FERNANDO BRIZ andMICHAEL W. DEGNER

Digital Object Identifier 10.1109/MIE.2011.941118

Date of publication: 17 June 2011

The elimination of rotor position/velocity sensors (and cabling)

in ac drives has long been desired and has been the focus of

intensive research for more than two decades [1]–[53]. The

methods developed to achieve this goal are commonly referred

to as sensorless control in the literature. Some of the expected

benefits of sensorless control that motivate this research are

cost reduction, increased robustness, and size reduction.

Sensorless control techniques for ac machines that rely on the fundamental

excitation have been shown to be capable of providing high-performance con-

trol, e.g., field-oriented control and direct torque control, in the medium- to

high-speed range [1]–[8]. However, as the speed decreases, the performance of

these methods decrease and eventually fail in the very low-speed range and/or

for dc excitation [6]–[8]. To overcome this limitation, sensorless control meth-

ods based on tracking the position of saliencies (asymmetries) in electric

machines have been proposed [6]–[52]. Such methods have the capability of

providing accurate, high bandwidth, position, speed, disturbance torque esti-

mates, and/or flux estimates in the low-speed range, including zero speed and

frequency. These techniques measure the response of the machine when high-

frequency excitation, distinct from the fundamental excitation used for torque

production, is applied via the inverter. The major differences between the meth-

ods are 1) the type of high-frequency excitation, 2) the type and number of sig-

nals measured, and 3) the signal processing used to estimate the rotor position.

Regardless of these differences, all of these methods share the same physical

principles, which create an expectation that they all would provide similar perform-

ance when implemented on the same drive/machine. However, this is not necessar-

ily true in practice. Practical implementation issues, including the nonideal behavior

of the inverter, parasitic effects in the cables, and machine windings, can have a

A Review of

High-Frequency Methods

© ARTVILLE

24 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011 1932-4529/11/$26.00&2011IEEE

significant impact on the overall per-

formance and can significantly vary

from method to method.

This article is a review of the high-

frequency signal injection methods that

have been proposed for the rotor posi-

tion/speed sensorless control of ac

machines. Although this article will

focus on rotor position estimation, the

same method can be used, and have

been reported, for flux angle estimation.

The main difference is the physical ori-

gin of the saliencies being tracked, i.e.,

rotor position dependent or magnetic

saturation dependent [15], [46].

High-FrequencyModeling of AlternatingCurrent MachinesThe high-frequency models, includ-

ing induction and permanent magnet

synchronous machines (PMSMs), used

for the analysis of high-frequency sen-

sorless control methods are often

derived from the corresponding funda-

mental frequency models. The high-

frequency excitation usually means

that the resistive terms are not sig-

nificant and can be eliminated from

the equations. In addition, the fact

that the high-frequency signal is

spectrally separated from the funda-

mental excitation frequency allows

the back electromotive force (EMF)

to be eliminated [14]. With these two

assumptions, the high-frequency model

is a pure inductive load, with the phase

inductance magnitudes being a func-

tion of rotor position [14]. With a

further assumption that the position-

dependent inductances consist of a

single harmonic component and the

fact that at low operating speeds the

high-frequency excitation signals occur

at frequencies significantly larger than

the fundamental frequency, means the

time rate of change of the inductances

is small and can be safely ignored. The

resulting high-frequency model of a

wye-connected machine is shown in

(1)–(3) [16], with ia þ ib þ ic ¼ 0.

va�vn ¼van ¼�X

Lrs

þ2DLrscos(hrhr)

�dia

dt

(1)

vb� vn ¼ vbn ¼�X

Lrs

þ 2DLrscos hr hr�2p3

� �� ��dib

dt

(2)

vc � vn ¼

vcn ¼X

Lrs þ 2DLrs

�

cos hr hr �4p3

� �� ��dic

dt

(3)

where va, vb, and vc are the voltages

applied by the inverter to the machines

terminals relative to the negative rail of

the dc bus, vn is the voltage induced in

the neutral point of the stator windings,PLrs and DLrs are the average and

differential stator high-frequency in-

ductances, hr is the harmonic order of

the saliency relative to electrical angu-

lar units, and hr is the angular position

of the rotor in electrical radians.

Figure 1 schematically shows the vari-

ation of the high-frequency phase

inductances in (1)–(3) as a function of

rotor position. The constant 2 for the

definition of DLrs is chosen as a mat-

ter of convenience [16].

