EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS
手工饰品制作
Earthquake Engng Struct.Dyn.(in press)
usherPublished online in Wiley InterScience(www.).DOI:10.1002/eqe.682
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Experimental verification of a wireless nsing and control system for structural control using MR dampers
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Chin-Hsiung Loh1,∗,†,Jerome P.Lynch2,Kung-Chun Lu1,Yang Wang3,
Chia-Ming Chang1,Pei-Yang Lin4and Ting-Hei Yeh1
1Department of Civil Engineering,National Taiwan University,Taipei106-17,Taiwan 2Department of Civil and Environmental Engineering,University of Michigan,Ann Arbor,MI,U.S.A.
3Department of Civil and Environmental Engineering,Stanford University,Stanford,CA,U.S.A.
4National Center for Rearch on Earthquake Engineering,Taipei,Taiwan
SUMMARY
The performance aspects of a wireless‘active’nsor,including the reliability of the wireless communi-cation channel for real-time data delivery and its application to feedback structural control,are explored in this study.First,the control of magnetorheological(MR)dampers using wireless nsors is examined. Second,the application of the MR-damper to actively control a half-scale three-storey steel building ex-cited at its ba by shaking table is studied using a wireless control system asmbled from wireless active nsors.With an MR damper installed on eachfloor(three dampers total),structural respons during ismic excitation are measured by the system’s wireless active nsors and wirelessly communicated to each other;upon receipt of respon data,the wireless nsor interfaced to each MR damper calculates a desired control action using an LQG controller implemented in the wireless nsor’s computational core. In this system,the wireless active nsor is responsible for the reception of respon data,determination of optimal control forces,and the issuing of command signals to the MR damper.Various control solu-tions are formulated in this study and embedded in the wireless control system including centralized and decentralized control algorithms.Copyright2007John Wiley&Sons,Ltd.
Received17January2007;Accepted17January2007
KEY WORDS:wireless active nsor;LQG control algorithm;MR-damper;decentralized control
∗Correspondence to:Chin-Hsiung Loh,Department of Civil Engineering,National Taiwan University,Taipei106-17, Taiwan.
†E-mail:u.edu.tw
Contract/grant sponsor:National Science Council;contract/grant numbers:NSC94-2625-Z-002-031,NSC95-2221-E-002-311
Contract/grant sponsor:National Science Foundation;contract/grant number:CMS-0528867
Contract/grant sponsor:Office of Naval Rearch
Copyright2007John Wiley&Sons,Ltd.
C.-H.LOH ET AL.
1.INTRODUCTION
For the installation of mi-active control devices(magnetorheological(MR)dampers)in structures,
extensive lengths of wires are often needed to connect nsors(to provide real-time state feedback)
with a controller where control forces are calculated.In contrast to this classical approach,wireless
nsors can be considered for controlling structures.In order to reduce the monetary and time
expens associated with the installation of wire-bad systems,the emergence of new embedded
np是什么意思system and wireless communication technologies have been adopted in academia and industry for
wireless monitoring.The u of wireless communications within a structural health monitoring
(SHM)data acquisition system was illustrated by Strar and Kiremidjian[1].More recently,
Lynch et al.have extended upon this work by embedding damage identification algorithms into
the wireless nsors[2]and have proven the reliability of the system in harshfield conditions [3–5].While the advantages of using wireless nsors for SHM have been verified in the structural monitoring area,many challenges must still be explored in greater detail before they can be adopted
for structural control.
To dissipate hysteretic energy and to indirectly apply control forces to a civil structure,mi-
active control devices,like MR dampers,have been developed and applied to various structures
in recent years[6–12].The voltage-dependent nonlinear hysteretic behaviour allows MR dampers
to be veryflexible in resisting different levels of external force.A number of control studies
have thoroughly investigated and modelled the command–force relationships for MR dampers[6].
Several analytical and experimental studies focusing upon the ismic protection of structures
using MR dampers have also been published[13,14].An inclusive goal of this study is to further
validate the effectiveness of MR dampers in the application of structural control.A prototype
wireless structural nsing and control system has been previously propod[15]for structural
respon mitigation.The software written to operate the wireless nsors under the real-time
requirements of the control problem is prented in detail herein.The promising performance
of wireless communication and embedded computing technology within a real-time feedback
structural control system is offered.
This paper prents the experimental verification of using both fully centralized control and
fully decentralized control strategies within a structural control system asmbled from mi-
active control devices(MR dampers)and a wireless nsor network consisting of wireless nsors
capable of actuation.An almost full-scale three-storey steel building with MR dampers installed
upon eachfloor of the structure is tested by applying ba motion using a six degree-of-freedom
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(DOF)shaking table.Structural respons are measured during ismic excitation by the wireless
nsors and wirelessly communicated to wireless nsors interfaced to the system’s MR damper.
Embedded within each wireless nsor’s computational core is linear quadratic Gaussian(LQG)
control solution.Specifically,the following two major rearch directions are emphasized in this
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study:
托福必备词汇1.The theoretical basis for fully centralized and fully decentralized control algorithms is offered
for implementation within a wireless structural control system.
