Comparative study of switching controls in vibration and ... · reluctance motor J.Y. Chai, Y.W....

Comparative study of switching controls in vibrationand acoustic noise reductions for switchedreluctance motor

J.Y. Chai, Y.W. Lin and C.M. Liaw

Abstract: A comparative study of vibration and acoustic noise reductions via electronic switchingcontrols for switched reluctance motor (SRM) is presented. First, studies concerning the acousticnoise and vibration sources, their effects and the existing mitigation approaches are given. Then fiveswitching control approaches, which belong to the magnetic and electronic remedies, are proposedand applied to the established SRM drive to comparatively evaluate their effectiveness andlimitations. These approaches include random frequency pulse width modulation with harmonicspectrum shaping, turn-on and turn-off angles advanced shift with fixed dwell angle, randomisingturn-off angle, current-tail profiling without and with advancing commutation shift. The theoreticalbasis, implementation and performance evaluation of each approach are presented in detail.Comparative evaluation shows that the hybrid approach combining the current-tail profiling andthe commutation advancing can yield the best compromise performance in vibration reduction,acoustic noise reduction and improved energy conversion efficiency.

1 Introduction

Similar to the variable reluctance stepping motor, theswitched reluctance motor (SRM) belongs to a doubly-salient and singly-excited machine [1–3]. It possesses a lot ofinherent structural advantages, such as rigid structure, highpower density, high reliability, low maintenance require-ment and suited for high-temperature and high-speedoperations. In addition, its converter is free from arm fed-through short circuit. However, the SRM also suffers frommany disadvantages: (i) high torque ripple; (ii) high acousticnoise and vibration; (iii) absolute rotor position informationis required for performing the converter switching for theSRM; (iv) nonlinear winding inductance and torquegenerating characteristics.

In dealing with the mechanical vibration and acousticnoise problems of an SRM, there has been much currentwork [4–19] concerning their origin, exploration andreduction. The studies in [2, 4–12] show that the sourcesof acoustic noise can be basically classified into fourcategories, namely magnetic, mechanical, aerodynamic andelectronic. Among these, it is shown that the radialattractive force between stator and rotor is the dominantone, particularly for the case in which the de-energisationoccurs at the aligned rotor position. In making performanceevaluation, it was found that vibration measurement can beused as an alternative to acoustic noise [4].

Basically, the existing solutions for vibration and acousticnoise reduction can be achieved via the motor design [5–7]and the converter control. Some typical research areas of

the former topic are: (i) the use of thicker back-iron,wherein the trade-off between noise and power density mustbe considered; (ii) applying an axial preload to reducebearing noise; (iii) dynamic rotor balancing to eliminatenoise due to rotor unbalance; (iv) the adoption of a slightlylarger airgap; and (v) suitable core laminations; in [6, 7] thefinite-element method is used for computer-aided analysisand design.

As to the converter control approaches, there exist threekey tunable parameters, namely the turn-on angle, the turn-off angle and the current shape. In the research reported in[8], the optimised current profile including turn-on and turn-off angles is generated using an artificial neural networkto yield performance compromise between acoustic noise,efficiency and average torque. As generally recognised,winding current-tail shaping is an effective means, whichhas been accomplished via voltage smoothing, and two-stage and three-stage commutation control [4, 9, 10, 12].Random PWM (RPWM) switching control [13, 14] andrandom turn-on and turn-off angles [15] have also beenstudied recently. However, owing to limited success, theoptimisation of the key parameters in random switchingschemes needs to be studied more deeply [13]. Accordingly,vibration reduction using random frequency PWM(RFPWM) with harmonic spectrum shaping is presentedin this paper.

Recently in [16], a hybrid excitation method waspresented. Overlap excitation is employed to reduce therapid change of radial MMF, and a C-damp converter isadded to reduce the decrease in efficiency. In [17], predictionand experimental transfer function estimation of thevibration caused by the magnetic force are presented, andaccordingly a vibration reduction control strategy isproposed. Intuitively, minimisation of ripple torque is adirect means, and this type of research is reported in[18–22]. In [18], the ripple torque reduction is achieved viatorque nonlinear control, associated with a suitable phasecommutation strategy. In [19], the current waveforms areE-mail: [email protected]

The authors are with the Department of Electrical Engineering, National TsingHua University Hsinchu, Taiwan, Republic of China

r The Institution of Engineering and Technology 2006

IEE Proceedings online no. 20050340

doi:10.1049/ip-epa:20050340

Paper first received 1st May and in final revised form 24th November 2005

348 IEE Proc.-Electr. Power Appl., Vol. 153, No. 3, May 2006

Authorized licensed use limited to: National Tsing Hua University. Downloaded on February 5, 2009 at 02:22 from IEEE Xplore. Restrictions apply.

optimised using computer search techniques to yield ripple-free torque. In [21], torque ripple minimisation is obtainedby optimum harmonic current injection, and in [22] thesame authors developed the online simplex optimisationtechnique to set the injected current harmonics, and it hasbeen verified to be effective in reducing steady-state torqueripple. Each approach described above possesses itsadvantages and limitations in implementation and effec-tiveness. In this paper, reductions of vibration and acousticnoise are achieved via commutation tuning, randomswitching and current profiling approaches and also theircombination.