It is useful to write (1)–(3) in

matrix form (4), with Lra, Lrb, and Lrc

standing for the inductance terms

within brackets in (1)–(3). By trans-

forming (4) to an equivalent qd0

model, (5) and (6) are obtained [16],

with superscript ‘‘s’’ standing for the

stationary reference frame.

va

vb

vc

0

26664

37775¼

Lra 0 0 1

0 Lrb 0 1

0 0 Lrc 1

1 1 1 0

26664

37775

dia

dt

dib

dt

dic

dt

vn

26666666664

37777777775

, (4)

vsqsv

sdsv

s0s

h iT

¼ Lsrqd0s

d

dtisqsi

sdsi

s0s

h iT

,

(5)

Lsrqd0S¼RLrS

1 0 0

0 1 0

0 0 1

264

375þDLrS

cos(hrhr) �sin(hrhr) 2cos(hrhr)

�sin(hrhr) �cos(hrhr) 2sin(hrhr)

cos(hrhr) sin(hrhr) 0

264

375:

(6)

The voltage induced in the neutral

point of the machine vn (7) can be

obtained from (4) [16], [36]. The

zero-sequence voltage, defined as the

mean value of the phase-to-neutral

voltages, is (8). For the case of

va þ vb þ vc ¼ 0, vrn ¼ �vn. However,

the previous equality never holds in

two-level inverters.

vn ¼ �vaLrbLrc þ vbLraLrc þ vcLraLrb

LrbLrc þ LraLrc þ LraLrb

,

(7)

vrn ¼van þ vbn þ vcn

3

¼ va þ vb þ vc

3� vn: (8)

Note that all the discussions given

earlier does not introduce any particular

restriction to the voltages feeding the

2ΔLσs

Lσa Lσb Lσ c

ΣLσs

θr (°)0 90 180 270 360

FIGURE 1 – Schematic representation ofthe high-frequency phase inductances as afunction of rotor position for the case ofhr ¼ 2.

Design of PMSMs for sensorless control is

receiving increasing attention and is expected to

be a field of great activity in the coming years.

JUNE 2011 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 25

machine, other than being high fre-

quency, meaning that these equa-

tions are valid for all high-frequency

excitation methods.

Saliencies inInduction MachinesInduction machines are not typically

designed to have a saliency, meaning

that the electromagnetic circuit seen

from the stator terminals is usually

assumed to be ideally symmetric.

However, saliencies exist in standard

induction machine designs because

of nonlinear magnetics (saturation)

and because of the effects of rotor

and stator slotting [6], [7], [12]–[16],

[22], [23], [25], [37]–[39], [42], [46].

The presence of stator and rotor slot-

ting in standard induction-machine

designs inherently creates saliencies

that offer the potential for use in sen-

sorless control. Semiopen or open

rotor slots are normally needed,

since the rotor slot bridges in closed

rotor slot machines offer a low-reluc-

tance path for the high-frequency

flux, making the rotor slots invisible

to the high-frequency excitation sig-

nals [15]. The relationship between

the pole number p, number of stator

S, and rotor slots R has to meet the

criteria shown in (9) for the slotting

saliency to couple with the stator

windings, assuming the machine has

an integer number of slots per pole

per phase [12].

n � p ¼ jR� Sj n ¼ 1, 2, 4, 5, . . . (9)

If the condition expressed in (9) is

met, the harmonic order of the sali-

ency variation with the rotor position

can be calculated as shown [12].

hr ¼ � R

p=2: (10)

In addition, the advent of high-

frequency sensorless control methods

has resulted in the development of

several methods for deliberately creat-

ing rotor-position-dependent salien-

cies [14], [42]; two examples of these

are shown in Figure 2. A key require-

ment for use of these saliencies in

sensorless control is that they cou-

ple with the windings in the stator.

This requires their spatial period to

match the fundamental or harmon-

ics of the stator windings’ spatial

distribution, with the modulation of

the rotor slots normally being chosen

to have a period equal to the pole

pitch. These modifications complicate

at a certain level the design and/or

manufacturing process of the mac-

hine but are viable for high-volume

production.

Saliencies in PermanentMagnet SynchronousMachinesPMSMs can be designed to be either

salient or nonsalient. Interior PMSMs

(IPMSMs) are intentionally salient as

part of their torque production mec-

hanism, which makes them natural

candidates for high-frequency-based

sensorless control. On the other hand,

surface PMSMs (SPMSMs) are not de-

liberately designed to be salient, which

means high-frequency-based sensor-

less control can be much more

complicated in terms of computa-

tional requirements, parameter sensi-

tivity, and even might not be possible

at all [9], [10].

The salient nature of IPMSM, and

consequently their suitability for sen-

sorless control, can be strongly af-

fected by the operating conditions.

While saturation in the d axis nor-

mally occurs due to the magnet and

does not significantly change when

fundamental current is injected, the

q-axis inductance can vary in a wide

range as the operating conditions

change [9]–[11]. The end result is

that the salient behavior of the mac-

hine seen by the high-frequency sig-

nals can dramatically change with

operating point. Two effects can be

distinguished: a reduction of the sali-

ency ratio, with a nonsalient behavior

in the limit, and a movement of the

minimum reluctance axis away from

the magnetic (d) axis because of cross

saturation. Both effects will result in a

deterioration of sensorless control,

and often instability, unless compen-

sating strategies are adopted [18],

[19], [32]–[34]. The design of PMSMs

(a) (b)

FIGURE 2 – Induction machines designs: (a) modulation of the rotor slots width and (b)double-cage induction motor with modulation of the outer cage resistance. (Figure takenfrom [42], used with permission.)

Methods that require additional signals and

associated hardware cost, e.g., sensors, cabling,

and A/D channels, in the end, replace a position/

speed sensor by a different type of sensor, which

obviously limits the intended benefits of

sensorless control.

