DECENTRALIZED WIRELESS SENSING AND CONTROL OF CIVIL STRUCTURES

Transcription

1 Smart Structures an Systems, submitte for publication, 2007 DECENTRALIZED WIRELESS SENSIN AND CONTROL OF CIVIL STRUCTURES Yang Wang a, R. Anrew Swartz b, Jerome P. Lynch b, Kincho H. Law a, Kung-Chun Lu c, Chin-Hsiung Loh c a Dept. of Civil an Environmental Engineering, Stanfor Univ., Stanfor, CA 94305, USA b Dept. of Civil an Environmental Engineering, Univ. of Michigan, Ann Arbor, MI 48109, USA c Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan * Corresponence Author: Prof. Kincho H. Law Department of Civil an Environmental Engineering Stanfor University Stanfor, CA , USA Tel. (650) Fax. (650) law@stanfor.eu ABSTRACT This paper iscusses the potential use of wireless communication an embee computing technologies for structural control applications. Specifically, control strategies base on linear quaratic regulator (LQR) algorithms are explore to assess the issues an performance for a prototype wireless structural sensing an control system. The system computes control ecisions base on ecentralize output feeback. The performance of this prototype system is first valiate in shake table experiments using a half-scale three-story steel structure instrumente with three magnetorheological ampers, which are commane by the prototype wireless sensing an control units. The experiments valiate the effectiveness of the ecentralize output feeback control algorithm. Further numerical simulations are conucte using the structural moels of a 5-story an a 20-story structure controlle by ieal actuators an semi-active hyraulic ampers. The simulation analyses are intene to stuy the effects of communication latencies an egrees of centralization on control performance. Experimental an numerical results emonstrate that ecentralize wireless control is viable for future structural control systems. Keywors: structural control, wireless communication, embee computing, ecentralize control, output feeback control.

2 Smart Structures an Systems, submitte for publication, 2007 INTRODUCTION For the past three ecaes, significant research an evelopment have been conucte in the fiel of structural control to mitigate excessive responses (Soong an Spencer 2002, Chu et al., 2005). Structural control systems can be categorize into three major types: (a) passive control (e.g. base isolation), (b) active control (e.g. active mass ampers), an (c) semi-active control (e.g. semi-active variable ampers). Passive control systems, e.g. base isolators, entail the use of passive energy issipation evices to control the response of a structure without the use of sensors an controllers. Active control systems use a small number of large ampers or actuators for irect application of control forces. In a semi-active control system, control evices are use for inirect application of control forces. Semi-active control is currently preferre over active control because it can achieve at least an equivalent level of performance, consumes orers of magnitue less power, an provies higher level of reliability. Examples of semi-active actuators inclue active variable stiffness (AVS) evices, semi-active hyraulic ampers (SHD), electrorheological (ER) ampers, an magnetorheological (MR) ampers. Aitional avantages associate with semi-active control inclue aaptability to real-time excitation, inherent Boune Input/Boune Output (BIBO) stability, an invulnerability against power failure. The shift from active control to semi-active control evices, which are smaller, less costly an more energy-efficient, will lea to the potential eployment of larger quantities of evices in a structure. In a semi-active control system, sensors are eploye in the structure to collect structural response ata uring ynamic excitation. Response ata is then fe into controllers to etermine require actuation forces an to apply control commans to system actuators. Commane by control signals, the actuators can generate control forces intene to mitigate unesirable structural responses. In traitional semi-active control systems, coaxial wires are normally use to provie communication links between sensors, actuators an controllers. With the rapi emergence of wireless

3 Smart Structures an Systems, submitte for publication, 2007 communication an embeing computing technologies, there have been extensive stuies towars the evelopment of wireless sensing technologies for structural monitoring applications (Straser an Kiremijian 1998, Lynch an Loh 2006, Wang et al. 2007a). The aoption of wireless sensing technologies can remey the high installation cost of commercial cable-base ata acquisition (DAQ) systems, which can cost up to a few thousan ollars per sensing channel (Celebi 2002). A natural extension of the wireless sensing technology, as it matures, is to explore its applicability for semiactive or active control evices by eraicating cables associate with traitional control systems, which may result in substantial cost in installation time an expense (Solomon et al. 2000). Extening the functionalities of a wireless sensor by incluing an actuation interface, the authors have evelope a prototype wireless sensing an control system an explore the application to real-time feeback control in a laboratory setting (Wang et al. 2006, Wang et al. 2007b). When replacing wire communication channels with wireless ones for feeback structural control, issues such as coorination of sensing an control units, communication range, time elay an potential ata loss nee to be examine. Time elay ue to wireless communication will cause egraation of the realtime performance of a control system (Lynch an Tilbury 2005). The time elay problem is common for any istribute network control systems, regarless of using wire or wireless communication (Lian et al. 2002). Decentralize control strategies may potentially resolve some of the ifficult issues (Sanell et al. 1978, Siljak 1991, Lynch an Law 2002). In ecentralize control, the control problem is ivie into a collective set of smaller, istribute control sub-systems. Controllers assigne to a subsystem require only local an neighboring sensor ata to make control ecisions. In a wireless network, this leas to reuce use of the communication channel an results in higher control sampling rates. Shorter communication ranges may also enable more reliable ata transmissions. Control computations can be performe in parallel using wireless sensors in ecentralize control architectures. However, ecentralize control may only achieve sub-optimal control performance when comparing to centralize control, because each subsystem only has local an neighboring sensor information to make control ecisions. The purpose of this work is to examine the effectiveness of ecentralize wireless sensing an control.