In this paper, a DSP-based SRM drive with the necessarysensors and interfacing circuits is first constructed. Thetuning and RPWM schemes for performing the requiredstudies are also established. Then the sources of acousticnoise and vibration of an SRM are included to facilitatethe development of these approaches. According to thephenomena being observed, five mitigation approachesfor acoustic noise and vibration have been developed andtheir performances are comparatively evaluated. Theseapproaches include random frequency PWM with harmo-nic spectrum shaping, commutation advanced tuning, turn-off instant randomisation, and current-tail profiling withoutand with commutation advancing shift. The last hybridmethod, which combines current-tail profiling and commu-tation advancing, is the most effective means in yielding acompromise performance in vibration reduction and torquegenerating capability. Theoretical bases and implementa-tions of all the proposed schemes are described in detail,and their performances are evaluated experimentally.

2 Sources of vibration and acoustic noise

Although there are many inherent structural advantages,the doubly-salient structure and non-ideal switched square-wave winding current give the SRM higher torque ripple,and thus lead to the generation of higher vibration andacoustic noise. In addition, the rotor position and current-dependent winding nonlinear inductance makes its torqueand dynamic behaviour highly nonlinear. Moreover,analysis of vibration behaviour is also difficult to performaccurately. For performing the development of keytechnologies, it is indispensable to understand thoroughlythe key features of an SRM. In this Section, the governingequations of an SRM are first introduced, and then thesources of vibration and acoustic noise are considered.

2.1 Governing equations

2.1.1 Voltage equation: By neglecting the couplingeffect between phases, the voltage equation of a particularphase winding can be expressed by:

v ¼ Riþ dlði; yrÞdt

¼ Riþ LðyrÞdidtþ eði; yr;orÞ ð1Þ

where v¼winding terminal voltage, i¼winding current,R¼winding resistance, LðyrÞ9@lði; yrÞ=@i¼ incrementalwinding inductance, and eði; yr;orÞ9½@lði; yrÞ=@yr�ðdyr=dtÞ¼ back electromagnetic force (EMF). The per-phase converter-fed equivalent circuit corresponding to (1)is shown in Fig. 1a.

Observation: As shown in Fig. 1a, the winding current isestablished via PWM switching control of the powerconverter. The non-ideal square-wave shape windingcurrent generally results in larger torque ripple comparedwith other types of motors. As the speed increases, thecurrent will even become single-pulse type.

2.1.2 Torque equation: By assuming the linearmagnetic system and neglecting the coupling effect betweenphases, the developed torque Tei (i) per phase can be derivedfrom its energy or coenergy WcðyrÞ as follows:

TeiðiÞ ¼@WcðyrÞ@yr

� �i¼constant

¼@1

2LðyrÞi2

@yr

¼ 1

2i2@LðyrÞ@yr

9KtðyrÞi2ð2Þ

where KtðyrÞ9 12@LðyrÞ=@yr denotes the torque generation

constant.The composite generating torque Te and mechanical

equation of an SRM can be derived by summing thetorques produced by all phases:

TeðiÞ ¼X4i¼1

TeiðiÞ ¼ TL þ Bor þ Jdor

dtð3Þ

where TL¼ load torque, J¼moment of inertia andB¼ damping ratio. The control system block diagramcorresponding to (3) is shown in Fig. 1b, where Ic¼ currentcommand magnitude, and Hi (s) denotes the ith phasecurrent hypothesised tracking transfer function. The typicalcomposite developed torque pattern of an SRM is shown inFig. 1c.

Observation: As far as the switching control of windingcurrent is concerned, some comments are:

� The current and torque waveforms given in Figs. 1b andc show that without special current waveform profiling,in addition to the torque ripple yielded by each phase dueto its non-ideal current waveform, large commutationripples also result because of the notch between adjacentphases.

� The extent of vibration generation depends on vibrationmode frequencies and the frequency components in thetorque ripples, which are affected by speed and currentwaveform.

� Torque ripple is considered to be one of the majorsources of vibration and acoustic noise. Some suitableswitching control and commutation tuning approachescan be employed for effectively reducing this noise.

2.2 Sources of acoustic noise and vibrationAs mentioned in Section 1, there are basically four types ofacoustic and vibration sources. Only two of these relate tothe studies reported in this paper and they are discussedbelow.

2.2.1 Magnetic sources: For the SRM shown inFig. 2 with a particular phase winding being excited, thegenerated magnetic flux across the airgap producesradial forces on the stator and rotor, and thus results inmagnetic noise and vibration. To simplify the derivation,it is assumed that: (i) the magnetic circuit is linear; and(ii) the reluctance of iron is neglected. Referring tothe configuration of motor structure shown in Fig. 2,one can find the airgap flux density at the overlapangle y [1]:

Bgðy; g; iÞ ¼ moHg ¼f

lry¼ mo

Nig

ð4Þ

where y¼ overlap angle between stator and rotor,g¼ airgap length between stator and rotor at overlap,r¼ rotor outer radius, l¼ iron axial length and N¼ numberof turns per phase winding. Since y is determined by the

IEE Proc.-Electr. Power Appl., Vol. 153, No. 3, May 2006 349


rotor position yr, Bg is also a nonlinear function of yr,i.e. Bg ¼ Bgðyr; g; iÞ, and the corresponding fluxfðy; g; iÞ ¼ Bgðy; g; iÞlry.