26 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011

for sensorless control is receiving

increasing attention and is expected

to be a field of great activity in the

coming years [9]–[11]. An example of

the different rotor designs was stud-

ied in [9] (Figure 3) where it was con-

cluded that an inset rotor design

[Figure 3(d)] showed the largest feasi-

ble operating region, i.e., a range of

operating conditions in the q–d cur-

rent plane for which the rotor remains

salient.

High-FrequencySignal InjectionThe main high-frequency sensorless

control methods proposed to date

are schematically shown in Figure 4,

organized as a two-dimensional ar-

ray, where the inputs to the array

are the form of high-frequency sig-

nal excitation (columns) and the

signals measured (rows). Boxes in

the array contain the papers from

the reference list in which the corre-

sponding methods were proposed

or analyzed. One interesting fact

deduced from Figure 4 is that, for

each form of high-frequency signal

excitation, there is more than one

type of signal from which the rotor

position can be estimated (although

not all of them have necessarily been

investigated). A review of the different

forms of high-frequency excitation

and signal measurement that have

been proposed is presented. All the

analysis will be based on the high-

frequency model (4), meaning that the

measured signals are expected to

contain the same rotor position

information. To make this explicit, a

standardized representation of the

measured signals will be used for all

cases.

Continuous Versus

Discontinuous Excitation

If the high-frequency signal used to

estimate the rotor position is always

present along with the fundamental

excitation, it is referred as continu-

ous excitation [14]–[40]. Discontinu-

ous excitation methods inject the

high-frequency signal periodically,

either because they require discon-

tinuing the regular operation of the

inverter [41] or to reduce its adverse

effects on the normal operation of

the machine [42], with the drawback

of not providing a continuous rotor

position estimate. Because of this, such

methods often require the use of a

supplementary observer to estimate

the rotor position when the high-

frequency signal is not being injected.

Periodic Versus PWM Excitation

Periodic injection methods inject a

periodic high-frequency carrier signal

(usually in the range of several

hundred hertz up to a few kilohertz)

superimposed on the fundamental exci-

tation, which is generally distinct from

the pulsewidth modulation (PWM)

switching excitation created by the

inverter [14]–[40]. A characteristic

of the periodic excitation methods is

that they encode the rotor position

information in the magnitude/phase

of the resulting high-frequency sig-

nals. The excitation caused by the

PWM switching of the inverter has

also been proposed and commonly

uses modified forms of PWM, and

the response to particular states of

the inverter is measured [35]–[41].

Signal Measurement

The number and type of signals that

can be measured and processed to

obtain the rotor position varies from

method to method, with more than

one option existing for each form of

high-frequency excitation. Figure 4

shows the options that have been

proposed, with Figure 5 showing the

configuration of the sensors for each

case. It is interesting to note that

most of industrial drives include

phase current sensors and often a dc

(a) (b)

(c) (d)

FIGURE 3 –Different PMSM designs: (a) two-barrier IPM, (b) and (c) one-barrier IPM, and(d) inset motor. (Figure taken from [9], used with permission.)

The nonideal behavior of the inverter has been

established as one of the primary sources of

error in carrier signal injection-based methods.

JUNE 2011 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 27

bus-voltage sensor. Sensorless meth-

ods that rely on only these signals

could be considered at no cost from a

hardware perspective. Opposite to

this are the methods that require

additional signals and associated

hardware cost, e.g., sensors, cabling,

A/D channels, and signal-conditioning

circuits. In the end, these methods

replace a position/speed sensor by a

different type of sensor, which obvi-

ously limits the intended benefits of

sensorless control. Methods using

zero-sequence components have an

additional drawback of requiring

access to the terminal box of the

machine, which is not typically avail-

able in industrial drives. However, it

should be noted that using only sen-

sors included for sensorless control

has the benefit of selecting and scal-

ing them for the specific task of

measuring the high-frequency signals.

The following sections discuss the

forms of high-frequency excitation that

have been proposed with a focus on

continuous excitation-based methods,

since the differences with discontinuous

excitation methods do not affect to

the physical principles but are mainly

related to the implementation details.

Processing of the measured high-

frequency signals is described later.

Wye-connected machines are first

considered, and differences for the

case of delta-connected machines

are also discussed.

Rotating Carrier-SignalVoltageWhen a rotating, high-frequency car-

rier-signal voltage (11) is applied to

the machine [14], it interacts with the

saliencies in the stator transient

inductance to produce two types of

[43] [14]–[25]

[35], [36][16], [26],

[27]

Current

ContinuousExcitation

Periodic

Rotating

DiscontinuousExcitation

AmplitudeModulated

Periodic

Rotating

Voltage VoltageVoltage

PWMPWM

[44]–[46]

Other

[29]–[34] [42]

[27]

[39], [40]

[28]

[37], [38]

[41]

(Y ) Zero-SequenceVoltage, (One Voltage

Sensor)

(Y ) Zero-SequenceVoltage (Three

Voltage Sensor)

(Δ) Zero-SequenceCurrent (One Current

Sensor)

(Δ) di/dt Zero-Sequence Current

(One di/dt Sensor)

(Y/Δ) PhaseCurrents (2/3

Current Sensors)

(Y/Δ) di/dt(2/3 di/dt Sensors or2/3 Current Sensors)

Y/Δ Stand for Wye- andDelta-Connected Machine

Sig

nal M

easu

rem

ent

High-Frequency Excitation

FIGURE 4 –Classification of high-frequency signal injection-based sensorless methods.

