessa, Ukraine

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 2 Contents Our contributions inOur contributions in structural control Pole Assignment algorithm Pole Assignment algorithm Sliding mode control Sliding mode control Active variable system Active variable system Time delay-Saturation control interaction Time delay-Saturation control interaction Current trends and developments in structural control Control devices Control algorithms Description of structural control for buildings subjected to dynamic loadingDescription of structural control for buildings subjected to dynamic loading

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 3 Nervous System Nerve Brain Muscle Description of structural control PC Data manipulation Control algorithm sensors Hybrid Actuator Active Tendons AVSD MR DAMPERS Semi-Active Control is a multidisciplinary research area What do we control? Relative displacement and acceleration between floors. How do we manage that? With devices which receive signal from the algorithm. Brain

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 4 Description of structural control Active control PC Data manipulation Control algorithm sensors Actuator Tendons AVSD MR DAMPERS Brain Active mass damper (AMD) Active control devices Active tendons

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 5 Active control - Control devices Current trends in structural control Active control - Control devices Active mass damper at Kyobashi Seiwa Building, Tokio, 1989

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 6 Active control - Control devices Current trends in structural control Active control - Control devices Brain Active mass damper at Nanging communication tower, China, 1999

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 7 Active control - Control devices Current trends in structural control Active control - Control devices Brain Active mass damper at Applause Tower, Osaca, 1992

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 8 Description of structural control semi-active control PC Data manipulation Control algorithm sensors Actuator Tendons AVSD MR DAMPERS Brain Semi-active control devices Magnetorheological/Electrorheologic al damper (MRD/ERD) Viscous damper with controllable valve Friction damper with controllable force Liquid damper with controllable pumpActive variable stiffness system AVS

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 9 Semi active control - Control devices Current trends in structural control Semi active control - Control devices Brain MR damper at National Museum of Emerging Science and Innovation, Tokyo, 2002 Max. damping force 300kN Operates by batteries

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 10 Semi active control - Control devices Current trends in structural control Semi active control - Control devices Brain Semi- active hydraulic damper at Kajima Shizuoka building, 2000 Max. damping force 1000kN The electric power per device is about 70 watts Response analysis has shown that this system can reduce both story shear forces and story drifts significantly Semi- active hydraulic damper at Kajima Shizuoka, improved at 2004 by wireless sensors

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 11 Semi active control - Control devices Current trends in structural control Semi active control - Control devices Brain AVS at Kajima Research Lab., Tokio, 1990 Open and close valve at 5ms

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 12 Semi active control - Control devices Current trends in structural control Semi active control - Control devices Brain MR fluid dampers at cable stayed Bridge on Dong Ting Lake, China, 2002 Reduce the vibration caused by wind and rain excitation

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 13 Description of structural control Hybrid control (Passive + semi active control) PC Data manipulation Control algorithm sensors Actuator Tendons AVSD MR DAMPERS Brain Hybrid control devices Hybrid seismic isolation (Base isolation+MRD) Hybrid Mass Damper (TMD+AMD)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 14 Hybrid control - Control devices Current trends in structural control Hybrid control - Control devices Brain V-shaped HMD at Shinjuku Park Tower Japan 1994

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 15 Hybrid control - Control devices Current trends in structural control Hybrid control - Control devices Brain Hybrid base isolation was experimented by University of Notre Dame, LORD and Takenaka Corporation, 2002

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 16 Description of structural control Control algorithms PC Data manipulation Control algorithm sensors Actuator Tendons AVSD MR DAMPERS LQR, LQG Pole Placement SMC On – Off control H 2 - H ∞ Fuzzy control Neural network control Bang- bang control ……. LQR, LQG Pole Placement SMC On – Off control H 2 - H ∞ Fuzzy control Neural network control Bang- bang control …. Time delay-Saturation control interaction Our contributions

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 17 Control strategy Pole placement Algorithm sensors Real time Fourier or Wavelet analysis Tendons Actuator AVSD MR DAMPERS Wired or wireless sensors ω1ω1 ωlωl ωhωh ω2ω2 ω3ω3 Re Im Control Force Pole placement algorithm => K f Data manipulation Control Algorithm Pole assignment On line selection of poles (eigenvalues), based on earthquakes characteristics Until now predetermined

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 18 Control of structure by pole placement algorithm Uncontrolled structure The well known Pole place algorithm find the matrix K f but requires the eigenvalues (poles) of the controlled system LQR, SMC, Pole Place, Fuzzy control, neural network control, bang- bang control, …….etc. Controlled structure