From Fig. 2, one can derive the incremental electricalenergy of the excited winding:

dWe ¼ idl ¼ gmolr

fy

df ð5Þ

The magnetic field stored energy can be expressed as:

Wsðy; g; iÞ ¼g

2molrf2

yð6Þ

By neglecting all electrical and magnetic losses, one can finddWe ¼ dWs þ dWm from the energy balance relationship.And then the incremental magnetic field energy correspond-ing to the change of y on the excited phase winding can be

a

L(�r )

e(i, �r , �r )

Tei

R

i

Pei ∼_Tei �r

Vd

converter leg

i+

−

+

−

�r

b

Js + B1Gc�(s)

Te2

Te3

Te4

Ic

TL

Te

speedcontroller

�r∗

� ′r

K�r

S4

Kt 4(i42)

�′r

Te1

S1

Kt1( i12)

i1∗

H1(s)

S2i2∗

S3

Kt 3(i32)

i3∗

i4∗

ii

�r

i = 1Te = ∑ Tei�r

i1

i2

i3

i4

∑ ∑∑+

−

H2(s)

H3(s)

H4(s)

++

−+

++×

×

×

×

Kt 2( i22)

4

i 1i 2

i 3i 4

�r = �r t

�r

�r

�r

�r

L1(�r )

L2(�r )

L3(�r )

L4(�r )

∂�ri = 1 i = 1

∂Li (�r )Te = ∑ Tei = ∑21

44

commutation ripple

phase ripple

c

Ic

I c

I c

I c I c

i i2

Fig. 1a Per-phase converter-fed winding equivalent circuitb Composite torque generating scheme and mechanical dynamic modelc Inductance, winding currents and composite developed torque at medium speed



derived from (6) as [1]:

dWs ¼ �dWm þ dWe ¼�g2molr

f2

y2dyþ g

molrfy

df ð7Þ

Tangential force:

From (5) and (7), the incremental mechanical energy is:

dWm ¼g

2molrf2

y2dy ð8Þ

Then, the electromagnetic tangential torque and thus forcecan be derived as:

Ft ¼Te

r¼ @Wm=@y

r¼ gl

2moB2ðy; g; iÞ ð9Þ

Radial force:

Similarly, the incremental magnetic field energy correspond-ing to the change of g can be derived from (6) as:

dWs ¼1

2molrf2

ydgþ g

molrfy

df ð10Þ

Then dWm and thus the radial force Fn can be found from(5) and (10) as:

Fn ¼@Wm

@g¼ � 1

2molrf2

y¼ � lry

2moB2ðy; g; iÞ ð11Þ

Thus, the ratio between radial and tangential forces isobtained from (9) and (11):

Fn

Ft¼ � ry

gð12Þ

Observation: Equation (12) indicates that the radial force inan SRM is proportional to the overlap angle y and it has animpact on the machine. Its effect is cancelled through therotor and stator bodies, subject to the generation ofvibrations. During driving operation, the largest Fn andhence vibration and acoustic noise will be generated at thede-energisation instant of a particular phase occurring at thealigned position. This fact can be used as a rough guide tofind suitable remedies, for example, the advanced commu-tation shift will let the overlap angle y decrease at thede-energisation instant.

2.2.2 Electronic sources: The winding current har-monic is a major factor. Additionally, the winding currentwaveform and thus the flux linkage during each switchingoperation vary significantly with time. Some featuresconcerning these vibration sources are [1, 3, 4]:

(i) At a given rotor position with the same currentmagnitude, the single-pulse mode may induce a higherpeak vibration than the current-chopping mode. And incurrent-chopping mode, a higher current-change rate causeslarger vibrations. Obviously, the higher current magnitudeinduces larger vibrations.

(ii) Vibrations are larger during the turn-off process owingto the higher current-chopping rate occurring near thealigned position where the maximum vibration is caused bythe radial force between stator and rotor. Turn-off beforefull alignment position may reduce vibrations. However,some negative phenomena will result, and the compromiseconsiderations should be taken into account. These issueswill be treated in detail later in this paper.

(iii) For a four-phase 8/6 SRM, the vibrations in a statorpole lagging 901 from the excited pole are out of phase withthe vibrations of the excited pole. The largest vibrationsmay occur when the ripple frequencies of the windingcurrent coincide with the resonant frequencies of the stator.Random PWM switching control [23] with proper spectrumshaping [24] may be an effective remedy. This controlstrategy will be studied in this paper.

3 Established DSP-based SRM drive and problemstatement

3.1 DSP-based SRM driveThe power circuit and the established DSP-based SRMdrive are shown in Figs. 3a and b. It mainly consists of anSRM, a 2(n+1) switch Miller’s converter and a DSPcontrol board. While the switches S1–S4 are in charge ofcommutation, SA and SB are used for performing the PWMswitching control for four phase windings. The SRMemployed in this paper is manufactured by TASC DrivesLtd., and is four-phase 8/6 pole with the ratings of 400V,1500 rpm, 4kW. The measured stator winding resistance Ris 0.96O, and the inductance varies between 14 and125mH. The DC-link voltage is set as Vd¼ 400V. Apermanent-magnet synchronous generator with resistiveload RL serves as the dynamic load of the SRM. The DSPADMC401 manufactured by Analog Devices Co. isemployed to build up the digital control environment.The PWM switching control signals are generated directlyby the PWM modulator in the DSP. Ramp-comparisoncurrent-controlled PWM (RC CCPWM) schemes withfixed and random switching frequencies are designed, andcommutation tuning is achieved by modifying the commu-tation signals for S1–S4.

