Sensorless Control of an IPM Synchronous Motor … Elettrici I...Sensorless Control of an IPM Synchronous Motor for City-Scooter Applications Marco Tursini, Roberto Petrella, Francesco

Sensorless Control of an IPM Synchronous Motor for City-Scooter Applications

Marco Tursini Roberto Petrella Francesco Parasiliti Department of Electrical Engineering

University of LAquila I-67040 Monteluco di Roio LrsquoAquila Italy

tursiniingunivaqit petrellaingunivaqit rockingunivaqit

Abstractmdash This paper presents the activity made by the

authors within the National Research Program ldquoPRIN 2000rdquo partially supported by the Italian Ministry of Instruction University and Research (MIUR) The research has concerned the development of a sensorless controller for interior permanent magnet (IPM) synchronous motors to be used in city-scooter application

The project result has been the design of a sensorless scheme suitable for general applications where low speed and standstill such as high speed operations are required The final solution consists in an hybrid technique employing an adaptive observer for mediumhigh speed operation and a signal injection based technique for low speed and standstill operation

The observer detects the rotor magnet flux components in the two-phase stationary reference frame using the motor electrical equations The motor speed is identified by a model reference adaptive scheme using an additional equation obtained by a Lyapunov function The analytical development of the observer is fully explained The convergence of the estimates at low speeds and standstill is achieved through the assistance of a high frequency signal injection technique

Realistic simulations accounting for the inaccuracy of an actual digital signal processor (DSP) implementation and the prototypal implementation on a commercial hardware for city-scooter application are presented and discussed

Keywordsmdash sensorless control adaptive observer interior PM synchronous motor signal injection

I INTRODUCTION Recent proposals in emerging application fields such as

electric vehicles have outlined an increasing interest in the so-called ldquointeriorrdquo permanent magnet (IPM) synchronous motor whose basic characteristic is represented by the construction with magnets displaced inside the rotor body [1]) The IPM motors share with their ldquonon-salientrdquo counterpart (the ldquocylindricalrdquo or ldquosurfacerdquo PM motors built with magnets displaced on the rotor surface) some interesting properties such as the absence of rotor losses (that calls for ldquocoolrdquo rotor and increasing efficiency) and the high torque vs weight ratio Additional features due to the particular design of IPMs are the robustness of the rotor structure (mechanically suited to high speed operation) and the presence of magnetic saliency In fact

from a magnetic point of view IPM motors exhibit a saliency ratio different from unity ie the direct d-axis inductance is substantially different from the quadrature q-axis inductance where the d-axis is usually selected to be aligned with the PM flux axis This characteristic is particularly suited for extending the speed operating region by proper ldquofield weakeningrdquo control techniques and also it allows the application of some interesting approaches to position and speed detection (self-sensing or ldquosensorlessrdquo control) Among the proposals in this field two kinds of approaches seem to be preferable depending on the speed operating range required by the application state observers and signal injection techniques

State observers are preferred for mediumhigh speed operation They require the use of a relatively accurate motor model the measurement of the motor currents (system output) and the knowledge of the feeding voltages (system input) The basic idea is to use the difference between the state variables and the estimated state variables to calculate the rotor position and speed directly or through related variables Several approaches are reported in literature most of them applied to non salient motors Both deterministic (Luenberger [5] [6]) non-linear (sliding mode [7]) and stochastic (extended Kalman filters [8]) observers have been proposed which exhibit different peculiarities in term of algorithm complexity and sensitivity to parameter variation and noise Adaptive approaches based on the model reference adaptive system (MRAS) theory have been also suggested [9] Basically the main limitations of the observer based solutions refer to standstilllow speed operations and safe starting

Signal injection techniques are the last frontier of research in sensorless control of IPM motors These methods take advantage of the constructive magnetic saliency of the machine to detect the rotor position through the injection and back-processing of proper test signals [10] [11] [12] They offer a solution both for standstill and low speed operations As drawbacks they require high precision in the measurement a certain degree of rejection to noise and disturbances and high accuracy in signal processing especially when full-digital solutions are considered andor low saliency motors are employed