2.Experimental verification of wireless communications for real-time structural control is made
and comparison of the control performance of the wireless control system is compared to
that of a traditional tethered control system.
Copyright2007John Wiley&Sons,Ltd.Earthquake Engng Struct.Dyn.(in press)
EXPERIMENTAL VERIFICATION OF A WIRELESS SENSING AND CONTROL SYSTEM
2.FORMULATION OF THE CONTROL PROBLEM
The equation of motion for a building control system can be expresd as the state-space formula-tion.If a large-scale simulation of the structure is conducted using thefinite element formulation, there would be many DOFs of the structure.However,to simplify the analysis of the system,a reduced-orde
r dynamic model of the system is pursued.In this study,the reduced-order model is derived bad upon a lumped mass system with lateral DOFs.The discrete-time reprentation of the reduced-order state-space equations can be reprented as
z d[k+1]=A d z d[k]+B d u[k]+E d¨x g[k]
y d,s[k]=C d z d[k]+D d¨x g[k]+F d u[k]
(1)
where z d[k]is the reduced-order state vector in discrete time,A d is the system matrix,B d is the matrix transformed from the continuous-time b matrix and E d is related to the inertial distribution vector.The measurement output,y d,s,consists of C d,D d,and F d matrices.In general, measurements such as displacement,velocity,and acceleration respons,can be chon arbitrarily as the system output.In this particular study,the reduced-order model is a three DOF lump mass shear structure model;two different control algorithms(centralized and decentralized)will be derived using the model and absolute acceleration measurements as feedback.
2.1.Fully centralized control of structural system
For fully centralized control,the entire structural system and all system outputs are available for the calculation of optimal control forces.Every control force is calculated as a function of the full state vector,z d.Since the full-state cannot be practically acquired in current structural control systems,the Kalman estimator is ud to transform the measured output vector of the system into an estimated state vector.The estimated state respon is then ud by the control system to calculate the control forces bad upon a linear gain matrix,G.Such an approach to feedback control is termed LQG regulation and bad upon H2control theory[16].The linear gain matrix is found by minimizing a global objective function defined as
J=
k→∞
k=initial time
collided
z T d[k]Qz d[k]+u T[k]Ru[k](2)
where Q and R are positive definite matrices that achieve a relative weighting between the system respon and the control effort needed to attain the respon,respectively.Minimization of the J funct
ion when constrained by the equation of motion of the system,the following Ricatti equation is derived:
A T d PA d−A T d P
B d(2R+B T d PB d)−1B T d PA d+2Q=P(3) The Ricatti equation is ud to calculate the Ricatti matrix,P,which is an integral component of the determination of the control force at the k th time step
u[k]=−(2R+B T d PB d)−1B T d PA d z d[k]=Gz d[k](4) Copyright2007John Wiley&Sons,Ltd.Earthquake Engng Struct.Dyn.(in press)
C.-H.LOH ET AL.
where G is the control gain(it should be noted that the gain matrix,G,will have dimension 3×6in this ca study).As is evident from Equation(4),the control force is calculated from the full-state vector.Considering the limited number of nsors in the structure that constitute the system output,y d,a Kalman estimator is adopted to estimate the full-state respon,ˆz d,bad upon the system output
z
d[k+1]=A d z d[k]+B d u[k]+L(y d,s[k]−C d z d[k]−F d u[k])(5) Here,L is the solution of the Ricatti equation corresponding to the Kalman estimator formulation [17].The control force can then be replaced by the following form:
u[k+1]=Gz d[k+1]=G(A d+B d G−LC c−L F d G)z d[k]+G Ly d[k]
=GˆA csˆz[k]+G L ms y[k](6)
whereˆA cs is the modified system matrix in relation to control and L ms is the Kalman estimator in relation to the system measurements.As en in Equation(6),the control force is generated using the full-state respon vector.Since each actuator(which corresponds to each row of the gain matrix)requires the full-state respon to determine its control action,this control approach assumes a fully centralized control architecture.
2.2.Fully decentralized control of structural system
Fully decentralized control emphasizes control of the local sub-system only using the sub-system’s actuators and nsor measurements.It is to mitigate the respon of the structure using limited information(partial state information)and independent controllers corresponding to sub-systems of th
e global structure.The control force generated by a sub-system controller would inherently be independent from tho of the other sub-systems.A main advantage of decentralized control architectures is that sub-system controllers are independent;the malfunction of an individual controller will not cau the failure of whole control system.In exchange for the reliability offered by decentralized control methods is that their control performance is below that of their centralized counterparts.Within the structural control community,a number of rearchers have explored decentralized approaches to the complex control problem[11,12].
