Simple Control Algorithms for MR Dampers and Smart Passive Control System

8/3/2019 Simple Control Algorithms for MR Dampers and Smart Passive Control System

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MR

Simple Control Algorithms for MR Dampers and

Smart Passive Control System

( Sang-Won Cho)

Department of Civil and Environmental Engineering

Korea Advanced Institute of Science and Technology

2 0 0 4

Doctoral Thesis


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SimpleControlAlgorithmsforMRDampersandSmartPassiveControlSystem

Advisor : ProfessorIn-Won Lee

by

Sang-Won Cho

Department of Civil and Environmental Engineering

Korea Advanced Institute of Science and Technology

A thesis submitted to the faculty of the Korea Advanced Institute of

Science and Technology in partial fulfillment of the requirements for the

degree of Doctor of Philosophy in the Department of Civil and

Environmental Engineering.

Daejeon, Korea

2003. 11. 27

Approved by

ProfessorIn-Won Lee

Major Advisor


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MR

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2003 11 27

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DCE

995353

. Sang-Won Cho. Simple Control Algorithms for MR Dampers

and Smart Passive Control System. MR

. Department of Civil and

Environmental Engineering. 2004. 101p. Advisor: Professor In-Won Lee.

Text in English.

ABSTRACT

This dissertation proposes simple and efficient control algorithms for seismically

excited structures using MR dampers and a smart passive system based on MR dampers.

Magnetorheological (MR) dampers are one of the most promising control devices for

civil engineering applications to earthquake hazard mitigation, because they have many

advantages such as small power requirement, reliability, and low price to manufacture.

A number of control algorithms have been adopted for semiactive systems

including the MR damper. In spite of good features of previous studies, some algorithms

have drawbacks such as poor performances or difficulties in designing the weighting

matrix of the controller. Thus, the control algorithm is required, which is simple to use

and efficient to give comparable or better performance over the previous algorithms.

As a simple and efficient control algorithm, a modal control scheme and a

maximum energy dissipation algorithm (MEDA) are implemented for the MR damper-

based control system.

Modal control reshapes the motion of a structure by merely controlling a few

selected vibration modes. Hence, a modal control scheme is more convenient to design

the controller than other control algorithms. Although modal control has been

investigated for the several decades, its potential for a semiactive control, especially for

the MR damper, has not been exploited. Thus, in order to study the effectiveness for the

MR damper system, a modal control scheme is implemented to seismically excited


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structures. A Kalman filter is included in a control scheme to estimate modal states from

physical measurements by sensors. Three cases of the structural measurement are

considered as a feedback to verify the effect of each measurement; displacement,

velocity, and acceleration, respectively. Moreover, a low-pass filter is applied to eliminate

the spillover problem. In a numerical example, a six-story building model with the MR

dampers on the bottom two floors is used to verify the proposed modal control scheme.The El Centro earthquake is used to excite the system, and the reduction in the drifts,

accelerations, and relative displacements throughout the structure is examined. The

performance of the proposed modal control scheme is compared with that of other control

algorithms that were previously suggested.

The maximum energy dissipation algorithm represents one control class which

employs the Lyapunovs direct approach to stability analysis in the design of a feedback

controller. However, their potential for civil engineering applications using semiactive

control, especially with MR dampers, has not yet been fully exploited. This paperinvestigates the performance and the robustness of the maximum energy dissipation

algorithm for civil engineering structures using MR dampers. The numerical examples

contain the cable-stayed bridge and the nonlinear building. Various earthquakes are used

to excite the systems. Through the series of numerical simulations, the performance is

compared with that of other control algorithms that are previously proposed: The

reduction in the drifts, accelerations, and relative displacements throughout the structure

are examined according to the evaluation criteria.

Meanwhile, to reduce the responses of the controlled structure by using MR

dampers, a control system including a power supply, controller, and sensors is needed.

However, it is not easy to apply the MR damper-based control system to large-scale civil

structures, such as cable-stayed bridges and high-rise buildings, because of the difficulties

of building up and maintaining the control system.


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Thus, this dissertation proposes a smart passive damper system. The smart

passive damper system is based on MR dampers. Of course, the MR damper is a

semiactive device that needs an external power source to change the damping

characteristics of the MR fluids. However, the smart passive damper system based on MR

dampers is not using an external power source, but self-powered by an electromagnetic

induction (EMI) system that is attached to the MR damper. The EMI system consists of apermanent magnet and a coil. According to the Faradays law of induction, the EMI

system changes the kinetic energy of the MR damper to the electric energy and then the

electric energy is used to vary the damping characteristics of the MR damper. Therefore,

it is easy to build up and maintain the proposed smart damper system that consists of the

MR damper and the EMI system, because it does not require any control system such as a

power supply, controller, and sensors. To verify the effectiveness of the proposed EMI

system, the performances are compared with those of the semiactive MR damper.


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TABLEOF CONTENTS

ABSTRACT .......................................................................................................................... i

TABLEOF CONTENTS ...................................................................................................... iv

LISTOF TABLES ............................................................................................................... vi

LISTOF FIGURES.............................................................................................................vii

CHAPTER1 INTRODUCTION........................................................................................1

1.1 Background......................................................................................................... 1

1.2 Literature Review ............................................................................................... 4

1.2.1 Magnetorheological (MR) Dampers......................................................... 4

1.2.2 Control Algorithms for MR Dampers....................................................... 7

1.3 MR Fluids and Dampers ................................................................................... 10

1.3.1 MR Fluids ............................................................................................... 10

1.3.2 MR Fluids Dampers................................................................................ 12

1.4 Objectives and Scopes ...................................................................................... 15

1.5 Organization ..................................................................................................... 17

CHAPTER2 MODAL CONTROL SCHEME................................................................18

2.1 Modal Control Scheme for MR Dampers......................................................... 18

2.1.1 Modal Control......................................................................................... 18

2.1.2 Design of Optimal Controller ................................................................. 21

2.1.3 Modal State Estimation .......................................................................... 23

2.1.4 Elimination of Observable Spillover ...................................................... 27

2.2 Numerical Example .......................................................................................... 29

2.3 Summary of Results.......................................................................................... 43


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CHAPTER3 MAXIMUM ENERGY DISSIPATION ALGORITHM ............................44

3.1 Control System ................................................................................................. 44

3.1.1 Control Devices ...................................................................................... 45

3.1.2 Maximum Energy Dissipation Algorithm for MR Damper.................... 47

3.2 Benchmark Problems........................................................................................ 49

3.2.1 Benchmark Cable-Stayed Bridge ........................................................... 493.2.2 Nonlinear Benchmark Building.............................................................. 55

3.3 Numerical Examples......................................................................................... 59

3.3.1 Control Performance............................................................................... 59

3.3.2 Controller Robustness............................................................................. 64


CHAPTER4 SMART PASSIVE CONTROL SYSTEM.................................................68

4.1 Electromagnetic Induction System for MR Damper ........................................ 68

4.2 Analytical Model and Design ........................................................................... 73

4.2.1 Analytical Model .................................................................................... 73

4.2.2 Design of the EMI System...................................................................... 76

4.3 Numerical Simulation Results .......................................................................... 80


CHAPTER5 CONCLUSIONS ........................................................................................88

SUMMARY (IN KOREAN) 90

REFERENCES 93

ACKNOWLEDGEMENTS

CURRICULUM VITAE


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LISTOF TABLES

1.1 Properties of MR and ER fluids.............................................................................. 11

2.1 Normalized controlled maximum responses

due to the scaled El Centro earthquake................................................................... 34

2.2 Normalized controlled maximum responses of the acceleration feedback


2.3 Normalized controlled maximum responses of the displacement feedback


2.4 Normalized controlled maximum responses of the velocity feedback


3.1 Parameters for MR damper model.......................................................................... 46

3.2 Comparisons of the evaluation criteria for benchmark cable-stayed bridge........... 61

3.3 Comparisons of the evaluation criteria for the nonlinear benchmark building....... 62

3.4 Evaluation criteria of modified location and number of MR dampers ................... 63

3.5 Evaluation criteria for7% stiffness perturbed system

under El Centro earthquake .................................................................................... 65

