Semi-Active Vibration Control Device Based on Superelastic

STRUCTURAL CONTROL AND HEALTH MONITORINGStruct. Control Health Monit. 2013; 20:890–902Published online 3 May 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.1500

Semi-active vibration control device based on superelasticNiTi wires

F. P. Amarante dos Santos1,*,†, C. Cismaşiu1 and J. Pamies Teixeira2

1Centro de Investigação em Estruturas e Construção–UNIC, Faculdade de Ciências e Tecnologia, Universidade Nova deLisboa, Quinta da Torre, 2829-516 Caparica, Portugal

2UNIDEMI–Unidade de Investigação e Desenvolvimento em Engenharia Mecânica e Industrial, Faculdade de Ciências eTecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal

SUMMARY

The present paper presents a physical prototype that simulates the response of a single degree of freedom dynamicsystem, equipped with a novel semi-active vibration control device. This device comprises two superelastic NiTielements working in phase opposition and aims to prevent deck unseating in simply supported bridges, during aseismic excitation. The special design of this device allows to avoid problems related to stress–relaxation phenomenaand material degradation because of cyclic loading that have been observed in similar passive dissipation devices. Theproposed design uses a strategy that permits the continuous adapting of the accumulated stress in the NiTi wires, on thebasis of the response of the device to external excitations. Although unloaded, the NiTi elements remain strain/stressfree, preventing stress–relaxation phenomena. With the occurrence of a dynamic excitation, a cumulative strain/stressprocess in the superelastic wires is initiated, enabling higher martensite transformation ratios and therefore increasingthe damping capacities of the system while keeping the stresses in the wires inside a narrower superelastic window.The strain/stress accumulation in the superelastic wires is a direct result of the motion of the structure itself, with noneed for external energy input. Copyright © 2012 John Wiley & Sons, Ltd.

Received 13 May 2011; Revised 9 January 2012; Accepted 12 March 2012

KEY WORDS: semi-active vibration control; energy dissipation systems; shape-memory alloys; superelasticity;seismic devices; unseating

1. INTRODUCTION

Past earthquakes have shown that the damage induced in bridges can assume several different forms,depending, among others, on factors such as the ground motion itself, conditions depending on thebuilding site, the adopted bridge structural solution, and its specific detailing provisions. Unseatingof the bridge superstructure at in-span hinges, or at simple supports, is one of the most severe formsof bridge seismic damage, leading to possible catastrophic consequences. In the case of simplysupported bridges, unseating brings about the toppling of the spans from their supports, causing thestructure to collapse. Bridges with inadequate seat lengths or restraints are more prone to spanunseating, requiring adequate seismic retrofitting to modify their dynamic response and control thedeck displacement. This is traditionally achieved using restraining systems built up of steel cables that,if designed to remain elastic, lack the ability to dissipate energy and are responsible for the transmissionof large seismic forces to other structural components. After yielding, these elements tend to accumulateplastic deformations in repeated loading cycles that can also result in unseating [1]. Several other unseat-ing prevention devices for bridges have been presented in the past decades, namely fluid-viscous

*Correspondence to: F. P. Amarante dos Santos, Centro de Investigação em Estruturas e Construção–UNIC, Faculdade deCiências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829–516 Caparica, Portugal.†E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd.

SEMI-ACTIVE VIBRATION CONTROL DEVICE BASED ON SUPERELASTIC NITI WIRES 891

dampers and metallic dampers [2]. Although these devices are able to dissipate energy, they lack thecapacity for re-centering, which is a very important asset to control hinge opening in bridges duringseismic actions. To overcome the limitations presented by these devices, alternative solutions forseismic retrofitting of structures have been proposed, on the basis of shape-memory alloys (SMAs) [1],a unique class of metallic alloys that exhibit a peculiar thermo-mechanical property, called superelasti-city. This property enables the material to withstand large cyclic deformations (up to 8%), withoutresidual strains while developing a hysteretic loop. This high inherent damping, combined withrepeatable re-centering capabilities and relatively high strength properties, has led several authors tostudy the retrofit and rehabilitation of bridges using SMA restraining cables [1–6]. Their efficacy whenused as seismic links has been confirmed, as they reduce the relative hinge displacements at theabutments much more effectively than conventional steel cable restrainers [4–6].

