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Sensors and Actuators A 225 (2015) 71–80

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

j ourna l h o mepage: www.elsev ier .com/ locate /sna

esign and control of a novel compliant differential shape memorylloy actuator

hao Guoa, Yongping Pana, Liang Boon Weeb, Haoyong Yua,∗

Department of Biomedical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575DSO National Laboratories, 20 Science Park Drive, Singapore 118230

r t i c l e i n f o

rticle history:eceived 6 January 2014eceived in revised form 14 January 2015ccepted 15 January 2015vailable online 11 February 2015

eywords:hape memory alloy

a b s t r a c t

This paper presents the design and control of a novel compliant differential shape memory alloy (SMA)actuator with significantly improved performance compared to traditional bias and differential typeSMA actuators. This actuator is composed of two antagonistic SMA wires and a mechanical joint coupledwith a torsion spring. The differential SMA wires are utilized to increase the response speed, and thetorsion spring is employed to reduce the total stiffness of SMA actuator and improve the output range.Theoretical models that include the stiffness equations of the SMA wire as well as the dynamics of threedifferent SMA actuation systems are introduced and compared. Simulation and experimental results have

ompliant SMA actuatorio-inspired designaturated PI control

proved that this new actuator can provide larger output angle compared to conventional SMA actuatorsunder the same conditions. Moreover, regulation and tracking control experiments have demonstratedthat this compliant differential SMA actuator achieves higher response speed compared to the bias SMAactuator using compatible PI controller. The tracking performance is further improved by the saturatedPI controller.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

Shape Memory Alloy (SMA) is an intelligent material that canemember its original shape at low temperature and return tohe pre-deformed shape by heating over a threshold temperature.ecause of this unique property, it has been receiving consider-ble attention as mini-actuator in recent years [1]. Among the SMAaterials, Nitinol (Ni–Ti) alloy has been widely employed for mini-

ctuator design due to its high strain (up to 8%). Compared toonventional (electric, hydraulic, and pneumatic) actuators, SMActuators have the advantages of high force to mass ratio, bio-ompatibility, small size, simple mechanical design, and silenceperation. These advantages make them suitable for a wide vari-ty of applications, like soft robotics [2,3], robotic surgical systems4,5], and grippers [6,7]. Nevertheless, SMA actuators present sev-ral disadvantages, such as, low energy efficiency, slow responseate, nonlinearity, which encourage additional effort in specialechanical design and advanced control strategy.

SMA wire can only achieve unidirectional actuation, thus it is

ecessary to provide a recovery force via a weight, a spring ornother antagonistic SMA wire to realize bidirectional movement.

∗ Corresponding author. Tel.: +65 6601 1590.E-mail address: bieyhy@nus.edu.sg (H. Yu).

ttp://dx.doi.org/10.1016/j.sna.2015.01.016924-4247/© 2015 Elsevier B.V. All rights reserved.

Typically, there are two classes of SMA actuators: bias type SMAactuator and differential type SMA actuator [8,9]. The former one,composed of a SMA element and a bias spring, has slow responseas the speed is determined by the cooling process and the passivespring. The latter one, which consists of two antagonistic SMA ele-ments, has faster speed of response than the bias actuator, but itconsumes more power and the angle is restricted by the stiff antag-onistic SMA elements. SMA actuators with large working range,contraction strain and quick response are desirable for differentpurposes in many fields [10]. To achieve this goal, a series of newSMA-based actuators or mechanisms have been developed. Forinstance, Grant and Hayward reported a differential SMA actua-tor which is comprised of 12 SMA wires in a helical arrangement toproduce larger strains [11]. Zhang and Yin presented a SMA-basedartificial muscle composed of 16 parallel SMA wires and a simplelinear spring to improve the driving force [12,13]. Paik and Woodintroduced a bidirectional SMA folding actuator to produce twoopposing 180◦ motions [14]. Park et al. [15] proposed a differen-tial spring-biased SMA actuator for a bio-mimetic artificial finger.In this design, the spring was directly connected to the SMA wire,which may absorb the contraction length of SMA wires.

Compared to stiff actuators, compliant actuators which incor-porate passive elastic element like spring or damper possess theability of absorbing shocks, storing and releasing energy, and safeinteractions with the environment [16]. These characteristics have

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2 Z. Guo et al. / Sensors and

ttracted strong interest from the areas of rehabilitation and sur-ical robotics. Many types of compliant actuators, such as serieslastic actuator [17,18], variable stiffness actuator [19], and pneu-atic artificial muscle [20] have been developed. Several advancedaterials such as ionic polymer metal composite (IPMC) [21],

lectro-active polymers (EAP) [22] are proposed as soft actuatorsor their large deformations, but they can generate only smallorces. Unlike these soft polymers, SMA wire can generate largeorces due to its large Young’s modulus [8]. However, the use ofuch SMA materials in compliant actuator design has not yet beenell investigated.