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 19 Control of structure continues and discrete formulation

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 20 Description of the Pole placement algorithm Low degree of freedom systemsLow degree of freedom systems

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 21 Description of the Pole placement algorithm Necessary and sufficient condition for arbitrary location of poles : Controllability condition a i coefficients of the characteristic polynomial |sI-A|

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 22 Description of the Pole placement algorithm The transformed and initial system has the same characteristic equation

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 23 Description of the Pole placement algorithm Ackermann’s formula

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 24 Selection of poles of the controlled structure based on dynamic signal Transformation of structure to the complex plane ωiωiωiωi ζ i =Cosφ i λiλiλiλi ω ci ζ ci =Cosφ ci λ ci Re Im

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 25 Im Re ωqωq Selection of poles of the controlled structure based on dynamic signal Selection of poles of the controlled structure based on dynamic signal λcλcλcλc ω q= ω ο ω q1…. ω qi ap%ap%ap%ap% ω qi ω q1 λoλo ζοωοζοωο ωcωc λcλc λcλc λcλc λcλcλcλc Transformation of loading to the complex plane Requirement: Equivalent control force from the devices

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 26 ωlωl ωhωh Im Re Selection of poles of the controlled structure based on dynamic signal Selection of poles of the controlled structure based on dynamic signal ω1ω1 0 λc,2λc,2 λc,1λc,1 C B A λ ο,3 λ ο,2 λo,1λo,1 ω2ω2 ω1ω1 ω3ω3 ω2ω2 ω3ω3 ωs1ωs1 ωs2ωs2 ap%ap% a p ; ω s or AB ; ζ c or BC ; Β΄ C΄C΄ A΄A΄ λ c,2 λc,3λc,3 A΄΄ C΄΄

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 27 Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal Selection of a p Selection of ω s Selection of ζ c

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 28 Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal f max[A g (f)] fifi a p max[A g (f)] IpIp Ag(f)Ag(f) f fifi max[A g (f)] a p max[A g (f)] IpIp Selection of a p a p max[A g (f)] IpIp fifi

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 29 ω s2 ω s1 ωiωi F max ω i /ω ο Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal Im Re ω s1 ω s2 λολο ω min U max ζ ωi ωi λοiλοi U max,i ω s2 ω s1 ωοωο Selection of ω s,i

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 30 ξ ωi ωi λοiλοi Im Re ω s2 ω s1 λ o, ω ο ωqωq u max /u o,max ωiωi ωmin ωmin 1 x Selection of poles of the controlled structure based on earthquake signal

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 31 F max /F max,i ζcζc Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal Im Re ω s2 ω s1 λολο ω min ζ ωi ωi λοiλοi ωοωο ζcζc Selection of ζ c xd=xd= U max U max,i

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 32 Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal Re Im u max /u o,max

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 33 Selection of poles of the controlled structure based on earthquake signal Selection of poles of the controlled structure based on earthquake signal Re Im F max /F o,max

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 34 Flow chart of control program Pole placement algorithm Flow chart of control program Pole placement algorithm pole_place_mdof_on_line.mdl Load System Response K fm Saturation Time delay Selection of poles.m FFT Selection of frequencies based on a p and Ι p Drawing of cycles of quake and the unsafe zone ω s in the complex plane Placement of poles of the uncontrolled structure Selection of poles of the controlled structure based on the rules:  If poles inside the unsafe zone put them out.  If poles outside of the unsafe zone leave them temporarily  If more reduction is desired, give artificial damping  If signal is too small no control Calculate the new values of poles based on the above new position λ c,i =α+βi. Control on line.m M, C, K State space formulation A, B Ti, ω i, ξ i Define parameters: a p Ι p, x, x d No of parts of signal. Define load signal Initial conditions For i th part of signal: Feedback Matrix K fm =poles(A,B, λ c,i ) Dynamic analysis 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

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 35 Numerical examples NamePGA (g) PGV (cm/s) MagnitudeDistance (Km) Station, component Kalamata EW Alkionides, Trans Aigio, Ν150 Athens, ΚΕDΕ Kozani, Grevena Loma Prieta, Outer Harbor Wharf Imperial Valley, El Centro USGS N, W Mexico City, Kobe, KJMA Duzce, Duzce Sinusoidal loading Sinusoidal loading with two frequencies Pulse All scaled at 0.3g Period, T sec Acceleration m/sec 2