In this research an hybrid sensorless solution for speed sensorless field-oriented control of interior permanent magnet (IPM) synchronous motors has been developed consisting in an adaptive observer for mediumhigh speed operation and a signal injection based technique for low speed and standstill operation The observer detects the rotor magnet flux components in the two-phase stationary reference frame using the motor electrical equations The motor speed is identified by a model reference adaptive scheme using an additional equation obtained by a Lyapunov function The convergence of the estimates at low speeds and standstill is achieved through the assistance of a high frequency signal injection technique Both simulation and experimental results are presented the last achieved by the implementation of a prototypal system using a commercial hardware for city-scooter application The system performance at different speed ranges are presented and discussed

II ADAPTIVE OBSERVER The adaptive speed and position observer for mediumhigh

speed and operation is presented in [2] and [3] The electrical equations of the IPM synchronous motor in terms of stator fixed axis components α-β are as follows

td

d αβαβαβ

ψiv += R (1)

( ) ( )rr θθ αβαβαβαβ Mψψ iL += (2)

where αβαβ iv and αβψ are vectors of the voltage current stator flux components respectively R is the resistance of the stator windings αβL is the matrix of the winding inductance and

( )

=

r

rMrM sin

cosψ

θθ

θαβψ (3)

is the vector of the flux linkage components due to the magnet whose position is measured by the angle rθ and whose amplitude is Mψ (see Figure 1)

The flux model can be expressed in a more useful form in term of rotor fixed axis components d-q as follows

N S

θr

q d

β

Aequivα

ψM

is

ψs

B

C

ωr

Figure 1 Flux and current space vectors in an IPM synchronous motor

( ) dqMdqdqrdq ψiLψTψ +== αβθ (4)

where ( )rθT is the α-β to d-q transformation matrix ][ qddq ii=i is the vector of the d-q current components

and

=

=

000 M

dqMq

ddq

ψL

L ψL (5)

being dL and qL the direct and quadrature synchronous inductances respectively

According to the previous relations the voltage equation in (1) and the flux model (4) can be arranged to build a flux observer as follows (Figure 2)

Voltage model

Flux model

αβi

αβψαβαβ iv

αβψ~

dqψ~Angle

calculation

K11

rθ~

ψe

Figure 2 Flux observer

( )αβαβ11αβαβαβ

ψψψ

Kiv ~ˆd

ˆdminus+minus= R

t (6)

( )( ) ( )

( )dqrdqr

dqdqdqr

dqr

M

M

)~()

~(

~~

~ ~~

ψ

ψ

ψψ

iTLT

iLT

T

+sdotsdot=

=+sdot=

=sdot=

minus

minus

minus

αβ1

1

1αβ

θθ

θ

θ

(7)

where αβψ is the stator flux achieved by the voltage model

(compare Equations (1) and (6)) αβψ~ and dqψ~ represent the same flux as provided by the flux model (respectively in terms of α-β and d-q components) 11K is a 2x2 gain matrix used to feedback the voltage model by the difference between the fluxes estimated by the same voltage model and by the flux model and rθ

~ is the rotor magnet position calculated as follows

sdot

and=

dq

dqr arctg

ψψ

ψψ~ˆ

~ˆ~

αβ

αβθ (8)

where the symbols ldquo^rdquo and ldquordquo represent the vector and dot products respectively

According to (3) the flux linkage due to the rotor magnet can be represented by the dynamical model

αβαβ ω

d

dMr

M ψψ

J=t

(9)

where

minus=

0110

J

From this assumption an adaptive observer which estimates the rotor magnet flux and the speed can be arranged as follows (Figure 3)

Inverse flux model

αβi

αβi

αβψ

αβˆ

Mψ

Angle calculation

rθ

ieRotor magnet

flux model

ψe

Speed identification

rωrθ

K21

K22

Figure 3 Adaptive magnet flux and speed observer

iMM

teer 22ψ21αβ

αβ ω KKψψ

++= ˆ

d

ˆdˆ J (10)

int+= dtˆ ωωω ekek IPr (11)

where )( ˆαβαβ iie minus=i is the difference between the

measured current and its estimate the latter obtained by the introduction of an inverse flux model )( ˆ~

