BENCH-SCALE EXPERIMENT FOR STRUCTURAL CONTROL · Bench-Scale Experiment for Structural Control...

September 9, 1998 1 Battaini, Yang, Spencer

BENCH-SCALE EXPERIMENT FOR STRUCTURAL CONTROL

M. Battaini,1 G. Yang2 and B.F. Spencer, Jr.,2

Abstract

Experimental verification of structural control strategies is essential for eventual full-scaleimplementations. However, few researchers have facilities readily available to them that are capa-ble of even small-scale structural control experiments. This paper demonstrates that appropriatelyconstructed bench-scale models can be used to study important aspects of full-scale structuralcontrol implementations, including: control-structure interaction, actuator and sensor dynamics,actuator saturation effects, limited availability of sensors, output feedback design, digital controlimplementation, control spillover,etc. The active control experiment considered herein is shownto be an effective tool for familiarizing students and practitioners with control system design andthe associated challenges.

Introduction

Experimental investigations are essential to obtain a fundamental understanding of manyphenomena. However, when physical systems are scaled down to a size appropriate for laboratorystudy, salient features of their behavior may be lost. This is particularly true for large civil engi-neering structures. For example, the load-carrying capacity of the steel beams increases as a resultof the decrease in beam depth; small size concrete specimen shrinks much more rapidly and uni-formly than a large and bulky member,etc.

In the area of control of civil structures, it is well-recognized that experimental verificationof control strategies is necessary to focus research efforts in the most promising directions (Hous-ner, et al. 1994a,b). However, few researchers have experimental facilities readily available tothem that are capable of even small-scale structural control experiments. Consequently, the major-ity of control studies to date have been analytical in nature, a substantial number of which haveemployed models that lacked important features of the physical problem. One such phenomenathat has been neglected for many years is control-structure interaction (CSI). Through a series ofanalytical and experimental studies, Dyke,et al. (1995) recognized that understanding CSI waskey to developing acceleration feedback control strategies and showed that accounting for CSI isfundamental to achieving high performance controllers.

This paper discusses the efficacy of a recently developed bench-scale structural controlexperiment. The model structure employed in the experiment represents a building controlled byan active mass driver (AMD) and consists of a steel frame with a controllable mass located at thetop. The model was chosen because of the large number of full-scale implementations of this class

1. Department of Structural Mechanics, University of Pavia, Via Ferrata 1, I27100 Pavia - Italy2. Department of Civil Engineering and Geological Sciences, University of Notre Dame, NotreDame, Indiana 46556-0767, U.S.A.

Bench-Scale Experiment for Structural Control


of systems (Soong 1990; Fujino,et al., 1996; Housner,et al., 1997; Spencer and Sain, 1997). Theexperiment is shown to allow for study of many intrinsic features of full-scale systems, includingcontrol-structure interaction, actuator and sensor dynamics, actuator saturation effects, limitedavailability of sensors, output feedback design, digital control implementation, control spillover,etc. It is envisioned that the total cost of this system, including the structural model, AMD, sen-sors, digital control system, power amplifier, spectrum analyzer, etc., is well within the range ofmost educational institution.

Experiment Setup

The equipment used for the active control experiment, performed in the Structural Dynam-ics and Control Earthquake Engineering at the University of Notre Dame, consisted of (see Figs.1 and 2):

• Structure: The structural specimen, manufacutured by Quanser Consulting Inc., is a model ofa flexible building, which can be configured to have either 1 or 2 floors. Herein, a 2-floor con-figuration of the model is employed. The interstorey height is 490 mm, with each columnbeing steel with a section of mm. The total mass of the structure is 4.259 kg, wherethe first floor mass is 1.689 kg, the second floor mass is 1.662 kg, and the mass of each columnis 0.227 kg. The structure has the natural frequencies of 1.24 Hz and 3.57 Hz which have cor-responding damping ratios of 0.02 and 0.055 respectively.