3.2 Problem statementIn this paper, magnetic and electronic remedies for redu-cing vibration and acoustic noise of an SRM drive areproposed and comparatively evaluated for their effective-ness. The RFPWM, an electronic approach, is used forrandomising the harmonic spectral distribution of phasewinding current. This is achieved digitally in the DSP by thedeveloped PWM modulator and RFPWM scheme shownin Fig. 3b.

As to the magnetic means, four approaches are studied inthis paper, these include (i) simultaneous advancing shift ofturn-on and turn-off angles; (ii) randomising turn-off angle;

r

+

−

vi

ii

1

1′

2

2 ′

3

3 ′

4 4′

Li (�r )

Li (�r )

�on�off

�r�(r + g)

de-energisation instant

�r = �r t

i i

Fig. 2 Relevant dimensions and geometrical parameters betweenrotor and stator teeth for particular excited phase winding



(iii) current-tail profiling; and (iv) current-tail profilingwith advancing commutation shift. All these tasks areaccomplished by the commutation tuning and current-tailprofiling schemes shown in Fig. 3b. Details concerning theanalysis, design and realisation of all the proposed controlschemes are presented in the next Section.

4 Proposed vibration and acoustic noisereduction approaches

4.1 Random PWM switching and harmonicspectrum shaping

4.1.1 Intuitive spectral analysis: The key to thismethod is to vary the winding current PWM switchingfrequency randomly, such that its harmonic spectrum canbe uniformly distributed. It follows that the effects ofharmonics on the acoustic noise and vibration are reduced.Among the existing random PWM techniques [13, 14, 23,24], the random frequency PWM (RFPWM) is the simplestone. In an RFPWM scheme, the frequency of its triangularcarrier vtri (t) is randomly changed according to theemployed random signal rðtÞ. The basic concept of this

approach can be understood from Fig. 4a. The frequency ofvtri (t) is set to be:

fs ¼ fs0 þ rðtÞDfs ð13Þwhere fs¼ instant switching frequency, fs0¼ averageswitching frequency, Dfs¼ switching frequency variationmagnitude, and r(t)¼ uniformly distributed random num-

bers in the range of [�1,+1]. In Fig. 4b, fhand f h denote

the lowest and highest harmonic frequency components of

winding current ii due to RFPWM, and Dfe9fh� f 1 is

the frequency range within which the current harmonicsshould be attenuated as far as possible [23, 24].

By randomly varying the triangular carrier frequency, theharmonic spectrum in winding current i01 (taking the firstphase winding as an example) under RC CCPWM controlcan be made to be uniformly distributed, as shown inFig. 4b. Realisation of the RFPWM scheme using ananalogue circuit is tedious. In this paper, the DSP-baseddigital RFPWM control algorithm is developed.

Comments: For a fixed switching frequency standard PWMscheme, one can choose the switching frequency to behigher than about 20kHz (ultrasonic frequency) to reduce

b

a

rectifier

3� ACEC

RL

SRM

HA HB

L1 L3 L2 L4

D1 D3 D2

DA

SA

(Hall position sensors)S2S3S1

DB

SB D4

Ld

−

CVd

Id

Pd

220 V60 Hz

+

S4

Ld

C

−�r

e�

SA SB

Gc�

(z)

SRM

EC

PMSG

RL

i4 i3 i2i1

Ic∗2v∗3

v∗4v

HB

HA

220 V 60 Hz

three-phase AC

∗1v

∗2i∗3i∗4i

∗1i

HB

HA

DSP ADMC401

S2 S3 S4S1

SA SBS2 S3 S4S1S2 S3 S4S1

A /D

A /D

encoderinterface

PIOS2 S3 S4S1

rectifier

PWMmodulator

andRFPWMscheme

commutationtuning and current

tail profilingschemes

S2 S3 S4S1

winding currentcommandsgenerator

gate driver

currentcontrollers

Gci (z)

speedcontroller

2(n +1) switchMiller

converter

commutationlogic

generator

Vd

Id

Pd

+

−

+

�∗r

Σ

PMSG

Fig. 3 Developed SRM drivea Power circuitb DSP-based control scheme



the acoustic noise. However, this is not helpful for thevibration reduction of an SRM, since its dominantvibration frequency is normally located far below theswitching frequency. On the other hand, the key purpose ofapplying RFPWM is to let the harmonic spectrum beuniformly distributed, and thus the possibility and extent ofvibration caused by the current harmonics with coincidedfrequencies can be reduced. However, similarly, theeffectiveness of vibration reduction by RFPWM is alsonot very significant [13]. The chief reason lies in theharmonics with frequencies within Dfe (in which thedominant vibration frequency is located) in Fig. 4b notbeing able to reduce via standard RFPWM [23]. Theimprovement is made as follows.

4.1.2 Robust harmonic spectrum shaping:For the four-phase 8/6 SRM employed in this paper, thevibration frequency range found from measurement isaround 1.43kHz. To allow the RFPWM be more effectivein vibration reduction, the robust spectrum shapingtechnique [24] is employed here. The proposed RFPWM

scheme with robust harmonic spectrum shaping is shown inFig. 4c. A bandpass filter is employed to extract the currentharmonics within the frequency range Dfe¼ 0.93–1.93kHz(centre frequency f0¼ 1.43kHz) from the winding current,

and then a compensation control signal i�1c ¼ W ði0eÞattenuates the harmonics to within Dfe.