αβαβψ ψψe minus= is the flux estimation error obtained by the flux observer

αββαω MiMi ψeψee ˆˆ minus= is the speed error achieved by a

Lyapunov approach 2221 KK are 2x2 gain matrices used in the rotor magnet flux observer IP kk are proportionalintegral gains used in the speed identification equation rr θω ˆˆ are the estimated rotor speed and position the latter given by

=

α

βθM

Mr arctg

ψ

ψˆ

ˆˆ (12)

The availability of the current error ie allows to introduce a current feedback also in the flux observer in order to improve the robustness of the overall system Thereafter equation (7) takes the form

iR eeψ

KKiv 12ψ11αβαβαβ ++minus=td

ˆd (13)

being 12K the gain matrix 2x2 used to feedback the current error

III SIGNAL INJECTION The signal injection technique employed for low speed

and standstill operation is presented in [2] It is based on the voltage injection principle and consists in a modified processing of the high frequency currents and the use of a Kalman filter observer for the extraction of the rotor speed and position information The method is briefly recalled in the following

The voltage injection principle was originally proposed by Corley and Lorenz in [10] It relies on the fact that by neglecting the saturation of the magnetic circuits and the related cross-coupling effect the d- and q-axis of the motor are magnetically decoupled from each other Moreover considering to inject an high frequency voltage the resistive voltage drops are negligible with respect to the reactive ones With these hypotheses the injected high frequency flux d-q components in the estimated ( rθ ) rotor position reference are given by

( )

=

01

ωωθ

θ

tsinV

ψ

ψi

i

si

dsi

qsi

r

r

ˆ

ˆ

(14)

where ωi and Vsi are the carrier pulsation and the amplitude of the injected voltage and Vsiωi is the magnitude of the corresponding flux As a result the high frequency current components in the estimated rotor position reference frame can be expressed as follows

( ) ][ )( rriidsi sintsinIi rand

minus=and

θθ2ω1θ

( ) ( ) ][ )( rriiiiqsi costsinItsinIi rand

minusminus=and

θθ2ωω 10θ

(15)

where

220 ∆ω LLLVI

i

sii

minus= 221 ∆

∆ω LL

LVIi

sii

minus= (16)

being

2dq LL

L+

= 2

∆ dq LLL

minus= (17)

the average value and the amplitude of the spatial modulation of the inductance respectively Ld and Lq the d- and q-axis inductances From (15) it can be seen that carrier frequency signals are produced both on the d- and q-axis components that are non-linearly amplitude-modulated by twice the difference between the estimated and the actual (θr) position In this proposal both the d- and q-axis components of the high frequency current in the estimated

reference frame are processed in order to extract the rotor position estimation error signal In fact the amplitude modulation of both (15)

][ )( rrid sinIand

minus= θθ2ε 1

][ )( rriiq cosIIand

minusminus= θθ2ε 10

(18)

can be evaluated by means of a proper demodulation engine [2]

Thereafter assuming the constant offset Ii0 is identified the rotor position error (εθ) can be expressed as follows

minus= minus

qi

d

Itan

εεε

0

121

θ (19)

where εd and εq denote the error signals extracted by each current component By this approach a straightforward relationship between the error signal and the actual rotor position estimation error is achieved

Once the error signal (19) has been evaluated it is used in a Kalman filter which provides the rotor position and speed estimation Figure 4 Details on Kalman filtering are given in [3]

qε

rω0iI

rθ

dε Eq (19) Kalman

filter

θε

Figure 4 Position and speed estimation by Kalman filter

(signal injection technique)

IV SIMULATION RESULTS In order to give a meaningful idea of the system

performance realistic simulations are carried out referring to the actual digital signal processor (DSP) implementation The commercial IPM motor for city scooter application is considered whose parameters are reported in TABLE I whereas the characteristics referring to the high-frequency signal injection are reported in TABLE II Synchronized control PWM and current sampling periods of 220 micros are considered with the consequent time-delays Moreover the problems related to current measurement have been accounted In fact the reliability of the sensorless scheme particularly for the signal injection technique is heavily affected by the accuracy of the high-frequency current components measurement