3.6 Evaluation criteria for30% stiffness perturbed system ........................................ 66

4.1 Normalized peak absolute accelerations and inter-story drifts ............................... 85

4.2 Percent increment compared to the better clipped-optimal controller case ............ 86


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LISTOF FIGURES

1.1 Behavior of MR fluid in magnetic field.................................................................. 10

1.2 Schematic of the prototype 20-ton large-scale MR fluid damper........................... 13

1.3 Small-scale SD-1000 MR fluid damper.................................................................. 14

1.4 Bypass type 20-ton MR fluid.................................................................................. 14

2.1 Schematic diagram of the MR damper implementation ......................................... 29

2.2 Frequency responses of the first floor for the uncontrolled structures

under the scaled El Centro earthquake.................................................................... 32

2.3 Frequency responses of the sixth floor for the uncontrolled structures

under the scaled El Centro earthquake.................................................................... 33

2.4 Variations of evaluation criteria with weighting parameters

for the acceleration feedback .................................................................................. 36


for the displacement feedback ................................................................................ 37


for the velocity feedback......................................................................................... 38

3.1 Mechanical model of the MR damper .................................................................... 45

3.2 Drawing of the Cape Girardeau Bridge .................................................................. 51

3.3 Cross section of bridge deck................................................................................... 51

3.4 Finite element model ............................................................................................. 54

3.5 Finite element model of the towers......................................................................... 54

3.6 Schematic of the 20-story benchmark building ...................................................... 56

4.1 Schematic of a MR damper-based control system.................................................. 68

4.2 Schematic of a MR damper with the EMI system .................................................. 70

4.3 Schematic of a MR damper with the EMI system implementation ........................ 70

4.4 Schematic of a MR damper implementation .......................................................... 73

4.5 Simple mechanical model of the normal MR damper ............................................ 75


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4.6 Design of EMI system with Sa under three earthquakes......................................... 77

4.7 Design of EMI system with Si under three earthquakes ......................................... 77

4.8 Design of theclipped-optimal controller with Sa under three earthquakes............. 794.9 Design of the clipped-optimal controller with Si under three earthquakes............. 79

4.10 Velocities and induced voltages under various earthquakes................................... 81

4.11 Normalized peak acceleration and inter-story drift ................................................ 83


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Chapter 1 Introduction 1

CHAPTER1

INTRODUCTION

1.1 Background

The tragic consequences of the recent earthquakes have underscored, in terms of

both human and economic factors, the tremendous importance of the way in which

buildings and bridges respond to earthquakes. In recent years, considerable attention has

been paid to research and development of structural control systems. Supplemental

passive, active, hybrid, and semiactive damping strategies offer attractive means to

protect structures against natural hazards. Passive supplemental damping strategies,

including base isolation systems, viscoelastic dampers, and tuned mass dampers, are

widely accepted by the engineering community as a means for mitigating the effects of

dynamic loading on structures. However, these passive-device methods are unable to

adapt to structural changes, varying usage patterns, and loading conditions.

For more than two decades, researchers have investigated the possibility of using

active, hybrid, and semiactive control methods to improve upon passive approaches to

reduce structural responses (Soong 1990; Soong and Reinhorn 1993; Spencer and Sain

1997; Housner et al. 1997; Kobori et al. 1998, 2003; Soong and Spencer 2002; Spencer

2002). The first full-scale application of active control to a building was accomplished by

the Kajima Corporation on 1989 (Kobori et al. 1991). The Kyobashi Center building is an

11-story (33.1m) building in Tokyo, having a total floor area of 423m2. A control system

was installed, consisting of two AMDs the primary AMD is used for transverse motion

and has a mass of 4 t, while the secondary AMD has a mass of 1 t and is employed to

reduce torsional motion. The role of the active system is to reduce building vibration

under strong winds and moderate earthquake excitations and consequently to increase

comfort of occupants of the building.


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Hybrid-control strategies have been investigated by many researchers to exploit

their potential to increase the overall reliability and efficiency of the controlled structure

(Housner et al. 1994; Kareem et al. 1999; Nishitani and Inoue 2001; Yang and Dyke

2003; Faravelli and Spencer 2003). A hybrid control system is typically defined as one

that employs a combination of passive and active devices. Because multiple control

devices are operation, hybrid control systems can alleviate some of the restrictions andlimitations that exist when each system is acting alone, Thus, higher levels of

performance may be achievable. Additionally, the resulting hybrid control system can be

more reliable than a fully active system, although it is also often somewhat more

complicated. To date, there have been over 40 buildings and about 10 bridges (during

erection) that have employed feedback control strategies in full-scale implementations

(Spencer and Nagarajaiah 2003).

Although nearly a decade has passed since construction of the Kobashi Seiwa

building, a number of serious challenges remain to be resolved before feedback controltechnology can gain general acceptance by the engineering and construction professions

at large. These challenges include: (i) reduction of capital cost and maintenance, (ii)

eliminating reliance on external power, (iii) increasing system reliability and robustness,

and (iv) gaining acceptance of nontraditional technology by the profession. Semiactive

control strategies appear to be particularly promising in addressing a number of these

challenges (Spencer 1996).

Control strategies based on semiactive control devices appear to combine the best

features of both passive and active control systems and to offer the greatest likelihood for

near term acceptance of control technology as a viable means of protecting civil

engineering structural systems against earthquake and wind loading. The attention

received in recent years can be attributed to the fact that semiactive control devices offer

the adaptability of active control devices without requiring the associated large power

sources. In fact, many can operate on battery power, which is critical during seismic

events when the main power source to the structure may fail. According to presently


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accepted definitions, a semiactive control device is one that can not inject mechanical

energy into the controlled structural system (i.e., including the structure and the control

device), but has properties which can be controlled to optimally reduce the responses of

the system. Therefore, in contrast to active control devices, semiactive control devices do

not have the potential to destabilize (in the bounded input/bounded output sense) the

structural system. Previous studies indicate that appropriately implemented semiactivesystems perform significantly better than passive devices and have the potential to

achieve the majority of the performance of fully active systems, thus allowing for the

possibility of effective response reduction during a wide array of dynamic loading

conditions (Spencer and Sain 1997; Symans and Constantinou 1999; Spencer 2002).

Most of the semiactive control devices have employed some electrically controlled

valves or mechanisms. Such mechanical components can be problematic in terms of

reliability and maintenance. Another class of semiactive devices uses controllable fluids.

The advantage of controllable fluid devices is that they contain no moving parts otherthan the piston, which makes them very reliable.

Two fluids that are viable contenders for development of controllable dampers are:

(1) electrorheological (ER) fluids; and (2) magnetorheological (MR) fluids. However,

recently developed MR fluids appear to be an attractive alternative to ER fluids for use in

controllable fluid dampers (Carlson 1994; Carlson and Weiss 1994; Carlson et al. 1995).

MR fluids are magnetic analogs of electrorheological fluids and typically consist of

micro-sized, magnetically polarizable particles dispersed in a carrier medium such as

mineral or silicone oil. When a magnetic field is applied to the fluid, particle chains form,

and the fluid becomes a semi-solid and exhibits viscoplastic behavior similar to that of an

ER fluid. Carlson and Weiss (1994) indicated that the achievable yield stress of an MR

fluid is an order of magnitude greater than its ER counterpart. Moreover, MR fluids are

not sensitive to impurities such as are commonly encountered during manufacturing and

usage. Therefore MR dampers have, over the last several years, been recognized having a

number of attractive characteristics for use in structural vibration control applications.


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1.2 Literature Review

1.2.1 Magnetorheological (MR) Dampers

Controllable fluid dampers generally utilize either electrorheological (ER) fluids or

magnetorheological (MR) fluids. These fluids are unique in their ability to reversibly

change from free-flowing, linear viscous fluids to semi-solids with a controllable-yield

strength in only a few milliseconds when exposed to an electric (ER fluids) or magnetic

field (MR fluids). These fluids can be modeled as Newtonian fluids in the absence of a

magnetic field. When a field is applied, the visco-plasticity model (Phillips 1969) may be

used to describe the fluid behavior.