Robustness analysis: Taking the first phase winding as anexample, let the PWM switching controlled winding currenti01 shown in Fig. 4b be modelled as:

i019Hii�19i01f þ i0e þ i0h ð14Þ

where Hi denotes an assumed winding current trackingtransfer function as described previously, i01f , i0e and i0hrepresent the current components in the fundamentalfrequency range, Dfe and high harmonic frequency range,respectively. Suppose that the component i0e within Dfe can

be perfectly extracted by the bandpass filter (i.e. i0e’ i0e) fromFig. 4c; one can derive:

i01 ¼ i01f þ i0e þ i0h ¼ Hiði�1 þ W i0eÞ ð15Þ

a

b

c

(i ′ 1) h

ff

(i′ 1) h

fsfs = mf f1

f1 f1

i ′1fi ′�

i ′h

�f�

f1 f1 fh fhf1 f1 fhfh2mf f1 3mf f1

−2 +2 −1 +1 −2 +2

v ∗2

v ∗3

v ∗4

v1∗

i ∗1

i ∗2

i ∗3

i ∗4

SA SB

C

A

B+1

−1

vtri (t )

t t t

+−

+−

+−

+−

vtri (t )

A C

r (t )

random signal

⇓

r (t )

vtri (t ) vtri (t )

currentcontrollers

t

+−

i ′1

i ′

1� Gci

B

Σ

�1

W

Gci

HBP

++ +

i∗1c

i ∗1 v∗1

PWM signal

i��

i∗11−Σ

+Σ

−

⇒

1 i ′2 i ′3 i ′4

f1f1

i1′

′ i1′

Fig. 4a Proposed random PWM modulatorb Resulting harmonic spectrac Proposed harmonic spectrum shaping scheme (per phase)



And thus the winding current after applying robustspectrum shaping control becomes:

i01 ¼ Hii�1 ¼ i01f þ ð1� HiW Þi0e þ i0h ð16Þ

Hence, the current i0e within Dfe has been reduced by afactor of ð1� HiW Þ.

4.1.3 Implementation of proposed randomswitching scheme and spectrum shapingscheme: For a standard PWMmechanism, its switchingfrequency is fixed and determined according to the programsetting. The PWM timer, which is clocked at the DSPinstruction rate, controls the internal operation of the PWMmodulator. The content (called PWMTM) is set in a 16-bitPWMTM register and used to control the PWM switchingfrequency. By randomly changing the content in the 16-bitPWMTM register, which has 32768 variations, accordingto the random variable r(t), the switch frequency can berandomised. In this study, fs0 ¼ 10 kHz and Dfs¼ 5kHzare set.

The key parameters and transfer functions in Fig. 4c arechosen to beW¼ 0.9999, HBP ðsÞ ¼ 6:29� 103s=ðs2 þ 6:29�103sþ 80:73� 106Þ (centre frequency f0¼ 1.43kHz, qualityfactor Q¼ 1.428, bandwidth¼ f0/Q¼ 1.0kHz), GciðsÞ ¼ 30þ8000=s. The proposed spectrum shaping scheme shown inFig. 4c is realised digitally in the DSP. All the continuoustransfer functions are transformed to the discrete-timedomain using the bilinear z-transform. The samplinginterval Ti is chosen to be 0.1ms.

4.1.4 Experimental results: With or¼ 700 rpm,RL¼ 158O, Pd ’ 1.6kW, Fig. 5a shows the measuredwinding current waveforms of the SRM drive and theirspectra by fixed switching frequency standard PWM( fs¼ 10kHz) and RFPWM ( fs¼ 5–15kHz) schemes. Theuniform harmonic spectrum due to RFPWM can beobserved from the result. Figure 5b shows the currentwaveforms and their spectra by RFPWM without and withrobust harmonic spectrum shaping. One can find from theresults that the harmonics within the frequency rangeDfe¼ 0.93–1.93kHz have been greatly attenuated. Thereduction of vibration is evaluated by the measuredacceleration, which is measured by an accelerometer,manufactured by Wilcoxon Research Company, USA,being mounted midway in the stator frame. The measuredaccelerations corresponding to the cases of Figs. 5a and bare compared in Fig. 5c. One can observe from Fig. 5c that,through applying the proposed harmonic spectrum shapingtechnique, the vibration reduction by RFPWM can beimproved, although its effectiveness has been considered tobe limited until now. The chief reason lies in the fact thatthe probability of coincidence of winding current ripplefrequencies with the stator resonant frequencies is reduced.Further comparison between the winding current wave-forms shown in Figs. 5a and b also shows that lower currentmagnitude and smaller changing rate at turn off areobtained by the RFPWM with spectrum shaping, which isequivalent to the current-tail profiling technique presentedin Subsection 4.4.

At another operation condition (or¼ 1500 rpm,RL¼ 104O,Pd ’ 2.2kW), the measured accelerations bystandard PWM, RFPWM and RFPWM with shaping areshown in Fig. 5d. The same phenomena in vibrationreduction can also be observed. Although the measuredresults at larger loads are not provided because of the ratinglimit of the dynamic load, the effectiveness of the proposedvibration reduction approach will also be predictable.