Figure 1: Bench-scale building model. Figure 2: Experimental set-up

xa2

xa1

ComputerController

uPower Amplifier

xra

m1

m2

ma

xg

2 108×



• Active Mass Driver (AMD): The AMD provides the control force to the structure. As shownin Fig. 3, it consists of a moving cart with a DC motor that drives the cart along a geared rack.The mass position control is obtained by a PD controller with displacement feedback. Themaximum stroke is cm and the total moving mass is 454 g.

• Sensors:Two Kistler K-Beam 8304A capacitive DC accelerometers with full scale range of 2g and sensitivity of 1024 mV/g were employed. The accelerometers are placed on each floorof the structure. Additionally, a potentiometer is attached to the motor to measure the cartposition relative to its base, with a full scale of V and a sensitivity of 0.362 V/cm.

• Digital Controller: Digital control is achieved by use of the MultiQ I/O board with the Win-Con realtime controller. The controller is developed using SIMULINK (1997) and executed inrealtime using WinCon. This board has a 13-bit analog/digital (A/D) and 12-bit digital/analog(D/A) converters with eight input/output analog channels. The SIMULINK code is automati-cally converted to C code and interfaced through the Wincon software to run the control algo-rithm on the CPU of the PC.

• Spectrum Analyzer: A 2-input/2-output PC-based spectrum analyzer manufactured by DSPTechnology is employed for data acquisition and analysis. The device has a 90 dB signal tonoise ratio and includes 8-pole elliptical antialiasing filters, programmable gains on the inputs/outputs, user selectable sample rates and a MATLAB (1997) user interface. These featuresallow for direct acquisition of high quality data and transfer functions for system identificationand response analysis.

• Computer: The computer used to house the MultiQ programmable I/O board and to interfacewith the spectrum analyzer is a 90 MHz Pentium-based Gateway 2000 computer configuredwith 40 MB of RAM.

Figure 3: Active mass driver (AMD).

9.5±

5±



Sensors, Actuators and Control-Structure Interaction

Accounting for sensor and actuator dynamics is well-known to be essential for the design ofhigh quality control systems. In particular, Dyke,et al. (1995) has shown that neglecting actuatordynamics can produce poor, or perhaps catastrophic, performance of the controlled system due tothe unmodeled or mismodeled dynamics of the actuator-structure interaction (i.e., control-struc-ture interaction). This section discusses models for the sensors/actuators employed in the bench-scale experiment and demonstrates that the bench-scale model can be used to effectively study thephenomena of control-structure interaction (CSI).

Until recently, most of the current active structural control strategies for aseismic protectionhave been based on either full-state feedback (i.e., all structural displacements and velocities) oron velocity feedback. However, accurate measurement of displacements and velocities is difficultto achieve directly in full-scale applications, particularly during seismic activity, since the founda-tion of the structure is moving with the ground. Alternatively, accelerometers can provide reliableand inexpensive measurement of accelerations at strategic points on the structure and haverecently been shown to be effective in structural control implementations (Spencer,et al., 1991,1994; Suhardjo,et al., 1992; Dyke,et al. 1995b, 1996). Therefore, floor accelerations will be theprimary measurements used to control the structure.

The capacitive accelerometers employed in this experiment have flat frequency responsewith zero phase lag from DC to 300 Hz. Therefore, in the frequency range of interest for thebench-scale structure, sensor dynamics can be neglected, and the acceleration can be treated as adirectly measured response as follows

(1)

where is the voltage measured from theith accelerometer, is the accelerometer offset volt-age, and is the sensitivity constant for the accelerometer.

The position of the AMD relative to the second floor is another readily available measure-ment. A potentiometer is mounted on the AMD cart and a small gear attached that rotates as theAMD moves. The response of the potentiometer is flat in the frequency range of interest for thisexperiment. Therefore, the AMD potentiometer can be related directly to the relative displace-ment of the AMD cart by

(2)

where is the voltage measured from the potentiometer, is the potentiometer offset voltage,and is the sensitivity constant for the potentiometer.