Although the discovery of ER and MR fluids dates back to the 1940s, only recently

have they been applied to civil engineering applications. To date, a number of ER fluid

dampers have been investigated (Burton et al. 1996; Gavin et al. 1996a, 1996b; Kamath

et al. 1996; Makris et al. 1996) for structural vibration control applications in civil

engineering. Gavin et al. (1996a, 1996b) designed and tested an ER damper that consisted

of a rectangular container and a moving plunger comprised of nine rigidly connected flat

plates. Makris et al. (1996) developed an ER damper consisting of an outer cylinder and a

double-20 ended piston rod that pushes the ER fluids through an annular duct.

Despite these advances in the development of ER fluid dampers, the development

of commercially feasible damping devices using these fluids is limited by several factors.

First, the fluids have a very limited yield stress; even the best ER fluids currently

available may only achieve stresses of 3.0 to 3.5 KPa. Also, common impurities that

might be introduced during manufacturing significantly reduce the capacity of the fluids.

Additionally, safety, availability and the cost of high-voltage (e.g. ~4000 volts) power

supplies required to control the ER fluids are further considerations. MR fluids, on the

other hand, have a 50 to 100 KPa maximum yield stress, are not affected by most

impurities, and are not sensitive to temperature. Moreover, MR fluids can be controlled


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with a low-power (e.g., less than 50 watts), low-voltage (e.g., ~12-24 volts), current-

driven power supply with ~1-2 amps output. Therefore, MR fluids are particularly

promising for natural hazard mitigation and cost sensitive applications (Carlson and

Spencer 1996a, 1996b; Spencer and Sain 1997).

Different techniques have been developed to model the behavior of the controllable

fluid dampers. Basically, two types of models have been investigated: non-parametric andparametric models. Ehrgott and Masri (1992) presented a nonparametric approach to

model a small ER damper that operates under shear mode by assuming that the damper

force could be written in terms of Chebychev polynomials. Gavin et al. (1996b) extended

this approach to model the ER damper. Chang and Roschke (1998) developed a neural

network model to emulate the dynamic behavior of MR dampers. However, the non-

parametric damper models are quite complicated. Stanway et al. (1987) proposed a

simple mechanical model, the Bingham model, in which a Coulomb friction element is

placed in parallel with a dashpot. Gamoto and Filisko (1991) extended the Binghammodel and developed a visoelastic-plastic model. The model consists of a Bingham

model in series with a standard model of a linear solid model. Kamath and Wereley

(1997), Makris et al. (1996), and Wereley et al. (1998) developed parametric models to

characterize ER and MR dampers. Dyke et al. (1996a,b), Spencer et al. (1997a) and Yang

et al. (2001a,b) presented the Bouc-Wen model whose versatility was utilized to describe

a wide variety of hysteretic behavior.

A number of experimental studies have been conducted to evaluate the usefulness

of MR dampers for vibration reduction under wind and earthquakes. Dyke et al. (1996a,b,

1998), Jansen and Dyke (2000), Spencer et al. (1996b), and Yi and Dyke (2000) used MR

dampers to reduce the seismic vibration of building structure model. Spencer et al.

(2000), Ramallo et al. (2001) and Yoshioka et al. (2001) incorporated an MR damper

with a base isolation system such that the isolation system would be effective under both

strong and moderate earthquakes. Johnson et al. (2001a,b) employed the MR damper to


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reduce wind-induced stay cable vibration. The experimental results indicate that the MR

damper is quite effective for a wide class of applications.

Moreover, the technology has been demonstrated to be scalable to devices

sufficiently large for implementation in civil engineering structures. Carlson and Spencer

(1996b), Spencer et al. (1999), and Yang et al. (2002) have developed and tested a 20-t

MR damper. Recently, Sodeyama et al. (2003) have also presented impressive resultsregarding design and construction of large-scale MR dampers. In 2001, the first full-scale

implementation of MR dampers for civil engineering application was achieved. The

Nihon-Kagaku-Miraikan, the Tokyo National Museum of Emerging Science and

Innovation has two 30-ton-MR fluid dampers installed between the third and fifth floors.

The dampers were built by Sanwa Tekki using the Lord Corporation MR fluid.

Retrofitted with stay-cable dampers, the Dongting Lake Bridge in Hunan, China

constitutes the first full-scale implementation of MR dampers for bridge structures. Long

steel cables, such as are used in cable-stayed bridges and other structures, are prone tovibration induced by the structure to which they are connected and by weather conditions,

particularly wind combined with rain, that may cause cable galloping. The extremely low

damping inherent in such cables, typically on the order of a fraction of a percent, is

insufficient to eliminate this vibration, causing reduced cable and connection life due to

fatigue and/or breakdown of corrosion protection. Two Lord SD-1005 MR dampers are

mounted on each cable to mitigate cable vibration. A total of 312 MR dampers are

installed on 156 stayed cables. Recently, MR dampers have been chosen for

implementation on the Binzhou Yellow River Bridge in China to reduce cable vibration.

The installation is expected to be completed in October 2003 (Spencer and Nagarajaiah

2003).


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1.2.2 Control Algorithms for MR Dampers

One challenge in the use of semiactive technology is in developing nonlinear

control algorithms that are appropriate for implementation in full-scale structures.

Numerous control algorithms have been adopted for semiactive systems. In one of the

first examinations of semiactive control, Karnopp et al. (1974) proposed a skyhookdamper control algorithm for a vehicle suspension system and demonstrated that this

system offers improved performance over a passive system when applied to a single-

degree-of-freedom system. Feng and Shinozukah (1990) developed a bang-bang

controller for a hybrid controller on a bridge. More recently, a control strategy based on

Lyapunov stability theory has been proposed for electrorheological dampers (Brogan

1991; Leitmann 1994). The goal of this algorithm is to reduce the responses by

minimizing the rate of change of a Lyapunov function. McClamroch and Gavin (1995)

used a similar approach to develop a decentralized bang-bang controller. This control

algorithm acts to minimize the total energy in the structure. A modulated homogeneous

friction algorithm (Inaudi 1997) was developed for a variable friction device. Clipped-

optimal controllers have also been proposed and implemented for semiactive systems

(Sack et al. 1994; Sack and Patten 1994; Dyke, 1996a,b,c). The effective utilization of

multiple control devices is an important step in the examination of semiactive control

algorithms. A typical control system for a full-scale structure is expected to have control

devices distributed throughout a number of floors. Because of the inherent nonlinear

nature of these devices, one of the challenging aspects of utilizing this technology to

achieve high levels of performance is in the development of appropriate control

algorithms.

As previously mentioned, a number of control algorithms have been adopted for

semiactive control systems using MR dampers (Jansen and Dyke 2000). Among many

control algorithms, modal control represents one control class, in which the motion of a

structure is reshaped by merely controlling some selected vibration modes. Modal control


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is especially desirable for the vibration control of civil engineering structure, which is

usually a large structural system, may involve hundred or even thousand degrees of

freedom, its vibration is usually dominated by the first few modes. Therefore, the motion

of the structure can be effectively suppressed by merely controlling these few modes

(Yang 1982). To date, numerous procedures and algorithms concerning modal control or

pole assignment have been proposed in literature. A modal control method using full statefeedback may not be practical for a structural system involving a large number of DOFs,

since the control implementation may requires a large amount of sensors. Thus a modal

control scheme, which uses modal state estimation, is desirable. To estimate the modal

states from the sensor output, Luenberger observer (Meirovitch 1990; Luenberger 1971)

and a Kalman-Bucy filter (Meirovitch, 1967) can be used for the case of low noise-to-

signal ratios and for high noise-to-signal ratios, respectively. The troublesome of

estimating the modal states for feedback in modal control is the problem of spillover.

Note, however, that a small amount of damping inherent in the structure is oftensufficient to overcome the observation spillover effect (Meirovitch and Baruh 1983). At

any rate, observation spillover can be eliminated if the sensor signals are prefiltered so as

to screen out the contribution of the uncontrolled modes.

On the other side, the maximum energy dissipation algorithm (MEDA) represents

one control class which employs the Lyapunovs direct approach to stability analysis in

the design of a feedback controller (Brogan 1991). The approach requires the use of a

Lyapunov function that must be a positive definite function of the states of the system.

