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Available online at www.sciencedirect.com

Sensors and Actuators A 141 (2008) 558–564

An LVDT-based self-actuating displacement transducer

Shang-Teh Wu ∗, Szu-Chieh Mo, Bo-Siou WuDepartment of Mechanical Engineering, National Yunlin University of Science & Technology,

Touliu, Yunlin 640, Taiwan

Received 23 June 2007; received in revised form 14 September 2007; accepted 8 October 2007Available online 18 October 2007

bstract

A novel linear actuator with inherent sensing capabilities is developed from a linear variable differential transformer (LVDT). By superpositionf dc currents upon high-frequency excitation signals, the coils of the LVDT are capable of exerting a push/pull force on the armature whileetaining the original displacement-sensing function. LC resonant circuits and active bandpass filters are designed to effectively isolate the sensingignals from the dc energizing sources. Linearity and sensitivity of the device are largely preserved compared to the original LVDT. For actuation,

t is found that the magnetic force on the armature can be maximized by energizing a specific combination of the three coils according to armatureositions. A simple control algorithm is developed for closed-loop control. It is implemented with an 8-bit microcomputer. Real-time testing showshat rest-to-rest control can be achieved with positioning errors of 0.02–0.04 mm and settling time below 0.2 s.

2007 Elsevier B.V. All rights reserved.

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eywords: Linear actuator; Displacement transducer; Linear variable differenti

. Introduction

In a servomechanism displacement or velocity transducersre essential components. However, installment of an externalensing device not only incurs expenses but also takes up spacehat may not be readily available. Various techniques of sen-orless or self-sensing actuation have been developed for theurpose of reducing cost, space, and increasing system robust-ess with fewer components. For electric motors, velocity ofhe rotor can be estimated from the back emf by observing theoltage–current relations. Displacements can then be obtainedy integration of velocities. Although most sensorless controlethods are designed for rotary machines, self-sensing tech-

iques have also been developed for linear actuators [1–5] andhe related loudspeakers [6–8]. Self-sensing control is also anctive research topic in magnetic levitated systems [9–12]. Itnvolves estimating air gaps of the magnetic bearing by mea-uring the coils’ inductance, which is inversely proportional

o the size of gap. To better estimate the inductance, a high-requency test signal could be injected into (i.e. superposedpon) the input power amplifier, generating a high-frequency

∗ Corresponding author. Tel.: +886 5 5342601 4111; fax: +886 5 5312062.E-mail address: wust@yuntech.edu.tw (S.-T. Wu).

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924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2007.10.027

nsformer (LVDT); Self-sensing; Self-actuating

urrent whose magnitude is inversely proportional to the coilnductance [10].

Instead of adding sensing capability to an electromagneticotor or actuator, this paper explores an alternative approach

hat equips a displacement sensor with “self-actuating” capabil-ties. A linear variable differential transformer (LVDT) will beonverted into a transducer that functions as a linear actuators well as a displacement sensor. The LVDT is a robust, high-esolution displacement sensor since it has no electrical contactetween the moving element and the transducer’s coils. LVDTsre usually installed on a linear motor or actuator for servo con-rol. A sub micron positioning system can be achieved by anVDT-equipped piezoactuator [13]. One drawback for a systemo install an LVDT is the extra space needed for the sensor. By

aking it function as an integrated sensor and actuator, the sizend cost of a servomechanism can be reduced.

The original LVDT operates by the principle that a harmonicxcitation signal applied to a primary coil will induce voltagesn two secondary coils. The voltage differential varies linearlyith the displacement of an armature moving inside the coils.he weak harmonic excitation has a negligible force on the arma-

ure, a magnetically permeable iron core. The idea behind theroposed LVDT actuator is to energize the coils by superim-osing dc (or low-frequency) voltages on the high-frequencyxcitation signals. The primary and secondary coils are

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S.-T. Wu et al. / Sensors and

eparately energized to obtain a force of the desired orienta-ion. While the magnetic force on the armature is not as strongs a conventional actuator, the resolution of sensing is largelyreserved. Using an LVDT signal conditioning IC, the armatureisplacement can be readily measured.

This paper presents the design of the LVDT actuator. A pro-otype is built for experiments. Linearity and sensitivity of theevice as a displacement sensor are tested. Actuation forcesxerted on the armature are also measured by a high-resolutionush–pull meter. It is found that the force can be maximizedy energizing a specific combination of the primary coil andhe two secondary coils according to armature positions. Awitching strategy for maximum force is established. A simpleontrol algorithm is then developed and implemented by an 8-biticrocomputer. It is shown that closed-loop control is achiev-

ble with settling time below 0.2 s and positioning errors of.02–0.04 mm.