To see the importance of accounting for actuator dynamics and how control-structure inter-action (CSI) is manifested in the bench-scale model, consider a simple two degree-of-freedommodel of the structure given by

xai αa vai va0–( )=

vai va0αa

xra αd vp vp0–( )=

vp vp0αd



(3)

where is the displacement of theith floor relative to the ground, , , are the mass, stiff-ness and damping, respectively of theith floor, is the ground acceleration, and is the forcegenerated by the AMD.

Next, a mathematical model for the AMD is developed. The torque (N-m) generated bythe DC motor employed in the AMD is given by (Kuo, 1987),

(4)

where is the voltage applied to the motor, V-sec is the back electromotiveforce constant, N-m/amp is the torque constant, is the internal gearratio, ohms is the armature resistance of the motor, Herry is the arma-ture inductance of the motor, cm is the motor gear radius, and is the velocity ofthe AMD relative to the second floor. Therefore the force generated by the AMD is

(5)

By neglecting the rotor inertia of the motor in comparison to the mass of the cart, Eq. (5) can alsobe written as

(6)

where is the mass of the AMD, is the absolute acceleration of the AMD mass, is theacceleration of the AMD mass relative to the second floor, and is the absolute acceleration ofthe ground. Combining Eqs. (4–6) yields

(7)

(8)

where is the time constant of the motor, , and .As can be seen from Eqs. (7–8), the dynamics of the AMD are tightly coupled to the

response of the structure to which it is attached. Figure 4 is a block diagram representation of theAMD model given in Eqs. (7–8). Here, denotes the transfer function from the force appliedby the actuator to the displacement of the second floor (i.e., the point on the structure where the

m1 0

0 m2

x1

x2 c1 c2+ c2–

c2– c2

x1

x2 k1 k2+ k2–

k2– k2

x1

x2

+ +m1 0

0 m2

–1

1

xg

0

f a

–=

xi mi ci ki

xg f a

Tm

dTm

dt-----------

Ra

La-----Tm–

KbK iKg

Larm-------------------- xar–

K i

La-----Vm+=

Vm Kb 7.67 103–×=

K i 7.67 103–×= Kg 3.7=

Ra 2.6= La 1.8 104–×=

rm 0.635= xraf a

f a

TmKg

rm--------------=

f a maxaa ma xra x2 xg+ +( )= =

ma xaa xraxg

d f a

dt--------- ε f a– β xra– γVm+=

xra

f a

ma------ x2 xg+( )–=

ε Ra La⁄= β KbK iKg2

Larm2⁄= γ K iKg Larm⁄=

Hx2 f a



actuator is attached) and there is no ground acceleration. Notice the presence of the “natural”velocity feedback in the open-loop system. Through this feedback interaction path, the dynamicsof the structure directly affect the characteristics of the control actuator (i.e., the phenomena ofCSI is intrinsic to this system).

To see the presence of CSI more explicitly, the transfer function from the motor voltageto the force applied to the structure is given by

(9)

where , and based on Eq. (3)

(10)

(11)

Note that the roots of are the natural frequencies (i.e., the poles) of the structure. Exam-ining Eq. (9) shows the classical control-structure interaction phenomena, where the poles of thestructure are zeros of the actuator transfer function.

As is the case with many control actuators employed in civil engineering applications (see,for example, Chung,et al. 1989 and Dyke,et al. 1995b, 1996), the open-loop dynamics of the

Figure 4: Block diagram of open-loop motor model.

sxra

MotorVoltage, Vm

Natural Velocity Feedback

–

+

1

mas2

-----------

–

+

f a

γf a

1s---

Hx2 f as( )

–

ε

β

x2

xra

+

Ha

Vmf a

H f aVms( ) sγd s( )

s2 εs

βma------+ +

d s( ) s2βn s( )–

-----------------------------------------------------------------------=

Hx2 f an s( ) d s( )⁄=

n s( ) m1s2

c1 c2+ s k1 k2+ + +=

d s( ) m1m2s4

m1c2 m2c1 m2c2+ +( )s3c1c2 m1k2 m2k1 m2k2+ + +( )s2

+ +=

c1k2 c2k1+( )s k1k2+ +

d s( ) 0=



bench-scale AMD are unstable. The typical approach stabilizing the system is to add a PD posi-tion feedback loop in which