Inspired by the biological structure of human joint driven byntagonistic muscles with tendons, this paper introduces a com-liant differential SMA actuator from the perspective of stiffness: aoft spring is integrated into an antagonistic SMA actuator, intend-ng to reduce the total stiffness and increase the compliance of theifferential SMA actuator, without compromising the advantagesf conventional SMA actuators.

The rest of this paper is organized as follows. Section 2 describeshe design of the compliant differential SMA actuator, along withhe implementation of two other different SMA actuators. Section

presents the mathematical models as well as a saturated PI con-roller developed for the compliant differential SMA actuator. Theimulation and experimental results are shown in section 4. Sec-ion 5 discusses the potential application of this actuator and theimitation of this study, with concluding comments presented inection 6.

. Actuator design

In this section, we introduce the design of the compliant dif-erential SMA actuator and the experimental testing bench. Wemplement three configurations using the same mechanical setupor the performance comparison of three kinds of SMA actuators.

.1. Compliant differential SMA actuator

Human elbow joint is actuated by antagonistic skeletal mus-les (biceps and triceps) which are connected to the bone throughhe tendon (Fig. 1(a)). Inspired by this biological structure, we pro-ose a new SMA-based compliant differential actuator to mimic thextension/flexion motion of human joint. As shown in Fig. 1(b), thisMA actuator is composed of two antagonistic SMA wires, a torsionpring and two cylindrical couplers. A load is applied on coupler #1y threaded connection. The antagonistic SMA wires, behaving likertificial human muscles, are directly connected to the couplers.MA wires provide the active force for bi-directional motion of thectuator. The torsion spring is used to mimic the human tendon ands packaged inside the couplers. As illustrated in Fig. 1(b), two legsf the torsion spring (0◦ deflection, left hand wind) are restrictedy the slots in the couplers. The active contraction force producedy the SMA wire can be transmitted from one coupler to the othery the torsion spring. In this design, we select a soft torsion spring.ts stiffness is lower than that of the SMA wires. The torsion springas two functions: one is to store the energy and provide the recov-ry force for the SMA wire; the other is to reduce the total stiffnessf the actuator. Fig. 1(c) and (d) shows the integrated Computerided Design (CAD) model and prototype of the compliant differ-ntial SMA actuator. The whole structure of this actuator is simplend easy to implement for different applications.

An experimental testing bench designed to evaluate the perfor-

ance of this compliant differential SMA actuator is presented in

ig. 2. The actuator is assembled into a base, supporting by twoearings on two sides. The coupler #1 is fixed on the axis by a smallcrew (not shown in this picture), while the coupler #2 can free

tors A 225 (2015) 71–80

rotate around the axis. An encoder is connected to the axis by acoupling. The rotational angle of the axis can be measured by theencoder. That means the position of the load and coupler #1 can bedetected. The working process of this actuator is described as fol-lows: when the upper SMA wire is activated by heating, the coupler#1 rotates due to the active contraction force of SMA wire, the loadfollows the rotation of coupler #1, thereby the torsion spring startsto twist and transmits the active force from coupler #1 to coupler#2, the lower SMA wire will be stretched to restrict the rotation, bycontrast, when the lower SMA wire is heated to contract, the activeforce is transmitted in the opposite direction. Based on this prin-ciple, we can heat the antagonist SMA wire and cool the oppositeone to increase the response speed of this actuator.

2.2. Comparison to other SMA actuators

To compare the performance of this actuator with the twotraditional SMA actuators, we implement three configurations torepresent three types of SMA actuators using the same mechanicalsetup. As shown in Fig. 3, they are (a) bias SMA actuator (coupler #1is connected with an SMA wire, coupler #2 is fixed by a hard ironwire, recovery force comes from the torsion spring), (b) differentialSMA actuator (two SMA wires are connected to coupler #1), and(c) compliant differential SMA actuator (two SMA wires are linkedto two couplers respectively, the torsion spring is hidden inside).Fig. 3 includes the CAD model of each actuator and its equivalentmechanical model. Two SMA wires generate the tensile force witha variable stiffness ki and a damping factor bi (here and the fol-lowing i = 1, 2). The torsion spring transmits the SMA force with aconstant stiffness ks. The system damping between two couplers isrepresented by bs. mi represents the mass of each coupler and themass of SMA wire can be neglected (mSMA � mi). The load appliedon coupler #1 is represented as a mass mload. Comparison of thesethree SMA actuators will be discussed in the experimental section.

3. Actuator modeling and controller design

In this section, we present general theoretical models thatinclude the equations of the SMA wire as well as the dynamics ofthe actuation system. These models are developed in several stepsfor clarity. First, the nonlinear stiffness of the SMA wire is givenbased on the constitutive model. And then, the dynamic equationsare developed for the controller design.