4.2 Commutation advanced shiftThe main problem of acoustic noise and vibrationgeneration in an SRM lies in the winding being turned offaround the aligned position with maximum radial force. Itis known that commutation tuning is an effective means ofimproving the torque generating characteristics of an SRM,including the maximum, RMS and ripple torques. Thereare many tunable variables and tuning approaches in thisarea. As far as the acoustic noise and vibration reductionare concerned, the advanced shift of turn-off angle iseffective and commonly employed. Figure 6a shows theidealised winding current and inductance profiles of aparticular phase under the simultaneous shift of yon and yoff

with fixed dwell angle yd.

Comments:(i) With the commutation advanced shift, it can be seenclearly from Fig. 6a that the overlap angle between statorand rotor is decreased, so the radial force at turn-off can bereduced from (11) and (12).

(ii) The advanced shift can also lead to a quicker windingcurrent buildup, and thus the commutation torque rippleand vibration are reduced accordingly. The researchreported in [25] indicated that the advanced shift angle yo1shown in Fig. 6a to enable the winding current to be linearlyraised to its command Ic is:

yo19yon � y0on ¼LminIcor

Vdð17Þ

Let the SRM operate at or¼ 700 rpm, RL¼ 158O. Themeasured vibrations are compared in Fig. 6b and the resultsindicate that, through applying the commutation advancedshift, the stator vibration is greatly reduced. The results (notshown here) also show that the magnitude of the currentcommand is reduced from Ic¼ 4.5 to 2.5A by the proposedapproach. For another operating condition (or¼ 1500 rpm,RL¼ 104O), the measured vibrations are shown in Fig. 6c.The results of Fig. 6c also show that the reduction ofvibration at higher speed can be effectively achieved bycommutation advanced shift.

4.3 Randomised turn-off angleThe randomised turn-on and turn-off angles to reduce thevibration and acoustic noise has been studied in [4, 15].Since the turn-off angle is the key variable relating to thevibration, only the randomised turn-off angle is consideredhere. In the proposed tuning control approach shownin Fig. 7a, the turn-on angle yon is fixed and the turn-offangle yoff is randomly varied around the average valueaccording to:

y0off ¼ yoff þ rðtÞDy ð18Þ

where yoff¼ original or average turn-off angle, y0off¼ thevaried turn-off angle, Dy¼magnitude of turn-off anglevariation, and r(t)¼ uniformly distributed random numberswith its magnitude being varied in the range of [�1,+1].

Comments: From (11), (12), Fig. 2 and Fig. 7a, one can findthat the equivalent overlap angle y is reduced owing torandomising yoff It follows that the vibration is reducedaccordingly. However, if the turn-on angle is fixed and theturn-off angle is advanced, the conduction period of thewinding current and thus the torque generating capabilitywill decrease. On the other hand, if the turn-off angle isreduced too much, the current-tail flowing in the decreasinginductance region may result in negative torque. It followsfrom the above observations that too large a value ofDy should be avoided in order to avoid the sacrifice of



a

b

c

d

2.5 kHz / div

2 A 2 A

2.5 kHz 2.5 kHz0

standard PWM RFPWM

i1i1

0

2 ms/div(2 ms/div)

NORM

2 ms/div(2 ms/div)

NORM

2.5 kHz/div

4 A4 A

500 Hz500 Hz 00

RFPWM RFPWM with specturm shaping

�f� �f�

i1 i1

0.93 ~ 1.93 kHz0.93 ~ 1.93 kHz

2 ms/div(2 ms/div)

NORM

2 ms/div(2 ms/div)

NORM

500 Hz / div500 Hz / div

T

2

1 ms

RFPWM

standardPWM RFPWM

RFPWMwith

spectrumshaping

0.98 m / s2

0.98 m / s2

0.98 m / s2

0.98 m / s2

1 ms

1 ms/div(1 ms/div)

AVG:100 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/s

1

1.96 m / s2

1.96 m / s2

1.96 m / s2

1.96 m / s2

1 ms1 ms

RFPWM

RFPWM

standardPWM

RFPWMwith

spectrum

shaping

1 ms/div(1 ms/div)

NORM:100 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/s

1T

1

Fig. 5a Measured winding current waveforms and their spectra by fixed frequency (standard) PWM ( fs¼ 10kHz) and proposed RFPWM ( fs¼ 5–15kHz)scheme at or¼ 700 rpm, RL¼ 158Ob Measured waveforms and spectra of winding currents by proposed RFPWM without (left) and with (right) robust harmonic spectrum shapingschemes at or¼ 700 rpm, RL¼ 158Oc Measured accelerations by standard SPWM, RFPWMwithout and with robust harmonic spectrum shaping schemes at or¼ 700 rpm, RL¼ 158Od Measured accelerations by same schemes as c at or¼ 1500 rpm, RL¼ 104O



torque-generating capability. In addition, the effects ofrandom signal attributes including magnitude and fre-quency range on the vibration and torque-generatingcapability are need to be studied deeply. In practice, forfixed yon, the randomisation of yoff can easily be achieved byrandomly changing the position register content, whichstores the information of dwell angle yd.

At or¼ 700 rpm, RL¼ 158O, the measured statoraccelerations for the normal case and yoff randomisationwith Dy¼ 41 are compared in Fig. 7b. The correspondingmeasured winding currents and their commands are shownin Fig. 7c. The results in Figs. 7b and c show that thevibration has been reduced subject to slight increase inwinding current from Ic¼ 4.0 to 4.8A. Further experi-

mental results indicate that, with the increase in extent ofrandomisation Dy, the vibration can be further decreasedsubject to a continuous increase in winding current. Themeasured accelerations at or¼ 1500 rpm, RL¼ 104Oshown in Fig. 7d also confirm the effectiveness of theproposed vibration reduction approach at higher speed.