28 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011

signals that can be used for rotor

position estimation: the negative-

sequence current and the zero-

sequence voltage [16].

vsqds c ¼ vs

ds cþ jvsqs c ¼ Vce jxct : (11)

Negative-Sequence

Carrier Current

The carrier-signal voltage (11)

produces a carrier-signal current

(12) that can be modeled using (4)

[14]. The carrier-signal current con-

sists of a positive- and negative-

sequence component (Figure 6), the

second of which contains the rotor

position information modulated in

its phase.

isqds c ¼ �jIcpejxct

� jIcnej(�xctþhrhr )

Icp ¼Vc

xc

PLrsP

Lrs2 � DLrs2

and

Icn

Vc

xc

DLrsPLrs2 � DLrs2

: (12)

Implementation of this method

requires the measurement of two

out of three phase currents [see

Figure 5(a)].

Zero-Sequence Voltage

The zero-sequence voltage (13) pro-

duced by the rotating carrier-signal

voltage (11) can also be modeled

using (4) [16]. The rotor position

information is again modulated in the

phase of this signal.

vs0sc ¼

1

3(van þ vbn þ vcn)

ffi V0ch cos (xct þ hrhr),

V0ch ¼ Vc

PLrsDLrsP

Lrs2 � DLrs2

: (13)

Implementation of this method

requires measurement of the three

phase-to-neutral voltages [see Figure 5(c)]

or the method shown in Figure 5(d)

using a single-voltage sensor [27].

Amplitude-ModulatedCarrier-Signal VoltageAn amplitude-modulated carrier-signal

voltage can also be used [29]–[34].

This method has been primarily used

with PMSMs. For this case, the ampli-

tude-modulated carrier-signal voltage

can be injected in the q axis [29], d axis

[30], or an arbitrary reference axis

[32], [33] of the estimated rotor-

synchronous reference frame. As-

suming that the injection angle is

aligned with the estimated d axis, the

injected voltage is given by (14), with

the superscript r standing for the

estimated rotor synchronous refer-

ence frame. The resulting current

(15) is calculated using (4), where

herr ¼ h1 � h is the error angle be-

tween estimated and real synchro-

nous (rotor) reference frames.

vr 0

qds c ¼ vr 0

ds c þ jvr 0

qs c ¼ Vc cos (xct),

(14)

ir 0

qds c¼1

2Icpþ Icnej2herr� �

sinðxctÞ: ð15Þ

Implementation of this method

requires measurement of two out

of the three phase currents [see

Figure 5(a)].

i0 /

(b)

iab

ibc

ica

vn − nR

(d)

(c)

(e)dtdi0 Current Sensor/

d i /dt Sensor

vc

vb

va

vc

vb

va

vn

vcn vbn van

vc

vb

va

vn

dic

vc

vb

va

dt

diadt

dibdt

Vdc /2

Vdc /2

ic

vc

vb

va

ib ia(a)

FIGURE 5 – Signal measurement: (a) phase currents using two/three sensors, (b) phasecurrents derivative using two/three sensors, (c) and (d) zero-sequence voltage using threevoltage sensors/a single sensor and an auxiliary resistor network (wye-connectedmachine), and (e) zero-sequence current/zero-sequence current derivative (delta-con-nected machine).

vqds_cs

iqdscs

q

d

ωc

ωc

Icn

Icp –ωc + hr θr

FIGURE 6 –Complex vector representationof the carrier voltage and the resulting car-rier current shown in the stationary refer-ence frame.

JUNE 2011 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 29

PWM-Based MethodsThe voltage variations produced by

the switching of the inverter during

PWM operation have also been

shown to be useful for saliency posi-

tion estimation. Two types of signals

have been proposed for use in wye-

connected machines: the derivative

of the current (di/dt) [39], [40] and

the zero-sequence voltage induced in

the stator windings [35], [36].

Derivative of the Phase Currents

It can be observed from (4) that the

derivatives of the phase currents are a

function of the instantaneous voltages

and the equivalent high-frequency in-

ductances. It is straightforward to cal-

culate the derivative of the currents

when a new inverter state is applied by

replacing va, vb, and vc in (4) with the

corresponding voltages applied by the

inverter. As an example, if the voltage

vectoru1 is applied (see Figure 7), then

va ¼ vdc=2 and vb ¼ vc ¼ �vdc=2, (16)

is obtained for phase a, similar expres-

sions can be derived for phases b and c.

disa(u1)

dt¼ vdc

Lrb þ Lrc

LrbLrc þ LraLrc þ LraLrb:

(16)

In [39], a complex vector quantity

pqd (17) was defined, where the terms

pa, pb, and pc are calculated from the

derivative of the phase currents for

different states of the inverter.

pqd ¼2

3pa þ pb ej2p=3 þ pc ej4p=3� �

¼ pejhchc : (17)

Implementation of this method

requires the use of di/dt sensors [39].