The first goal of simulations is to compare the different performance of the signal injection technique and the adaptive observer in terms of speed response and position estimation error The tested cases refers to a standstill operation (with initial rotor position and estimation error

equal to 45 degrees) followed by a step variation of the speed reference from zero to a given set point with 117 Nm (02 pu) load torque For the sake of comparison this kind of test is repeated in the following cases

1) (Figure 5 to Figure 7) assuming for the sensorless operation the signal injection technique described in Section III only in this case the lowmedium speed operating region is explored assuming 450 rpm and 750 rpm set points respectively 015 and 025 pu

2) (Figure 8 to Figure 9) assuming for the sensorless operation the signal injection at standstill and the adaptive observer described in Section II after startup in this case the mediumhigh speed operating region is explored assuming 1500 rpm and 2250 rpm set points respectively 05 and 075 pu As for the signal injection technique a rotor position

estimation error is present at steady state which increases with the operating speed (Figure 5 and Figure 6) Such an error which is independent on the load (ie current) conditions (see Figure 7) is due to the delays of the digital implementation and can assume excessive values with increasing speed leading to a lack of control In a practical case it must be compensated for operation at medium speed whereas it can be accepted if operation at very low speed and standstill is assumed In Figure 5 and Figure 6 the influence of the Kalman filter acceleration parameter a( is presented Assuming a value different from zero proportional to the difference between the reference and the estimated speed allows to improve the preciseness of the speed estimation during the fast transients while it does not affect the steady state operation and rotor position error

-005

0

005

01

015

02

025

03

035

0 02 04 06 08

T [s]

[pu]rω

)(sirωrω

-10

0

10

20

30

40

50

0 01 02 03 04 05 06 07 08

T [s]

[degrees]

pu025015=rω)(sirr θθ minus

Figure 5 Sensorless operation with signal injection technique

(Kalman filter parameter 0=a( )

-005

0

005

01

015

02

025

03

035

0 02 04 06 08

T [s]

[pu] rω

)(sirωrω

-10

0

10

20

30

40

50

0 01 02 03 04 05 06 07 08

T [s]

[degrees]

)(sirr θθ minus pu025015=rω

Figure 6 Sensorless operation with signal injection technique

(Kalman filter parameter )( )(sirr ωωka minussdot=( )

-14

-12

-10

-8

-6

-4

-2

00 02 04 06 08 1

load torque [pu]

[deg

rees

]

pu045-025-015=rω

)(sirr θθ minus Figure 7 Rotor position estimation error at steady state

(signal injection technique)

As for the adaptive observer the rotor position estimation error at steady state seems to be independent on the operating speed Nevertheless it is strongly affected by the choice of the several observer gains As an example the counteracting influence of the integral gain Ik used in the speed identification equation is shown by the comparison of Figure 8 and Figure 9 If this gain is too small the speed and the position estimates assume an oscillatory behavior which can lead to instability during large (and fast) transients

From the presented results it arises that the signal injection technique can be used to achieve good operation at standstill and (eventually) very low speed while the adaptive observer with proper gains in the remaining speed range The strategy adopted to manage the operation of the hybrid observer is resumed as follows

0

025

05

075

1

0 02 04 06 08

T [s]

[pu]rω

)(obsrωrω

-10

0

10

20

30

40

50

0 01 02 03 04 05 06 07 08

T [s]

[degrees]

pu07505=rω

)(obsrr θθ minus

Figure 8 Sensorless operation with adaptive observer

(integral gain 0750= kI used in the speed identification equation)

0

025

05

075

1

0 02 04 06 08

T [s]

[pu]rω

)(obsrωrω

T [s]

[degrees]

pu07505=rω

)(obsrr θθ minus

-10

0

10

20

30

40

50

0 01 02 03 04 05 06 07 08 Figure 9 Sensorless operation with adaptive observer

(integral gain 10= kI used in the speed identification equation)