Taking advantage of the superelastic (SE) effect, SMA-based seismic damping devices are aimed to con-centrate the energy dissipation in controlled locations. These energy dissipation capabilities can be enhancedby the introduction of an initial prestress in the SE wires. Prestress enables the system to work at highermartensite transformation ratios and, hence, to exhibit higher damping [7,8]. However, when thematerial agesat constant strain, in the coexistence domain, stress–relaxation occurs, leading to a stress step in the forwardtransformation plateau of the hysteretic cycle [9,10], decreasing the effectiveness of the original prestress.

It is also known that SE elements exhibit permanent deformation because of progressive cumulativecreep during cyclic loading, before the full stabilization of the SE hysteresis [11,12]. This causes thenet strain produced by a given structural oscillation to be reduced, decreasing the energy dissipationcapabilities of the material. Cumulative creep in NiTi alloys is related to dislocations and other latticedefects, generated at high stress during the preceding loading cycle [13,14], and because of the repeatedmotion of the parent-martensite interface [15]. Wang et al. have shown that with the same number ofcycles, the residual strain increases with strain amplitude [16].

The novel semi-active vibration control device, proposed in the present paper, originates from theNiTi-based passive dissipation device reported by Dolce et al. [7]. As to increase its energy dissipationcapabilities, the original device was made of sets of prestressed wires working in phase opposition. Toavoid problems related to relaxation phenomena and cyclic loading, usually associated with similarpassive control devices, the proposed design uses a strategy that allows the continuous adapting ofthe accumulated strain in the SE wires, on the basis of the response of the device to external excitations.Although unloaded, the NiTi elements remain strain/stress free, preventing the stress–relaxationphenomena. With the occurrence of a dynamic excitation, strain/stress starts to accumulate in the SEwires, enabling higher martensite transformation ratios and increasing the damping capacities of thesystem. The cumulative strain/stress in the SE wires is a direct result of the motion of the structure itself,with no need of external energy input.Moreover, the device is able to limit the stresses in the wires inside anarrower SE window, mitigating the degradation of the material because of cyclic loading.

2. PRESTRESS, STRESS–RELAXATION, AND CYCLIC LOADING IN NITI WIRES

Shape-memory alloys in practical use are almost limited to three types: NiTi alloys, Cu-based alloys,and ferrous alloys. For applications regarding the use of SMAs in bridge restrainers, under the directaction of external ambient factors (i.e., wet weather, direct rain), NiTi exhibits an excellent corrosionbehavior, when compared with the moisture sensitive Cu-based alloys [17]. NiTi also presents goodfatigue properties, high corrosion resistance, similar to stainless steel, and ductility [8]. For this reason,NiTi is used in most of the SE-based civil engineering applications.

2.1. Prestress in superelastic NiTi wires

To analyze the influence of prestress on the dissipation capabilities of a SE control system comprisingtwo NiTi restraining wires working in phase opposition, one uses a simplified version of the physicalprototype described in Section 3, corresponding to the configuration presented in Figure 1(a). Thedevice uses 0.406mm diameter NiTi Euroflex SE508 wires (EUROFLEX GmbH, Pforzheim, Germany),with a chemical composition of 51 at% Ni. The device is subjected to a quasi-static harmonic displace-ment yielding the full extent of the martensitic transformation in the wires. The evolution of the

Copyright © 2012 John Wiley & Sons, Ltd. Struct. Control Health Monit. 2013; 20:890–902DOI: 10.1002/stc

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Figure 1. Influence of prestress on superelastic hysteresis: (a) device; (b) prestress = 0; (c) prestress = 50MPa;(d) prestress = 100MPa; and (e) prestress = 200MPa.