L(�r )

Lmax

Lmin

�on �off

�dL(�r )

�r

iadvanced ioriginal

�r = A �r = B

R

S

R

S

A

B

a

Ic

� ′on �′off

�o1

� �

1 ms

shifting (4°)advanced

normalcase

shifting (4°)advanced

normalcase

b

0.98 m / s2

0.98 m / s2

1 ms/div(1 ms/div)

AVG:100 kS/s

c

1.96 m / s2

1.96 m / s2

1 ms

1 ms/div(1 ms/div)

NORM:100 kS/s

1

Fig. 6a Idealised winding current and inductance profiles before and aftercommutation advanced shiftb Measured stator accelerations at or¼ 700 rpm, RL¼ 158O withoutand with advanced shift of 41c Measured stator accelerations at or¼ 1500 rpm, RL¼ 104O withoutand with advanced shift of 41

1 ms/div(1 ms/div)

AVG:100 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/s

r (t )

t

�r �r�r

�d �d

�on�on �on�off �off

�off

�off

normal case

normal case

0.98 m / s2

0.98 m / s2

1.96 m / s2

1.96 m / s2

1 ms

1 ms

1 ms

5 A

i aA4

5 A

i a∗

i a∗

i a4.8 A

C

B

B

A

CA

randomising�off (4

°)


°)

normal case


°)

a

b

c

d

′

′ �d′

�off′

Fig. 7a Employed random signal r(t) and angles of y0off corresponding to

r(t)¼A, B and Cb Measured stator accelerations at or¼ 700 rpm, RL¼ 158O withoutand with yoff randomisation with Dy ¼ 4�

c Measured winding currents and their commands corresponding to bd Measured stator accelerations at or¼ 1500 rpm, RL¼ 104O withoutand with yoff randomisation with Dy ¼ 4�



4.4 Current-tail profilingTo understand this control methodology, from (4) and (11)the radial force is expressed as:

Fn ¼�lrm0N

2

2g2yi2 ð19Þ

After demagnetisation at yr ¼ yoff , the vibration behaviourof the stator can be characterised by a second-order

dynamic equation [9]:

€Fn

m¼ €aþ 2xon _aþ ona ð20Þ

where m¼ equivalent mass, a¼ vibration acceleration of

stator, on ¼ffiffiffiffiffiffiffiffiffik=m

p, x ¼ b=ð2

ffiffiffiffiffiffikmpÞ, k¼ stiffness and

b¼ viscous damping coefficient. From (19) and (20), one

can see that the reduction of €Fn via smoothing of thewinding current-tail is an effective remedy in vibrationreduction. As mentioned previously, many existing methodscan be applied. For example, one can apply a narrow pulsewith proper width before the turn-off instant. Thiscorresponds to the three-stage commutation methodpresented in [10]. Two types of current-tail profiling controlapproaches are studied in this paper.

4.4.1 Fixed commutation instant: The proposedcurrent-tail profiling control approach without advancedshifting of the commutation instant is shown in Fig. 8a. Anarrow pulse width DyT behind the turn-off instant smallangle yT is added to let the winding be re-excited by Vd witha narrow duration of DyT. It follows that the current-tailchanging rate will become slower, as shown in Fig. 8a. Thetwo tunable parameters in this approach are yT and DyT,which are dependent on the speed and loading condition,

and they are determined by trial-and-error here. Fn and €Fnwith added narrow pulse are also shown in Fig. 8a. The

generation of the positive rectangular pulse in €Fn due to

b

L(�r )

�r

�r

commutationwithout

advanced shifting

winding currentwithout

advanced shifting

�on�off

�r

�d

�T

�r

F n

� ′on

�on� ′on

�off�on� ′on

�on

∆�T

�r

commutationwith

advanced shifting

winding currentwith

advanced shifting

�on

� ′on � ′off

� ′on

�off� ′on

� ′off

�r

�r

a

Fn¨

Fig. 8 Proposed current-tail profiling control approaches

a Inductance profile, commutation signal, winding current, Fn and €Fn

without advanced commutation shiftb Commutation signal and winding current with advanced commu-tation shift

1 ms

5 Ai1∗

i1∗

i13.9 A

a

b

5 A

i14 A

0.5 ms

S1

S1

1 ms/div(1 ms/div)

NORM:100 kS/s

500 µs/div(500 µs/div)

NORM:200 kS/s

T

3

1

Fig. 9a Measured winding current and its command for normal case(without making current-tail profiling) at or¼ 700 rpm, RL¼ 158Ob Same as a at or¼ 1500 rpm, RL¼ 104O



1 ms

5 A

�T = 0.82° ∆�T = 0.33°

normal case

fixed �T

i ∗1 i1

5 A

1.96 m / s2

1.96 m / s2

1 ms

S1


NORM:200 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/sT

1

3

1

1 ms

5 A

�T = 0.82° ∆�T = 0.33°

i∗1 i14.2 A

1 ms

normal case

fixed �T0.98 m / s2

0.98 m / s2

S1

1 ms/div(1 ms/div)

NORM:100 kS/s

1 ms/div(1 ms/div)

AVG:100 kS/s

a

b

1 ms

5 A

i∗1 i12.5 A

�T = 0.82° ∆�T = 0.33°S1

advancedcommutationshifting (4°)

normal case

0.98 m / s2

0.98 m / s2

1 ms

1 ms/div (1 ms/div)