. Design of the LVDT actuator

.1. LVDT as a displacement sensor

An LVDT has three solenoidal coils wound around a cylindri-al tube, as shown in Fig. 1. A sinusoidal signal is applied at therimary coil, inducing voltages on the two secondary coils. Ashe armature moves inside the tube, the induced voltage associ-

ted with one secondary coil increases while the other decreases.he armature displacement can thus be determined by measuring

he differential of the two induced voltages. In practice a signalonditioning IC such as AD598 (by Analog Devices, Inc.) is used

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ig. 1. Linear variable differential transformer: the coils (top left), the armature whicxperimental setup (right).

tors A 141 (2008) 558–564 559

o convert the sinusoidal differential to a dc voltage proportionalo the armature displacement.

Dimensions of the LVDT experimented in this paper are indi-ated in Fig. 1. The dimensions are close to those of the Schaevitz200 (by Measurement Specialties, Inc.), an LVDT with a lin-ar range of ±5 mm. Note that the three coils are of the sameimension, and the length of the armature is about the lengthf two coils. When the armature is at the leftmost position (i.e.,hen the left end of the armature reaches the left end of Sec-ndary coil 1), mutual inductance between the primary coil andecondary coil 1 is maximal while mutual inductance between

he primary coil and Secondary coil 2 is minimal. The opposites true when the armature is moved to the rightmost position.

.2. Superposition of sensing signals and actuatingurrents

Fig. 2 shows the basic configuration of the proposed LVDTctuator, where a set of inductors and capacitors are used tosolate the high-frequency sensing signal from the dc actuatingoltages. The excitation signal vs will be set at a relatively highrequency between 10 and 20 kHz. Note that the impedance of annductor with inductance L is equal to jωL, where ω is the radianrequency of the signal, and the impedance of a capacitor withapacitance C is equal to 1/jωC. Hence the inductor appears as aigh impedance to high-frequency ac signal but a low impedance

o the dc sources (u1, u2 and u3). The harmonic signals arelocked away from the dc sources while the dc currents areassed through the inductor to energize the coils. In other words,f the inductance is large enough, the high-frequency excitation

h moves inside the coils (middle left), the casing (bottom left), and photo of the

560 S.-T. Wu et al. / Sensors and Actuators A 141 (2008) 558–564

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asvIas the excitation signal. Signals of other frequencies, lower or

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ig. 2. Basic configuration of the LVDT actuator: vs is a harmonic excitationignal; v1 and v2 are the induced signals; ui’s are the actuating voltages.

ignal and the induced signals on the secondary coils will notleak” into the dc sources. On the other hand, the capacitorsppear as a low impedance to high-frequency signals but a highmpedance to the dc sources, so that the induced harmonic volt-ges (v1 and v2) are passed through to reach the measurementircuits while the dc currents are blocked away. Note that by “dc”e mean at frequencies much lower than that of the excitation

ignal.Fig. 2 illustrates the basic idea but has some problems in

ractice. First it needs a large inductor to effectively block thec excitation signal. For example, to have an impedance of 100 k

to a 10 kHz signal, an inductor of 1.59 H has to be used. Largenductors are undesirable because they take up space and slowown response. The second problem is with the coupling capac-tors. While the actuating voltages (u1, u2, and u3) are primarilyf low frequencies, high-frequency switching occurs in the tran-ient state. The transient actuating voltage may have frequencyomponents close to or larger than that of the ac excitation signal.

single coupling capacitor can hardly distinguish the sensingignal from the transient voltage.

