DECENTRALIZED CIVIL STRUCTURAL CONTROL USING A REAL-TIME WIRELESS SENSING AND CONTROL SYSTEM

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1 4 th Worl Conference on Structural Control an Monitoring 4WCSCM-252 DECENTRALIZED CIVIL STRUCTURAL CONTROL USIN A REAL-TIME WIRELESS SENSIN AND CONTROL SYSTEM Abstract Y. Wang 1, R. A. Swartz 2, J. P. Lynch 2, K. H. Law 1, K.-C. Lu 3, C.-H. Loh 3 1 Dept. of Civil an Environmental Engineering, Stanfor Univ., Stanfor, CA 94305, USA 2 Dept. of Civil an Environmental Engineering, Univ. of Michigan, Ann Arbor, MI 48109, USA 3 Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan Over the last few ecaes, structural control technologies have attracte great interest from the earthquake engineering community as a means of reucing ynamic structural responses. Traitional structural control systems employ large quantities of cables to connect structural sensors, controllers, an actuators into one system. To reuce the high-cost an labor-intensive installations, wireless communication technology can serve as an alternative to provie real-time ata links among the noes in a control system. A prototype wireless structural sensing an control system has been physically implemente an its performance verifie in large-scale shake table tests. Our previous stuy shows that as multiple ata links share a common communication channel, communication latency appears to be an important issue with respect to the wireless control system s performance. This paper investigates the feasibility of employing ecentralize an partially ecentralize control strategies to eraicate communication latency problems associate with wireless sensor networks. Control algorithms are embee in a wireless sensor prototype esigne for use in a structural control system. To valiate the integration of ecentralize control algorithms with wireless sensors, a 3-story half-scale steel structure is use with a magnetorheological (MR) amper installe on each floor. Introuction Structural control is currently consiere by many structural engineers as an effective means of mitigating ynamic structural responses (Soong an Spencer, 2002). After ecaes of evelopment, structural control technologies have mature an 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). Among these three types of control technologies, semi-active control has the avantage of achieving consierable control performance while consuming relatively low power. In a semi-active control system, sensors are eploye in the structure to collect real-time structural response ata uring a ynamic excitation. Response ata is then fe into control ecision moules (controllers) in orer to etermine an apply control commans to system actuators. Commane by control signals, the actuators can generate control forces intene to reuce unwante structural responses. Examples of semi-active actuators inclue active variable stiffness (AVS) evices, semi-active hyraulic ampers (SHD), electrorheological (ER) ampers, an magnetorheological (MR) ampers. Semi-active control systems are inherently stable because they o not apply mechanical energy irectly to the structure. Furthermore, because of their power efficiencies, semi-active actuators can easily be implemente without epening on a structure s native electric system, which can fail uring strong earthquakes. In orer to acquire real-time sensor ata for control ecisions, cables are traitionally use to connect sensors with a controller. For a typical low-rise builing, the installation of a commercial wire-base ata acquisition (DAQ) system can cost upwars of a few thousan ollars per sensing channel (Celebi, 2002). As the size of the control system grows (increase in the number of sensors or actuators an their istribution in a structure), or the actuator ensity rises, aitional cabling may result in significant increases in installation time an expense. Thus, wireless communication has been wiely explore for use in structural monitoring applications (Straser an Kiremijian, 1998; Lynch an Loh, 2004; Wang et al., 2006a); however, application to real-time feeback control systems has been scarce. In a previous paper (Wang et al., 2006b), the authors propose a prototype wireless structural sensing an control system. The system consists of multiple stan-alone wireless sensors an controllers that form an integrate wireless network through a common-use wireless communication channel. In the propose Wang, Swartz, Lynch, Law, Lu an Loh 1