According to Lyapunov stability theory, if the rate of change of the Lyapunov function is

negative semi-definite, the origin is stable in the sense of Lyapunov. Thus, in developing

the control law based on Lyapunov stability theory, the goal is to choose control inputs

for each deice that will result in making the rate of change of the Lyapunov function as

negative as possible. Jansen and Dyke (2000) suggested MEDA as a variation of the

decentralized bang-bang approach proposed by McClamroch and Gavin (1995). It is


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noticeable that this control law requires only local measurements, which means MEDA is

simply implemented without any design process.


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1.3 MR Fluids and Dampers

1.3.1 MR Fluids

The initial discovery and development of MR fluids can be credited to Jacob

Rabinow (1948, 1951) at the US National Bureau of Standards in the late 1940s. These

fluids are suspensions of micron-sized, magnetizable particles in an appropriate carrier

liquid. Normally, MR fluids are free flowing liquids having a consistency similar to that

of motor oil. However, in the presence of an applied magnetic field, the iron particles

acquire a dipole moment aligned with the external field that causes particles to form

linear chains parallel to the field, as shown in Fig. 1.1. This phenomenon can solidify the

suspended iron particles and restrict the fluid movement. Consequently, yield strength is

developed within the fluid. The degree of change is related to the magnitude of the

applied magnetic field, and can occur only in a few milliseconds.

Figure 1.1 Behavior of MR fluid in magnetic field

There are basically two types of controllable fluids MR fluids and ER fluids. The

primary advantage of MR fluids stems from their high dynamic yield strength due to the

high magnetic energy density that can be established in the fluid. Energy density in MR

fluids is limited by the magnetic saturation of iron particles. From a practical

implementation perspective, although the total energy requirements for the ER and MR


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devices are almost equal, only MR devices can be easily driven by common low-voltage

power sources (Carlson and Spencer 1996a). MR devices can be controlled with a low-

voltage, current-driven power supply outputting only ~1-2 amps. ER devices, on the other

hand, require a high-voltage power source (~2000-5000 volts) that may not be readily

available, especially during strong earthquake events. Moreover, such a high voltage may

pose a safety hazard. The properties of both MR and ER fluids are given in Table 1.1.

Table 1.1 Properties of MR and ER fluids (Spencer and Sain 1997)

Property MR Fluids ER Fluids

Max. yield Stress 50-100 kPa 2-5kPa

Maximum field ~250kA/m ~4kV/mm

Plastic viscosity, p 0.1-1.0Pa-s 0.1-1.0Pa-s

Operable temp. range -40 to 150C +10 to 90C

Stabilityunaffected by most

impurities

cannot tolerate

impurities

Response time milliseconds milliseconds

Density 3 to 4 g/cm3 1 to 2 g/cm3

2

)(/ fieldyp 10-10-10-11 s/Pa 10-7-10-8 s/Pa

Maxi. energy density 0.1 Joules/cm3 0.001 Joules/cm3

Power supply (typical)2-25V

1-2A

2000-5000V

1-10 mA


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1.3.2 MR Fluid Dampers

The maximum force that an MR damper can deliver depends on the properties of

MR fluids, their flow pattern, and the size of the damper. Virtually all devices that use

MR fluids can be classified as operating in: (a) a valve mode, (b) a direct shear mode, (c)

a squeeze mode, or a combination of these modes (Carlson and Spencer 1996a). To date,several MR fluid devices have been developed for commercial use by the LORD

Corporation (Carlson et al. 1996; Jolly et al. 1998). Linear MR fluid dampers have been

designed for use as secondary suspension elements in vehicles. MR fluid rotary brakes

are smooth-acting, proportional brakes which are more compact and require substantially

less power than competing systems. MR fluid vibration dampers for real-time, active

control of damping have been used in numerous industrial applications.

In civil engineering applications, the expected damping forces and displacements

are rather large in magnitude. Therefore, MR dampers primarily operating under direct

shear mode or squeeze mode might be impractical. Usually valve mode or its

combination with direct shear mode is employed. Some examples of recently developed

MR dampers are given below. These dampers are capable of meeting real-world

requirements and are presently either in commercial production or in production

prototype trials.

A 20-ton prototype large-scale seismic MR fluid damper was developed under

cooperation between the LORD Corporation and the Structural Dynamics and

Control/Earthquake Engineering Laboratory (SDC/EEL) at the University of Notre Dame

(Carlson and Spencer 1996a; Spencer et al. 1997b,1998; Yang et al. 2000a,b). The MR

fluid damper schematic is given in Fig. 1.2. For the nominal design, a maximum damping

force of 200,000 N (20 tons) were chosen. The damper has an inside diameter of 20.3 cm

and a stroke of 8 cm. The completed damper is approximately 1 m long, has a mass of

250 kg, and contains approximately 6 liters of MR fluid. However, the amount of fluid

energized by the magnetic field at any given instant is approximately 90 cm3.


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Fig. 1.3 shows a small-scale SD-1000 MR fluid damper manufactured by the

LORD Corporation (Carlson and Spencer 1996a; Dyke 1996a,b; Jolly et al. 1998;

Spencer 1997a). In this damper, MR fluids flow from a high-pressure chamber to a low-

pressure chamber through an orifice in the piston head. The damper is 21.5 cm long in its

extended position, and the main cylinder is 3.8 cm in diameter. Forces of up to 3,000 N

can be generated with this device.Fig. 1.4 shows a bypass-type 20-ton MR fluid damper designed by the Sanwa

Tekki Corporation (Fujitani et al. 2000; Sunakoda et al. 2000). Unlike dampers

mentioned previously, MR fluids in this damper flow from a high-pressure chamber to a

low-pressure chamber in valve mode through a bypass outside the main cylinder. The

bypass has an annular gap between the outside of the magnetic pole and the inside of the

bypass cylinder. The magnetic field is generated by a 10-stage electromagnet and is

perpendicular to the fluid flow.

Figure 1.2 Schematic of the prototype 20-ton large-scale MR fluid damper


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Figure 1.3 Small-scale SD-1000 MR fluid damper

Figure 1.4 Bypass type 20-ton MR fluid

Bearing & SealMR Fluid

CoilDiaphragm

Accumulator

Wires to

Electromagnet


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1.4 Objectives and Scopes

The purpose of this study is to implement simple and efficient control algorithms

for seismically excited structures using MR dampers and to develop a smart passive

system based on the MR damper. The objectives and scopes of this study can be

summarized as follows.

First, the objectives and scopes of the study on implementations of simple and

efficient control algorithms can be summarized as follows:

(1) Implementation of modal control for seismically excited structures using MR

dampers:

In order to study the effectiveness for the MR damper-based semiactive, a modal

control scheme is implemented to seismically excited structures. A Kalman filter is

included in a control scheme to estimate modal states from measurements by

sensors. A low-pass filter is applied to eliminate the spillover problem. In a

numerical example, a six-story building model with the MR dampers on the bottom

two floors is used to verify the implemented modal control scheme. The

performance of the proposed modal control scheme is compared with that of other

control algorithms previously studied.

(2) Implementation of maximum energy dissipation algorithm for seismic response

reduction of large-scale structures using MR dampers:

The performance and the robustness of the maximum energy dissipation algorithm

for civil engineering structures using MR dampers are investigated. The numerical

examples contain the cable-stayed bridge and the nonlinear building. Various

earthquakes are used to excite the system. Through the series of numerical

simulation, the performance and the robustness are compared with that of other


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control algorithms that are previously proposed: The reduction in the drifts,

accelerations, and relative displacements throughout the structure are examined

according to the evaluation criteria.

Next, the objectives and scopes of the study on development of a smart passive

system based on the MR damper can be summarized as follows:

(1) Development of a smart passive system based on the MR damper to reduce

structural responses:

The smart passive damper system is based on MR dampers. The MR damper is a

semiactive device that needs an external power source to change the damping

characteristics of MR fluids. However, the smart passive damper system based on

MR dampers is not using an external power source, but self-powered by an

electromagnetic induction system (EMI) that is attached to the MR damper. TheEMI system for MR dampers consists of a permanent magnet and a coil. According

to the Faradays law of induction, the EMI system changes the kinetic energy of

the MR damper to the electric energy and then the electric energy is used to vary

the damping characteristics of the MR damper. The theoretical backgrounds and

the designing process are presented. To verify the effectiveness of the proposed

smart passive control system, the performances are compared with those of the

semiactive MR damper using clipped-optimal controller.