3.1. SMA modeling

3.1.1. Constitutive equationAccording to Liang and Rogers [8,23], the constitutive equation

of SMA wire can be described as the relation of stress �, strain ε,temperature T and martensite fraction � (0 ≤ � ≤ 1, � = 1 means SMAtotally in martensite phase, � = 0 means SMA in austenite phase).The general form is written as

� = Eε + ˝� + �T (1)

where E, and � represent the Young’s modulus, phase transfor-mation constant and thermal expansion coefficient, respectively.For SMA material, is a constant and can be expressed as =−εLE, where εL is the maximum recoverable strain of SMA. Sincethe influence of � on the strain is much smaller than that of ˝, the

thermal expansion part in Eq. (1) can be neglected. The constitutiveequation is simplified as

� = Eε − εLE�. (2)

Z. Guo et al. / Sensors and Actuators A 225 (2015) 71–80 73

Fig. 1. (a) Structure of human elbow joint; (b) the proposed bio-inspired human joint mechanical model, two SMA wires, two couplers and a torsion spring play as theantagonistic muscles, bones and tendon respectively; (c) the integrated design in CAD model and (d) the prototype of the compliant differential SMA actuator.

totyp

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E

wt

t

�

F

F

Fig. 2. (a) CAD model and (b) pro

The Young’s modulus is the function of martensite fraction,xpressed in following expression

= �EM + (1 − �)EA (3)

here EM and EA are the Young’s modulus constants correspondingo martensite and austenite phases, respectively.

Taking into account the initial condition of SMA wire (�0, ε0, �0),he constitutive Eq. (2) is given by

=∫ t

E(ε − εL�)dt + �0. (4)

0

The contraction force of SMA wire satisfies

= A� = kεl (5)

ig. 3. CAD models and equivalent mechanical models for three SMA actuators: (a) bias S

e of the experimental test bench.

where A and l are the cross-sectional area and the initial length ofSMA wire, respectively. k is the stiffness of SMA wire, from Eq. (5),which is written as

k = �A

εl. (6)

Considering two terminal conditions, where the SMA wire intwinned martensite phase without load (�0 = 0, ε0 = 0, � = 1), andfull austenite without load (�0 = 0, ε0 = 0, � = 0) [24], since thephase transformation rate is equal to zero, thereby from Eq. (4),

the SMA stiffness in full martensite phase and austenite phase aregiven by

kM = EMA

l, kA = EAA

l. (7)

MA actuator; (b) differential SMA actuator; (c) compliant differential SMA actuator.

74 Z. Guo et al. / Sensors and Actuators A 225 (2015) 71–80

Table 1Parameters of the SMA wire and the compliant actuator.

Parameter Value Parameter Value

EM 28 GPa CA 10MPa/◦KEA 75 GPa CM 10MPa/◦KAs 88 ◦C Tamb 20 ◦CAf 98 ◦C A 4.9 × 10–8 m2

Ms 72 ◦C Aw 290.45 × 10–6 m2

Mf 62 ◦C Cp 320 J/Kg ◦Cmw 6.8 × 10−4 kg/m εL 2.3%R 20 �/m εA 5%l0 0.37 m h0 20m1, m2 8 g h2 0.001mload 100 g rl 20 mmJ , J 0.38 kg (mm)2 r ,r 15 mm

3

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equations involved in the overall mathematical models of the com-pliant actuation system is shown in Fig. 5. This model clearlyillustrates a complex multiple-input multiple-output (MIMO) sys-tem with cross-coupling effects. Two independent output variables

1 2 1 2

bs 0.5 b1 ,b2 2ks 0.0018 N m/1◦ rs 7.5 mm

.1.2. Heat transformation modelSMA has inherent hysteresis during the transformation between

artensite phase and austenite phase. The martensite fraction � isodeled by SMA temperature and stress [8,23].During the heating transformation (martensite phase to austen-

te phase) � is given by

� = �M

2

{cos[aA(T − As) + bA�] + 1

}for As + �

CA≤ T ≤ Af + �

CA

(8)

nd during the cooling transformation (austenite phase to martens-te phase) � is given by

� = 1 − �A

2cos[aM(T − Mf ) + bM�] + 1 + �A

2

for Ms + �

CM≤ T ≤ Mf + �

CM

(9)

here Ms, Mf, As, Af are the start and finish transition temperaturesssociated with martensite and austenite phase transformations.A, bA, aM and bM are constants derived from four transition tem-eratures, aA = �/(Af − As), bA = −(aA/CA), and aM = �/(Ms − Mf ),M = −(aM/CM). CA, CM are material coefficients. �M,�A are the ini-ial martensite fractions for each transformation.