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 36 Numerical examples Eigenperiods: {0.45, 0.16, 0.12}sec Eigenfrequencies: {2.217, 6.212, 8.977}sec -1 Poles: {-2.48  i,  39.0 i,  i} m i =1 t k i = 980 kN/m c i =1.407 kNs/m Eigenperiod: 0.2s Eigenfrequenc: 5 sec -1 Damping ratio: ζ=0.05 Poles: n=-2±31.35i F F3F3 F2F2 F1F1 F3F3 F1F1 cs3 F1F1 F8F8 F5F5 cs1cs2cs3

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 37 Numerical examples m i =345.6 t k i = 6.8x10 5 kN/m c i =734 kNs/m Eigenperiods: { 0. 77, 0.26, 0.15, 0.12, 0.09, 0.08, 0.075, 0.07 } sec Eigenfrequencies f i : {1.29, 3.86, 6.29, 8.50, 10.43, 12.00, 13.16, }sec -1 Poles: {-4.10 ± i, ± 82.64i, ± 75.36i, ± 65.32i, ± 53.44i, ± 39.53i, ± 24.27i, ± 8.18i} F3F3 F2F2 F1F1 F8F8 F6F6 F5F5 F4F4 F7F7 F3F3 F1F1 F8F8 F5F5 F7F7 F1F1 F8F8 F5F5 cs1cs2cs3

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 38 Numerical examples Eigenperiods : {0.45, 0.16, 0.12}sec Eigenfrequencies : {2.217, 6.212, 8.977}sec -1 Poles : {-2.48  i,  39.0 i,  i} m i =1 t k i = 980 kN/m c i =1.407 kNs/m Eigenperiods : 0.2s Eigenfrequency : 5 sec -1 Damp.ratio.: ζ=0.05 Poles : n=-2±31.35i F F3F3 F2F2 F1F1 F3F3 F1F1 F3F3 F2F2 F1F1 F8F8 F6F6 F5F5 F4F4 F7F7 F3F3 F1F1 F8F8 F5F5 F7F7 F1F1 F8F8 F5F5 cs1 cs2cs3 m i =345.6 t k i = 6.8x10 5 kN/m c i =734 kNs/m Eigenperiods : { 0. 77, 0.26, 0.15, 0.12, 0.09, 0.08, 0.075, 0.07 } sec Eigenfrequencies f i : {1.29, 3.86, 6.29, 8.50, 10.43, 12.00, 13.16, }sec -1 Poles : {-4.10 ± i, ± 82.64i, ± 75.36i, ± 65.32i, ± 53.44i, ± 39.53i, ± 24.27i, ± 8.18i}

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 39 Kalamata SDOF earthquake Video Time (s) Acceleration ( m / s 2 ) Time (s) Displacement ( m) Time (s) Force ( kN)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 40 Kalamata earthquake, MDOF Video Χρόνος (s) Displacement 3 rd ( m) Χρόνος (s) Acceleration 3 rd ( m / sec 2 ) Χρόνος (s) Force 3 rd ( kN)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 41 A Β C A C Sinusoidal SDOF loading A Β C

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 42 Kalamata SDOF earthquake Time (s) Acceleration ( m / sec 2 ) Time (s) Displacement ( m) Time (s) Force ( kN)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 43 Kalamata MDOF earthquake Time (s) Displacement 3 rd ( m) Time (s) Acceleration 3 rd ( m / sec 2 ) Time (s) Force 3 rd ( kN)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 44 Numerical examples SinusoidalNo controlControl u 1 (mm) (m/sec 2 ) F (kN) Kalamata earthquake No controlControl u 1 (mm) (m/sec 2 ) F (kN)126 Kalamata earthquake No control Control cs1cs2cs3 u 1 (mm) (m/sec 2 ) F 1 (kN) u 2 (mm) (m/sec 2 ) F 2 (kN)3.59 u 3 (mm) (m/sec 2 ) F 3 (kN)

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 45 Conclusions The is based on the frequency content from the incoming part of signal and on the non resonance theoryThe strategy is based on the frequency content from the incoming part of signal and on the non resonance theory The numerical examples show reduction to both the displacement and the acceleration for reasonable demand for control force.The numerical examples show reduction to both the displacement and the acceleration for reasonable demand for control force. Strategy for on-line control of structures against earthquakes, were developed

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 46 MR Dampers or Actuators Pole placement algorithm based on the frequency content of the incoming signal Α, Β, λ ci POLE PLACEMENT => K fm ν l, ν h, => ν ci =κ ν h, ν l ν h FFT Non linear behavior Estimate the new Κ

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 47 FFT part of the earthquake signal Acceleration and the relative spectrum of Mexico earthquake /4 of signal 1/4 of signal /3 of signal /2 of signal Total signal