892 F. P. AMARANTE DOS SANTOS, C. CISMAŞIU AND J. PAMIES TEIXEIRA

resulting boxforce-displacement diagrams and the shape of the corresponding SE hysteresis ispresented in Figure 1(b)–(e), as the prestress in the wires increases from 0 to 200MPa.

The capacity of a given system to mitigate vibrations is usually evaluated through the equivalentviscous damping, defined as zeq ¼ ED= 4pES0ð Þ , where ED is the energy dissipated in a cycle ofharmonic vibrations and ES0 is the maximum strain energy [18]. The behavior of the system with noprestress is represented in Figure 1(b), where the NiTi wires enable the development of a fulltension/compression SE hysteresis, with an equivalent viscous damping of about 10%. When the NiTiwires are prestressed, Figure 1(c), (d), and (e), the equivalent viscous damping gradually increases asthe hysteresis changes from two distinct SE areas to a single hysteretic curve. The equivalent viscousdamping associated with the SE hysteresis obtained for a prestress of 200MPa is 23%. This means thatby prestressing the NiTi wires, the SE damping available in the system has doubled.

2.2. Stress–relaxation in shape-memory alloys

Superelasticity is a property associated with a diffusionless phase transformation in solids calledmartensitic transformation. During this transformation, the atoms are cooperatively rearranged into adifferent crystalline structure with identical chemical composition, through a displacive distortion pro-cess [19]. In SMAs, the martensitic transformation changes the material from the parent phase, a high-temperature phase called austenite, to a low-temperature phase called martensite. Being a first-orderphase transition, parent and product phases coexist during the phase transformation [20]. In the stress-free state, an SMA is characterized by four transformation temperatures: Ms and Mf during coolingand As and Af during heating. The first two (with Ms > Mf) indicate the temperatures at which theforward transformation starts and finishes, respectively. The last two (with As < Af) are the tempera-tures at which the inverse transformation starts and finishes, Af being the temperature above whichthe martensite becomes completely unstable [15]. The transformation temperatures of the EuroflexSE508 NiTi wires are Mf=�45 �C, Ms=�35 �C, As=�15 �C, and Af=�5 �C. When an SE alloy issubmitted to a given constraint (stress or strain), in its coexistence phase, the critical stress to inducemartensite decreases by a certain amount (Δs). This decrease is due to residual stresses that promotethe formation of martensite, which remains in the material once the applied constraint is removed.These residual stresses are a function of the intensity of the constraint and of its duration [10]. By usingthe Clausius–Clapeyron coefficient (CCC), which translates the relation between temperature and thecritical stress to induce the martensitic transformation, the variation of the transformations temperaturesMs and Mf can be expressed as a function of Δs, yielding ΔMs=ΔMf=�Δs/CCC. Hence, the



transformation temperatures increase when an SE alloy ages under loading�Mf

s > Mis and Mf

f > Mif

�.

The CCC of the Euroflex SE508 NiTi wires is 6.5MPaK� 1.If the material ages at constant strain in the coexistence domain, a stress step occurs, leading to the

stress–relaxation of the material. Figure 2 represents the simplified stress–temperature phase diagrampath associated with aging at constant strain in the coexistence domain, together with the variation inthe corresponding isothermal hysteresis. Three major regions can be identified in the stress–temperaturephase diagram: Md region, where only detweened martensite exists, A region, where only austeniteexists, and Mt, dA region, the coexistence domain where all phases can coexist. One can also identifythe two transformation strips,[M] and [A], for the direct and inverse transformations, respectively.

If an SE cycle is interrupted after describing the first initial path (o-a-b), the martensitic transforma-tion slowly continues to develop, and strain tends to increase. Because the strain is blocked, a set ofauto balanced compressive forces develops within the SE specimen, causing the stress to decrease.If, after a certain period of time, the mechanical tensile cycle is continued, the SE hysteresis deviatesfrom the original path. The stress step reduction is a function of time and austenitic fraction of thematerial during aging. Estimates of the time constants and amplitudes of changes in the transformationtemperatures for NiTi SE alloys are very difficult to obtain because of the large time scales involved inthe aging process. In Cu-based alloys, given the smaller time scales involved, variations of Ms areeasier to obtain and have been reported to reach about 15% [21].