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1.5 Organization

This dissertation consists of four chapters. Chapter 1 discusses the background, the

literature review, the characteristics of MR fluids and dampers, and the objectives and

scopes of this study.

In Chapter 2, a modal control scheme is implemented for the MR damper-based

control system. A low-pass filter and the Kalman filter as a modal state estimator are

reviewed and included in the modal control scheme for the MR damper-based control

system in Section 2.1. Reduced design procedure is presented, also, in this section. To

evaluate the proposed modal control scheme for usage with the MR damper, a numerical

example is considered, in which a model of a six-story building is controlled with four

MR dampers in Section 2.2. The results are summarized in Section 2.3.

In Chapter 3, the maximum energy dissipation algorithm (MEDA) is implemented

for the MR damper-based control system. The control system including the MR device

and MEDA is reviewed in Section 3.1. In Section 3.2, the cable-stayed bridge and the 20-

story nonlinear building are shown as representative structures of civil engineering and

numerical examples. In Section 3.3, the applicability of the MEDA-based semiactive

control system is examined from the viewpoint of the performance and the robustness

through the numerical examples. The results are summarized in Section 3.4.

In Chapter 4, a smart passive control system is proposed. In Section 4.1, an

electromagnetic induction (EMI) system is proposed for the MR damper. An analytical

model and a design procedure of the proposed EMI system are described in Section 4.2.

To show the effectiveness of the proposed smart passive control system, a set of

numerical simulations are performed for the four historical earthquakes in Section 4.3.

Section 4.4 summarizes the results.

Finally, the conclusions of this dissertation are summarized in Chapter 5.


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Chapter 2 Modal Control Scheme 18

CHAPTER2

MODAL CONTROL SCHEME

2.1 Modal Control Scheme for MR Dampers

In this section, a modal control scheme with a Kalman filter and a low-pass filter is

implemented to a seismically excited structure. A Kalman filter is included in a control

scheme to estimate modal states from various measurements. Moreover, a low-pass filter

is applied to eliminate the spillover problem. After the implementation of the modal

control scheme, numerical simulations are presented in subsequent sections for

comparisons between control algorithms.

2.1.1 Modal Control

Consider a seismically excited structure controlled with m MR dampers. Assuming

that the forces provided by the control devices are adequate to keep the response of the

primary structure from exiting the linear region, the equations of motion can be written

gMfKxxCxM xtttt &&&&& =++ )()()()( (2.1)

whereM, Cand Kare the nn mass, damping, and stiffness matrices, respectively; x is

the n-dimensional vector of the relative displacements of the floors of the structure; f=

[f1,f2,,fm ]T

is the vector of measured control forces generated by m MR dampers; gx&& is

ground acceleration; is the column vector of ones; and is the matrix determined by

the placement of MR dampers in the structure. This equation can be written in the state-

space form as


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gx&&& NGfFzz ++= (2.2a)

vMfHzy ++= (2.2b)

wherezis a state vector;y is a vector of measured outputs; and v is a measurement noise

vector. The displacement can be expressed as the linear combination

x ===

n

r

rr tt1

)()( , r= 1, 2,, n (2.3)

where )(tr is a rth modal displacement; r is a rth eigenvector; is a eigenvector set;

and is a modal displacement vector. The eigenvectors are orthogonal and can be

normalized so as to satisfy the orthonormality conditions

rsr

T

s = M , rsrrT

s 2

=K , r= 1, 2,, n (2.4)

where rs is the Kronecker delta and r is a natural frequency. Thus inserting (2.3) into

(2.1), multiplying byT

r and considering orthogonal condition between eigenvectors, we

obtain

g

T

r

T

rr

2

rrrrr x2 &&&&& Mf=++ , r= 1, 2,, n (2.5)

where r are modal damping ratios. (2.5) can be written in the matrix form as

gxtttt &&&&& ')()()()( EfB'2 +=++ (2.6)

where is the diagonal matrix listing 2rr ; 2

is the diagonal matrix listing2

1 ,,

2

n ;B= T

; andE= MT . (2.6) can be written in the modal space-state form as


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gxttt &&& EBfAww ++= )()()( (2.7a)

)()( tCwty = (2.7b)

where w(t) = [ T& T ] is the modal state vector and

=

I0A

2,

=

B'

0B ,

=

E'

0E (2.8)

In modal control, only a limited number of lower modes are controlled. Hence, l

controlled modes can be selected with l< n and the displacement may be partitioned into

controlled and uncontrolled parts as

)()()( tttRC

xxx += (2.9)

where xC and xR represent the controlled and uncontrolled displacement vector,

respectively. We refer to the uncontrolled modes as residual. Then, (2.7) can be rewritten

gCCCCC xttt &&& EfBwAw ++= )()()( (2.10a)

)()( tt CCC wCy = (2.10b)

where wC is a 2l-dimensional modal state vector by the controlled modes and

=

C

2

C

C

C

I0A ,

=

C

CB'

0B ,

=

C

CE'

0E (2.11)

are the 2l2l, 2lm matrixes and a 2l1 vector, respectively.


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For a feedback control, the control vector is related to the modal state vector according to

f(t) = KCwC(t) (2.12)

where KC is an m2l control gain matrix. Note that, in using the control law given by

(2.12), the closed-loop modal equations are not independent.

Because the force generated in the i th MR damper depends on the responses of the

structural system, the MR damper cannot always produce the desired optimal control

forcefCi. Only the control voltage vi can be directly controlled. Thus, the strategy of the

clipped-optimal control (Dyke et al. 1996a) is used, in which a force feedback loop is

incorporated to induce the force in the MR damperfi to generate approximately the

desired optimal control force fCi. To this end, the i th command signal vi is selected

according to the control law

][(max ii H )fffVv iiC = (2.13)

where Vmax is the voltage to the current driver associated with saturation of the MR effect

in the physical device, andH(w) is the Heaviside step function.

2.1.2 Design of Optimal Controller

Referring to the discussions in above section, control gain matrix KC should be

decided. Although a variety of approaches may be used to design the optimal controller,

H2/LQG (Linear Quadratic Gaussian) methods are advocated because of their successful

application in previous studies (Dyke et al. 1996a,b,c).

For the controller design, gx&& is taken to be a stationary white noise, and an infinite

horizon performance index is chosen that weights the modal states by controlled modes

such as


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+= )dt(E

1limJ

0

T

C

T

C

RuuwQw (2.14)

whereR is a 2 2 identity matrix because the numerical example has two MR dampers,

and Q is a 2l 2ldiagonal matrix. It should be noted that the size ofQ is reduced from 2n

2n to 2l 2lbecause the limited lower modes are controlled. Therefore, it can be said

that it is more convenient to design the smaller weighting matrix of modal control. For

example, when the lowest one mode is selected for calculating the modal control action,

Q is a 2 2 diagonal matrix such as

=

mv

md

q

q

0

0Q (2.15)

where qmd is a weighting element for a modal displacement and qmv is for a modal

velocity. When the lowest two modes are controlled, Q is the 4 4 diagonal matrix.

=

mv2

mv1

md2

md1

q0

q

q

0q

Q (2.16)

The measurement noise is assumed to be identically distributed, statistically independent

Gaussian white noise processes, and 100/ == iigg vvxx SS &&&& . Then, the controller is

CCCCC ss BLCAIKG)]([)( 1= (2.17)

where ][ LDBLB = . Here,KC is the state feedback gain matrix for the deterministic

regulator problem given by


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PBK CC '= (2.18)

wherePis the solution of the algebraic Ricatti equation given by

0''' =++ CCCCCC QCCPBPBPAPA (2.19)

and

)'( SCL C= (2.20)

whereSis the solution of the algebraic Ricatti equation given by

0=++ CCCCCC E'ESCSC'SASA' (2.21)

2.1.3 Modal State Estimation

An observer for modal state estimation should be provided, since real sensors may

not estimate the full modal states directly or the system may be expensive to prepare the

sensors for the full states. To estimate the modal state vector wC (t) from the measured

output y(t), we consider an observer. Luenberger observers are used for low noise-to-

signal ratios and Kalman-Bucy filters for high noise-to-signal ratios (Meirovitch, 1990).