.1.3. Heat dynamicsThe heat for phase transformation is generated by applying a

oltage to the SMA wire. A SMA heat transfer model is formulated toescribe the rate of temperature change due to a change in voltagef the wire and the convective heat loss to the environment. Thisodel can be defined by the first-order dynamic equation [25].

wcpT = V2

R− hAw(T − Tamb) (10)

here mw is the mass per unit length, cp is the specific heat con-tant, R is the SMA’s resistance per unit length, V is the appliedoltage, Aw is the wire surface area, Tamb is the ambient temper-ture and h is the heat convection factor, which is a function ofhe temperature with the parameters h0 and h2, h = h0 + h2T2.wo NiTi SMA wires (0.25 mm diameter, the initial length is 0.37 mTwinned martensite phase), Flexinol, Dynalloy, Inc.) are selectedor our actuator design. Their properties are summarized in Table 1.

.2. Actuator modeling

A simplified schematic diagram and its equivalent mechanicalodel of the compliant differential SMA actuator are presented in

ig. 4. The couplers are actuated under the function of the uppernd lower SMA wires. The rotational angle of each coupler, relative

Fig. 4. (a) Simplified schematic diagram, drawing with applied forces and (b) theequivalent mechanical model of the compliant differential SMA actuator.

to the y axis, is defined as �i. Fi is the SMA contraction force and riis its moment arm, respectively. s is the torque of torsion spring.The moment arm of the load is r1. Ji represents the inertia constantof each coupler.

The main parameters of the compliant actuator are shown inTable 1. Taking into account the damping and stiffness in the actu-ation system, the dynamic equation of each coupler is given by

{J1�1 = F1r1 − b1�1 − ks(�1 − �2) − bs(�1 − �2) − mloadgrl cos �1

J2�2 = ks(�1 − �2) + bs(�1 − �2) − F2r2 − b2�2

.

(11)

For comparison, we build the dynamics of the two other SMAactuators based on the mechanical model in Fig. 3, the equation ofthe bias SMA actuator is written as

J1�1 = F1r1 − b1�1 − ks�1 − bs�1 − mloadgrl cos �1. (12)

The differential SMA actuator’s dynamic model is given by

J1�1 = F1r1 − b1�1 − F2r1 − b2�1 − mloadgrl cos �1. (13)

Hence, the contraction force is related to the SMA stiffness andstrain. The strain rate of SMA wire εi is derived from kinematics asa function of its joint velocity �i

εi = ri�i/li. (14)

Based on the modeling process, a schematic diagram of the

Fig. 5. Block diagram of the mathematical model of the actuation system.

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ig. 6. (a) Flow diagram of the position control system for the compliant differentialMA actuator, and (b) structure of the SPI control strategy.

1 and �2 can be controlled by applying voltages on two SMA wireseparately. Since the load is applied on coupler #1, � = �1 representshe output angle of the actuator. �r is the reference angular position.

.3. Saturated PI Controller design

From the actuation system modeling derived in Section 3.2, it islear that the SMA actuator position can be controlled by the volt-ge signals. It is worth noting that the actuation model is importantor the simulation and controller parameters selection although it isot directly applied to controller design. In this section, a saturatedroportional Integral (PI) controller is designed to demonstrate theerformance of the proposed compliant differential SMA actua-or. The flow diagram of the position control system is presentedn Fig. 6(a). Two control voltages produced by the controller arepplied to the upper and lower SMA wires to get the desired posi-ion.

The structure of the saturated PI controller is shown in Fig. 6(b). basic control law si for each SMA wire is defined as follows:

i = ci + cPi� + cIi

∫�dt, (15)

here � = � − �r is the position error. cpi, cIi are the proportional

nd integral gains, respectively. These parameters are chosen foresired tracking performance. It has been observed that the pas-ive SMA wire in the different SMA actuator can produce a fewillimeters of slack when it cools [10]. This will cause the wire to

ontract enough to take up the slack before it begins to pull theoupler. Slack in the wire will slow the response speed of the con-rol system. To solve this problem, ci is set in a small voltage toeep SMA wires in tension when the position error is zero, for theurpose of reducing the slack of SMA wires. Each si is restricted by

boundary layer between a high voltage ViH and zero. Thus, theontrol voltage Vi for each SMA wire is defined as⎧

i =

⎪⎨⎪⎩

ViH if si ≥ �i

si if 0 ≤ si < �i

0 if si < 0

. (16)

tors A 225 (2015) 71–80 75

Specifically, the tracking performance can be improved byadjusting the thickness of the boundary layer. If si is over the bound-ary layer �i, SMAs are activated by the high voltage ViH to get quickresponse. If si enters the boundary layer, within proper tuning ofthe control gains, the voltage is reduced to avoid overshoot forsmoother and more stable response. If the value si is lower thanzero, the controller switches to zero for cooling the SMA wire. Themagnitude of the boundary layer is determined experimentally toprotect the SMA wire from overheating.

4. Simulation and experimental results

In this section, we provide a description of the experimentalsetup. Three types of experiments have been performed to test andcompare the performance of the compliant actuator with the othertwo conventional actuators.