2.3. Cyclic loading in NiTi alloys

To evaluate the stabilization process, a 2.40mm diameter Euroflex SE508 NiTi wire sample is subjectedto an experimental program, consisting of 60 consecutive loading cycles, performed at ambient tempera-ture (’20 �C) and with four different strain rates, ranging from quasi-static conditions up to a strain rate of0.333%/s. The tests are carried out using a Zwick/Roell Z050 (Zwick GmbH & Co. KG, Ulm, Germany)testing machine, and the resulting stress–strain diagrams are presented in Figure 3.

Figure 2. Aging under constant strain in the coexistence zone: phase diagram path and correspondent hysteresis.

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Figure 3. Cyclic tensile tests at increasing strain rates: stress–strain diagrams.



It can be seen that during the cyclic loading, the starting point of the stress–strain diagrams tends todrift away from the origin because of cumulative creep deformation. This drifting is explained by theaccumulation of slip deformations during stress-induced transformation, resulting in residual strains,which increase during the first cycles and tend to stabilize with saturation. The slip deformationsinduce internal stresses that can assist the formation of stress-induced martensite and, as a conse-quence, decrease the critical stress needed to induce martensite [13]. Conversely, the level of thereverse transformation stresses changes very little. As a consequence, the width and size of thehysteretic loop is significantly reduced upon cycling [9] as well as the damping capabilities ofthe material. As the number of cycles continues to grow, the slip deformations increase the densityof dislocations within the crystal structure. These dislocations obstruct the formation of martensite ina way similar to strain hardening in plasticity. As a consequence, the slope of the strain–stress curveincreases during loading [13]. The key parameters defining the extent of the hysteretic loop, namelythe cumulative creep deformation (ep), the variation of the critical stress needed to induce martensite(Δs), and the equivalent viscous damping (xeq), are quantified and plotted in Figure 4.

It can be seen that the variation of these parameters with the number of cycles is rather important.However, an asymptotic behavior is observed, meaning that they tend to gradually stabilize. It can alsobe seen that, for a given number of cycles, changes of these parameters increase with the strain rate.

3. PHYSICAL PROTOTYPE

3.1. General description of the prototype

The physical prototype presented in this section simulates the response of a single degree of freedomdynamic system, equipped with a novel semi-active vibration control device made up of two SE NiTiwire elements working in phase opposition.

The objective of the proposed semi-active control device is to limit the hinge opening during adynamic event, while keeping the stress in the wires inside a prescribed SE window, to mitigate thedegradation of the material because of cyclic loading but guaranteeing a minimal threshold to theirstress level. As the strain is self-adjusting, the wires are strain/stress-free when not subjected to adynamic excitation, limiting aging problems.

The stress in the SE wires is adjusted by controlling the displacements of the wires at their supports. Thetwo wire supports can assume, independently, two configurations, locked or unlocked. By default, thesupports are locked, restraining the SE wires. If the system needs to compensate for an excessively low orhigh stress in a givenwire, it momentarily unlocks the wire through a controlled velocity process andwithoutintroducing additional forces into the system. The semi-active system bounds the stresses in the SE wiresbetween an upper and a lower stress limit. During the dynamic oscillations, if the stress in a given wirereaches one of these values, the corresponding support is unlocked until the displacement of the mass isreversed. The process of unlocking and subsequent locking of an SE wire allows the system either toincrease their cumulative stress, when compensating for excessively low stresses, or to decrease them, whencompensating for excessively high stresses. As the compensation for lower stresses is larger and usuallymorefrequent than the compensation for higher stresses, the net accumulated stress in the SE wires is positive.

