Vibration Control of Structures using Semi-

active MR Dampers

Contents

Introduction Types of controls Semi-active controls Semi-active control devices MR Fluid Dampers Mathematical models of MR dampers Semi-active control algorithms Closure

2

Introduction

Seismically-excited Structures

3

Contd….

Wind-excited Structures Human-excited Structures

4

Tacoma Narrows Bridge, Tacoma, Washington

Millennium Foot Bridge, London, England

Control System

Structure

Structure

SensorsSensors

Controller

Controller

Actuator

Actuator

Seismic InputSeismic Input

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Control Input

Seismic Response Control Principles Reduce the effect of seismic excitation

Prevent a structure from exhibiting the

resonance vibration

Transfer the vibration energy of a main

structure to the secondary oscillator

Put additional damping effect to a structure

Add a control force to a structure

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Classification of Structural Control

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Active control + External control force to reduce the responses

(i.e., provides input voltage)+ Voltages required are computed by controller

using certain algorithms with inputs from sensors.

+ Sensors measure motion (strains, displ, vel, accl.)

+ Actuators apply forces to structure, thereby adding or dissipating energy

Destabilization possible. External power may not be available during

earthquake. 8

Passive control

+ Passive control device imparts forces that are developed directly as a result of motion of structure (i.e., no actuator involved).

+ No external power+ Total energy (structure + passive device)

cannot increase, hence inherently stable. No adaptability to various external load Not as effective as active, hybrid, semi-

active control

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Semi-active control

As an active control system, it monitors the

feed-back measurement, and generates

appropriate command signal.

As a passive control system, control forces are

developed as a result of the motion of the

structure.

Reliability of passive system with adaptability of

active system

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Semi-active control devices

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Variable-Orifice Dampers

Variable friction dampers

Controllable fluid dampers

MR dampers

ER dampers

Semi-active control devices

Variable-Orifice Dampers

Variable friction dampers

Controllable fluid dampers

MR dampers

ER dampers

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Semi-active control devices

Variable-Orifice Dampers

Variable friction dampers

Controllable fluid dampers

MR dampers

ER dampers

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MR Fluid Dampers

Characteristics of MR fluid

Without Magnetic Fields

With Magnetic Fields

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Attractive features

High dissipative force at low velocity Inherent stability and failure-safety Continual optimization High dynamic range Mechanical simplicity Fast response-time Small device size Large temperature range

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Annular Orifice

Force vs Displacement curve of MRD

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Wang et.al,” Magnetorheological fluid dampers: a review of parametric modelling”, Smart Mater. Struct. 20 (2011)

Force vs Velocity curve of MRD

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Wang et.al,” Magnetorheological fluid dampers: a review of parametric modelling”, Smart Mater. Struct. 20 (2011)

Models of MR damper

Bingham Model Bouc-Wen Model Modified Bouc-Wen Model

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00)sgn(. fxcxff cmr

Models of MR damper

Bingham Model Bouc-Wen Model Modified Bouc-Wen Model

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mrmrmrc zxxkxcf 000

xAzxzzxz nmr

nmrmrmr |||||| 1

Models of MR damper

Bingham Model Bouc-Wen Model Modified Bouc-Wen Model

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)()()( 0100 xxkyxkyxczf

Semi active control system

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Semi-active control algorithms

Clipped-optimal Control Algorithm Lyapunov Stability Theory-based

Control Algorithm(LYAP) Maximum Energy Dissipation

Algorithm (MEDA) Cost Function-based Semi-active

Neuro-control Algorithm Fuzzy Logic control (FLC)

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Indirect control command to MR damper Control voltage v , instead of control force

Clipped algorithm

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maxVvff iic 0 iic vff

fc

fi

fc-fi=0

ν =0 ν =0

ν =0ν =0

ν =Vmax

ν =Vmaxνi = Vmax H ([fc-fi]fi)

fc : calculated optimal control force fi : control force of MR damper H : Heaviside step function vi : control voltage

Clipped algorithm

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maxVvff cic

ccic fvff

fc

fi

fc-fi=0

ν =0 ν =0

ν =0ν =0

ν =µfc

ν =µfc

νi = Vc H ([fc-fi]fi)

fc : calculated optimal control force fi : control force of MR damper H : Heaviside step function vi : control voltage

Lyapunov Control Algorithm(LYAP) Primary method of testing the stability of

nonlinear or linear system with uncertainty. Any scalar function V(x) that satisfies the 2

conditions V(x) is a positive definite, V’(x) is a negative definite function

is a lyapunov function. If V(x) fulfill the conditions means the

trajectories are bounded → system is stable. Lyapunov equation

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ATP+PA+Q=0

Fuzzy Logic control (FLC)

Fuzzy Logic is all about relative importance of precision

Minimization of some objective function, which tends to reduce the structural response

Neural nets tend to provide control forces, which would reduce the response of the structure when subjected to unknown future earthquakes

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FLC-Contd…

The advantage of this approach is its inherent robustness and its ability to handle the non-linear behaviour of the structure

A FLC is incorporated into a closed-loop control system similar to conventional controllers where R=reference input, E=input signal error, u=output control force, W=earthquake excitation, and Y=response after control.

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FLC-Contd… “if-then” rule

MI : if X1=Ai and X2=Bi then Y=Cii

i is number of control rules, X1 and X2 are variables of the antecedent

part and Y is a variable of the consequent part.

Ai, Bi, and Ci are linguistic values of the fuzzy variables.

Components: fuzzification, rule base, decision making and defuzzification

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Closure

Structural control technologies has been developed to mitigate vibration of civil engineering structures

Structural control can improve serviceability as well as safety of structures

Semi-active control is promising for civil engineering applications with the use of MR dampers

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