4.1. Experimental setup

The experimental setup has been developed to evaluate theperformance of this compliant differential SMA actuator. Beforeto set the experimental setup, each actuated SMA wire (twinnedmartensite state) is passively extended to the fully de-twinnedmartensite state. As shown in Fig. 7(b), an iron stick linked with astandard weight (100 g) is connected to the coupler #1 of the actua-tor as the testing load. The pre-strain of each SMA wire is extendedto 0.03. Including the load force, the initial strain of the upper wireis equal to 0.0336.

Fig. 7(a) and (b) shows the schematic diagram of the control sys-tem and a picture of the experimental setup, respectively. Lab VIEWsoftware (National Instruments Corp., TX) on a computer controlsthe position of the actuator using a power supply (Dual-trackingDC 6306D, Topward Electric Instrument Co., TW), an NI-PCI-6221Data Acquisition (DAQ) card (National Instruments Corp., TX) anda voltage amplifier. The angular position of the actuator, measuredby a shaft encoder (Omron E6B2-CWZ1X, Omron Inc., Japan) witha resolution of 2500 pulses per turn, was collected by the DAQcard. This DAQ card also provided two 16-bit resolution analog volt-age outputs with a full-scale range of ± 10 V to the amplifier. Twoanalog voltage channels were augmented by the amplifier with again of 3.125 V/V and applied on two SMA wires separately. Forcomparison, saturated PI and PI (without boundary layer and ini-tial constant value) control strategies were programmed in the LabVIEW software and experimental tests have been conducted in thefollowing.

4.2. Comparison for the three kinds of SMA actuators

A comparison between this new compliant differential SMAactuator and the other two SMA actuators was performed in twoaspects: stiffness and output angle. A Simulink model was devel-oped in MATLAB/Simulink to simulate the joint motion of the threedifferent SMA actuators with the same load and same input voltagein open loop. Based on the mathematical models of the actuationsystem and the SMA stiffness definition, we can get the stiffnessof the upper SMA wire. Fig. 8 presents the simulated SMA stiff-ness for the three different SMA actuators in a function of recoverystrain (0 → 0.015) and martensite fraction (1 → 0). It displays thatthe stiffness increases from martensite phase to austenite phaseduring heating process. The minimal value is equal to 3.7 kN/mwhen the SMA wire is in fully martensite phase. In this compli-ant actuator design, the stiffness of the torsion spring ks is chosen

as 0.0018N m/1◦; its equivalent stiffness of an extension spring is1.03 kN/m. This value is determined by the parameters of the spring(including the mean coil diameter, diameter of spring wire, num-ber of turns, elastic modulus of the material, and so on), depending

76 Z. Guo et al. / Sensors and Actuators A 225 (2015) 71–80

Fig. 7. (a) Block diagram configuration of the position control system and (b) experimental setup for testing.

Fig. 8. Stiffness of upper SMA wire during heating process, in which blue line,bda

osecattoshS

aeptwahaisSmwSdem

lack line and red line, represent the results of the bias, differential, and compliantifferential, SMA actuators, respectively. Abbreviation in the figure: BS: bias SMActuator; DI: differential SMA actuators; CD: compliant differential SMA actuators.

n the limited space between the two couplers. Thus, this springtiffness is lower than the SMA stiffness (ks < kM). According to thequivalent mechanical models in Fig. 3, the passive stiffness of theompliant actuator includes the stiffness of the unheated SMA wirend the bias spring, which is equal to (k2 · ks)/(k2 + ks) (because theorsion spring and lower SMA wire are connected in series). Thus,he values of passive stiffness of the three SMA actuators follow therder (k2 · ks)/(k2 + ks) < ks < k2. This compliant actuator has themallest passive stiffness. I.e. the actuator presented in this paperas the smallest passive stiffness and is thereby the most compliantMA actuator.

The simulation angles for the three actuators during heatingnd cooling phases are shown in Fig. 9(a). Since it has the small-st passive stiffness, the compliant differential SMA actuator canrovide larger output angle than the other two actuators. To provehis hypothesis and the simulation results, a constant voltage (1 V)ith the same load was applied to the upper SMA wire of the three

ctuators in open loop, raising the temperature of the SMA wire byeating. The lower SMA wire was not activated and remained as

passive spring. The experimental results for the three actuators,ncluding heating and cooling phases of the upper SMA wire, arehown in Fig. 9. The results confirm that the compliant differentialMA actuator provides the largest angle. The maximum angularotion of the compliant differential SMA actuator is close to 30◦,hile the bias SMA actuator is limited to 20◦ and the differential

◦

MA actuator provides only 13 . This limitation in angular motion isue mainly to the high stiffness of the antagonist SMA wire. Thesexperimental results provide strong evidence for the theoreticalodels and simulation results in Fig. 9(a). The dynamic response

Fig. 9. (a) Simulation and (b) experimental results of the three SMA actuators underthe same applied voltage, showing the load angular position over the time.

of the three actuators shows a slight position overshoot beforereaching steady-state, see Fig. 9(b). This behavior is explained withthe aid of the heat dynamics, Eq. (10). During the heating phase,the SMA wire undergoes a phase change that persists until anenergy balance between the power input and the power loss isreached. This energy transfer also corresponds to the temperatureresponse of the SMA wire. Interesting, during the cooling phase,we observed that the three actuators have almost the same cool-ing time. It means that the rate at which the compliant differentialSMA actuator returned to the relaxed state is faster than the otheractuators. This faster rate of the compliant differential SMA actu-ator is provided by stored energy in the torsion spring. The aboveresults clearly indicate that the compliant differential SMA actuatorprovides larger working range under the same voltage stimulatingcondition and a faster system response.

