Gürsoy Turan İzmir Yüksek Teknoloji Enstitüsü active hydraulic damper Control Design Linear Quadratic Regulator(LQR) Upper Controller Response simulation Results 3/22 Introduction

Hybrid Control of a 3-D Structure by using Seismic isolators and Semi-Active Dampers

Role of Research Infrastructers in seismic rehabilitationFebruary 8-9, 2012 – İTÜ – İstanbul

Gürsoy Turanİzmir Yüksek Teknoloji Enstitüsü

[email protected]

(sponsored by TÜBİTAK, Grant No: 107M353)

mailto:[email protected]

Goal

During strong seismic ground motions

➲ Base isolators shall not rupture

➲ Structural response should not be badly affected

Seismic Isolator - Structural displacement displacement

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Goal





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Goal





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Outline

➲ Intro: Control of Seismic isolated Structures➲ 3-story building model➲ semi active hydraulic damper➲ Control Design

● Linear Quadratic Regulator(LQR)● Upper Controller

➲ Response simulation➲ Results

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Outline




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Outline




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Outline




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Outline




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Outline




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Introduction

➲ Kurata et al. (1999) → response of full scale building model with semi active

damper

➲ Wongprasert & Symans (2005) → Building model with variable orifice damping - using

fuzzy logic

➲ Aldemir & Bakioğlu (2000) → Time scale controller design for semi active damper

➲ Ribakov & Glück (2002) →MR damper control + ON-OFF upper controller

➲ Çetin et.al (2009) → MR damper control

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Introduction


damper


fuzzy logic




15/545/22

Introduction


damper


fuzzy logic




16/545/22

Introduction


damper


fuzzy logic




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Introduction


damper


fuzzy logic




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Building Model

➲ 3 stories4 columns, H=0.82m / story, rigid beamsMass 200kg/story

➲ Seismic isolator, H= 4cmE

y= 4000 Pa

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Building Model

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f9 = 6.68 Hz

f10

= 7.60 Hz

f11

= 8.02 Hz

f12

= 9.22 Hz

f13

=111.00 Hz

f14

=111.80 Hz

f15

=112.50 Hz

f16

=124.50 Hz

f1 = 0.31 Hz

f2 = 0.32 Hz

f3 = 0.34 Hz

f4 = 3.11 Hz

f5 = 3.33 Hz

f6 = 3.60 Hz

f7 = 5.92 Hz

f8 = 6.05 Hz

➲ 3 stories4 columns, H=0.82m / story, rigid beamsMass 200kg/story

➲ Seismic isolator, H= 4cmE

y= 4000 Pa

Control Design: Linear Quadratic Regulator (LQR)

M xCdC d dT xK x =−M eq xeq

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M x+(C+ΓdC d ΓdT ) x+K x =−MΓeq xeq+Γd u

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2nd order diff. Equation --> 1st order diff.Eqn.



q=AqB1 x gB2u

M xCdC d dT xK x =−M eq xeq d u

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q=AqB1 x gB2u

A= [ 0 I−M−1 K −M−1 CdC d d

T ] B1= [ 0eq ] B2= [ 0

M−1 d]

2nd order diff. Equation --> 1st order diff.Eqn.

Here, q= [ x x ]T

M xCdC d dT xK x =−M eq xeq d u

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V q=∫0

∞

qTQquT Ru dt

Minimization problem

Kontrol force contribution

Structural response contribution

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Control Design: (LQR)

uo=−R−1B2T P qo

The optimal control force that minimizes the problem definition

AT PP AQ−P B2 R−1B2

T P=0

Here, P is the solution to the following Ricatti equation

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Control Design: (LQR)

Control Design: Upper Controller

➲ Damping levels: 5000 : 5000 : 25000 Ns/m5 positions / damper

➲ No. of dampers = 4

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Therefore➲ 625 damping configurations, and thus➲ 625 optimal control equations

(The minimization problem is solved for 625 different configurations)


➲ Damping levels: 5000 : 5000 : 25000 Ns/m5 positions / damper

➲ No. of dampers = 4

Therefore➲ 625 damping configurations, and thus➲ 625 optimal control equations

(The minimization problem is solved for 625 different configurations)

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➲ dbase

< 15mm → minimum damping

➲ dbase

> 15mm → optimal damping


At time ti, the upper controller

➲ calculates the optimal control force, u

➲ calculates the closest damping force to achieve the desired optimal control force

➲ switches to the calculated damping state

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19.05.1940 Imperial Valley (El Centro) 12.11.1999 Düzce (Bolu)17.08.1999 Kocaeli (Sakarya)

Selected Earthquakes

Response simulation

0.62s 3.2s

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Response simulation

0.62s 3.2s

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Response simulation

Response simulation

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Base Displacement: 1940ELCentroD

ispl

acem

ent,

{m

}

time, {s}

controlled

Response simulation

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Dis

plac

emen

t, {

m}

time, {s}

1st story Displacement: 1940ELCentro

controlled

Response simulation

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Base Displacement: 12KasBoluD

ispl

acem

ent,

{m

}

time, {s}

controlled

Response simulation

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Dis

plac

emen

t, {

m}

time, {s}

1st story Displacement: 12KasBolu

controlled

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Dis

plac

emen

t, {m

}

time, {s}

Base Displacement: 17AguSKR

controlled

Response simulation

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Dis

plac

emen

t, {

m}

time, {s}

1st story Displacement: 17AguSKR

controlled

Ccontr

– Cmax

Cmax

69 %

-37 %

117 %

-24 %

90 %

-16 %

d Cmin Cmax CcontrC

contr – C

min

Cmin

El CentroBase {m} 0.035 0.013 0.022 -35 %

1st story {m} 0.016 0.033 0.020 26 %

BoluBase {m} 0.067 0.016 0.035 -48 %

1st story {m} 0.022 0.048 0.036 69 %

SakaryaBase {m} 0.047 0.012 0.023 -50 %

1st story {m} 0.0076 0.0126 0.0106 39 %

Response simulation

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Results

Benefits of using base isolators together with semi active dampers

➲ Isolator displacement is reduced (%35-%50 reduction w.r.t. min. damping case).

➲ No significant increase in 1st story displacement response (%16-%37 w.r.t. max. damping)

➲ This control system is robust because energy is only introduced to change the valve positions of the dampers

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Results


➲ Isolator displacement is reduced (%35-%50 reduction w.r.t. min. damping case).



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Results


➲ Isolator displacement is reduced (min. sönümlemeye göre 35-%50 azalmıştır.).



53/5422/22

Thank you

Gürsoy Turanİzmir Yüksek Teknoloji Enstitüsü

[email protected]

(TÜBİTAK 107M353)

mailto:[email protected]

Gürsoy Turan İzmir Yüksek Teknoloji Enstitüsü active hydraulic damper Control Design Linear Quadratic Regulator(LQR) Upper Controller Response simulation Results 3/22 Introduction

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