4 Smart Structures an Systems, submitte for publication, 2007 In this stuy, a linear quaratic regulator (LQR) feeback control algorithm is employe for both experimental an numerical simulations. A ecentralize LQR control algorithm taking into consieration of time elays is first introuce. Experimental results from large-scale shake table structural control experiments conucte on a 3-story steel frame structure installe with MR ampers using a prototype wireless sensing an control system are then briefly reviewe (Wang et al. 2007b). The purpose of the experiments is to assess the viability of a wireless sensing an control system, an the performance of ifferent ecentralize an centralize control schemes. To further examine the issues involve in ecentralize control an communication time elays, numerical simulations are conucte using a 5-story an a 20-story structural moel controlle by ieal actuators an semi-active hyraulic ampers (SHD) (Kurata et al. 1999). LQR CONTROL ALOIRTHMS WITH TIME-DELAY USIN OUTPUT FEEDBACK A linear quaratic regulator (LQR) output feeback control algorithm that takes into consieration of time elay is summarize below. Consier a lumpe-mass structural moel with n egrees-offreeom (DOF) an m actuators. The system state-space equations consiering l time steps of elay can be state as: z [ k+ 1] = A z [ k] + B p [ k l], where z [ k] [ k] [ k] x = x (1) In Eq. (1), z [ k] an [ k l] p represent, respectively, the 2n 1 iscrete-time state-space vector at time k an the m 1 control force vector with time elay. The matrices A an B are the 2n 2n system matrix an the 2n m actuator location matrix, respectively. The objective to minimize a cost function J:

5 Smart Structures an Systems, submitte for publication, 2007 T T ( [ ] [ ] [ ] [ ]) 2 2 J = z k Qz k + p k l Rp k l, where Q 0 an R > 0 (2) p k= l n n m m by selecting an optimal control force trajectory p. Let the system output be enote by a q 1 system vector y [ k] measure at time k. The state-space vector z [ k] an output vector [ k] relate by a q 2n linear transformation, D, that is: y can be [ k] = [ k] y D z (3) The optimal output feeback control force p can be compute using an m q gain matrix as: [ k] = [ k] p y (4) where the gain matrix is esigne so that the cost function J is minimize. For the output feeback control problem with time elay (say, l time steps), Chung et al. (1995) propose a solution by introucing a moifie first-orer ifference equation: [ k + 1] = [ k] + [ k] z A z B p (5) This moifie first-orer ifference system is equivalent to the original system (Eq. 1) by proper efinitions of the augmente matrices an vectors: A I A = 0 I 0 0, 0 0 I 0 B 0 B = 0 0, z [ k] [ k] [ k 1], [ k] = [ k l] z z = z [ k l] p p (6)

6 Smart Structures an Systems, submitte for publication, 2007 where 0 an I represent, respectively, the zero an ientity submatrices of proper imensions. Corresponingly, the weighting matrix in Eq. (2) an the output matrix in Eq. (3) are also augmente an enote by Q an D, respectively, as: Q Q = , D = [ D ] (7) In orer to make the optimization problem inepenent of the initial state, z [ l], which contains the state space vectors z [0],, z [l], is consiere as a ranom vector. The esign objective is altere to minimize the expecte value of the original cost J: J = E{ J} (8) where E{ i } enotes the expectation. Let initial state: Z l represent the secon statistical moment of the augmente { [ ] T [ ]} Zl = E z l z l (9) It can be shown that by introucing an auxiliary matrix H, the expecte cost is equivalent to (Chung et al 1995): T { [ ] [ ]} { [ ]} J = E z l Hz l = trace HZ l (10)

7 Smart Structures an Systems, submitte for publication, 2007 In practice, it is generally assume that initial state [ l] z is a ranom variable uniformly istribute on the surface of the unit sphere, i.e. Zl = I. Finally, the control problem with time elay can be pose as solving the following nonlinearly couple matrix equations: T T T ( ) ( ) ( ) A + BD HA + BD H+ Q+ D RD = 0 (11a) ( ) ( ) T l A + B D L A + B D L+ Z = 0 (11b) ( ) T T T 2B H A + B D LD + 2R D LD = 0 (11c) where is the optimal output feeback gain matrix, L is the Lagrangian matrix an H is an auxiliary matrix. Details on the erivation of the time-elay optimal control solution have been escribe by Chung et al. (1995). In this stuy, an iterative algorithm escribe by Lunze (1990) is employe for the time elay problem. Furthermore, the algorithm is moifie for ecentralize control by constraining the structure of the gain matrix to be consistent with the ecentralize architecture. As shown in Fig. 1, the iterative algorithm starts from an initial estimate for the gain matrix. Within each iteration step i, the matrix H i an L i are solve respectively using the current estimate of the gain matrix i. Base on the H i an L i matrices compute, a search graient i is calculate an the new gain matrix i+ 1 is compute by traversing along the graient from i. An aaptive multiplier, s, is use to ynamically control the search step size. At each iteration step, two conitions are use to ecie whether i+ 1 is an acceptable estimate. The first conition is trace( Hi+ 1Z l) < trace( HZ i l) which guarantees that i+1 is a better solution than i eigenvalues of the matrix ( + i+1 ) augmente system. To fin the gain matrix. The secon conition is that the maximum magnitue of all the A B D nees to be less than 1 to ensure the stability of the that is consistent with the ecentralize architectural constraints, the graient matrix i compute using Eq. 11c is moifie by zeroing out those entries