4.2.1. RemarkThe maximum speed of response of this actuator mainly

depends on the input current/voltage through the SMA wire andthe SMA wire’s stiffness. Larger current can increase the responsespeed, while the current should be limited to protect the SMA

wire. In addition, the maximum working range of this compliantmechanism depends on the mechanical range of two couplers, thede-twinned strain of the SMA wire and the stiffness of the SMA wire.When all wires are subjected to provide the same initial conditions

Z. Guo et al. / Sensors and Actuators A 225 (2015) 71–80 77

Fig. 10. Step response of two actuators with different controllers, blue thick dashedline, red thin solid line, dark green thick solid line, and light green thick dash-dot linerepresent the reference (abbreviated as Ref), real value, current on upper SMA wire,ccS

(trct

4

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easoatmafra

Table 2Performance comparison of step response for different control methods.

Step response angle (◦) Time to the stable state (s) Total reductionpercentage

PI BS PI CD SPI CD

0 → 10 4 4.2 0.6 85%10 → 20 4.5 3.5 0.5 89%20 → 10 6 2 1 83%10 → 0 6 2.5 1 83%

Note: Total reduction percentage: from SPI control on CD actuator to PI control onBS actuator. PI BS: PI control for bias SMA actuator, PI CD: PI control for compliant

urrent on lower SMA wire, respectively: (a) bias SMA actuator using PI control, (b)ompliant differential SMA actuator using PI control, and (c) compliant differentialMA actuator using saturated PI control.

pre-strain, current, temperature, length, etc.), the actuator withhe softer joint will have a larger working range motion because theesistance force will be smaller and the wires can experience largerontraction. This is clearly shown in the simulation and experimen-al results.

.3. Regulation results

In the following sections, we compare the tracking performanceetween the bias SMA actuator and the compliant differential SMActuator. The differential SMA actuator will not be compared inhis test due to its limited angle range. Firstly, the experimentalesponses to a series of step inputs were examined. For compar-son, the same PI controller for the two actuators and differentontrollers (PI and saturated PI) for the same compliant differ-ntial SMA actuator have been implemented. The gains of bothontrollers were optimized to minimize the position response timend improve the output accuracy. The voltage boundary value isimited under 4 V.

Fig. 10 shows position responses of both actuators with differ-nt controllers to desired steps of 10◦ and 20◦, and the currentspplied on both SMA wires, respectively. Fig. 10(a) illustrates thetep response of the bias SMA actuator with PI controller. Webserve that this actuator can follow the reference within a rel-tively long time just under one channel current driving. Duringhe heating phase, the rise time to the 10◦ step input is approxi-

ately 4 s. For the response to 20◦, it is slightly longer and requires

pproximately 4.5 s. This is expected as the set point is further awayrom the zero position, so it takes a longer time for the actuator toeach the desired 20◦ set point. During the cooling phase, the aver-ge fall time from 20◦ to the 10◦ and from 10◦ to 0◦ is approximately

differential SMA actuator, SPI CD: saturated PI control for compliant differentialSMA actuator.

6 s. The joint angle reduces slowly to reach the set point under therecovery force from the torsion spring.

Fig. 10(b) shows step response of the compliant differentialSMA actuator using the same PI controller. It is observed that theresponse speed is increased under the function of two channelscurrents. Compared to the bias SMA actuator, the compliant actua-tor reaches the set point faster, while it costs in average 4 s to reachthe stable value during the heating phase, and also an overshoottakes place in this tracking. The rise time is almost the same as thebias SMA actuator. Specifically, to increase the response speed ofthis actuator, the lower SMA wire was heated with a second channelcurrent during the cooling phase. This reduces the fall time to 2.5 s.To further improve the performance, the saturated PI controller wasemployed to control the compliant actuator.