Zero-Sequence Voltage

In the technique proposed in [35] and

[36], the instantaneous line-to-neutral

voltages (see Figure 5) were measured.

The zero-sequence voltage, after ap-

plying a particular inverter state, can

be obtained from (7) by substituting

va, vb, and vc by the corresponding

voltage levels applied by the in-

verter. Based on this, three different

zero-sequence voltage vectors can

be defined, vra ¼ vr(1) ¼ �vr(4);

vrb ¼ vr(2) ¼ �vr(5); vrd ¼ vr(3) ¼�vr(6), each obtained by applying

inverter states in the a, b, and c direc-

tions (see Figure 7) of the complex

plane. A complex voltage vector, vqdr

(18) is defined using the three measure-

ments, which can be shown to be of

the form (19) and contains information

on the saliency position in its phase.

vqdr ¼2

3vra þ vrb ej2p=3 þ vrc ej4p=3� �

,

(18)

vqdr ¼3DLrs

PLrsvdc

LrbLrc þ LraLrc þ LraLrb

ejhr hr

¼ k1ejhrhr : (19)

Implementation of this method

requires measurement of three phase-

to-neutral voltages [see Figure 5(c)].

Other Forms of High-Frequency ExcitationThe discussion on periodic excitation

methods was restricted to rotating

(11) and amplitude-modulated (14)

voltage-injection methods. Other forms

of periodic high-frequency excitation

signals have been proposed, including

carrier-signal current injection [43],

high-frequency square-wave injection

[44], [45], and other forms of rotating

voltage injection [46]. Similar consid-

erations can be made with respect to

PWM methods. The use of PWM har-

monics without modification of the

PWM pattern was proposed in [53].

However, the proposed method has

the drawback of requiring measure-

ment for both phase voltages and cur-

rents at relatively high sampling rates.

All of these methods share the same

physical principles with the methods

previously discussed and are not

discussed further because of space

restrictions.

Delta-Connected MachinesAll of the discussions presented so

far are essentially valid for delta-con-

nected machines. However, in delta-

connected machines, no zero-sequence

voltage can be induced in the stator

windings. In this case, the zero-

sequence current replaces the zero-

sequence voltage [see Figure 5(e)].

Sensorless control using the zero-

sequence current and carrier-signal

injection/PWM excitation can be

found in [28] and [37], respectively.

These implementations require mea-

surement of the zero-sequence cur-

rent and the derivative of the zero-

sequence current, respectively [see

Figure 5(e)].

Processing ofHigh-Frequency SignalsThis section describes the basics of

the signal processing used to estimate

the rotor position from the measured

high-frequency signals. One major dif-

ference between carrier-signal injec-

tion methods and PWM methods is

that the measured signals provided

by the first are modulated by the car-

rier frequency while the second are

already demodulated to around dc by

their measurement method. Because

of this, the first step in the processing

of the carrier signals normally in-

cludes a coordinate transformation

v3 (− + −)v2 (+ + −)

v1 (+ − −)

v6 (+ − +)v5 (− − +)

v4 (− + +) a

b

c

FIGURE 7 – Switching state vectors (thesign of the phase potentials is indicated inbrackets).

Most of industrial drives include phase current

sensors. Sensorless methods that rely on only

these signals could be considered no cost from a

hardware perspective.

30 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011

and separation of the carrier signals

(see Figure 8), which is not needed

for the case of PWM excitation. The

next two steps are common to all

methods: compensation of second-

ary saliencies and rotor position

estimation.

Coordinate Transformationand Separation of theCarrier Signals

Negative-Sequence

Carrier-Signal Current

Equation (12) only included the cur-

rent that resulted from the carrier-sig-

nal voltage. In normal operation, the

measured stator current will also in-

clude the fundamental current used

for current regulation [see Figure 8(a)].

Preventing interference between the

negative-sequence carrier-signal cur-

rent and the fundamental current is of

great importance and can be effec-

tively achieved using the scheme

shown in Figure 8(a) [20]. Band-stop

filters (BSFs) are used to eliminate the

carrier-signal current from the feed-

back signal used for current regula-

tion, eliminating reaction of the current

regulator to the carrier-signal current.

To isolate the negative-sequence car-

rier-signal current, (20) (Figure 9), BSFs

are used to eliminate the fundamental

current and the positive-sequence car-

rier-signal current [20].

icnqds cn ¼ �jIcnejhr hr : (20)

Zero-Sequence

Carrier-Signal Voltage

It is useful to convert the zero-

sequence carrier-signal voltage in

(13) to a zero-sequence complex vec-

tor (21), which can be done with the

signal processing shown in Figure

8(b) [27].

vc0qd c ¼ �jV0chejhr hr : (21)

Amplitude-Modulated

Carrier-Signal Voltage

A similar approach as was used for

the negative-sequence carrier-sig-

nal current can be made for this

form of excitation. Once the funda-

mental current has been eliminated

[see Figure 8(c)] and (15) is obtained,

its imaginary component (22) can

then be demodulated and low-pass

filtering [see Figure 8(c)] with (23)

being the output [30]. It can be seen

that this signal is proportional to

sinðherr), which for the case of small

estimation errors is� herr.