(12)

where is the control signal, is the proportional gain, is the differential gain, and is thesensitivity of the potentiometer. Equation (7) then becomes

(13)

and the transfer function from the command signal to the force can be written as

(14)

Equation (14) also shows that the poles of the structure are the zeros of the stabilized actua-tor transfer function. Fig. 5 shows the transfer function from the AMD command signal

to its absolute acceleration , which is proportional to the AMD force . As predicted, thezeros of this transfer function are at 0, 1.24, and 3.57 Hz. The two zeros at origin are due to the

Vm kp uxra

αd------–

kd

xra

αd------–=

u kp kd αd

d f a

dt--------- ε f a– β

γkd

αd--------+

xra–γkpxra

αd---------------– γ kpu+=

u f a

H f aus( )

s2γ kpd s( )

s3 εs

2 αdβ γ kd+

αdma

------------------------sγkp

αdma

-------------+ + +

d s( ) s2 β

γkd

αd--------+

sγkp

αd--------+ n s( )–

-------------------------------------------------------------------------------------------------------------------------------------------------------------=

Figure 5: Transfer function from the command signal to the AMDacceleration .

uxaa

0 1 2 3 4 5 6 7 8 9 10−40

−30

−20

−10

0

10

20

30

Frequency (Hz)

Mag

nitu

de (d

B)

AMD mounted to groundAMD mounted to structure

Hxaaus( )

u xaa f a



rigid body mode of the AMD mass. The other two zeros correspond to the two natural frequenciesof the structure. For comparison, the transfer function corresponding to the case in which theAMD is rigidly connected to the ground is superimposed on Fig. 5. As can be seen, the zerospresent in the actuator transfer function when it was mounted to the structure are no longerpresent in the transfer function when the AMD is mounted to the ground.

The implication of the presence of CSI shown here are profound: at the frequencies wherethe structural response is the greatest (i.e., the poles), the actuator has the least ability to inputforces to the structure. Note that for many years the role of control-structure interaction in protec-tive system designs was not well recognized, but was incorrectly viewed to be a time delay. Aswas shown in Dyke,et al. (1995a), accounting for control-structure interaction is essential toachieving high quality control.

Experimental Model Identification

One of the most important and challenging components of control design is the develop-ment of an accurate mathematical model of the structural system. There are several methods bywhich to accomplish this task. One approach is to directly identify the unknown constants in aparametric model such as given in Eqs. (3, 7–8). The approach employed in this study for devel-oping the necessary dynamical model of the structural system is to measure the input/output rela-tionships of the system and construct a mathematical model that can replicate this behavior. Suchinput-output models obtained directly from data have been shown to be effective for designinghigh-performance controllers (Dyke,et al.1995a,b, 1996). Note that this identification procedureautomatically incorporates control-structure interaction into the resulting model.

The first step in the system identification process is to experimentally determine the transferfunctions (also termed frequency response functions) from each of the system inputs to each ofthe outputs. A block diagram of the structural system (Fig. 1) to be identified is shown in Fig. 6.The two inputs are the ground excitation and the command signal to the actuator . The threemeasured system outputs include the absolute accelerations, , , of the two floors of the teststructure and the actuator displacement . Thus, a transfer function matrix (i.e., six input/output relations) must be identified to describe the characteristics of the system in Fig. 6.

Figure 6: System identification block diagram.

xg

u

xra

xa1

xa2

System

Structural

xg uxa1 xa2

xra 3 2×



Subsequently, each of the experimental transfer functions is modeled as a ratio of two poly-nomials in the Laplace variables (i.e., the poles, zeros and gain) and then used to determine a statespace representation for the structural system. Because the system under consideration is a multi-input/multi-output system (MIMO), construction of the state space model is not straightforward.First, two separate systems were formed, each with a single input corresponding to one of the twoinputs to the system. Once both of the component system state equations were generated, theMIMO system was formed by stacking the states of the two individual systems. However, thedynamics of the test structure itself were redundantly represented in this combined state spacesystem, and the state space system had repeated eigenvalues for which the eigenvectors were notlinearly independent (i.e., the associated modes were not linearly independent). A minimal real-ization of the system was found by performing a model reduction. This approach is described inmore detail in Dyke,et al. (1994).