The proposed semi-active device uses a control strategy that allows the continuous adapting of theaccumulated stress in the wires, on the basis of the response of the device to external excitations. As in

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Figure 4. Influence of cycling on superelasticity: (a) cumulative creep; (b) critical stress to induce martensite; and(c) equivalent viscous damping.



an active control system, a controller monitors the feedback measurements and generates appropriatecommand signals for the device and, as in a passive control system, the control forces are developed as aresult of the motion of the structure itself, with no need of external energy input. As the control forces actas to oppose the motion of the structural system, they promote the global stability of the structure [22–26].

The prototype is used to simulate the dynamic response of a simple supported bridge with SErestraining cables in the deck–abutment interfaces, as illustrated in Figure 5.

For the system to be able to continuously read and adjust the stress values in the SE wires, each wireis equipped with a load cell and a linear actuator placed at opposite endings of the wire. The design andmanufacturing of the physical prototype was carried out using an educational version of SolidWorks.Its kernel elements are shown in Figure 6.

The moving mass module (MMM), which accommodates the load cells, is mounted on rails, enablingthe displacement of the module in the direction of the dynamic loading. This displacement and thecorresponding acceleration are monitored by a Solartron DC25 (Solartron Metrology, Bognor Regis,United Kingdom) long-stroke linear variable differential transformer displacement transducer and anaccelerometer. The rails are fixed to a set of bars that also support both of the linear actuators through thickend plates. The linear actuators comprise a clamping device that constrains the movement of the remainingextremity of the SE wires. The bars are rigidly connected to a shake-table by means of four brackets. Thebase of the MMM (10� 20� 20� 30 cm) is made of steel and can accommodate a series of additionalsteel plates, with different dimensions and weights, which are fixed by two metallic pins. The MMM isprovided with a set of four steel beveled shape wheels, with RHP 618/8 bearings (ARN TradingLtd t/a AHR International, St Albans, UK) and is mounted on a set of two 40� 10� 300mmaluminum bars, with wedge-shaped rails. As the angle presented by the wedge-shaped rails is widerthan the one shown by beveled wheels, the contact area between the two pieces is minimized, reducingthe mechanical friction developed in this interface.

3.2. Description of the miniature load cells

To cope with the limited dimensions of the MMM, two miniature load cells were designed, one foreach SE wire. The load cells clamp the SE wires into thin aluminum plates, which are laterally fixed

Superelasticrestrainer cables

Superelasticrestrainer cables

Abutment Abutment

Deck

Figure 5. Simple supported bridge with a superelastic restraining system.

Bar

Clamp

End plate

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Load cell

Wedged rail

Moving mass module

Pin

Linear actuator

Figure 6. General design concept for the physical prototype.



to the MMM. These aluminum plates are equipped with a set of four strain gauges disposed in aWheatstone-bridge configuration to enable accurate force readings. The Wheatstone-bridge configura-tion is used to help the measurement of small variations in the resistance that the four strain gaugesproduce, corresponding to a change in the specimen’s strain field. This bridge configuration is usuallycalled a full-bridge because it has four active strain gauges. In this particular case, two are mounted inthe direction of the bending strain, with one on the maximum strain zone of the plate and the other onthe minimum strain zone. The other two acts as Poisson gauges and are mounted transversely to theprincipal axis of strain, adjacent to the other two strain gauges. To build this bridge, two HBMT-rosetteswith two measuring grids, model 1-XY13-1.5/350, were used. Figure 7 represents a schematic drawingshowing the position of the two T-rosettes on the force sensor, together with the correspondingfull-bridge circuit diagram. In this circuit diagram, VCH is the measured voltage of the signal and VEX isthe excitation voltage.

An Finite element (FE) model of the force sensor was analyzed in ANSYS (ANSYS, Inc.,Canonsburg, Pennsylvania, USA) to obtain the strain field corresponding to the loading of the SE wire.This FE model enables not only to define the positioning of the T-rosettes on the force sensor but alsoto calibrate the thickness of the aluminum plate to obtain an adequate signal from the bridge. The forceused in the FE simulation corresponds to a stress level of about 300MPa in a NiTi SE508 wire with0.406mm diameter, which corresponds to half of the maximum stress associated with the loadingplateau. The resulting dimensions for the aluminum plate were 60� 17� 2mm.