ir 0

qs c ¼1

2Icnsin(herr)sin(xct)

� 1

2Icnherrsin(xct), (22)

Ierror ¼1

4IcnsinðherrÞ �

1

4Icnherr: ð23Þ

Modeling, Effects,and Decoupling ofSecondary SalienciesAll the modeling and discussion

presented so far has assumed that

the saliency in the machine consisted

of a single, sinusoidally varying, spatial

harmonic (1)–(3). With this assump-

tion, all of the methods discussed, with

the exception of amplitude-modulated

carrier-signal voltage, provide a signal

of the form (24), with Xrotor standing

for Icn, V0ch, p, and k1 in (17), (19), (20),

and (21), respectively, from which the

rotor angle can be directly obtained.

xqd ¼ Xrotor ejhr hr : (24)

However, the assumption of a sin-

gle saliency is not realistic in practice.

Secondary saliencies and nonsinusoi-

dal variation of the desired saliency

always exist [19]–[22], [25], [36].

Although they can have different sour-

ces, saturation of the magnetic paths

is recognized as the main one. Second-

ary saliencies cause the measured sig-

nal to have an expression of the form

(25), where the first term on the right

Negative-Sequence

BSF

Positive-Sequence

BSF

−

va

ia

ib

vb

vc

CurrentReg.

PWMInverter

CurrentVector

HF Signal Injection

FundamentalBSF ejωc t

s∗iqdss∗vqds

siqds −f

cniqd −cn

iqdss

s∗vqds −f

siqds −fsiqd −cn+

d

q

LPF sin(ωct )

Ierroriqdss

^e– jhrθr

FundamentalBSF ×

(a)

(c)

v0ss v0qd_s

c v0qd_cc

e – jωc t

(b)

FIGURE 8 – Schematic representation of the signal processing of the (a) negative-sequencecarrier-signal current, (b) zero-sequence carrier-signal voltage, and (c) amplitude-modu-lated carrier signal current. BSF: band-stop filter.

d

Icn

q

iqds_cncn

hrθr –π /2

FIGURE 9 –Negative-sequence carrier-sig-nal current. Superscript ‘‘cn’’ stands for car-rier negative reference frame.

JUNE 2011 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 31

side of the equation is the desired

signal containing the rotor position

information (24) and the rest of com-

ponents are secondary saliencies

(noise), which are normally harmon-

ics of the fundamental excitation

frequency xe, for saturation-induced

saliencies.

xqd¼Xrotorejhrhr þ

XXh ss ejhxet : (25)

The performance (stability, accu-

racy, and robustness) of a particular

sensorless control method primarily

depends on the relationship between

xqd rotor (signal) and xqd ss (noise)

[22], [17]. The magnitudes of second-

ary saliencies normally present in

real implementations typically result

in unacceptable levels of estimation

error and very often lack the desired

stability, requiring, therefore, some

form of compensation. Several meth-

ods have been developed to address

this issue [19]–[22], [25], [36], most

of them having the form shown in

Figure 10. An estimation of the sec-

ondary components, xqd ss, is first

calculated and decoupled from the

measured signal, xqd. The main differ-

ences between the proposed methods

are 1) the structure of the model, 2)

the number inputs, and 3) the storing

and computational requirements. In

these methods, the behavior of the

secondary saliencies is measured and

stored (either using time-based [25],

[36] or frequency-based [17], [19],

[22] lookup tables), for different

operating conditions, as part of the

commissioning process. The stored

information is later accessed during

normal sensorless operation of the

drive. Figures 11 and 12 show an

example implementation of a time-

based lookup table using the zero-

sequence voltage (19). Figure 13

shows an example implementation

of a frequency-based lookup table

using the zero-sequence carrier-sig-

nal voltage (21) [27]. An induction

machine in which the rotor–stator

slotting saliency was tracked was

used in both cases.

Artificial neural networks (ANNs)

have also been proposed as an alter-

native to the use of lookup tables for

secondary saliencies decoupling;

examples of the use of classical and

structured ANN can be found in [51]

and [52], respectively.

Rotor Position EstimationOnce the signal containing the rotor

position information (24) has been

isolated, the rotor position informa-

tion is contained in the phase angle of

−

Position/Velocity

Estimation

SecondaryComponent

Model

SignalProcessing

xqdxqd_rotor^

ΣXh–ss^

SecondaryComponent Decoupling

ωr^

θr^

SignalMeasurement

Inputs

FIGURE 10 – Schematic representation of secondary saliency decoupling and positionestimation.