NORM:100 kS/s

1 ms/div(1 ms/div)

AVG:100 kS/s

1 ms/div(1 ms/div)

NORM:100 kS/s

c

1 ms

5 A

i∗1 i13 A

1 ms

1.96 m / s2

1.96 m / s2

advancedcommutationshifting (4°)

normal case

�T = 0.82° ∆�T = 0.33°S1


NORM:200 kS/s

1T

1

d

Fig. 10a Measured winding current, its command and stator vibrations at or¼ 700 rpm, RL¼ 158O by current-tail profiling with fixed yT ¼ 0:82� andDyT ¼ 0:33�

b Same as a at or¼ 1500 rpm, RL¼ 104Oc Same as a by advanced commutation shift of 41d Same as c at or¼ 1500 rpm, RL¼ 104O



current-tail profiling is helpful in the reduction of vibration[9, 10].

4.4.2 Advanced commutation instant: Althoughthe current-tail profiling approach shown in Fig. 8a canbe applied to reduce the axial force between stator androtor, the long current-tail will reduce the developedtorque. The proposed improved current-tail profilingapproach is shown in Fig. 8b. By simultaneously advanceshifting the whole switching pattern including the mainand the auxiliary pulses, the generated negative torquecan be reduced. It follows that the negative effects ofcurrent-tail profiling are compensated for.

4.4.3 Experimental results: Fixed commutationinstant: For convenience of comparison, Figs. 9a and bshow the winding currents and their commands withoutmaking current-tail profiling at or¼ 700 rpm, RL¼ 158Oand or¼ 1500 rpm, RL¼ 104O, respectively. Figures 10aand b show the winding currents and stator accelerationsunder current-tail profiling with yT¼ 0.821 and DyT¼ 0.331.The results indicate that, by applying fixed current-tailprofiling, the vibration is reduced at different motor speeds,but the winding currents are increased respectively fromIc¼ 3.9 to 4.2A (or¼ 700 rpm,RL¼ 158O) and Ic¼ 4.0 to5.0A (or¼ 1500 rpm, RL¼ 104O).

4.4.4 Experimental results: Advanced commuta-tion instant: Let the advanced commutation shift be 41;the measured winding currents and accelerations ator¼ 700 rpm, RL¼ 158O are shown in Fig. 10c. Themeasured results at a higher speed (or¼ 1500 rpm,RL¼ 104O) are shown in Fig. 10d. The results indicatethat, through applying current-tail profiling with advancedcommutation shift, both the current magnitudes ( from4.2 to 2.5A for or¼ 700 rpm, from 5.0 to 3.0A foror¼ 1500 rpm) and the stator vibrations are greatly reducedsimultaneously. The reduction in winding current under thesame load condition implies an increase in developedtorque.

5 Comparative evaluation

Having performed the studies concerning five approaches inacoustic noise and vibration reduction, some observationsand comments are now made. These five approaches are(i) RFPWM with harmonic spectrum shaping; (ii) simulta-neously advanced yon and yoff with fixed yd ; (iii) random-ising yoff ; (iv) current-tail profiling; and (v) current-tailprofiling with advanced commutation shift.

These five approaches all can reduce the acoustic noiseand vibration. Although the RFPWM approach isconsidered to be less effective until now and the relatedresearch is scarce, the application of the proposed spectrumshaping technique can improve this effectively. However,further studies to yield better results are still worthperforming.

Among the five studied approaches, approaches (i) and(ii) can reduce vibration through the reduction of torqueripple and, moreover, the former can reduce the probabilityof the coincidence of current ripple frequencies with thestator resonant frequencies. As to approaches (iii) to (v),the radial force at turn-off and thus the vibration can beeffectively reduced.

Current-tail profiling is very effective in acoustic noiseand vibration reduction subject to an increase in therequired winding current, i.e. a reduction in torquegenerating capability. However, by applying the proposed

hybrid tuning approach, i.e. current-tail profiling withadvanced commutation shift, good compromise perfor-mances in the increase of torque generating capability andthe reduction of acoustic noise and vibration are obtained.

6 Conclusions

This paper has presented studies concerning reductions ofacoustic noise and vibration of an SRM. A DSP-basedSRM drive with properly mounted acceleration sensor isestablished and used as a test platform. Studies concerningthe sources of acoustic noise and vibration find that theradial attraction force is the major reason, and effectivemagnetic and electronic remedies are also understood.Accordingly, this paper then proposed five mitigationapproaches, including RFPWM with robust harmonicspectrum shaping, advanced turn-on and turn-off angleswith fixed dwell angle, randomising turn-off angle, current-tail profiling, and current-tail profiling with commutationadvanced shift. It has been found that, through applyingthe developed spectrum shaping technique, RFPWM canbe made more effective in the reduction of acoustic noiseand vibration. Current-tail profiling with advanced shiftdeveloped in this paper possesses the best compromiseperformance in the increase of torque generating capabilityand reduction of acoustic noise and vibration. Theoreticalbasis, design and implementation of all the proposedcontrol schemes are described in detail, and the perfor-mance for all the schemes has been confirmed experimen-tally. In addition, the limits and key issues for furtherstudies concerning all control approaches have also beenconsidered.

7 Acknowledgment

The research was supported by the National ScienceCouncil, Taiwan, ROC, under the Grant of # NSC 93-2213-E-007-107.

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