The corresponding strain field in the longitudinal direction of the plate and the displacementsalong the direction of the SE wire is presented in Figure 8(a) and (b), respectively. The maximumabsolute strain in the plate yields 0.25me, corresponding to a stress of about 18MPa. The maximumdisplacement in the plate along the wire’s axis yielded 0.013mm.

To guarantee that the strain gauge is able to perform its task properly, the strain to be measuredhas to be transferred faultlessly and free of loss. To achieve this purpose, an intimate connection isrequired between the strain gauge and the aluminum plate. The surface of the metal was firstcleaned, and a special cyanoacrilate cold curing adhesive (Z70) was used to guarantee the requiredbonding between the strain gauge and the plate.

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Figure 7. Schematics of the load cell. Full-bridge circuit diagram.

(a) Strain field (b) Displacement field

Figure 8. Finite element simulation of the aluminum plate: (a) strain field and (b) displacement field.



The strain gauges were connected to a National Instruments SCXI-1520 8-Channel Universal StrainGage Input Module (National Instruments Corporation, Austin, Texas, USA). A virtual instrument (VI)was created using a LabView framework, enabling the signal acquisition from the force sensor and,once calibrated, yielding the desired force readings. A DAQ Assistant Express VI (National InstrumentsCorporation, Austin, Texas, USA, using NI-DAQmx Software), was used to create, edit, and run theanalog input corresponding to the voltage measurement task. By using an averaging process, a samplecompression of the data points was performed to attenuate the noise derived from the readings. Tocalibrate the force-sensor VI, strain readings associated with reference weights were scaled and offset.

3.3. Description of the linear actuators

Two Bosh Rexroth EMC 32-12�5 L100 OF01 precision rolled ball screw actuators were used to adjustthe stress level in the SE wires. They are coupled with two SIGMA II Omron-Yaskawa cylindricalservo-motors (Bosch Rexroth AG, Lohr am Main, Germany), model SGMAH-02AAA61D-OY. ASIGMA-II Omron-Yaskawa SGDH-02AE-OY servo-drive is used to control the servo-motor, allowingfor analog and pulse inputs for speed, torque, and position control.

A special clamping system was designed, allowing the connection of SE the wires to the linearactuators. The clamps are cylindrical-shaped elements made of steel, with 20mm diameter. They arebuilt up of two main components that when pressed together constrain the SE wire from moving.One of these pieces displays a narrow, longitudinal indentation that helps to fix the wire into place.The linear actuator modules are supported by two aluminum plates, measuring 135� 80� 20mm.These plates are rigidly fixed to a pair of 720mm long, load bearing aluminum Bosch-Rexroth30� 30 strut profiles weighing 0.80 kg/m. These bars also accommodate the rails for the MMM.The Bosch-Rexroth profiles are fixed on the top stage of the Quanser Shake-Table II, as illustratedin Figure 9, where a view of the complete prototype is shown.

3.4. Description of the control system

The control system of the physical prototype is presented next. The control variable of the system is theanalog voltage level for the servo-drive’s speed reference, ranging from zero to 6V, which correspondsto the highest allowable rotating speed for continuous operation (3000 rpm). The implemented control-ler, combining proportional, integral, and derivative control actions, can assume two possible states:PID-OFF and PID-ON, which correspond to the unlocked and locked support conditions. Two differ-ent setpoints are possible for PID-ON state, corresponding to the upper and lower force limits definedfor SE wire. The controller chooses the setpoint depending on the force level in the SE wire at a giveninstant. This state is activated above or below the two prescribed force thresholds, the high and lowPID thresholds, respectively. Between these two force delimiters, the controller sets the PID-OFF state.The differential gap existing between the force thresholds that activate the PID controller, and thecorresponding force setpoints, works as an anticipatory feature of the system. It provides the controllerwith a reference force input while the force in the SE wire is still approaching this value.