8 Smart Structures an Systems, submitte for publication, 2007 which correspon to the zero terms in the ecentralize output feeback gain matrix. The iteration then procees to compute the next estimate i+ 1 by traversing along this constraine graient. A PROTOTYPE WIRELESS STRUCTURAL SENSIN AND CONTROL SYSTEM The prototype wireless sensing an control system is built upon the previous evelope wireless sensing unit esigne for structural sensing an monitoring applications (Wang et al. 2005, 2007a). The wireless sensing unit consists of three basic functional moules: the sensor signal igitizer, the computational core, an the wireless transceiver (see Fig. 2a). A simple two-layer printe circuit boar (PCB) is esigne for the wireless sensing unit, which, incluing the batteries, fits within an 10.2cm by 6.5cm by 4.0cm off the shelf weatherproof plastic container (see Fig. 2b). To exten the functionality of the wireless sensor for actuation, an off-boar control signal generation moule (Fig. 2c) is esigne an fabricate. A separate 5.5cm by 6.0cm PCB is esigne for the control signal generation moule which consists of a single-channel 16-bit igital-to-analog converter (Analog Device AD5542) an other support electronics. As shown in Fig. 2, the control signal moule is attache to the wireless sensing unit via two multi-line wires one for analog signals an the other one for igital signals. The moule can output an analog voltage from -5V to 5V at rates as high as 100 khz. Detaile esign of the wireless sensing an control unit an the control signal generation moule has been escribe by Wang et al. (2006, 2007b). To stuy the potential application of the wireless sensing an control system for structural control, valiation tests on a 3-story frame structure instrumente with MR ampers are conucte at the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan (see Fig. 3). This section first introuces the experimental setup, an then presents the test results. The three-story steel frame structure has a 3m by 2m floor plan, 3m inter-story height, an a weight ajuste to 6,000 kg per each floor using concrete blocks. Both the beams an the columns of the structure are

9 Smart Structures an Systems, submitte for publication, 2007 constructe with H steel I-beam elements. The three-story structure is mounte on a 5m 5m 6-DOF shake table. For this stuy, only longituinal excitations are use. Along this irection, the shake table can excite the structure with a maximum acceleration of 9.8m/s 2. The test structure is heavily instrumente with accelerometers, velocity meters, an linear variable isplacement transucers (LVDT) installe on each floor of the structure to measure the ynamic response. These sensors are interface to a high-precision wire-base ata acquisition (DAQ) system resie at the NCREE facility; the wire-base DAQ system is set to a sampling rate of 200 Hz. The basic architecture of the prototype wireless sensing an control system is schematically shown in Fig. 3a. Wireless sensors an controllers are mounte on the structure for measuring structural response ata an commaning the actuators in real-time. In aition to the wireless sensing an control units, a remote ata an comman server with a wireless transceiver is inclue as an optional element responsible for logging the flow of wireless ata. During an experimental test, the comman server first notifies the wireless sensing an control units to initiate automate operations. Once the start comman is receive, the wireless units that are responsible for collecting sensor ata start acquiring an broacasting ata at a specifie time interval. Accoringly, the wireless units responsible for commaning the actuators receive the sensor ata, calculate esire control forces in real-time, an apply control commans at the specifie time interval. For this experimental stuy, three 20 kn MR ampers are installe with V-braces on each story of the steel structure (Fig. 3c). The amping coefficients of the MR ampers can be change by issuing a comman voltage between 0V to 1.2V. This comman voltage etermines the electric current of the electromagnetic coil in the MR amper, which in turn, generates a magnetic fiel that sets the viscous amping properties of the MR amper. Calibration tests are first conucte on the MR ampers before mounting them to the structure so that moifie Bouc-Wen amper moels can be formulate for each amper (Lin et al. 2005). In the real-time feeback control tests, hysteresis moel parameters for the MR ampers are an integral element in the calculation of amper actuation voltages. For

10 Smart Structures an Systems, submitte for publication, 2007 wireless sensing an control, a separate wire is use to output the appropriate voltage from the offboar control generation moule to comman the MR ampers (see Fig. 3). For the wireless system, a total of four wireless sensors are installe, following the schematic shown in Fig. 3(a). Each wireless sensor is interface to a Tokyo Sokushin VSE15-D velocity meter to measure the absolute velocity response for each floor of the structure as well as the base. The sensitivity of this velocity meter is 10V/(m/s) with a measurement limit of ±1 m/s. The three wireless sensors on the first three levels of the structure (C 0, C 1, an C 2 ) are also responsible for commaning the MR ampers. Besies the wireless control system, a traitional wire-base control system is installe in the structure for comparative tests. Centralize an ecentralize velocity feeback control schemes are use for the wire an the wireless control systems. For the centralize control tests, the output vector inclues the relative velocities (but not the relative isplacements) on all floors with respect to the groun; the output matrix, D, thus has the form: [ ] D = 0 I (12) For ecentralize control tests, the inter-story velocities between ajacent floors are efine as the output vector, an the output matrix D is set to have the form: D [ 3 3] = 0 (13) Furthermore, to represent a fully ecentralize, partially ecentralize an centralize control schemes, the output feeback gain matrices for the 3-story test structure are constraine to the following respective patterns:

11 Smart Structures an Systems, submitte for publication, 2007 * 0 0 * * 0 * * * = 0 * 0, = 0 * * 1 2 an 3 * * * = (14) 0 0 * 0 * * * * * When combine with the output matrix D efine in Eq. (12) or (13), the pattern in 1 specifies that when computing control ecisions, the actuator at each floor only nees the entry in the output vector y corresponing to that floor. The pattern in 2 specifies that the control ecisions require information from a neighboring floor. Finally, the pattern in 3 inicates all entries in the output vector participate in the centralize control ecisions. Table 1 summarizes the ifferent patterns of the gain matrix, the output matrices D, an the achievable sampling times for the centralize, partially ecentralize an fully ecentralize control strategies (which are enote by egrees of ecentralization, 3, 2 an 1, respectively). For this test structure, the wire-base system can achieve a sampling rate of 200Hz, or a time step of 0.005s. Mostly ecie by the communication latency of the 24XStream wireless transceivers, the wireless system can achieve a sampling rate of 12.5Hz (or a time step of 0.08s) for the centralize control scheme. This sampling rate is ue to each wireless sensor waiting in turn to communicate its ata to the network (about 0.02s for each transmission). An avantage of the ecentralize architecture is that fewer communication steps are neee, thereby reucing the time for wireless communication. To ensure that appropriate control ecisions are compute by the wireless control units, one necessary conition is that the real-time velocity ata use by the control units are reliable. Rarely experiencing ata losses uring the experiments, our prototype wireless sensor network proves to be robust. In case ata loss happens, the wireless control unit is currently esigne to simply use a previous ata sample. For the experimental results presente herein, the groun excitation is the 1940 El Centro NS earthquake recor (Imperial Valley Irrigation District Station) scale to a peak groun acceleration of 1m/s 2. To illustrate the performance of ifferent ecentralize schemes with ifferent communication