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 48 Decision of the eigenfrequencies of the controlled system λ i : eigenvalues of A λ ci : eigenvalues of

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 49 Control strategy Sliding mode control algorithm sensors Real time Fourier or Wavelet analysis Tendons Actuator AVSD MR DAMPERS Wired or wireless sensors ω1ω1 ωlωl ωhωh ω2ω2 ω3ω3 Re Im Data manipulation Control Algorithm Sliding mode control Sliding surface S=PX Control Force Pole place algorithm =>Sliding matrix P On line selection of sliding surface based on earthquakes characteristics Until now predetermined

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 50 Flow chart of control program, SMC Flow chart of control program, SMC Selection of poles.m FFT Selection of frequencies based on ap and Ιp Drawing of cycles of quake and the unsafe zone ωs in the complex plane Placement of poles of the uncontrolled structure Selection of poles of the controlled structure based on the rules:  If poles inside the unsafe zone put them out.  If poles outside of the unsafe zone leave them temporarily  If more reduction is desired, give artificial damping  If signal is too small no control Calculate the new values of poles based on the above new position λc,i=α+βi. Control on line.m M, C, K State space formulation A, B Ti, ωi, ξi Define parameters: a p Ι p, x, x d No of parts of signal. Define load signal Initial conditions For ith part of signal: Estimation of sliding surface matrix P Δυναμική ανάλυση στο SIMULINK, Sim(SMC_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 SMC_mdof_on_line.mdl

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 51 Numerical examples Χρόνος (s) Μετακίνηση ( m) Επιτάχυνση ( m / sec 2 ) Χρόνος (s) Δύναμη ( kN) Χρόνος (s) Kalamata Earthquake,SDOF

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 52 Control strategy Control strategy On off control algorithm sensors Tendons Actuator AVSD MR DAMPERS Wired or wireless sensors Data manipulation Control Algorithm On off control algorithm Yes No Close valves Open valves Real time Fourier or Wavelet analysis ω1ω1 flfl fhfh ω2ω2 ω3ω3

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 53 Control strategy Control strategy On off control algorithm AgAg TcTc TiTi T Non resonance theory αfαf

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 54 Control strategy Control strategy On off control algorithm Τ 0 Ι, Τ 1 Ι, Τ 2 Ι,…, Τ ndof Ι f 0 Ι, f 1 Ι, f 2 Ι,…, f ndof Ι Type Ι Type ΙΙ α f, quake f L f h Τ 0 ΙI, Τ 1 ΙI, Τ 2 ΙI, …, Τ ndof ΙI f 0 ΙI, f 1 ΙI, f 2 ΙI, …, f ndof ΙI Proposed relation for designing the stiffer type II:

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 55 Control strategy Control strategy On off control algorithm Avoiding resonance cfcf bfbf 3)3) afaf bfbf 4)4) afaf cfcf 5)5) bfbf afaf cfcf 6)6) bfbf afaf cfcf 2)2) bfbf afaf cfcf 7)7) bfbf afaf cfcf 1)1) bfbf afaf cfcf bfbf f 0 Ι, f 1 Ι, f 2 Ι,…, f ndof Ι cfcf f 0 ΙI, f 1 ΙI, f 2 ΙI,…, f ndof ΙI a f, quake f f L f h YES NO Choice of type II Choice of type I

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 56 Flow chart of control program Active Variable Stiffness algorithm, AVS Flow chart of control program Active Variable Stiffness algorithm, AVS SIMULATION_AVS_MDOF_online Load System Type I Response Time delay Selection of stiffness.m FFT Selection of frequencies based on a p and Ι p Selection of f h and f L of loading part Control on line.m M, C, K State space formulation A, B Ti, ω i, ξ i Define parameters: a p Ι p, No of parts of signal. Define load signal Initial conditions For i th part of signal: K=K I or K=K II Dynamic analysis Sim( SIMULATION_AVS_MDOF_online ) Keep the response for this part of load. Update the initial conditions with the final of the previous part. Continue to the next part of load Yes No Choose type I Choose type II K=K I K=K II System Type II

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 57 Harmonic load, SDOF Video Type II, 10 Hz Type I, 5Hz AVSD T1 = 5HzT2 = 10Hz

Erasmus + International mobility program 9-13 July 2018Odessa, Ukraine 58 Time delay-Saturation control interaction Saturation level of control force (kN) u max /u max, uncontrolled t d (sec) Region of pairs of saturation level of control force and time delay where the control is effective. (Design specifications) Properties of the control devices and total actual control system should meet the design specifications