Exploiting the fact that the excitation frequency is constant

nd known, more efficient stop/pass circuits are constructed, ashown in Fig. 3. In this refined design, an LC pair is used insteadf the single inductor to block a constant-frequency signal. This

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ig. 3. Refined design of the LVDT actuator: vs is a signal of frequency 15.9 kHz,and-pass filters is also set at 15.9 kHz.

ig. 4. Frequency response of the bandpass filter. Note the unity (0 dB) gain at5.9 kHz for the dashed curve (calculated response); solid curve is the measuredesponse.

s because the impedance of the LC pair is

jωL

1 − ω2LC. (1)

rom Eq. (1) the LC pair appears as an infinite impedance for aignal of 1/

√LC rad/s (1/2π

√LC Hz), which is the resonant

f the LC circuit. The inductance and capacitance are choseno be 10 mH and 0.01 �F, respectively, so that the resonant fre-uency is 15.9 kHz. The harmonic excitation signal is set at thisrequency so that it will be well isolated from the dc sources.he inductance chosen for the LC pair is much smaller than is

equired for a single inductor.In place of the coupling capacitors of Fig. 2, a narrow-band

ctive filter is used in Fig. 3 to pass the induced harmonicignals. It is a second-order tuned-circuit filter that can be con-eniently built using an active-filter IC such as UAF42 (by Texasnstruments, Inc.). The center frequency is set at 15.9 kHz, same

igher, are effectively attenuated. Such a design prevents high-requency transient signals (due to switching of the “dc” powernput) as well as low frequency actuating currents from contam-

same as the resonant frequency of the LC pairs; center frequency (fs) of the

S.-T. Wu et al. / Sensors and Actuators A 141 (2008) 558–564 561

Fig. 5. Output voltage of the signal conditioner versus armature displacementfor various dc energizing voltages (a), and the close-up view (b)

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Fig. 7. Three different methods of energization (for rightward force). In Type 3 Seco

Fig. 6. Force measurement by a digital push–pull meter.

nating the LVDT signal conditioning circuits. Fig. 4 shows therequency response of the band-pass filter constructed with anAF42.

. Sensitivity and force–displacement curves

The sensitivity curves of the LVDT actuator are measuredith the signal conditioning IC (Fig. 3). The harmonic excita-

ion signal for the primary coil is also generated by this IC. Fig. 5hows the curves of the output voltage from the signal condi-ioner versus armature positions. The measurements are repeatedor different dc energizing voltages from 0 to 5 V. It is seen thathe lines shift slightly upward with the applied voltage. Whilehis is an undesirable phenomenon, for high-precision applica-ions the measured signals can be calibrated against the appliedoltage, which is a controlled quantity and is constant in steadytate. For instance, in rest to rest operation the applied voltageill tend toward zero.Let linearity of the sensing curves be defined to be

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here δ(xi) denotes the voltage deviation of the ith measuredata from the least-squares line, and S denotes the range of output

oltage. In our device the output voltage varies from 0 to 5 Vor a stroke of ±5 mm, so that S = 5 V. The linearity for theata curves shown in Fig. 5 is calculated to be between 0.25 and.33%.

ndary coil 1 is energized in one direction and the other two coils in another.

562 S.-T. Wu et al. / Sensors and Actuators A 141 (2008) 558–564

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ig. 8. Force versus armature displacement for an applied dc voltage of 15 V: (a)ightward force; (b) leftward force. Solid curves are the quadratic least-squarest of the measured data.

Next is measurement of magnetic forces on the armatureFig. 6). Each of the primary and secondary coils can be inde-endently energized according to the position of the armaturend the intended force orientation. Three different energizingethods are tested. The first one is energizing a single coil (one

econdary coil on either side); the second method is energizingwo neighboring coils (the primary coil and one secondary coil);he third is energizing two neighboring coils in one direction andhe remaining coil in the opposite direction (Fig. 7). Figs. 8 and 9ompare the force–displacement curves for the three differentnergizing methods (types). It is seen that, depending on theosition of the armature, either Type 2 or Type 3 yields theaximum force.Refer to Fig. 7 and denote displacement of the center of the

rmature by x. Fig. 9 indicates that, when x > −2.5 mm, therimary coil and Secondary coil 2 should be energized in oneirection and Secondary coil 1 be energized in the opposite direc-

ion (Type 3) in order to generate maximum positive forces. (Foregative forces the process is reversed.) This can be explainedy the phenomenon that energizing the two coils on one sidef the armature not only pulls the armature toward them but

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ig. 9. Least-squares fitted curves for voltages from 14 to 16 V: (a) rightwardorce; (b) leftward force.

lso polarizes the armature, so that energizing the third coil inhe opposite direction helps push the armature. In the design ofhe closed-loop controller, the switching law will be based onhe maximum force curves. That is, the coil(s) to be energizednd the directions will be determined from a table based on therossing points shown in Fig. 9. Note that an average will beaken for the crossing points since they vary slightly with theoltages: For positive force the crossing is set at −2.5 mm andor negative force it is set at 2.3 mm.