2 prototype system, sensor ata is wirelessly propagate within the wireless control system, an processe by wireless sensors esignate as controllers. Appropriate control commans are then applie to semiactive actuators by the wireless controllers. As the size of the control system grows large, one major ifficulty encountere by both wireless an wire structural control systems is the egraation of the system s real-time characteristics. In particular, when a common channel is use for the communication of ata between sensors, actuators, an controllers, as is the case in a networke control system, communication latencies can seriously egrae the performance of the system. Communication latencies have been wiely explore in the network control fiel with many solutions propose (Lian et al., 2002; Ploplys et al., 2004). One such remey is to consier fully an partially ecentralize control system architectures. In a ecentralize control system, the sensing an control network is ivie into multiple subsystems. Controllers are assigne to each subsystem an require only subsystem sensor ata for control ecisions. Shorter communication ranges an reuce use of the communication channel require by ecentralize control architectures benefit both wireless an wire-base network control systems. Compare with centralize control, ecentralize control architectures only offer sub-optimal control performance because each subsystem has incomplete sensor ata available to make control ecisions. In contrast, centralize control provies an optimal control solution. However, the overhea neee to communicate ata in a centralize system results in a reuction in the system s sampling rate. So while ecentralize control solutions might be sub-optimal, their reuce communication latencies allow them to operate at higher sampling rates thereby enhancing their control effectiveness. This stuy attempts to investigate the traeoff between the completeness of sensor ata offere by centralization an the low communication latencies offere by ecentralization. Centralize an ecentralize output feeback control algorithms are first introuce. In orer to compare the performance of ifferent ecentralize an centralize control schemes, an extensive set of large-scale shake table tests are conucte, using a baseline wire control system an the prototype wireless structural sensing an control system. The test structure is a 3-story steel builing in which an MR amper is installe on each floor. The wireless control system is shown to be as reliable an as effective as the wire baseline system. Centralize an Decentralize Linear Output Feeback Control Design An optimal feeback control esign normally requires aequate real-time structural response ata to compute optimal control forces. For example, if a multi-story builing is moele by a lumpe-mass structural system with actuators eploye among ajacent floors, real-time floor isplacements an velocities that constitute the state-space vector are neee for a typical linear quaratic regulator (LQR) controller (Franklin et al., 2003). However, ue to instrumentation complexity an cost, not all structural response ata may be available in practice. To aress this ifficulty, output feeback control methos can be use to provie a sub-optimal control strategy uner the constraint that only part of the state-space variables are measure in real-time. This section first presents the basic formulation of an optimal centralize output feeback control solution, an then proposes a moifie algorithm that allows the output feeback gain matrix to be constraine. The output feeback gain matrix is then formulate for various ecentralize control architectures using the constraine gain matrix algorithm etaile herein. Formulation for Centralize Linear Output Feeback Control The output feeback igital-omain LQR control solution can be briefly summarize as follows. For a lumpe-mass structural moel with n egrees-of-freeom (DOF) an m actuators, the system state-space equations consiering l time steps of elay can be state as: Wang, Swartz, Lynch, Law, Lu an Loh 2

3 z [ k+ 1] = A z [ k] + B p [ k l], where z [ k] [ k] [ k] x = x (1) where z [ k] represents the 2n 1 iscrete-time state-space vector, [ k l] p is the elaye m 1 control force vector, A is the 2n 2n system matrix (containing the information about structural mass, stiffness an amping), an B is the 2n m actuator location matrix. The primary objective of the time-elay LQR problem is to minimize a cost function J by selecting an optimal control force trajectory p : 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 In an output feeback control esign, when control ecisions are compute, only ata in the system output vector y [ k] are available. The output vector is efine by a q 2n linear transformation, D, to z k : the state-space vector [ ] [ k] = [ k] y D z (3) For example, if the relative velocities on all floors are measurable an no relative isplacement is measurable, D can be efine as: The m q optimal gain matrix [ ] D = 0 I (4) _cen n n n n is require to provie a linear output feeback control law: [ k] = [ k] p y (5) Chung et al. (1995) propose a solution to the above output feeback control problem consiering the time elay (l time steps). An augmente system in the first-orer ifference equations is introuce: [ k + 1] = [ k] + [ k] z A z B p (6) This system is equivalent to the original system (Eq. 1) by proper efinitions of the augmente matrices an vectors (enote with over bars). As a result, the following nonlinearly couple matrix equations are solve for an optimal output feeback gain matrix, the Lagrangian matrix, L, an the Hamiltonian matrix, H: T T T ( ) ( ) ( ) A + BD HA + BD H+ Q+ D RD = 0 (7a) ( ) ( ) T l A + B D L A + B D L+ Z = 0 (7b) ( ) T T T 2B H A + B D LD + 2R D LD = 0 (7c) Derivation etails are referre to Chung et al. (1995). Heuristic Solution for Centralize an Decentralize Output Feeback ain Matrices An iterative algorithm to solve the continuous-time feeback control problem has been presente by Lunze (1990). The algorithm (Fig. 1) starts from an initial guess for the gain matrix. Within each Wang, Swartz, Lynch, Law, Lu an Loh 3