A modal control method using the full state feedback may not be practical for a

structural system involving a large number of DOFs, since the control implementation

may requires a large amount of sensors. Thus a modal control scheme that uses a modal

state estimation, is desirable. Moreover, accurate measurements of displacements and

velocities are difficult to achieve directly in full-scale applications, particularly during

seismic activity, since the foundation of the structure is moving with the ground. Hence,

it is ideal to use the acceleration feedback because accelerometers can readily provide

reliable and inexpensive measurements of accelerations at arbitrary points on the structure


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(Dyke et al. 1996a, b). Not only, the acceleration feedback is considered, but also the

state feedback including velocities and displacements, is implemented for the modal state

estimation using a Kalman-Bucy filter. In any case, we can write a modal observer in the

form

)]()()([)()()( tttxttt CCCgCCCCC fDwCyLEfwAw +++= &&& (2.22)

where )( tCw is the estimated controlled modal state and L is the optimally chosen

observer gain matrix by solving a matrix Riccati equation, which assumes that the noise

intensities associated with earthquake and sensors are known. CC is changeable according

to the signals that are used for the feedback and DC is generally zero except the

acceleration feedback. For modal state estimation from the displacements, CC in (2.22) is

as follows;

CC= ]0[ C (2.23)

For control with the velocity feedback,

CC= ]0[ C (2.24)

For control with the acceleration feedback,

CC=

C

CCMKM

00][ 11 andDC=

1M (2.25)

Upon obtaining the estimated controlled modal state from (2.22), we compute the

feedback control forces

f(t) = KC )( tCw (2.26)


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Until now, the uncontrolled modes are ignored. In reality, however, the sensor signals

will include contributions from all the modes, so that the output vector is corrected to

)()()( ttt RRCC wCwCwCy +== (2.27)

To examine the effect of the control forces on the uncontrolled modes, residual modes

can be written

gRRRRR xttt &&& EfBwAw ++= )()()( (2.28)

where wR is a residual state vector by uncontrolled modes. Substituting (2.26) into (2.10a)

and considering (2.28), we obtain

gCCCCCCC xttt &&& EwKBwAw += )()()( (2.29a)

gRCCRRRR xttt &&& EwKBwAw += )()()( (2.29b)

Moreover, substituting (2.26) and (2.27) into (2.22), we can write the observer equation

in the form

gCRRCCCCCCCC xttttt &&& EwLCwwLCwKBAw +++= )(])()([)()()( (2.30)

Then the error vector is defined

)()()( ttt CCC wwe = (2.31)

so that (2.29) and (2.30) can be rearranged


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gCCCCCCCCC xttt &&& EeKBwKBAw += )()()()(

gRCCRRRCCRR xtttt &&& EeKBwAwKBw ++= )()()()( (2.32)

)()()()( ttt RRCCCC wLCeLCAe +=&

(2.32) can be written in the matrix form

gR

R

C

R

C

CCR

CRRCR

CCCCC

C

R

C

x

t

t

t

t

t

t

&&

&

&

&

+

=

0

E

E

e

w

w

LCALC0

KBAKB

KB0KBA

e

w

w

)(

)(

)(

)(

)(

)(

(2.33)

Note that the term CRKB in (2.33) is responsible for the excitation of the residual

modes by the control forces and is known as control spillover (Balas, 1978). If RC is

zeros, which means the sensor signal only include controlled modes, the term CRKB

has no effect on the eigenvalues of the closed-loop system. Hence, we conclude that

control spillover cannot destabilize the system, although it can cause some degradation in

the system performance. Normally, however, the above system cannot satisfy the separate

principle because the term LCR affects eigenvalues of the controlled system by the

observer. This effect is known as observation spillover and can produce instability in the

residual modes. However, a small amount of damping inherent in the structure is often

sufficient to overcome the observation spillover effect.(Meirovitch and Baruh, 1983). At

any rate, observation spillover can be eliminated if the sensor signals are prefiltered so as

to screen out the contribution of the uncontrolled modes (Meirovitch, 1990)


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2.1.4 Elimination of Observable Spillover

(2.33) in above section should be further improved for eliminating the observable

spillover. A low-pass filter is introduced to measure the filtered response vectoryfdefined

as

)()(

)()()(

tt

ttt

yzf

yz

yMzHy

yGzFz

+=

+=&(2.34)

or in the frequency domain

)()()( jyjHjy yf = (2.35)

where ])([)( 1 yyzzy jj MGFIHH +=

. Substituting (2.27) into (2.35), the new

sensor dynamics becomes

)]()()[()( jjjj RRCCyf wCwCHy += (2.36)

If the low-pass filter dynamics Hy(j) can be selected as a diagonal matrix, (2.36)

becomes

)]()([)]()([)( jjjjj RyRCyCf wHCwHCy += (2.37)

The pole of the low-pass filter dynamics can be placed by proper selection of the

parameters, Hz, Fz, Gy, My, then the roll-off can be occurred forth the lowest modal

frequency of the residual dynamics. The second term of right-hand side of (2.37), which

represents the residual modal state, may have the following characteristics.

|)(||)()(| 1 jjj RRy wwH for


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where 01 . Otherwise, the first term of right-hand side of (2.37), which represents the

controlled modal state, may also have the following characteristics.

|)(||)()(| jjj CCy wwH for


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2.2 Numerical Example

To evaluate the proposed modal control scheme for use with the MR damper, a

numerical example is considered in which a model of a six-story building is controlled

with four MR dampers (Fig. 2.1). This numerical example is the same with that of Jansen

and Dyke (2000) and is adopted for direct comparisons between the proposed modal

control scheme and other control algorithms. Two MR dampers are rigidly connected

between the ground and the first floor, and two MR dampers are rigidly connected

between the first and second floors.

Figure 2.1 Schematic diagram of the MR damper implementation

(Jansen and Dyke 2000)


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Each MR damper is capable of producing a force equal to 1.8% the weight of the

entire structure, and the maximum voltage input to MR devices is Vmax = 5V. The

governing equations can be written in the form of (2.7) by defining the mass of each

floor, mi, as 0.227 N/(cm/sec2), the stiffness of each floor, ki, as 297 N/cm, and a damping

ratio for each mode of 0.5%. MR damper parameters used in this study are c0a = 0.0064

Nsec/cm, c0b = 0.0052 Nsec/cmV, a = 8.66 N/cm, b = 8.86 N/cmV, g = 300 cm

-2

, b =300 cm

-2, A = 120, and n = 2. In simulation, the model of the structure is subjected to the

NS component of the 1940 El Centro earthquake. Because the building system considered

is a scaled model, the amplitude of the earthquake was scaled to ten percent of the full-

scale earthquake.

Figs. 2.2 and 2.3 show the uncontrolled responses of the first and sixth floors,

respectively, in frequency domain. From Fig. 2.2, it can be seen that the first mode is

dominant in relative displacement and velocity of the first floor, whereas the lowest three

modes are dominant in the absolute acceleration. In Fig. 2.3, however, we can find that

the first mode is dominant in all responses of the sixth floor. Thus, it will be possible to

reduce the responses through modal control that control using the lowest one or two

modes.

The various control algorithms were evaluated using a set of evaluation criteria

based on those used in the second generation linear control problem for buildings

(Spencer et al., 1997a). The first evaluation criterion is a measure of the normalized

maximum floor displacement relative to the ground, given as

=

max

i

it,1

x

|t|xJ

)(max (2.43)

wherexi(t) is the relative displacement of the i th floor over the entire response, and xmax

denotes the uncontrolled maximum displacement. The second evaluation criterion is a

measure of the reduction in the interstory drift. The maximum of the normalized

interstory drift is


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=

max

n

ii

it,2

d

|/ht|dJ

)(max (2.44)

where hi is the height of each floor (30cm), di(t) is the interstory drift of the above ground

floors over the response history, andmax

nd denotes the normalized peak interstory drift in

the uncontrolled response. The third evaluation criterion is a measure of the normalized

peak floor accelerations, given by

=

max

a

ai

it,3

x

|tx|J

&&

&& )(max (2.45)

where the absolute accelerations of the ith floor, )(txai&& , are normalized by the peak

uncontrolled floor acceleration, denoted )(txmaxa&& . The final evaluation criteria considered

in this study is a measure of the maximum control force per device, normalized by the

weight of the structure, given by

=

W

(t)||fJ i

it,4 max (2.46)

where W is the total weight of the structure (1335 N). The corresponding uncontrolled

responses are as follows:xmax = 1.313 cm,max

ad = 0.00981 cm,max

ax&& = 146.95 cm/sec2.