The analytical models of three representative transfer functions are compared with theexperimentally obtained transfer function in Figs. (7–9). The transfer function from theground acceleration to the absolute acceleration of the second floor is shown in Fig. 7, the transferfunction from the cart command signal to the absolute acceleration of the second floor isshown in Fig. 8, and the transfer function from the actuator command to the cart dis-placement relative to the second floor is shown in Fig. 9.

The identified model of the structural system, which includes the structure and the AMD, isfinally given by

Hxa2xgs( )

Figure 7: Transfer function from the ground acceleration to the second floorabsolute acceleration .

xgxa2

0 1 2 3 4 5 6 7 8 9 10−60

−40

−20

0

20

40

Frequency (Hz)

Mag

nitu

de (d

B)

ExperimentalModel

0 1 2 3 4 5 6 7 8 9 10−400

−300

−200

−100

0

100

Frequency (Hz)

Phas

e (d

eg)

Hxa2us( )

Hxraus( )



Figure 8: Transfer function from cart command signal to the second floorabsolute acceleration .

uxa2

0 1 2 3 4 5 6 7 8 9 10−60

−40

−20

0

20

Frequency (Hz)

Mag

nitu

de (d

B)

ExperimentalModel

0 1 2 3 4 5 6 7 8 9 10−200

−100

0

100

200

Frequency (Hz)

Phas

e (d

eg)

Figure 9: Transfer function from cart command signal to the cartdisplacement relative to the second floor .

uxra

0 1 2 3 4 5 6 7 8 9 10−15

−10

−5

0

5

10

15

Frequency (Hz)

Mag

nitu

de (d

B)

ExperimentalModel

0 1 2 3 4 5 6 7 8 9 10−150

−100

−50

0

50

Frequency (Hz)

Phas

e (d

eg)



(15)

(16)

where is the state vector of the system, is the vector of measured respons-es, andv represents the noise in the measurements. Note that there are 7 state variables in the statevector , in which 4 states correspond to the structure, 2 states correspond to the AMD, and theother one corresponds to the dynamic of the motor.

H2/LQG Controller Design

To illustrate some of the constraints and challenges that can be studied through the bench-scale model, an infinite horizon, linear quadratic Gaussian (LQG/ ) control design is presented.The LQG/ approach is an output feedback design method that has been shown to be effectivefor design of acceleration feedback control strategies for this class of systems(Spencer,et al.,1991, 1994; Suhardjo,et al., 1992; Dyke,et al. 1995b, 1996). Note that although the ground accelera-tion is an available measurement,this design will not make use it.

To simplify design of the controller, is taken to be a stationary white noise, and an infi-nite horizon performance index is chosen that weights the accelerations of the three floors,i.e.,

(17)

where all of the elements of the weighting matrixQ are zero, except for and . Further,the measurement noise is assumed to be identically distributed, statistically independent Gaussianwhite noise processes, and . Note that the infinite horizon LQG approach isequivalent to control method (Spencer,et al., 1994).

The separation principle allows the control and estimation problems to be considered sepa-rately, yielding a controller of the form (Stengel 1986; Skelton 1988)

(18)

where is the Kalman Filter estimate of the state vector based on the reduced order model. Bythe certainty equivalence principle (Stengel 1986; Skelton 1988), is the full state feedback gainmatrix for the deterministic regulator problem given by

(19)

where is the solution of the algebraic Riccati equation given by

(20)

x Ax Bu E xg+ +=

y Cx Du F xg v+ + +=

x y xa1 xa2 xra[ ]′=

x

H2H2

xg

J lim1τ--- E Cx Du+( )′Q Cx Du+( ) ru

2+{ } td

0

τ

∫=τ ∞→

Q11 Q22

SxgxgSvivi

⁄ γ 25= =H2

u Kx–=

xK

K N ′ B′P+( ) r⁄=

P

0 PA A ′P PBB′P r⁄ Q+–+=



and

(21)

(22)

(23)

(24)

Calculations to determine were done using the MATLAB (1997) routinelqry.m within the con-trol toolbox.