12 Smart Structures an Systems, submitte for publication, 2007 latencies, the same groun excitation is applie to the original uncontrolle structure an the structure controlle by the four ifferent wireless an wire control schemes as efine in Table 1. Fig. 4 illustrates the structure s peak inter-story rifts an floor accelerations uring these experimental runs. Compare with the uncontrolle structure, all wireless an wire control schemes achieve significant reuction with respect to maximum inter-story rifts an absolute accelerations. Among the four control cases, the wire centralize control scheme shows better performance in achieving the least peak rifts an secon least overall peak accelerations. This result is rather expecte, because the wire system has the avantages of lower communication latency an utilizes complete sensor ata from all floors. The wireless schemes, although running at longer sampling steps, achieve control performance comparable to the wire system. The fully ecentralize wireless control scheme (case #1), results in uniform peak inter-story rifts an the least peak floor accelerations. This illustrates that in the ecentralize wireless control cases, the higher sampling rate (from lower communication latency) can potentially compensate the loss of ata from ignoring the sensor ata from faraway floors. NUMERICAL SIMULATIONS ON DECENTRALIZED STRUCTURAL CONTROL With encouraging results from the experimental tests, further investigations of the ecentralize output feeback control strategies are performe with numerical simulations. Specifically, ifferent ecentralization patterns an sampling time elays are being investigate for two structural moels, namely a 5-story Kajima-Shizuoka builing (Kurata et al 1999) an a 20-story benchmark structure esigne for the Structural Engineers Association of California (SAC) project (Spencer et al 1998). Numerical simulation results are performe for the cases when the structures are instrumente with ieal actuators that are capable of proucing any esire forces an with semi-active hyraulic ampers (SHD). The actuators are installe as a V-brace on each floor of the structures (see Fig. 5). For the SHD ampers, the Maxwell element propose by Hataa et al. (2000) is employe to moel the amping force an is escribe by the following ifferential equation:

13 Smart Structures an Systems, submitte for publication, 2007 keff p () t + p() t keff x() t c () t = (15) SHD where p(t) an x() t enote the amping force an the inter-story velocity, respectively, k eff represents the effective stiffness of the amper in series with the V-brace, an c () t is the ajustable amping coefficient of the SHD amper. If the esire amper force is in an opposite irection to the interstory velocity, as shown in Fig. 5, the amping coefficient is ajuste so that a amper force closest to the esire force is generate. If the esire force is in the same irection to the inter-story velocity, the amping coefficient is set to its minimum value. SHD DECENTRALIZED STRUCTURAL CONTROL SIMULATIONS OF A 5-STORY BUILDIN A five-story moel similar to the Kajima-Shizuoka Builing is employe (Kurata et al., 1999). The steel-structure builing has a total height of about 19m (Fig. 6). For this stuy, two semi-active hyraulic ampers (SHD) are installe at each floor. In the numerical simulations, it is assume that both the inter-story isplacement an inter-story velocity relative to the lower floor are measurable. Similarly, the state-space system is formulate such that the state-space vector contains inter-story isplacements an inter-story velocities, rather than the isplacements an velocities relative to the groun. In orer to reflect this requirement on sensor ata, the output matrix D is efine to be a 2n 2n ientity matrix. The simulations are conucte for ifferent egrees of centralization (DC), as illustrate in Fig. 6(b); the case where DC equal to i represents that the neighboring i floors constitute a communication subnet an share their sensor ata. For example, the case where DC=1 implies each group consists of only one floor. For the case where DC=3, each group consists of three floors, resulting in 3 wireless subnets for the 5 story builing. For DC=5, all 5 floors share their sensor ata, resulting in a centralize information architecture. Base on the above efinitions for output matrix D an egrees of centralization, the

14 Smart Structures an Systems, submitte for publication, 2007 gain matrix consists of two square submatrices with the same symmetric shape constraints. In each square submatrix, the iagonal entries an the j th (j = 1,.., i-1) entry above an below the iagonal entry are non-zero. For example, when DC = 2, the gain matrix has the following shape constraint: * * * * * * * 0 0 * * * * * * 0 0 * * * 0 = (16) 0 0 * * * 0 0 * * * * * * * 510 The left submatrix an the right submatrix correspon to the isplacement part an the velocity part, respectively, of the output vector y. The various combinations of centralization egrees (1 through 5) an sampling time steps ranging from 0.005s to 0.06s (at a resolution of 0.005s) are simulate. Four groun motion recors are use for each simulation: the 1940 El Centro NS recor (Imperial Valley Irrigation District Station) scale to a peak groun acceleration (PA) of 1m/s 2, the same 1940 El Centro NS recor scale to a PA of 2m/s 2, the 1999 Chi-Chi NS recor (TCU-076 Station) scale to a PA of 1m/s 2, an the 1995 Kobe NS recor (JMA Station) scale to a PA of 1m/s 2. Performance inices propose by Spencer et al. (1998) are aopte. In particular, the two representative performance inices employe are: PI max () t i ti, 1 = max Earthquakes max ˆ i () t ti, J LQR, an PI2 = max Earthquakes Jˆ LQR (17) Here PI 1 an PI 2 are the performance inices corresponing to inter-story rifts an LQR cost inices, respectively. In Eq. (17), () t represents the inter-story rift between floor i (i = 1,, 5) an its i lower floor at time t, an max i () t is the maximum inter-story rift over the entire time history an ti, among all floors. The maximum inter-story rift is normalize by its counterpart max ˆ i () t, which is the maximum response of the uncontrolle structure. The largest normalize ratio among the ti,