The resulting evaluation criteria are presented in Table 1 for the control algorithms

previously studied (Jansen and Dyke, 2000). The numbers in parentheses indicate the

percent reduction as compared to the best passive case. To compare the performance of

the semiactive system to that of comparable passive systems, two cases are considered in

which MR dampers are used in a passive mode by maintaining a constant voltage to the

devices. The results of passive-off (0V) and passive-on (5V) configurations are included.


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0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

PSD

frequency, Hz

104

PowerSpectrumo

f

Velocity

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

x 106

PS

D

frequency, Hz

PowerSpectrumo

f

Acceleration

Frequency, Hz

Figure 2.2 Frequency responses of the first floor for the uncontrolled structures

under the scaled El Centro earthquake

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

PSD

frequency, Hz

PowerSpectrumo

f

RelativeDisplacement

102

x 105


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Figure 2.3 Frequency responses of the sixth floor for the uncontrolled structures

under the scaled El Centro earthquake

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2.0

2.5

3.0

PSD

frequency, Hz

102

Pow

erSpectrumo

f

RelativeDisplacement

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

x 105

PSD

frequency, Hz

PowerSpectrumo

f

Velocity

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

x 106

PSD

frequency, Hz

PowerSpectrumo

f

Acceleration

Frequency, Hz


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Table 2.1 Normalized controlled maximum responses

due to the scaled El Centro earthquake*

Control strategy J1 J2 J3 J4

Passive-off 0.862 0.801 0.904 0.00292

Passive-on 0.506 0.696 1.41 0.0178

Lyapunov controller A 0.686(+35) 0.788(+13) 0.756(16) 0.0178

Lyapunov controller A 0.326(35) 0.548(21) 1.39(+53) 0.0178

Decentralized bang-bang 0.449(11) 0.791(+13) 1.00(+11) 0.0178

Maximum energy dissipation 0.548(+8) 0.620(11) 1.06(+17) 0.0121

Clipped-optimal A 0.631(+24) 0.640(8) 0.636(29) 0.01095

Clipped-optimal B 0.405(20) 0.547(21) 1.25(+38) 0.0178

Modified homogeneous friction 0.421(17) 0.599(20) 1.06(+17) 0.0178

(* Jansen and Dyke 2000)


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For modal control, three cases of the structural measurements are considered;

displacements, velocities and accelerations. Using each structural measurement, a

Kalman filter estimates the modal states. Fig. 2.4 represents the results of the stochastic

response analysis for the acceleration feedback case. The variations of each evaluation

criteria for increasing weighting parameters are shown in a 3-dimensional plot.

Previously mentioned, J1 is evaluation criteria for the maximum displacement, J2 is forthe maximum interstory drift and J3 is for the maximum acceleration. In Fig. 4, JT is the

summation of evaluation criteria,J1,J2 andJ3. From the variations ofJT, we can find the

weighting for reduction of overall structural responses whereas fromJ1,J2 andJ3, we can

find the weighting for reduction of related responses. In Fig. 2.4, it can be seen that J1 is

minimum at qmd = 400 and qmv = 1500,J2 is at qmd = 1 and qmv = 500,J3 is at qmd = 2200

and qmv = 100 and J4 is at qmd = 500 and qmv = 600. Designer can decide which to use

according to control objectives. By using the controller (H2/LQG) with designed

weighting matrices from Fig. 2.4, we can get the results in Table 2.2.Figs. 2.5 and 2.6 represent the results for the displacement and velocity feedback

cases, respectively. Tables 2.5 and 2.6 summarize the results for each minimum

evaluation criteria of the designed weighting matrices from Figs. 2.5 and 2.6.

For each feedback case, in Tables 2.2 to 2.4, four modal control designs with

different capabilities are considered. In Table 2.2, the modal controllerAJ1,AJ2,AJ3 and

AJT with acceleration feedback use a weighting that minimize the evaluation criteria J1,

J2, J3 and JT, respectively. In Tables 2.3 to 2.4, the modal controllerDJ1, DJ2, DJ3, and

DJT with displacement feedback and VJ1, VJ2,VJ3, and VJT with velocity feedback use a

weighting which minimize the evaluation criteria J1,J2,J3 andJT, respectively. For each

weighting, the lowest one and two modes cases are given in Tables 2.2 to 2.4. In the

lowest two modes case, we place identical weighting on the each mode; qmd1 = qmd2 = qmd

and qmv1 = qmv2 = qmv.


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Figure 2.4 Variations of evaluation criteria with weighting parameters

for the acceleration feedback

J1 J2

J3 JT=J1+ J2 + J3

qmd qmv qmd qmv

qmd qmvqmdqmv


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for the displacement feedback

J1 J2

J3 JT=J1+ J2 + J3

qmd qmv qmd qmv

qmd qmvqmd qmv


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for the velocity feedback

J1 J2

J3 JT=J1+ J2 + J3

qmd qmv qmd qmv

qmdqmv qmdqmv


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The calculated evaluation criteria for various control strategies are compared in

Tables 2.1 to 2.4. The performance of the proposed modal control scheme is generally

better than that of other control strategies. The results show that the modal controllerA

and V appear to be quite effective in achieving significant reductions in both the

maximum displacement and interstory drift over the passive case. In fact, the modal

controllerAJ1 achieves a 39% reduction in the relative displacement as compared to thebetter passive case. If further reductions in interstory drift and acceleration are desired in

the controller, modal controllerAJ2 and AJ3 can achieve the reductions in the interstory

drift and absolute acceleration of 30% and 23%, respectively, over the best passive cases,

although the maximum displacement increased. The reduction by modal controllerAJ2 is

resulting in the lowest interstory drift of all cases considered here. In Table 2.4, modal

controller VJ1 using the lowest two modes and VJ3 achieve reductions in relative

displacement and absolute acceleration of 41% and 30%, respectively, resulting in the

lowest values of all cases considered here. The modal controllerAJT and VJT do notachieve any lowest value of evaluation criteria, but have competitive performance in all

evaluation criteria. Notice that the designer has some versatility depending on the control

objectives for the particular structure under consideration.

The modal controllerD compared with the modal controllerA and Vappears to be

worse in achieving reductions, which agrees with the fact that the variations of evaluation

criteria are more sensitive to weighting parameterqmv than qmdfrom Figs. 2.4 to 2.6.

Comparing the lowest one mode case with two-mode case, every lowest value of

evaluation criteria occurs at the lowest one mode case, except the modal controller VJ1

that achieves further reductions by 6% from one mode case (reductions of 41% over the

best passive case) in the relative displacement.