4 [ ] = 1 0 ; m q s = 1; for i = 1,2, Solve equation (7a) for H i ; Solve equation (7b) for L i ; Fin graient using equation (7c): ( 2 T ( ) T 2 T i = B H A + BD LD + RDLD ) ; iterate { = + i+ 1 i s i ; Solve equation (7a) again for H using i+ 1 i+ 1 ; if trace ( H i+ 1 Z l) < trace( HZ i l) an max ( 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. 7) for centralize optimal time-elay output feeback control (Lunze, 1990). iteration step i, the Hamiltonian matrix H i an the Lagrangian matrix L i are solve respectively using the current guess i. Base on compute H i an L i, a searching graient i is calculate, an the new gain matrix i+ 1 is compute by traversing along a 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 guess. The first conition is trace( H i+ 1 Z l) < trace( HZ i l), which guarantees that i+ 1 is a better solution than i. The secon conition is that the maximum magnitue of all the eigenvalues of the matrix A + Bi+ 1D is less than 1, which ensures the stability of the augmente system. The iterative algorithm put forth by Lunze (1990) has an attractive feature, i.e. the algorithm can also formulate an optimal control solution for a ecentralize system simply by constraining the structure of to be consistent with the ecentralize architecture. The following equation illustrates two ecentralize output feeback gain matrices for a simple 3-story lumpe-mass structure. * 0 0 * * * 0, 2 0 * * _ec = _ec = (8) 0 0 * 0 * * The pattern in _ec1 specifies that when computing control ecisions, the actuator on each floor only nees the entry in the output vector y that correspons to that floor. The pattern in _ec2 specifies the control ecisions also require information from a neighboring floor. In orer to fin a ecentralize gain matrix that satisfies certain shape constraint, the algorithm escribe in Fig. 1 is moifie by zeroing out the corresponing entries in the graient matrix i. The next estimate i+ 1 is compute by traversing along the constraine graient. Using the above ecentralize gain matrices an the following output matrix D, inter-story velocities between ajacent floors can be use for ecentralize control ecisions: D _ec = (9) Wang, Swartz, Lynch, Law, Lu an Loh 4

5 Valiation Tests using a Real-time Wireless Sensing an Control System In orer to examine the traeoff between the amount of sensor ata available to a controller an the communication latency using various ecentralize control schemes, valiation tests are conucte at the National Center for Research on Earthquake Engineering (NCREE) in Taipei, Taiwan. Both a baseline wire control system an a prototype wireless structural sensing an control system are use to implement the real-time feeback control of a 3-story steel frame instrumente with three MR ampers. Design of the Wireless Structural Sensing an Control System The feasibility of the propose wireless structural sensing an control system has been previously valiate in a simpler set of control tests (Wang et al., 2006b). Wireless sensing an control units are the builing blocks of the real-time wireless feeback control system. The major responsibilities assume by the wireless sensing an control units inclue: (a) collect real-time structural sensor ata; (b) wirelessly transmit or receive the sensor ata within a wireless communication network; (c) process ata an compute control ecisions; an () apply control signals to semi-active actuators. The harware esign of the wireless sensing an control unit (Fig. 2) is base upon a wireless sensing unit previously propose for use in wireless structural monitoring systems (Wang et al, 2006a). The three original functional moules inclue in the wireless sensing unit esign are the sensor signal igitizer, the computational core, an the wireless transceiver. To exten the functionality of the wireless sensor for actuation, an offboar control signal generation moule is esigne an fabricate. The control signal generation moule consists of a single-channel 16-bit igital-to-analog converter an support electronics. The moule can output an analog voltage from -5V to 5V at rates as high as 100kHz. A challenge associate with employing wireless sensors for use in a structural control system is the performance of the wireless communication channel. Because of local frequency ban requirements in Taiwan, the MaxStream 24XStream wireless transceiver (MaxStream, 2005) operating at 2.4Hz spectrum