15 Smart Structures an Systems, submitte for publication, 2007 simulations for the four ifferent earthquake recors is efine as the performance inex PI 1. Similarly, the performance inex PI 2 is efine for the LQR control inex J LQR, as given in Eq. (2). When computing the LQR inex over time, a uniform time step of 0.001s is use to collect the structural response ata points, regarless of the sampling time step of the control scheme; this allows one control strategy to be compare to another without concern for the ifferent sampling time steps use in the control solution. Fig. 7 an Fig. 8 show the values of the two control performance inices for the 5-story structure instrumente with ieal actuators an SHD ampers, respectively. Different combinations of egrees of centralization an sampling time steps are employe for the simulations. The plots clearly illustrate that the egrees of centralization an sampling steps coul have significant impact on the performance of the control system. enerally speaking, control performance is better for higher egrees of centralization an shorter sampling times. To better review the simulation results, the performance inices for the five ifferent control schemes are also plotte as a function of sampling time. For example, as shown in Fig. 8(c), if a partially ecentralize control system with DC equal to 2 can achieve 0.01s sampling step an a centralize system can only achieve 0.03s ue to aitional communication latency, the partially ecentralize system can result in much lower maximum interstory rifts. Similar trens are observe in Fig. 8() for the LQR performance inices. DECENTRALIZED STRUCTURAL CONTROL SIMULATIONS OF A 20-STORY BUILDIN A 20-story benchmark structure esigne for the Structural Engineers Association of California (SAC) project is also selecte for numerical simulations (Spencer et al.,1998). To simplify the analysis, the builing is moele as an in-plane lumpe-mass structure (Fig. 9). In the numerical simulations, it is assume that both the inter-story isplacements an inter-story velocities between every two

16 Smart Structures an Systems, submitte for publication, 2007 neighboring floors are measurable. The system state-space equations are formulate such that the state-space vector contains inter-story isplacements an velocities, rather than the isplacements an velocities relative to the groun. The output matrix D is efine as a 2n 2n ientity matrix, as in the case of the 5-story structure, so that the state-space vector is use for control feeback irectly. The simulations are conucte for ifferent egrees of centralization (DC), as illustrate in Fig. 9(c). The egrees of centralization reflect ifferent communication network architectures, with each channel representing one communication subnet. The actuators covere within a subnet are allowe to access the wireless sensor ata within that subnet. For example, the case where DC=1 implies each wireless channel covers only five stories an a total of four wireless channels (subnets) are utilize. Of all the ifferent egrees of centralization, the case where DC=1 represents the lowest requirement to the wireless communication range an achieves lowest communication latency as a smaller number of wireless sensors nee to broacast their ata in the subnet. Constraine by this ecentralize information structure, the gain matrix for the case where DC=1 has the following sparsity pattern: ( 1,1) ( 1,5) ( 2,2) ( 2,6) =, when DC 1 ( 3,3) ( 3,7) = ( 4,4) ( 4,8) (18) The left submatrix an the right submatrix correspon to the inter-story isplacement an the interstory velocity components, respectively, of the output vector y. The left an right submatrices are block-iagonal, with every block ( i, j) being a 5-by-5 square matrix. For the case where DC=2, each wireless channel covers ten stories an a total of three wireless channels are utilize. Constraine by the overlapping information structure, the gain matrix for DC=2 has the following sparsity pattern:

17 Smart Structures an Systems, submitte for publication, 2007 ( 1,1) ( 1,2) ( 1,5) ( 1,6) ( 2,1) ( 2,2) ( 2,3) ( 2,5) ( 2,6) ( 2,7) =, when DC 2 ( 3,2) ( 3,3) ( 3,4) ( 3,6) ( 3,7) ( 3,8) = ( 4,3) ( 4,4) ( 4,7) ( 4,8) (19) For the case when DC=3, the number of stories covere by each of the two wireless subnets increases accoringly. That leas to fewer communication subnets an fewer zero blocks in the gain matrices. The case where DC=4 specifies that one wireless channel covers all twenty floors, which results in a centralize information structure. Fig. 10 shows the numerical simulation results for the 20-story structure instrumente with ieal actuators. Various combinations of centralization egrees (DC = 1,,4) an sampling time steps ranging from 0.01s to 0.06s (at a resolution of 0.01s) are simulate. Three groun motion recors are use for each simulation: the 1940 El Centro NS recor (Imperial Valley Irrigation District Station), the 1995 Kobe NS recor (JMA Station), an the 1999 Chi-Chi NS recor (TCU-076 Station), all scale to a peak groun acceleration (PA) of 1m/s 2. The two performance inices introuce in Eq. (17) are plotte in Fig. 10 for ifferent combinations of egrees of centralization an sampling time steps. Similar to the simulations for the 5-story structural moel, when computing the LQR inex over time, a uniform time step of 0.001s is use to collect the structural response ata points, regarless of the sampling time step of the control scheme. enerally speaking, the results are similar to the previous results for the 5-story structure where the control performance is better for higher egrees of centralization an shorter sampling times. The plots show that except for the case where DC=1, the control schemes with certain overlapping information structures achieve comparable performance. As shown in Fig. 10(c), if a partially ecentralize control system with DC equal to 2 can achieve a sampling step of 0.02s an a centralize system can only achieve 0.04s ue to aitional communication latency, the partially ecentralize system can result in lower maximum inter-story rifts. Similar trens are observe in Fig. 10(), except that the plots are smoother ue to the summation process for computing the LQR inices.