The Kalman Filter optimal estimator is given by

(25)

(26)

where is the solution of the algebraic Riccati equation given by

(27)

and

(28)

(29)

(30)

(31)

Calculations to determine were done using the MATLAB routinelqew.mwithin the controltoolbox. Sample code to design these controllers are available athttp://www.nd.edu/~quake/ underthe “Benchmarks” heading (Spencer,et al., 1998).

Control Implementation Issues

The controllers used in this experiment were implemented on the PC and interfaced with theexperiment using the MultiQ programmable I/O board. There are a number of issues that shouldbe understood and addressed to successfully implement a control design digitally, several ofwhich are discussed in this section. Further information regarding implementation concepts isprovided in Quast,et al. (1995).

N C′QD=

r r D′QD+=

Q C′QC NN′ r⁄–=

A A BN ′ r⁄–=

K

x Ax Bu L y Cx– Du–( )+ +=

L [R˜

1– γFE′ CS+( )] ′=

S

0 SA˜

A˜

′S SG˜

S H˜

+–+=

R˜

I γFF′+=

A˜

A ′ C′R˜

1– γFE′( )–=

G˜

C′R˜

1– C=

H˜

γE( )E′ γ2EF′R˜

1– FE′–=

L



The method of “emulation” is used for the design of the discrete-time controller. Using thistechnique, a continuous-time controller was first designed which produced satisfactory controlperformance (see control design section). The continuous-time controller is then approximated or‘emulated’ with an equivalent digital filter using the bilinear transformation. Typically, with theuse of emulation, if the sampling rate of the digital controller is at least 10-25 times the closed-loop system bandwidth, the discrete equivalent system will adequately represent the behavior ofthe emulated continuous-time system over the frequency range of interest. Such a sampling rateperformance was successfully achieved by the system used in this experiment.

Once the final controller has been designed using SIMULINK, it is converted to C codeusing RTW and run in realtime using WinCon. The controller sampling rate is fixed at 1000 Hz inorder to satisfy the digital controller implementation issues.

The sampling rate that is achievable by a digital control system is limited by such things asthe rate at which A/D and D/A conversions can be performed, the speed of the processor and thenumber of calculations required to be performed by the processor during a sampling cycle (Quast,et al., 1995). For this experiment, all I/O processes, control calculations, and supervisory func-tions were performed in less than 1 msec, allowing for sampling rates on the order of 1 kHz,although such high sampling rates are not required for this application.

The model on which the control design was based was acceptably accurate below 5 Hz, butsignificant modeling error was present at higher frequencies. If one tries to affect high-authoritycontrollers at frequencies where the system model is poor, catastrophic results may occur. Thus,for the structural system under consideration, no significant control effort was applied above 5 Hz.

The loop gain transfer function (breaking the control loop at the input to the system) wasexamined in assessing the various control designs. By “connecting” the measured outputs of theanalytical system model to the inputs of the mathematical representation of the controller, theloop gain transfer function from the actuator command input to the controller command outputwas calculated. The loop gain was used to provide an indication of the closed loop stability for thecontroller implemented on the physical system. For stability purposes, the loop gain should beless than one at the higher frequencies where the model poorly represents the structural system(i.e., above 5 Hz). Thus, the magnitude of the loop gain transfer function should roll off steadilyand be well below unity at higher frequencies. A control design was considered to be acceptablefor implementation if the magnitude of the open loop transfer function at high frequencies waswell below 0 dB at frequencies greater than 5 Hz. Figure 10 shows the measured loop gain trans-fer functions of the controller.

Results

The response of the bench-scale structure for the uncontrolled and controlled cases are pre-sented. Figures. 11–12 show the transfer functions from the ground acceleration to the first andsecond floor acceleration, respectively.

The structure was subjected to the El-Centro earthquake scaled to 35% amplitude as showin Fig. 13. Figures 15–14 show the absolute acceleration of the first floor and the second floorxa1



Figure 10: Loop-gain transfer functions.