SaturationCompens.

v ∗ ω ∗

ψ ∗

ψr

v∧

v∧

vr

Pr(vr)

ω

ωrωs

∧

ω∧

– – lm

D

N÷

τ1id

iq

iq

is(F)

is(S)

i ∗s u∗

s

e jδ

e – jδ

∧δ

∧δ

∧δ

p /ωsR ls∠x

uσ

uk

uk

usEquation(20)

l

M3~

~

~

Mains

PWM

r

SaturationCompens.

v ∗ ω ∗

ψ ∗

ψrψψ

v∧

v∧

vrvv

PrPP (vrvv )

ω

ωrωωωsωω

∧

ω∧

– – lmll

D

N÷

τ1ττidii

iqii

iqii

isii(F)

isii(S)

i ∗s u∗

suu

e jδ

e – jδ

∧δ

∧δ

∧δ

p /ωsRωωls

∠xuσuu

uk

uk

usuuEquation

(20)

l

M3~

~

~

Mains

PWM

rψψ

FIGURE 11 – Sensorless control implementation. (Figure taken from [36], used with permission.)

32 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011

(24). Different methods have been

proposed to obtain this angle, which

can differ in the bandwidth of the esti-

mation and computational require-

ments. It is important to point out in

this regard that all the discussion

presented so far has focused on the

estimation of the rotor position hr ,

while often the rotor speed xr is also

needed for control purposes.

The use of a tan�1 function is very

likely the most intuitive solution to

obtain the phase angle of xqd rotor [36],

[46]. In addition to being conceptually

simple, it provides instantaneous re-

sponse. One inconvenience of this

method is that it only provides hr . If

xr is also needed, discrete differ-

entiation of hr can be required (see

Figure 11), which is problematic in

practice because of the noise present

in the signals. To alleviate the prob-

lems with noise, the output of the

tan�1 function is often low-pass fil-

tered at the price of further limiting

the estimation bandwidth. A differ-

ent approach for obtaining hr is the

use of tracking filter/observers.

In these methods, a vector cross-

product (see Figure 14) is used to gen-

erate an error signal (26) that drives a

controller from which the rotor posi-

tion hr is obtained [14], [22], [29].

e ¼ Xrotorsin(hr(hr � hr))

� Xrotor(hr(hr � hr)): (26)

An example of a tracking observer

is shown in Figure 14 [22], [29]. Since

the tracking filters are based on feed-

back, they would suffer from the

bandwidth limitations imposed by

the controller. The system shown in

Figure 14 includes a feed-forward

term (transforming the filter to an

observer) that drives the mechanical

model based on an estimate of the

torque produced by the drive, theo-

retically providing the capability of

zero lag response. Another important

characteristic of the system in Figure 14

is that the rotor speed xr can be ob-

tained as an internal variable, eliminat-

ing the need of digital differentiation of

the estimated rotor position.

All the discussions earlier assumed

that the signal tracked consisted of a

single saliency, which was obtained

using some of the methods for

secondary saliency decoupling. How-

ever, it is possible to design a tracking

observer capable of tracking a signal

that contains more than one compo-

nent, with the block diagram being

similar to Figure 14 but with the ‘‘sali-

ency model’’ modeling having more

than one saliency [22].

ImplementationAlthough the high-frequency injec-

tion-based sensorless control meth-

ods respond to the same physical

principles, there are a number of

practical implementation issues that

influence the performance of each

method.

The nonideal behavior of the

inverter has been established as one

2π

0

0

1

0.5

0

0

0 1 2 st

1

δ∧

μσα

Sα

prα

(a)

(b)

(c)

(d)

FIGURE 12 – Elimination of saturation-induced components from the position signal (Fig-ure taken from [36], used with permission.) (a) Field angle, (b) disturbed position signal,(c) saturation component, and (d) filtered position signal.

–3

0

3

(A)

–1

0

1

(V)

–1

0

1

(V)

0 0.1 0.2 0.3

–1

0

1

Time (s)(d)

(c)

(b)

(a)

(V)

FIGURE 13 –Compensation of saturation-induced harmonics of the zero-sequence carrier-signal voltage vector (from [27]). (a) isqs, isds, (b) distributed position signal, (c) saturationcomponent, and (d) filtered position signal.

JUNE 2011 n IEEE INDUSTRIAL ELECTRONICS MAGAZINE 33

of the primary sources of error in car-

rier-signal injection-based methods.

Commutation events, especially in-

verter dead time, produce distortion

in the high-frequency carrier-signal

excitation, [(11)/(14)], which creates

additional current/zero-sequence com-

ponents in the measured signals and

reduces the accuracy of the estimated

position. Strategies to overcome

these effects can be found in [32],

[33], and [47]–[50].

PWM methods are not sensitive

in general to effects such as dead

time, since they measure the high-

frequency response in the time domain,

which allows waiting until the effects

due to the dead time of the inverter

have passed before making measure-

ments. However, PWM methods are

very sensitive to parasitic effects

induced in the cables and windings

caused by the issues such as long

cables, shielding of the cables, and

grounding strategy, which can cause

poorly damped, high-frequency oscil-

lations in the measured signals, and

strategies to mitigate these effects can

be found in [35].

Another important issue is the

interference that the injection of

the high-frequency signals has with

the regular operation of the drive.

Injection of a carrier signal [(11)/(14)]

results in a high-frequency current

that can create objectionable noise,

vibration, and additional losses. In

general, high-frequency, low-magni-

tude carrier-signal voltages are pre-

ferred, since this reduces the adverse

effects and makes filtering easier.