To formulate a decentralized control solution,the discrete-time state-space equation is
rewritten as
z d[k+1]=A d z d[k]+英语口语培训哪家好
(B d)i u i[k]+E d¨x g[k]
(y d,s)j[k]=(C d)j z d[k]+(D d)j¨x g[k]+
(F d)j,i u i[k]
(7)
where‘j’indicates j th sub-system and‘I’indicates i th locations of actuator,and y j indicates the measured output of the j th sub-system of the measurement system.Let it be assumed that for each sub-system,there is one control actuator which applies a control force.The control force of the i th actuator is denoted as u i and its control action eks to minimize the following objective function:
J i=
k→∞
k=initial time
z T d[k]Qz d[k]+u T i[k] Ru i[k](8)
Copyright2007John Wiley&Sons,Ltd.Earthquake Engng Struct.Dyn.(in press)
EXPERIMENTAL VERIFICATION OF A WIRELESS SENSING AND CONTROL SYSTEM Here, R is a scalar weighting term and may be different for each actuator depending upon the objectives of the specific actuator.The number of objective functions is the same as the number of sub-systems defined in the global structure.
Consider a three-storey structure where eachfloor is considered a sub-system within the control system.If an actuator and nsor(measuring acceleration)are collocated upon eachfloor of the structure,eachfloor can be considered its own sub-system.Provided three sub-systems,the global state-space equation and the measurement output equations corresponding to each floor)can be written as follows:
z d[k+1]=A d z d[k]+
3
i=1
(B d)i u i[k]+E d¨x g[k]
y1[k]=(C d,1)1×6z d[k]+(D d,11)1×1u1[k]+
3
j=2
(D d,1j)1×1u j[k]+(F d,1)1×1¨x g[k]
y2[k]=(C d,2)1×6z d[k]+(D d,22)1×1u2[k]+
j=1,3
(D d,2j)1×1u j[k]+(F d,2)1×1¨x g[k]
y3[k]=(C d,3)1×6z d[k]+(D d,33)1×1u3[k]+
2
j=1
(D d,3j)1×1u j[k]+(F d,3)1×1¨x g[k]
(9)
Here,the matrix(C d,1)1×6corresponds to thefirst row(with dimensions1×6)of the discrete-time matrix C d of Equation(4);the other matrix notations follow the same convention.The objective function,J i,for the i thfloor can be written for all threefloors as
J1=∞
k=0
z T d[k]Q6×6z d[k]+u T1[k] R1×1u1[k]
J2=∞
k=0
z T d[k]Q6×6z d[k]+u T2[k] R1×1u2[k]
J3=∞
k=0
z T d[k]Q6×6z d[k]+u T3[k] R1×1u3[k]
(10)
Each objective function will derive an optimal gain matrix that corresponds to the objectives of the sub-system actuator.The Ricatti equation derived from the i th sub-system objective function can be prented as
A T d PA d−A T d P(
B d,i)6×1(2 R1×1+B T d P(B d,i)6×1)−1(B d,i)T6×1PA d+2Q=P(11) Bad upon the solution of the Ricatti equation,the control gain of the sub-system can be described as
u i[k]=−(2 R+B T d,i PB d,i)−1B T d,i P A(z d)i[k]=G1×6(z d)i[k](12) It should be noted that the gain matrix relating the full-state respon to the i th control force,u i, has the dimensions of1×6.To maintain the fully decentralized architecture,the communication of respon data between the sub-systems does not occur.Therefore,a Kalman estimator is ud to estimate the full-state respon,ˆz d,bad upon the measured system output
( z d)i[k+1]=A d z d[k]+(B d)i u i[k]+L j((y d,s)j[k]−(C d)j( z d)i[k]−(F d)j,i u i[k])(13) Copyright2007John Wiley&Sons,Ltd.Earthquake Engng Struct.Dyn.(in press)
C.-H.LOH ET AL.
If control force of Equation(12)is substituted into Equation(13),the estimator can be rewritten as
( z d)i[k+1]=(A d+(B d)i G i−L j(C d)j−L j(F d)j,i G i)( z d)i[k]+L j(y d,s)j[k](13a) here subscript i indicates the full state estimated by the i th sub-system Kalman estimator.The estimated full state is t
hen ud to determine the optimal control force to be applied by the sub-system actuator
u i[k+1]=G i( z d)i[k+1](14)
3.THE EXPERIMENTAL SET-UP
3.1.Test structure
A three-storey half-scale steel structure is designed and constructed at the National Center for Rearch on Earthquake Engineering(NCREE)in Taipei,Taiwan.As shown in Figure1,the three-storey structure consists of a single bay with a3m×2mfloor area and3m tall stories. The structure is constructed using H150×150×7×10steel I-beam elements with each beam–column joint designed as a bolted connection.Concrete blocks are added and fastened to the floor diaphragms until the total mass of eachfloor is precily6000kg.The entire structure is constructed upon a large-scale NCREE shaking table capable of applying ba motion in six independent DOFs.The structural behaviour is modelled using a lumped mass shear structure reduced-order structural model defined by three he lateral displacement of eachfloor). Bad on the respon of the bare frame,the damping and stiffness matrices of a reduced-order model were identified using system identification techniques.The identified natural frequencies
corresponding to thefirst three modes of the structure are1.08,3.25,and5.06Hz,
respectively.
Figure1.Benchmark structure for structural control rearch.
Copyright2007John Wiley&Sons,Ltd.Earthquake Engng Struct.Dyn.(in press)