18 Smart Structures an Systems, submitte for publication, 2007 Numerical simulations are also conucte for the four control strategies where semi-active hyraulic ampers (SHD) are employe on the structure. The arrangement of SHD ampers is shown in Fig. 9(); the number of instrumente SHD ampers ecreases graually from 4 to 1 in the higher floors. Fig. 11 presents the simulate maximum inter-story rifts when the structure is excite using the same three groun motions, except that the PAs are scale up to 5m/s 2, instea of 1m/s 2. To compare the performance of ecentralize versus centralize control, the case where DC=2 (partially ecentralize) an the case where DC=4 (centralize) are plotte. As shown in Fig. 9, each subnet covers ten floors when DC=2, or twenty floors when DC=4. That is, the inuce time elay when DC=2 is about half of the elay when DC=4, an the time elays of 20ms an 40ms are assigne, respectively, for these two cases. As shown in Fig. 11, both of the two control schemes significantly reuce the maximum inter-story rifts compare with the uncontrolle case. For the Kobe an Chi-Chi groun motions, the partially ecentralize case where DC=2 achieves equivalent performance compare with the centralize case where DC=4, while for the El Centro recor, the case with DC=2 achieves slightly better performance than the case where DC=4. These results illustrate that although ecentralize control has the isavantage of computing control ecisions without complete sensor ata, the lower time elay in ecentralize control coul make the control scheme perform as well as centralize control, given that the centralize case, using wireless communication, requires longer latencies. CONCLUSIONS In this paper, a prototype wireless structural sensing an control system is presente. The performance of the prototype system has been successfully valiate in real-time feeback control experiments using a 3-story steel structure instrumente with MR ampers. The experiments have also shown the potential effectiveness of ecentralize output feeback control. Using the LQR-base ecentralize control algorithm, simulation results are obtaine for a 5-story an a 20-story builing structure instrumente with ieal actuators an SHD ampers, by varying the egrees of centralization an the

19 Smart Structures an Systems, submitte for publication, 2007 sampling time steps of the control system. Both the experimental results an the simulations results emonstrate that ecentralize wireless sensing an control is viable for future structural control systems. It is also illustrate that ecentralize control strategies may provie equivalent or even superior control performance, given that their centralize counterparts coul suffer longer feeback time elay ue to wireless communication latencies. Future research will continue to investigate both the theory an implementation of wireless ecentralize structural control. Besies LQR, other ecentralize control algorithms that may achieve better control performance are worth exploring. Initial progress has been mae in eveloping ecentralize H control algorithms, where ecentralize controllers are esigne to minimize the norm of the close-loop system transfer matrix (Zhou et al. 1996). For implementation, system performance can be greatly improve by employing more powerful embee computing evices, an aopting wireless technologies that have lower communication latency (such as IEEE an stanars). Further wireless structural sensing an control experiments using a larger-scale laboratory structure are being planne to gain better unerstaning of ecentralize control strategies. H ACKNOWLEDMENTS This research is partially fune by the National Science Founation uner grants CMS (Stanfor University), CMS (University of Michigan), an the Office of Naval Research Young Investigator Program aware to Prof. Lynch at the University of Michigan. Aitional support is provie by National Science Council in Taiwan uner rant No. NSC Z The authors wish to thank the two fellowship programs: the Office of Technology Licensing Stanfor rauate Fellowship an the Rackham rant an Fellowship Program at the University of Michigan. This paper is an extension of the article presente at the US-Taiwan Workshop on Smart Structures an Structural Health Monitoring in Taipei, Taiwan, October, 2006; the authors woul like to acknowlege the travel supports provie by the National Science Founation for attening the workshop.

20 Smart Structures an Systems, submitte for publication, 2007 REFERENCES Çelebi, M. (2002). Seismic Instrumentation of Builings (with Emphasis on Feeral Builings). Report No , Unite States eological Survey, Menlo Park, CA. Chu, S.Y., Soong, T.T. an Reinhorn, A.M. (2005), Active, Hybri, an Semi-active Structural Control: a Design an Implementation Hanbook, Wiley, Hoboken, NJ. Chung, L.L., Lin, C.C. an Lu, K.H. (1995). "Time-elay control of structures," Earthq. Eng. Struct. D., 24(5), Hataa, T., Kobori, T., Ishia, M. an Niwa, N. (2000). "Dynamic analysis of structures with Maxwell moel," Earthq. Eng. Struct. D., 29(2), Kurata, N., Kobori, T., Takahashi, M., Niwa, N. an Miorikawa, H. (1999). "Actual seismic response controlle builing with semi-active amper system," Earthq. Eng. Struct. D., 28(11), Lian, F.-L., Moyne, J. an Tilbury, D. (2002). "Network esign consieration for istribute control systems," IEEE T. Contr. Syst. T., 10(2), Lin, P.-Y., Roschke, P.N. an Loh, C.-H. (2005). "System ientification an real application of the smart magneto-rheological amper," Proceeings of the 2005 International Symposium on Intelligent Control, Limassol, Cyprus, June Lunze, J. (1992), Feeback Control of Large Scale Systems, Prentice-Hall, New York. Lynch, J.P. an Law, K.H. (2002). "Decentralize control techniques for large scale civil structural systems," Proceeings of the 20th International Moal Analysis Conference, Los Angeles, CA, February 4-7. Lynch, J.P. an Tilbury, D.M. (2005). "Implementation of a ecentralize control algorithm embee within a wireless active sensor," Proceeings of the 2n Annual ANCRiSST Workshop, yeongju, Korea, July Lynch, J.P. an Loh, K.J. (2006). "A summary review of wireless sensors an sensor networks for structural health monitoring," Shock Vib. Dig., 38(2), Sanell, N., Jr., Varaiya, P., Athans, M. an Safonov, M. (1978). "Survey of ecentralize control methos for large scale systems," IEEE T. Automat. Contr., 23(2), Siljak, D.D. (1991), Decentralize control of complex systems, Acaemic Press, Boston. Solomon, I., Cunnane, J. an Stevenson, P. (2000). "Large-scale structural monitoring systems," Proceeings of SPIE Non-estructive Evaluation of Highways, Utilities, an Pipelines IV, Newport Beach, CA, March 7-9. Soong, T.T. an Spencer, B.F., Jr. (2002). "Supplemental energy issipation: state-of-the-art an stateof-the-practice," Eng. Struct., 24(3), Spencer, B.F., Jr.,, Christenson, R.E. an Dyke, S.J. (1998). "Next generation benchmark control problem for seismically excite builings," Proceeings of the 2n Worl Conference on Structural Control, Kyoto, Japan, June 29 -July 2. Straser, E.. an Kiremijian, A.S. (1998). A Moular, Wireless Damage Monitoring System for Structures. Report No. 128, John A. Blume Earthquake Eng. Ctr., Stanfor University, Stanfor, CA. Wang, Y., Lynch, J.P. an Law, K.H. (2005). "Wireless structural sensors using reliable communication protocols for ata acquisition an interrogation," Proceeings of the 23r International Moal Analysis Conference (IMAC XXIII), Orlano, FL, January 31 - February 3. Wang, Y., Swartz, R.A., Lynch, J.P., Law, K.H., Lu, K.-C. an Loh, C.-H. (2006). "Wireless feeback structural control with embee computing," Proceeings of the SPIE 11th International