As shown in Fig. 10(c), with properly adjusting the parameters,(set the original current on the SMA wire and increase the currentduring the cooling process), this controller eliminates the overshootand further reduces the response time. Compared to PI controller,during the heating phase, the saturated PI controller reduces therise time on the 10◦, 20◦ step input from 4.2s to 0.6 s, and 3.5 s to0.5 s, respectively. Note that, during the cooling phase, the fallingtime of step response from 20◦ to 10◦, 10◦ to 0◦ reduces from 2.5 s tolower than 1 s. Step response comparisons between bias SMA actu-ator with PI controller, compliant differential SMA actuator withPI controller and compliant differential SMA actuator with satu-rated PI controller are shown in Table 2. The results clearly indicatethat the rise and fall times of step response are decreased signif-icantly, as well as the response speeds both in the heating andcooling phases are increased. The consumed time during coolingphase is reduced over 50% from bias actuator to compliant differ-ential actuator with the same PI controller. Therefore, the compliantSMA actuator has better performance than the bias SMA actuator.Furthermore, our proposed saturated control method can furtherimprove the response results over conventional PI controller. So weachieve a step response time reduction of more than 80%.

4.4. Tracking results

This section presents the comparison of tracking responses toa series of sine inputs with varying frequencies. Fig. 11 showsthe tracking results with 0.05 Hz sinusoidal reference trajectory.Fig. 11(a), is the result of PI control for bias SMA actuator, showinga little disturbance in the rising period of tracking and 2◦ error inthe peak value. Some fluctuations appear in the recorded current ofSMA wire, which cause the disturbance in tracking. The actuator cantrack the reference in the falling process with the help of the torsionspring. Fig. 11(b) illustrates the tracking results of the compliant dif-ferential SMA actuator under PI control. The tracking performance

is improved obviously by controlling two current channels on theSMA wires. The real position smoothly follows the reference tra-jectory, while a time lag is observed at the beginning of rising andfalling time of the sine wave. As shown in Fig. 11(c), the tracking

78 Z. Guo et al. / Sensors and Actuators A 225 (2015) 71–80

Fig. 11. Experimental tracking results for 0.05 Hz sinusoidal reference trajectoryshowing (a) PI control for bias SMA actuator, (b) PI control for compliant differentialSMA actuator, (c) saturated PI control for compliant differential SMA actuator, and(

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Fig. 12. Experimental tracking results for 0.1 Hz sinusoidal reference trajectoryshowing (a) PI control for bias SMA actuator, (b) PI control for compliant differentialSMA actuator, (c) saturated PI control for compliant differential SMA actuator, and

d) error comparison.

esult using the saturated PI controller on compliant SMA actua-or is presented. It illustrates that the saturated PI control methodbtains more accurate and smooth tracking results than the PI con-rol on the same actuator. Fig. 11(d) displays the error comparisonmong the three different tracking. With the same PI controller forhe two different actuators, the error range is reduced from −1◦

o 2◦ to −1◦ to 1.5◦, and the error is further decreased to −0.8◦ to◦ with the saturated PI control method on compliant differentialMA actuator.

Fig. 12 shows the results with 0.1 Hz sinusoidal reference tra-ectory tracking with the three previous ways for 0.05 Hz tracking.ig. 12(a) illustrates the tracking of bias SMA actuator under PIontrol. By adjusting the current on the upper SMA wire, the actu-tor can track the reference with a disturbance during the risingime, while it follows the reference in the falling time with a largerrror. A time lag comes out because of the increased frequency. Tomprove the tracking performance during the falling time, the lowerMA wire in the compliant differential SMA actuator is activated.he real position can follow the reference with some fluctuations,

resented in Fig. 12(b). However, it is hard to catch the peak valueith this simple PI control. We introduce the saturated PI controller

or the compliant differential SMA actuator, and a smooth, stablend accurate tracking is obtained in Fig. 12(c). Fig. 12(d) shows the

(d) error comparison.

error comparison among the different control ways. It is shown thatthe saturated PI method for compliant differential SMA actuatorhas the lowest error, limiting its range among −1◦ to1◦. The out-put error of the compliant differential SMA actuator is smaller thanthe error of the bias SMA actuator, using for both the same PI con-troller. The error is reduced from −2.5◦ to1.5◦ to −1.5◦ to1.5◦. Theerror has been further minimized with the saturated PI controller.In addition, it is obviously observed that the tracking performanceis smooth and the actuator is able to reach the peak of the sinusoidalreference trajectory.

Comparing the results of the same actuator with the same con-troller and different reference frequencies (from 0.05 Hz to 0.1 Hz),it is observed that each tracking error rises gradually as the fre-quency increases. It takes a finite amount of time for the actuatorsto track for the limited cycle time. The actuators begin to lagbehind the desired trajectory due to the slow response speedof the SMA wire. Nonetheless, these figures demonstrate bettertracking performance for the compliant differential SMA actua-tor over the bias SMA actuator with the same PI controller, andthe tracking performance has been further enhanced with the

substitution of the conventional PI controller for the saturated PIcontroller.