is employe for the wireless sensing unit. The 450m inoor communication range of the 24XStream wireless transceiver is sufficient for installation in most small an meium-size civil structures. The peer-to-peer communication capability of the wireless transceiver makes it possible for the wireless sensing an control units to communicate with each other, thus supporting flexible information flow among multiple wireless units. As previously iscusse, one critical issue in applying wireless communication technology into real-time feeback structural control is the communication latency while transmitting sensor ata from the wireless sensing units to the wireless control units. Previous analysis an experimental valiation show that each peer-to-peer wireless transmission takes Wireless Sensing Unit Computational Core Structural Sensors Sensor Signal Digitization 4-channel 16-bit Analog-to-Digital Converter ADS8341 SPI Port 128kB External SRAM CY62128B Parallel Port 8-bit Microcontroller ATmega128 UART Port Wireless Communication Wireless Transceiver: 20kbps 2.4Hz 24XStream, or 40kbps 900MHz 9XCite SPI Port Actuation Signal eneration 16-bit Digital-to-Analog Converter AD5542 Structural Actuators Figure. 2. Functional iagram etailing the harware esign of the wireless sensing unit interface to the actuation signal generation moule. Wang, Swartz, Lynch, Law, Lu an Loh 5

6 roughly 20ms using the 24XStream transceivers. Valiation Test Setup an Results Experimental tests were conucte at the National Center for Research on Earthquake Engineer (NCREE) in Taipei, Taiwan. A three-story steel frame structure is esigne an constructe by researchers affiliate with NCREE (Fig. 3). The floor plan of this structure is 3m 2m, with each floor weight ajuste to 6,000 kg using concrete blocks; inter-story heights are 3m. The three-story structure is mounte to a 5m 5m 6-DOF shake table. For this stuy, only longituinal excitation is use in the tests. The test structure is heavily instrumente with various types of sensors. For example, accelerometers, velocity meters, an linear variable isplacement transucers (LVDT) are installe on each floor of the structure. These sensors are interface to a high-precision wire-base ata acquisition (DAQ) system native to the NCREE facility; this wire DAQ system is set to a sampling rate of 200 Hz. For this experimental stuy, three 20 kn MR ampers are installe in a V-brace upon each story of the steel structure (Fig. 3). 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 (Lin, 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. Two control systems are installe in the test structure: the wireless control system an a traitional wirebase control system. For the wireless system, a total of four wireless sensors are installe (Fig. 3). Each wireless sensor is interface to a velocity meter to measure the absolute velocity response for each floor of the structure as well as the base. 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. As escribe by Lynch et al. (2006), Bouc-Wen hysteresis moels an LQR gain matrices are embee in these wireless control units to C i: Wireless control unit (with one wireless transceiver inclue) S 3 C 2 V 3 Floor-3 S i: Wireless sensing unit (with one wireless transceiver inclue) D 2 V 2 Floor-2 T i : Wireless transceiver C 1 D i: MR Damper V i: Velocity meter D 1 V 1 Floor-1 (b) Lab experiment comman server T 0 D 0 C 0 V 0 Floor-0 (a) (c) Figure. 3. Laboratory setup: (a) sensor, MR amper, an wireless unit eployment; (b) the three-story test structure; (c) a wireless control unit commaning an MR amper. Wang, Swartz, Lynch, Law, Lu an Loh 6

7 etermine MR amper comman signals using real-time structural response ata. Centralize an ecentralize velocity feeback control algorithms presente before are use for both the wire an the wireless control systems. Tokyo Sokushin VSE15-D velocity meters are selecte for measuring velocities on each floor of the structure. The sensitivity of this velocity meter is 10V/(m/s) with a measurement limit of ±1 m/s. An LQR weighting matrix Q esigne to minimize inter-story rifts over time, an a iagonal weighting matrix R are use for all the wireless an wire control tests that are presente herein. As shown in Table 1, ifferent ecentralization patterns an sampling steps are teste using the two control systems. For the test structure, the wire-base system can achieve a short sampling step of 5ms. Mostly ecie by the communication latency of the 24XStream wireless transceivers, the wireless system can achieve a sampling step of 80ms for the centralize control scheme. This is ue to each wireless sensor waiting in turn to communicate its ata to the network (20ms for each transmission). An avantage of the ecentralize architecture is that fewer communication steps are neee, thereby reucing the time for communication. The El Centro NS (1940) earthquake recor is scale to a peak acceleration of 1m/s 2 for the experimental results shown in Fig. 4. Fig. 4 illustrates the peak