21 Smart Structures an Systems, submitte for publication, 2007 Symposium on Nonestructive Evaluation for Health Monitoring an Diagnostics, San Diego, CA, February 26 - March 2. Wang, Y., Lynch, J.P. an Law, K.H. (2007a). "A wireless structural health monitoring system with multithreae sensing evices: esign an valiation," Struct. an Infrastructure Eng., 3(2), Wang, Y., Swartz, R.A., Lynch, J.P., Law, K.H., Lu, K.-C. an Loh, C.-H. (2007b). "Decentralize civil structural control using real-time wireless sensing an embee computing," Smart Struct. Syst., in press. Zhou, K., Doyle, J.C. an lover, K. (1996), Robust an optimal control, Prentice Hall, Englewoo Cliffs, N.J.

22 Smart Structures an Systems, submitte for publication, 2007 Keywors: structural control, wireless communication, embee computing, ecentralize control, output feeback control. LIST OF FIURES AND TABLES Figure. 1. Heuristic algorithm solving the couple nonlinear matrix equations (Eq. 11) for ecentralize optimal time-elay output feeback control (Lunze, 1990). Figure 2. Overview to the prototype wireless sensing an actuation unit: (a) printe circuit boar for the wireless sensing unit ( cm 2 ); (b) package wireless sensing an control unit ( cm 3 ); (c) printe circuit boar of the signal generation moule ( cm 2 ); () control signal moule connecte to wireless sensor. Figure 3. Laboratory setup: (a) eployment scheme of wireless sensors an actuators; (b) the 3-story test structure mounte on the shake table; (c) the MR amper installe between the 1st floor an the base floor of the structure; () a wireless control unit an an off-boar control signal generation moule. Figure 4. Experimental results of ifferent control schemes using the El Centro excitation scale to a peak acceleration of 1m/s 2 : (a) peak inter-story rifts; (b) peak accelerations. Figure 5. Key parameters of the SHD amper employe. Figure 6. A five-story moel similar to the Kajima-Shizuoka Builing: (a) sie elevation of the builing; (b) information group partitioning for ifferent egrees of centralization (DC). Figure 7. Simulation results for the five-story Kajima-Shizuoka Builing instrumente with ieal actuators. The plots illustrate performance inexes for ifferent sampling time steps an egrees of centralization (DC): (a) 3D plot for performance inex PI 1 ; (b) 3D plot for performance inex PI 2 ; (c) conense 2D plot for PI 1 ; () conense 2D plot for PI 2. Figure 8. Simulation results for the five-story Kajima-Shizuoka Builing instrumente with semiactive hyraulic ampers (SHD). The plots illustrate performance inexes for ifferent sampling time steps an egrees of centralization (DC): (a) 3D plot for performance inex PI 1 ; (b) 3D plot for performance inex PI 2 ; (c) conense 2D plot for PI 1 ; () conense 2D plot for PI 2. Figure. 9. Twenty-story SAC builing for numerical simulations: (a) builing elevation; (b) moel parameters of the lumpe mass structure; (c) wireless subnet partitioning for ifferent egrees of centralization (DC); () layout of semi-active hyraulic ampers (SHD) ampers on the floor plans. Figure. 10. Simulation results for the 20-story SAC structure instrumente with ieal actuators. The plots illustrate performance inexes for ifferent sampling time steps an egrees of centralization (DC): (a) 3D plot for performance inex PI 1 ; (b) 3D plot for performance inex PI 2 ; (c) conense 2D plot for PI 1 ; () conense 2D plot for PI 2. Figure. 11. Maximum inter-story rifts for cases where DC=2 with 20ms time elay an DC=4 with 40ms time elay. Table 1. Different ecentralization patterns an sampling time for the wireless an wire-base control experiments.