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. Discussion

From above experimental investigation, the compliant differ-ntial SMA actuator possesses the merits of both conventionalMA actuators. Although the differential SMA actuator has fasteresponse than bias SMA actuator, its working range is limited forhe increasing stiffness in the inverse phase transformation. In theurrent study, a soft spring is employed in the actuator design toeduce the stiffness as well as to enlarge the working range ofifferential SMA actuator. A saturated PI law has been developedhat demonstrated better tracking performance by introducing twowitching surfaces into the control structure. Experimental resultslso reveal that saturated PI controller has quicker response speednd higher accuracy than the PI controller in the position tracking ofhe same compliant differential SMA actuator. With this saturatedI controller, 0.1 Hz sinusoidal tracking on 0.25 mm diameter SMAire has been implemented. The tracking frequency can be fur-

her improved with smaller diameter SMA wires, since these haveower heating and cooling times. Nevertheless, the smaller diam-ter SMA wires also provide lower contraction force. Therefore, inractical application, a tradeoff between the response speed andutput force should be considered.

In this study, we introduced a mechanical solution to improvehe performance of conventional SMA actuators with a sim-le prototype. Such a design has the potential applications inobotic systems, such as for flexible multi-section surgical toolsr rehabilitation finger design. According to real application,echanical modification could be considered to meet the spe-

ific requirements: the size of coupling elements can be reducedo couple a smaller spring, multi-section SMA actuated joints cane connected together to increase the degree of freedom of theobot.

Due to the limited strain of SMA wire, long wire was usu-lly used to obtain large rotational angle in the traditional SMActuators. Since our method increased the angle of the SMA actu-tor, it would be valuable to reduce the length of SMA wire forhe desired motion. This study will be investigated in the future.t is also noteworthy mentioning that de-twinned strain of SMA

ire is an important factor [26]. It can affect the working rangef the SMA based actuator. In the current work, to minimize anyossible influence on our results, the same loading and currentondition to all three actuators were adopted to provide the samenitial conditions. However, considering the importance of thisactor, a further study is under consideration. In addition, theysteresis phenomenon can be found in the open loop experi-ent for the SMA actuator during heating and cooling process.

ince the primary focuses of the present study was the compari-on of working range, response rate and control performance, weill pay more attention to the hysteresis testing and compensa-

ion of this SMA actuator using advanced control strategy in theuture work.

. Conclusion

In this work, we introduced a novel compliant differential SMActuator incorporating two antagonistic SMA wires and a torsionpring. This design allows a wider range of angular motion com-ared to conventional SMA actuators. Experimental comparisonetween the new compliant SMA actuator vis-à-vis conventionalMA actuators has been conducted to evaluate the performance

nhancement in terms of tracking accuracy and settling time.uture work will focus on the design of advanced control strategies27–29] and the applications to robotic systems for this compliantMA actuator.

tors A 225 (2015) 71–80 79

Acknowledgment

This research was supported by MINDEF-NUS/NTU-JPP-11-03.

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Biographies

Zhao Guo received his Ph.D. degree in mechanical Engineering from the Institute

of Robotics, Shanghai Jiao Tong University (SJTU), Shanghai, China, in 2012. He iscurrently a Research Fellow at the Department of Biomedical Engineering, NationalUniversity of Singapore (NUS). His research interests include compliant actuatordesign, SMA actuator for bio-inspired robots, exoskeleton, and neuromuscular-model based robotic control.

8 Actua

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ongping Pan received the Ph.D. degree in Control Theory and Control Engineer-ng from the South China University of Technology, Guangzhou, China, in 2011.rom 2011 to 2013, he was a Research Fellow of the School of Electrical and Elec-ronic Engineering, Nanyang Technological University, Singapore. He is currently aesearch Fellow of the Department of Biomedical Engineering, National Universityf Singapore, Singapore. He serves as the Reviewer for several flagship internationalournals. His research interests include adaptive control, computational intelligence,ehabilitation robots and embedded systems.

iang-Boon Wee received his PhD in Space Robotics at The University of Michigan,nn Arbor, in 1993. Liang-Boon started his career as a project engineer in 1987,orking on design of computer simulation and the development of flight control

ystems. Throughout his career in DSO, National Laboratories he has worked on var-ous acquisition and development projects. His area of expertise has also expanded

tors A 225 (2015) 71–80

to include guidance research, systems architecture research as well as computervision and image processing research. His current appointment is Chief Engineer inthe Guided Systems Division.

Haoyong Yu received his PhD in Mechanical Engineering from the MassachusettsInstitute of Technology (MIT), Cambridge, in 2002. He is an Assistant Professor ofDepartment of Biomedical Engineering at National University of Singapore (NUS).Before joining NUS in September 2010, he worked in Defense Science Organization(DSO), National Laboratories of Singapore as a Principal Member of Technical Staff,

where he worked on exoskeleton and humanoid robots as well as intelligent groundand aerial robots. His current research at NUS focuses on robotics for robotics insurgery, neuro rehabilitation, assistive technologies, and bio-inspired robots. Dr. Yuis a member of IEEE. He received the Best poster award in the 2013 IEEE Life SciencesGrand Challenges Conference.