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Table 2.2 Normalized controlled maximum responses of the acceleration feedback

due to the scaled El Centro earthquake


1 mode 0.310(-39) 0.529(-24) 1.07(+18) 0.0178

Modal control AJ1(qmd=400, qmv=1500) 2 modes 0.392(-23) 0.543(-22) 1.05(+16) 0.0178

1 mode 0.398(-21) 0.485(-30) 0.870(-4) 0.0178Modal control AJ2

(qmd=1, qmv=500) 2 modes 0.413(-18) 0.510(-27) 0.781(-14) 0.0178

1 mode 0.549(+8) 0.618(-11) 0.697(-23) 0.0178Modal control AJ3(qmd=2200, qmv=100) 2 modes 0.548(+8) 0.585(-16) 0.741(-18) 0.0178

1 mode 0.380(-25) 0.488(-30) 0.823(-9) 0.0178Modal control AJT(qmd=500, qmv=600)

2 modes 0.423(-16) 0.533(-23) 0.876(-3) 0.0178


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Table 2.3 Normalized controlled maximum responses of the displacement feedback



1 mode 0.403(-20) 0.560(-20) 0.765(-15) 0.0178Modal control DJ1(qmd=100, qmv=4900) 2 modes 0.325(-36) 0.504(-28) 1.06(+17) 0.0178

1 mode 0.403(-20) 0.560(-20) 0.769(-15) 0.0178Modal control DJ2(qmd=100, qmv=4900) 2 modes 0.325(-36) 0.504(-28) 1.06(+17) 0.0178

1 mode 0.702(+39) 0.728(+5) 0.671(-26) 0.0178Modal control DJ3(qmd=200, qmv=4900) 2 modes 0.678(+34) 0.689(-1) 0.796(-12) 0.0178

1 mode 0.408(-19) 0.566(-19) 0.721(-20) 0.0178Modal control DJT(qmd=3300,qmv=4700)2 modes 0.329(-35) 0.510(-27) 1.04(+15) 0.0178


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Table 2.4 Normalized controlled maximum responses of the velocity feedback



1 mode 0.327(-35) 0.554(-20) 1.06(+17) 0.0178Modal control VJ1(qmd=700, qmv=800)

2 modes 0.301(-41) 0.530(-24) 1.07(+18) 0.0178

1 mode 0.383(-24) 0.487(-30) 0.874(-3) 0.0178Modal control VJ2

(qmd=1, qmv=400)2 modes 0.351(-31) 0.510(-27) 0.941(+4) 0.0178

1 mode 0.541(+7) 0.611(-12) 0.632(-30) 0.0178Modal control VJ3(qmd=1300, qmv=100)

2 modes 0.522(+3) 0.583(-16) 0.553(-39) 0.0178

1 mode 0.354(-30) 0.502(-28) 0.825(-9) 0.0178Modal control VJT(qmd=600,qmv=500)

2 modes 0.323(-36) 0.510(-27) 0.827(-9) 0.0178


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2.3 Summary of Results

In this study, modal control was implemented to seismically excited structures

using MR dampers. To this end, a modal control scheme was applied together with a

Kalman filter and a low-pass filter. A Kalman filter considered three cases of the

structural measurement to estimate modal states: displacement, velocity, and acceleration,

respectively. Moreover, a low-pass filter was used to eliminate spillover problem. In a

numerical example, a six-story structure was controlled using MR dampers on the lower

two floors. The responses of the system to a scaled El Centro earthquake excitation were

found for each controller through a simulation of the system.

Modal control reshapes the motion of a structure by merely controlling a few

selected vibration modes. Hence, in designing phase of controller, the size of weighting

matrix Q was reduced because the lowest one or two modes were controlled. Therefore, it

is more convenient to design the smaller weighting matrix of modal control. This is one

of the important benefits of the proposed modal control scheme.

The numerical results show that the motion of the structure was effectively

suppressed by merely controlling a few lowest modes, although resulting responses

varied greatly depending on the choice of measurements available and weightings. The

modal controllerA and V achieved significant reductions in the responses. The modal

controllerAJ2, VJ1 and VJ3 achieve reductions (30%, 41%, 30%) in evaluation criteriaJ1,

J2 and J3, respectively, resulting in the lowest values of all cases considered here. The

modal controllerAJT and VJT fail to achieve any lowest value of evaluation criteria, but

have competitive performance in all evaluation criteria. Based on these results, the

proposed modal control scheme is found to be suited for use with MR dampers in a multi-

input control system. Further studies are underway to examine the influence of the

number of controlled modes on the control performance.


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Chapter 3 Maximum Energy Dissipation Algorithm 45

3.1.1 Control Devices

The MR damper with capacity of 1000KN is considered as control devices. To

accurately predict the behavior of controlled structure, an appropriate modeling of MR

dampers is essential. Several types of control-oriented dynamic models have been

investigated for modeling MR dampers. Herein, the Bouc-Wen model is considered. TheBouc-Wen model (Spencer et al, 1997a), which is numerically tractable and has been

used extensively for modeling hysteretic system, is considered for describing the behavior

of the MR damper (Figure 3.1).

Figure 3.1 Mechanical model of the MR damper

The force generated by the damper is given by

xczf &0+= (3.4)

where the evolutionary variablezis governed by

xAzxzzxz nn &&& += |||||| 1 (3.5)

By adjusting the parameters of the model , , n, and A, the degree of linearity in the

unloading and the smoothness of the transition from the pre-yield to the post-yield region


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can be controlled. Some of the model parameters depend on the command voltage u to

the current driver as follows.

uba += and uccc ba 000 += (3.6)

Parameters for both benchmark problems are listed in Table 3.1. Each parameter is

adopted from Yoshida and Dyke (2002) for the nonlinear benchmark building and from

Moon et al. (2003) for the cable-stayed bridge.

Table 3.1 Parameters for MR damper model

Value

ParameterFor non-linear building For cable-stayed bridge

a 1.087e5 N/cm 500 N/m

b 4.962e5 N/(cmV) 671.41 N/(mV)

c0a 4.40 N s/cm 0.15 N s/m

c0b 44.0 N s/(cmV) 1.43 N s/(cmV)

50 s-1

300 s-1

3 cm-2 300 m-2

3 cm-2 300 m-2

A 1.2 120

n 1 1


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3.1.2 Maximum Energy Dissipation Algorithm for MR Damper

This control algorithm is presented as a variation of the decentralized bang-bang

approach proposed by McClamroch and Gavin (1995). Lyapunovs direct approach

requires the use of a Lyapunov function, denoted V(x), which must be a positive definite

function of the states of the system x. In the decentralized bang-bang approach, theLyapunov function was chosen to represent total vibratory energy in the system. Jansen

and Dyke (2000) instead consider a Lyapunov function that represents the relative

vibratory energy in the structure as in

MxxKxxVTT

2

1

2

1+= (3.7)

According to Lyapunov stability theory, if the rate of change of the Lyapunov function

)(xV& is negative semi-definite, the origin is stable in the sense of Lyapunov. Using

(3.7), the rate of change of the Lyapunov function is then

f)MKxxCM(xxKxVTT

++= gx&&&&&& (3.8)

In this expression, the only way to directly effect V& is through the last term containing

the force vectorf. To control this term and make V& as large and negative as possible, the

following control law is obtained:

)(max iii fxHVv &= (3.9)

where i is ith column of the matrix; fi is i th column of the fmatrix.

Note that MEDA is very simple because only local measurements (i.e., the velocity

and control force) are required to implement this control law. In (3.9), there is no design

parameter to decide, which is essential part in other control laws. In other words, complex


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design process can be skipped. This is the important benefit of using MEDA. Otherwise,

the more structures are complex, the more design parameters are considered. Therefore, it

can be said that it is more convenient to use MEDA for structural control, especially for

the large-size civil structures.


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3.2 Benchmark Problems

In this study, we consider two kinds of benchmark problem: a cable-stayed bridge

and a 20-story nonlinear building. The cable-stayed bridge and the high-rise nonlinear

building model are representative structures of civil engineering. Using both benchmark

problems, we exploit MEDA for civil engineering applications. For the completeness, this

section briefly summarizes both benchmark problems, respectively. More details can be

found in Dyke et al (2003) and Ohtori et al (2000, 2002).

3.2.1 Benchmark Cable-Stayed Bridge

At the Second International Workshop on Structural Control (Dec. 18-20, 1996,

Hong Kong), the Working Group on Bridge Control developed plans for a "first

generation" benchmark study on bridges. The cable-stayed bridge used for this

benchmark study is the Missouri 74Illinois 146 bridge spanning the Mississippi River

near Cape Girardeau, Missouri, designed by the HNTB Corporation (Hague, 1997). The

bridge is currently under construction and is to be completed in 2003. Seismic

considerations were strongly considered in the design of this bridge due to the location of

the bridge (in the New Madrid seismic zone) and its critical role as a principal crossing of

the Mississippi River. In early stages of the design process, the loading case governing

the design was deter

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Simple Control Algorithms for MR Dampers and Smart Passive Control System

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