inter-story rifts an floor accelerations for the original uncontrolle structure an the structure controlle by four ifferent wireless an wire control schemes. Compare with the uncontrolle structure, all wireless an wire control schemes illustrate obvious reuction in peak rifts an accelerations. Among the four control cases, the wire scheme shows superior performance by achieving the least peak rifts an secon least overall peak accelerations. This is as expecte, because the wire system has avantages in terms of both low communication latency an sensor ata completeness. The wireless system, although running at longer sampling steps, achieves Wireless System Wire System Decentralization #1 Decentralize #2 Partially Decentr. #3 Centralize Centralize ain Constraint _ec1 in Eq. (8) _ec2 in Eq. (8) N/A N/A Output Matrix D _ec in Eq. (9) D _ec in Eq. (9) D _cen in Eq. (4) D _cen in Eq. (4) Sampling Step/Rate 20 ms / 50 Hz 60 ms / Hz 80 ms / 12.5 Hz 5 ms / 200 Hz Table 1. Different ecentralization patterns an sampling steps for the wireless an wire-base control systems use in the valiation experiments. 3 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) (a) Acceleration (m/s 2 ) 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. (b) Wang, Swartz, Lynch, Law, Lu an Loh 7

8 control performance comparable to the wire system. The wireless case #1, a fully ecentralize control scheme, results in uniforme peak inter-story rifts an the least peak floor accelerations. This shows that in the ecentralize wireless control cases, the isavantage of incomplete sensor ata is compensate by the benefit erive from lower communication latency (an hence higher sampling rate). Conclusions This paper investigates the feasibility an effectiveness of ecentralize control strategies in civil structures. We first present a heuristic computational algorithm for an optimal output feeback structural control esign using both centralize an ecentralize communication patterns. Experimental tests are conucte to examine the traeoff between sensor ata completeness offere by centralization an low communication latencies offere by ecentralization. The results show that ecentralize wireless control strategies may provie equivalent or even superior control performance, given that their centralize counterparts suffer longer sampling steps ue to communication latencies. The experiments also successfully valiate the reliability of the prototype wireless structural sensing an control system. Acknowlegements 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 uner rant No. NSC Z an Central Weather Bureau in Taiwan. 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. References Celebi, M. (2002), Seismic Instrumentation of Builings (with Emphasis on Feeral Builings), Report No , Unite States eological Survey (USS), Menlo Park, CA, USA. Chung, L.L., C.C. Lin, an K.H. Lu (1995), Time-elay Control of Structures, Earthquake Engineering & Structural Dynamics, 24(5), Franklin,.F., J.D. Powell, an M. Workman (2003), Digital Control of Dynamic Systems, Pearson Eucation, New Jersey. Lian, F.-L., J. Moyne, an D. Tilbury (2002), Network Design Consieration for Distribute Control Systems, IEEE Transactions on Control Systems Technology, 10(2), Lin, P.-Y., P.N. Roschke, an C.-H. Loh (2005), System Ientification an Real Application of a Smart Magneto-Rheological Damper, Proceeings of the 2005 International Symposium on Intelligent Control, Limassol, Cyprus, June 27-29, Lunze, J. (1992), Feeback Control of Large-scale Systems, Prentice Hall, Hertforshire, UK. Lynch, J.P. an K. Loh (2005), A Summary Review of Wireless Sensors an Sensor Networks for Structural Health Monitoring, Shock an Vibration Digest, 38(2), Lynch, J.P., Y. Wang, R.A. Swartz, K.-C. Lu, C.-H. Loh (2006), Implementation of a Close-loop Structural Control System using Wireless Sensor Networks, Journal of Structural Control an Health Monitoring, in review. MaxStream, Inc. (2005), XStream OEM RF Moule Prouct Manual, Linon, UT, USA. Ploplys, N.J., P.A. Kawka, an A.. Alleyne (2004), Close-loop Control over Wireless Networks, IEEE Control Systems Magazine, 24(3), Soong, T.T. an B.F. Spencer, Jr. (2002), Supplemental Energy Dissipation: State-of-the-art an State-of-the-practice, Engineering Structures, 24(3), Straser, E.. an A.S. Kiremijian (1998), A Moular, Wireless Damage Monitoring System for Structures, Ph.D. thesis in Dept. of Civil an Environmental Eng., Stanfor University, Stanfor, CA, USA. Wang, Y., J.P. Lynch, an K.H. Law (2006a), A Wireless Structural Health Monitoring System with Multithreae Sensing Devices: Design an Valiation, Structure an Infrastructure Engineering, in press. Wang, Y., A. Swartz, J.P. Lynch, K.H. Law, K.-C. Lu, an C.-H. Loh (2006b), Wireless Feeback Structural Control with Embee Computing, Proceeings of the SPIE 11th International Symposium on Nonestructive Evaluation for Health Monitoring an Diagnostics, San Diego, CA, USA, February 26 - March 2, Wang, Swartz, Lynch, Law, Lu an Loh 8