The controller transfer function Gc(s) comprehends three terms, each one associated with thecorresponding control action,

Figure 9. Physical prototype.



Gc sð Þ ¼ Kp þ Ki

sþ Kds ¼ Kp 1þ 1

Tisþ Tds

� �(1)

where s is a complex variable, Kp, Ki, and Kd are constants called gains, Ti =Kp/Ki is the integraltime, and Td =Kd /Kp is the derivative time.

Being a closed-loop control system, the stress output signal C(s) is fed back to the summing point,where it is compared with the reference stress input R(s), yielding the actuating error signal E(s). Theoutput signal of the controller, U(s), is the analog speed reference input for the servo-drive. Thefeedback-path transfer function, H(s), corresponds to the force-sensor, which measures the outputvariable to make it comparable with the reference input signal, resulting in the feedback stress signal,B(s). The controlled process is defined by the transfer function Gcp(s).

The implementation was performed using the LabView PID Control Toolset Applications, on thebasis of a basic PID algorithm, having as main inputs the setpoint, which is the reference input stress,R(s), the process variable, B(s), the PID gains, and the output range. The PID gains consist of a clusterof three values, corresponding to Kp, Ti, and Td. The over-travel limit function is used to prevent the SEwire from failure by limiting the maximum allowing stress to a prescribed value.

The resulting block diagram is presented in Figure 10. The main controller is divided into twoindependent controllers, each one responsible for one of the SE wires. Each of these controllers hastwo reference stress inputs, delimiting the effective SE window, and yield a reference speed output

Figure 10. Block diagram of the superelastic vibration control system with two restraining elements.



for the corresponding servo-drive. The global output signal from the controller comprehends thereference speeds for both servo-drives, U(s) =U1(s) +U2(s).

In the design process of a control loop, to meet given performance specifications, the constants Kp,Ti, and Td in Eq. (1) have to be adequately tuned. When the mathematical model of the process cannotbe easily obtained, an analytical approach to this tuning is not possible, and experimental approacheshave to be used. To improve the performance of the controller, a tuning algorithm based on theZiegler–Nichols [27] stability boundary rule was implemented. In this tuning method, the Ki and Kd

gains are first set to zero, and the Kp gain is increased until it reaches the ultimate gain, Ku, at whichthe output of the loop starts to oscillate. The corresponding period of oscillation, Pu is called theultimate period. For the proposed prototype, the ultimate gain yields Ku= 0.30 and the ultimate periodPu= 0.7 s. To obtain a quarter decay ratio, which corresponds to a decay of 25% on the transientresponse in one period, yielding a good compromise between quick response and adequate stabilitymargins [28], the PID gains were set to Kp= 0.18, Ti = 0.35, and Td= 0.084.

4. EXPERIMENTAL RESULTS

To assess the performance of the proposed control system, the physical prototype is subjected to aharmonic excitation with a frequency of 1Hz and an amplitude of 5 cm, using a shake-table. Thelow and high setpoints of the PID controller are set to 11% and 22% of the maximum force (Fmax = 60N), and the PID threshold limits are set to 13% and 24% of the maximum force, respectively, resultingin a gap of 2%. In spite of this anticipatory feature of the controller, a small overshoot is observed forboth the upper and lower stress limits.

To analyze the response of the system to the external excitation, the force time history in one of theSE wires is presented in Figure 11. At the beginning of the dynamic loading, the SE wires are stress/strain-free. When the MMM starts to move, and during the first 10 s of the experiment, the controlsystem is switched off. As the stresses induced in the SE wires are in phase opposition, the wires arestrained alternately. After the controller is switched on, the system rapidly starts to compensate forlow stresses in the SE wires, and the corresponding force readings are shifted upwards. When theMMM moves in one direction and the stress in one of the SE wires decreases below a given threshold,the corresponding linear actuator shifts in the same direction, as it tries to accommodate the displace-ment introduced by the external excitation. During the controlled phase, the force values in the SE wiresare delimited by the two reference stress inputs, also limiting the force which is transmitted to thesupports. These values correspond to the low and high setpoints of the PID controller, respectively.