0 1 2 3 4 5 6 7 8 9 10−30

−25

−20

−15

−10

−5

0

5

10

15

20

Frequency (Hz)

Mag

nitu

de (d

B)

Experimental loop gainAnalytical loop gain

Figure 11: Transfer function from the ground acceleration to the first floorabsolute acceleration .

xgxa1

0 1 2 3 4 5 6 7 8 9 10−50

−40

−30

−20

−10

0

10

20

Frequency (Hz)

Mag

nitu

de (d

B)

Experimental uncontrolledExperimental controlledAnalytical controlled



Figure 12: Transfer function from the ground acceleration to the secondfloor absolute acceleration .

xgxa2

0 1 2 3 4 5 6 7 8 9 10−50

−40

−30

−20

−10

0

10

20

30

Frequency (Hz)

Mag

nitu

de (d

B)Experimental uncontrolledExperimental controlledAnalytical controlled

Figure 13: Measured table acceleration due to 35% El Centro drive signal.

0 10 20 30 40 50 60−150

−100

−50

0

50

100

150

Time (sec)

Acce

lera

tion

(cm

/s2 )



Figure 14: Second floor absolute acceleration due to 35% El Centroearthquake excitation.

xa2

0 10 20 30 40 50 60−400

−300

−200

−100

0

100

200

300

400

Time (sec)

Acce

lera

tion

(cm

/s2 )

UncontrolledControlled

Figure 15: First floor absolute acceleration due to 35% El Centroearthquake excitation.

xa1

0 10 20 30 40 50 60−250

−200

−150

−100

−50

0

50

100

150

200

250

Time (sec)

Acce

lera

tion

(cm

/s2 )

UncontrolledControlled



of the bench-scale structure when excited by the 35% N-S component of the 1940 El Centroearthquake. Figures 16–17 show the relative displacement and the acceleration of theAMD when controller is on. Table 1 provides a summary of the peak responses for the controlledand uncontrolled systems. As can be seen from these results, the acceleration feedback controlsystems are quite effective. Note that at 116% El Centro earthquake, the AMD reaches its strokelimit ( i.e., the actuator saturation). Therefore, this benchscale model can provide an effective plat-form for studying such phenomenon. Research is currently underway at University of NotreDame focusing on this issue.

Table 1: Peak responses due to 35% El Centro earthquake.

Controller(cm/s2) (cm/s2) (cm) (cm/s2) (V)

uncontrolled(mass locked)

230.67 314.09 — 314.09 —

controlled 124.38 204.99 2.871 452.85 1.900

xa2

Figure 16: AMD relative displacement due to 35% El Centro earthquakeexcitation.

xra

0 10 20 30 40 50 60−3

−2

−1

0

1

2

3

Time (sec)

Disp

lace

men

t (cm

)

xra xaa

xa1 xa2 xraxaa u



Conclusions

This paper has shown that appropriately constructed bench-scale models can be used tostudy important aspects of full-scale structural control implementations. Important issues such assensor/actuator dynamics, control-structure interaction, actuator saturation, output feedback con-trol design, digital control implementation, etc., are all readily examined using the bench-scalemodel, making it an effective tool for familiarizing students and practitioners with control systemdesign and the associated challenges. It is envisioned that the total cost of this system, includingthe structural model, AMD, sensors, digital control system, power amplifier, spectrum analyzer,small-scale shaking table etc., is well within the range of most educational institution.

Acknowledgment

The partial support of the National Science Foundation under Grant Nos. CMS 95–00301and CMS 95–28083 (Dr. S.C. Liu, Program Director) is gratefully acknowledged. We also wish tothank Quanser Consulting Inc. for providing the bench-scale structure, the active mass driver, theMultiQ I/O board and the WinCon software used in this work.

Figure 17: AMD absolute acceleration due to 35% El Centro earthquakeexcitation.

xaa

0 10 20 30 40 50 60−400

−300

−200

−100

0

100

200

300

400

500

Time (sec)

Acce

lera

tion

(cm

/s2 )



References

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