. Closed-loop control

Employing both the sensing and actuating capabilities, onean devise a closed-loop controller to move the armature of theVDT actuator to a desired position. A modified proportionalnd derivative control algorithm is designed as follows:

= −kpe − kdx (2)

˙ = −αe + αe (3)

= x − xd (4)

S.-T. Wu et al. / Sensors and Actuators A 141 (2008) 558–564 563

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ig. 10. Driving circuits for energizing the three coils. The control input is fromn 8-bit microcontroller (0–5 V). Four analog switches (controlled by digital out-ut pins sw1 − sw4) are used to select the coil(s) to be energized and determinehe current directions.

here xd is the desired displacement of the armature, kp, kdnd α are positive constants. The velocity of the armature (x) isstimated by calculating the difference of two consecutive x’s.

Since the initial transient currents (due to the proportionalain) may “penetrate” the band-pass filter and contaminate theisplacement signals, a low-pass filter of cutoff frequency α (Eq.3)) is included to smooth out the proportional control input. Thelter slows down the initial response but does not affect steady-tate performance. In the experiments the sampling time is 4 ms,p = 3, kd = 0.068, and α = 62.5.

The simple control algorithm is implemented by an 8-biticrocontroller (PIC16F877 by Microchip, Inc.). The IC is

quipped with 10-bit A/D converters and two PWM output chan-els. The latter are used as D/A converters with an external RCow-pass filter. That is, the output from the microcontroller is ato 5 volt analog signal, which is directed to three power opera-

ig. 11. Closed-loop response: (a) armature displacements; (b) control input aspercentage of the full-scale voltage.

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Fig. 12. Responses for target displacements of 1, 2, 3, and 4 mm.

ional amplifiers (OPA547) that in turn drive the three coils. Ashown in Fig. 10, a set of analog switches are used to select theoil(s) to be energized (sw1 and sw3) and determine the direc-ion of currents (sw2 and sw4). The selection is based on theaximum force curves discussed in the previous section. The

oltages from the microcontroller are amplified five times, sohat the maximum driving voltage on each coil is 25 V.

Fig. 11 shows the response of the armature moving fromto 1 mm and the corresponding control command. The set-

ling time is 0.11 s and the steady-state error is about 0.02 mm.ig. 12 shows the responses for target displacements of 1–4 mmsing the same control parameters. The settling time varies from.093 to 0.196 s, and the steady-state errors are between 0.02 and.04 mm.

. Conclusions

By superposition of dc voltages on the original high-requency excitation signal of an LVDT, a self-actuatinginear-displacement sensor is devised. With the additional powerurrents, linearity and sensitivity of the original LVDT areargely preserved. It is found that energizing two consecutiveoils in one direction and the third coil in the reverse direc-ion yields maximum force for most of the moving range ofhe armature. Rest-to-rest positioning is achievable with a mod-fied PD control algorithm, that can be implemented by an 8-bit

icrocomputer.The experimental results also indicate that there is room for

mproving in the prototype’s steady-state precision, speed ofesponse, and the magnetic force. This may involve a refinementf the filtering circuits and the control algorithm. To raise theagnetic force, different dimensions of coils and armature may

e explored.

cknowledgment

This research was supported by the National Science Council,aiwan, ROC, under grant number NSC95-2221-E-224-031-Y2.

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iographies

hang-Teh Wu was born in Changhua, Taiwan, in 1963. He received the BSnd MS degrees in mechanical engineering from National Taiwan University,n 1985 and 1989, respectively, and the PhD degree in mechanical engineer-ng from Massachusetts Institute of Technology in 1993. He joined Nationalunlin University of Science & Technology since 1993, and is currently arofessor in the Department of Mechanical Engineering. His research inter-sts include vibration and control, design of electromechanical sensors andctuators.

zu-Chieh Mo was born in Taipei, Taiwan, in 1983. He received the BS degreerom Ta Hua Institute of Technology in 2005 and the MS degree in mechan-cal engineering from National Yunlin University of Science & Technologyn 2007. He is currently working at Foxlink Image Technology Inc., Taipei,aiwan.

o-Siou Wu was born in Taichung, Taiwan, in 1982. He received the BS and MSegrees in mechanical engineering from National Yunlin University of ScienceTechnology, in 2004 and 2006, respectively. He is currently working at Avision

nc., Hsinchu, Taiwan.