23 Smart Structures an Systems, submitte for publication, 2007 [ ] = 1 0 ; m q s = 1; for i = 1,2, Solve equation (11a) for Solve equation (11b) for H i ; L ; ( ) i Fin graient using equation (11c): 2 T ( ) T 2 T i = + + Apply shape constraint to i ; iterate { = + i+ 1 i s i ; Solve equation (11a) again for i+ 1 if trace ( Hi+ 1Z l) < trace( i l) max B H A B D LD R D LD ; H using i+ 1 ; HZ an ( eigen ( A + Bi+ 1D ) ) < 1 exit the iterate loop; else s = s / 2; If (s < machine precision), then exit the iterate loop; en }; s = s 2; If i+ 1 i < acceptable error, then exit the for loop; en Figure. 1. Heuristic algorithm solving the couple nonlinear matrix equations (Eq. 11a-c) for ecentralize optimal time-elay output feeback control (Lunze, 1990).

24 Smart Structures an Systems, submitte for publication, 2007 ATmega128 Microcontroller Connector to Wireless Transceiver Sensor Connector Octal D-type Latch AHC573 SRAM CY62128B A2D Converter ADS8341 (a) (b) Digital Connections to ATmega128 Micro-controller Integrate Switching Regulator PT5022 Analog Connections to ATmega128 Microcontroller Comman Signal Output Digital-to-Analog Converter AD5542 (c) Operational Amplifier LMC6484 () Figure 2. Overview to the prototype wireless sensing an actuation unit: (a) printe circuit boar for the wireless sensing unit ( cm 2 ); (b) package wireless sensing an control unit ( cm 3 ); (c) printe circuit boar of the signal generation moule ( cm 2 ); () control signal moule connecte to wireless sensor.

25 Smart Structures an Systems, submitte for publication, 2007 S3 V3 Floor-3 Ci: Wireless control unit (with one wireless transceiver inclue) 3m C2 Si: Wireless sensing unit (with one wireless transceiver inclue) D2 V2 Floor-2 Ti: Wireless transceiver Di: MR Damper 3m C1 Vi: Velocity meter D1 V1 Floor-1 Lab experiment comman server T0 3m D0 C0 V0 Floor-0 (a) (b) (c) () Figure 3. Laboratory setup: (a) eployment scheme of wireless sensors an actuators; (b) the 3- story test structure mounte on the shake table; (c) the MR amper installe between the 1st floor an the base floor of the structure; () a wireless control unit an an offboar control signal generation moule.

26 Smart Structures an Systems, submitte for publication, Maximum Inter-story Drifts No Control Wireless #1 Wireless #2 Wireless #3 Wire 3 Maximum Absolute Accelerations No Control Wireless #1 Wireless #2 Wireless #3 Wire Story 2 Floor Drift (m) Acceleration (m/s 2 ) (a) (b) Figure 4. Experimental results of ifferent control schemes using the El Centro excitation scale to a peak acceleration of 1m/s 2 : (a) peak inter-story rifts; (b) peak accelerations.

27 Smart Structures an Systems, submitte for publication, 2007 x () t SHD p(t) Maximum Control Force Maximum Displacement Stiffness of the SHD Maximum Damping Coefficient Minimum Damping Coefficient Maximum Shaft Velocity Power Consumption 1,000 kn +/- 6 cm 400,000 kn/m 200,000 kn-s/m 1,000 kn-s/m 25 cm/s 70 Watts Figure 5. Key parameters of the SHD amper employe.

28 Smart Structures an Systems, submitte for publication, 2007 Floor-5 4.2m 4 x 3.6m Floor-1 F5 Ch5 Ch4 Ch3 Ch2 Ch1 DC = 1 F5 Ch4 Ch3 Ch2 Ch1 DC = 2 F5 Ch3 Ch2 Ch1 DC = 3 F5 Ch2 Ch1 DC = 4 F5 DC = 5 Ch1 (a) (b) Figure 6. A five-story moel similar to the Kajima-Shizuoka Builing: (a) sie elevation of the builing; (b) information group partitioning for ifferent egrees of centralization (DC).

29 Smart Structures an Systems, submitte for publication, 2007 Maximum Drift Among All Stories LQR Inex Performance Inex PI Sampling Time(s) 0 1 (a) Degree of Centralization Performance Inex PI Sampling Time(s) 0 1 (b) Degree of Centralization Performance Inex PI Maximum Drift Among All Stories 0.4 DC = 1 DC = 2 DC = DC = 4 DC = Sampling Time (s) (c) Performance Inex PI DC = 1 DC = 2 DC = 3 DC = 4 DC = 5 LQR Inex Sampling Time (s) () Figure 7. Simulation results for the five-story Kajima-Shizuoka Builing instrumente with ieal actuators. The plots illustrate performance inexes for ifferent sampling time steps an egrees of centralization (DC): (a) 3D plot for performance inex PI 1 ; (b) 3D plot for performance inex PI 2 ; (c) conense 2D plot for PI 1 ; () conense 2D plot for PI 2.

30 Smart Structures an Systems, submitte for publication, 2007 Maximum Drift Among All Stories LQR Inex Performance Inex PI Sampling Time(s) (a) Degree of Centralization Performance Inex PI Sampling Time(s) 0 1 (b) Degree of Centralization Performance Inex PI Maximum Drift Among All Stories 0.6 DC = 1 DC = 2 DC = DC = 4 DC = Sampling Time (s) (c) Performance Inex PI DC = 1 DC = 2 DC = 3 DC = 4 DC = 5 LQR Inex Sampling Time (s) () Figure 8. Simulation results for the five-story Kajima-Shizuoka Builing instrumente with semiactive hyraulic ampers (SHD). The plots illustrate performance inexes for ifferent sampling time steps an egrees of centralization (DC): (a) 3D plot for performance inex PI 1 ; (b) 3D plot for performance inex PI 2 ; (c) conense 2D plot for PI 1 ; () conense 2D plot for PI 2.