The force accumulation in the SE wires enhances the damping capability of the system becausethe extent of the martensitic transformation is increased. This can be seen in the correspondingforce-displacement diagram depicted in Figure 12. When the controller is switched off and theSE wires work alternately, they remain in their austenitic form. This is translated by a linear

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Figure 11. Force time history in one of the superelastic wires.


20

15

10

5

0

-5

-10

-5 0 5 10 15

1

2Initial cycle

Final cycle[mm]

Figure 12. Force-displacement diagram evolution.

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.40 10 20 30 40 50 60 70 80 90

CONTROL-OFF CONTROL-ON

¨

Figure 13. Acceleration time history.


relation between the total force yielded by the system and the corresponding displacements of theMMM, the initial cycle in Figure 12. When the control system is switched on and the SE wires startworking simultaneously, as they begin to accumulate force, the overall stiffness of the system isincreased. This increase is represented in Figure 12 by step 1, during which the slope of the linerepresenting the force-displacement relation becomes steeper because both of the austenitic SE wiresstart contributing to the system’s stiffness. After this initial stiffening, as the SE wires continue toaccumulate force, stress-induced martensite starts to develop and the system becomes gradually moreflexible. This process is described by step 2 and leads to the appearance of a stabilized SE hystereticloop. The shifting of the center of the loop to the negative displacement region means that the systemhas sustained a rigid-body movement to the left, with respect to its original position.

The acceleration time history of the MMM, as monitored during the experimental test, is shown inFigure 13. According to this register, the acceleration levels in the MMM are decreased when thecontrol system is switched on, which is consistent with the additional damping provided to the systemby the SE wires. When the external excitation ceases to exist, the acceleration rapidly tends to zero.

5. CONCLUSIONS

A physical prototype that simulates the response of a controlled single degree of freedom dynamicsystem allows to illustrate the potential of a novel semi-active vibration control device on the basis ofSE NiTi wires. The design of the semi-active vibration control device is based on two main guidelines:

1. SE wires are stress-free until the beginning of the dynamic excitation to prevent stress–relaxation;2. Control of the stress levels in the SE wires during the dynamic excitation. For low stress levels

in the wires, a process of stress accumulation enables higher martensite ratios and thereforehigher dissipation capabilities. In the case of high stress levels, a stress relieve process prevents



the wires from yielding while also limiting the force transmitted to the adjacent structural ele-ments. By limiting the stress levels in the SE wires, one also helps to mitigate the degradationeffects in the SE material because of cyclic loading.

A thorough description of the kernel parts of the prototype provides an extended insight into thedeveloped approach to meet these guidelines. The integration of the control algorithms into theprototype is also addressed. The control algorithms, on the basis of a PID approach, are implementedusing a LabView platform. Several considerations regarding this type of control systems are made,including relevant aspects related to controller tuning.

To assess the performances of the proposed semi-active vibration control device, the physicalprototype was subjected to an external harmonic excitation, induced by a shake-table. Analyzing theresults of these experimental tests, one can conclude that the control device performed adequately. Itpromotes the force accumulation in the SE wires, enabling the development of a wide SE hystereticloop and also controls their maximum force and decreases the acceleration of the MMM.

The main drawback of the presented mechanism consists in the fact that the stress control in the SENiTi wires is achieved through the use of electromechanical actuators. The compensation either forhigh or low stresses in the SE wires is achieved by the movement of these actuators, which are placedin series with the wires, in the force flow path. This means that the actuators have to be able to sustainthe forces developed in the SE wires during the dynamic loading, which, in the case of civil engineer-ing structures, are considerable high. To comply with these forces, it would be necessary to use highbearing capacity electromechanical actuators, with high costs and high energy demands, undesirableto a restraining mechanism. To meet the requirements of fast response and low power consumption,promising alternatives are currently being studied.

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Semi-Active Vibration Control Device Based on Superelastic

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