PWM methods also produce a distor-

tion because of the modification intro-

duced in the PWM pattern. The

possibility of using PWM methods

with no interference to the regular

operation of the inverters has been

suggested [38], [40]. In actual prac-

tice, all PWM methods require a

minimum duration of an inverter

state to perform the measurement.

This cannot be met if the inverter

state time interval is too small,

which occurs when the voltage vec-

tor crosses a sector in the space vec-

tor modulation (SVM) hexagon or

for very low-modulation indices. The

Saliency Model (Unit Vector)

+

+ + ωr^ θr

^

Te1s

++

^1

Js

VectorCross

Product

ε

Controller Mechanical System Model

J

+

Ki

Kp

Kd

1s

xqds_rotor

^

^

^e j(hr θr )

FIGURE 14 – Tracking observer for estimating rotor position in a machine with a single rotorposition-dependent saliency implemented in a stationary reference frame.

0

90

180

(Mec

h. D

eg.)

0 0.2 0.4 0.6 0.8

–2

0

2

Time (s)(b)

(a)

(Mec

h. D

eg.)

θr∧

∧θrθr –

FIGURE 15 – Sensorless position control using the zero-sequence carrier-signal currentwhen a position step from 0 to 180� is commanded. (a) The estimated rotor position and(b) estimation error. A carrier of xc ¼ 3;750 Hz, Vc ¼ 15 V was used. The machine wasoperated at rated flux and 80% of rated load (from [28]).

0 1 2 st

0

–2

–π

–π

π

π

Δυ

υ

2°

υ∧

FIGURE 16 – (From top): measured and estimated rotor positions and position angle errorat zero stator frequency and 1-Hz slip frequency. (Figure taken from [39], used withpermission.)

34 IEEE INDUSTRIAL ELECTRONICS MAGAZINE n JUNE 2011

commutation interval needs to be

increased in that case and extra volt-

age vectors can be needed, which

creates a distortion of the current

and increase the losses in the power

devices and the electric machine

[35]–[40].

Figures 15 and 16 show examples

of sensorless control using high-

frequency signal injection. The sta-

tor–rotor slotting saliency of an

induction machine was tracked in

both cases. Rotating carrier-signal

voltage and zero-sequence current

with a delta connection was used

for the results in Figure 15 [28], with

a carrier-signal frequency of xc ¼3; 750 Hz (the switching frequency

was xs ¼ 15 kHz) and a carrier-sig-

nal voltage magnitude of Vc ¼ 15 V

(peak), with the carrier-signal current

being only 1% of the rated current.

PWM excitation and derivative of the

phase currents (17) were used for the

results in Figure 16 [39]. Stable, accu-

rate control is observed in both cases.

ConclusionsHigh-frequency excitation sensorless

control methods measure the

response of the machine to some

form of high-frequency excitation

from which the rotor position is esti-

mated. The utilization of these meth-

ods is feasible in both induction and

PMSMs. The design of the machine

strongly influences its salient behav-

ior, meaning that not all designs are

adequate for their use in sensorless

applications. All the methods

respond to the same physical princi-

ples, with the main differences

among them being the type of high-

frequency signal excitation and the

type and number of signals that are

measured. Stable operation, with

similar values of accuracy, has been

reported for PWM-based methods

and for carrier-signal injection-based

methods.

AcknowledgmentsThis work was supported in part by

the Research, Technological Devel-

opment, and Innovation Programs

of the Spanish Ministry of Science

and Innovation (MICINN) under

grant MICINN-10-CSD2009-00046, and

MICINN-ERDF under grant MICINN-

10-ENE2010-14941.

BiographiesFernando Briz received his M.S.

and Ph.D. degrees from the Univer-

sity of Oviedo, Gijon, Spain, in 1990

and 1996, respectively. From June

1996 to March 1997, he was a visit-

ing researcher at the University of

Wisconsin, Madison. He is currently

an associate professor in the Depart-

ment of Electrical, Computer, and

Systems Engineering, University of

Oviedo. His research interests in-

clude control systems, power con-

verters, ac drives, sensorless control

of ac drives, magnetic levitation, diag-

nostics, and digital signal processing.

He is a Senior Member of the IEEE.

Michael W. Degner received his

B.S., M.S., and Ph.D. degrees in

mechanical engineering from the

University of Wisconsin, Madison, in

1991, 1993, and 1998, respectively,

with a focus on electric machines,

power electronics, and control sys-

tems. His Ph.D. dissertation was on

the estimation of rotor position and-

flux angle in electric machine drives.

In 1998, he joined the Ford Research

Laboratory, Dearborn, Michigan,

working on the application of elec-

tric machines and power electronics

in the automotive industry. He is

currently the manager of the Elec-

tric Machine Drive Systems Depart-

ment, Electrification Research and

Advanced Engineering Laboratory,

Ford Research and Advanced Engi-

neering, where he is responsible for

the development of electric mac-

hines, power electronics, and their

control systems for hybrid and fuel

cell vehicle applications. His research

interests include control systems,

machine drives, electric machines,

power electronics, and mechatronics.

He is a Senior Member of the IEEE.

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