1) At standstill the speed command is zero the estimates employed for sensorless control are provided by the signal injection technique In the meantime the adaptive observer is tuned by substituting the estimated position ( rθ~ ) (see the scheme in Figure 2) with the one provided

by the signal injection observer

2) Once the motor starts the estimated speed increases When a first commutation level is reached (ie estimated speed greater than 01 pu plus an additional hysteresis band) the controller switches to the estimates provided by the adaptive observer From this point on the signal injection observer is tuned by substituting at each control step the integral components of the Kalman filter (both speed and position estimates) with the corresponding values provided by the adaptive observer

3) Thereafter when a second commutation level is reached (ie estimated speed greater than 02 pu plus an additional hysteresis band) the high frequency signal injection is removed Since this instant the adaptive observer acts alone Once signal injection ceases the full voltage capacity of the feeding DC bus is available for the fundamentals operation ie the maximum speed range can be attained Moreover the power losses due to the high frequency currents and the vibrations due to the high frequency torque ripple finish

V EXPERIMENTAL RESULTS The sensorless solution developed within the research

project has been implemented and experimentally tested using a commercial drive (and IPM motor) for city-scooter application Figure 10 shows the experimental set-up The sensorless controller has been realized using a TMS320C240 Evaluation Module (EVM) The EVM has been interfaced with the commercial hardware in order to read the current signals (from the Hall sensors) and generate the pulse pattern for the MOSFET inverter whereas the controller of the commercial drive has been fully disabled In order to improve the accuracy of current measurement an analog band-pass filter has been implemented for the extraction of the high frequency currents injected in two of the motor phases This solution allows the separate and independent conditioning and sampling of both the instantaneous currents and the respective high frequency currents on two couple of channels (2+2) with optimized scaling for each couple

The MOSFET inverter is fed through an external DC power supply at the rated voltage of 48 V Being the commercial motor for city scooter equipped with position sensors (both Hall sensors and an incremental encoder rating 64 pulses per mechanical round) the related signals have been also interfaced with the EVM board to achieve the measurement of the actual rotor position and calculate the position estimation error Due to the (relatively) low resolution of the encoder although quadrupled by the DSP quadrature encoder unit the precision in the measurement of the electrical position is in the order of 3 degrees The basic parameters of the DSP implementation and signal injection are depicted in TABLE II The PWM and current sampling periods have been set to 220 micros which is the time necessary for the execution of the whole control algorithm (adaptive observer signal injection Kalman filter) The algorithm include the carrier recovery strategy presented in [3] for the demodulation of the high frequency currents

Figure 10 Experimental prototype of the drive for city-scooter application

The experimental results are presented in Figure 11 to Figure 16 All the tests are carried out at no load Figure 11 shows the speed transient from 0 to 015 pu In this range (low speed operation) signal injection is always active and the related position estimation is used to assist the adaptive observer One notices the position error during the transient and the estimated (smooth) speed tracking the actual one this last affected by the noise due to the calculation from the low resolution encoder The position peak error is in the order of 14 degrees

Figure 12 shows the speed transient from 015 to 03 pu In this range at 02 pu there is the transition form the low to the ldquohighrdquo speed region signal injection is removed as shown by the lack of injected voltage signal The inverse transition form high (03 pu) to low (015 pu) speed range with restart of the signal injection is shown in the subsequent Figure 13

Figure 11 Speed transient from 0 to 015 pu

(inside the low speed range)

Figure 12 Speed transient from 015 to 03 pu

(with transition from the low to high speed region at 02 pu speed)

Figure 13 Speed transient from 03 to 015 pu

(with transition from the high to low speed region at 02 pu)

Figure 14 shows the digital demodulation technique used to achieve the error signals (18) in the case of the d-axis component According to the chosen injection-to-control frequency ratio eight samples of the high frequency currents are available for each period of the injection carrier which has proved to be the minimum number of samples to assure a satisfactory behavior of the digital demodulation Figure 15 shows a speed reversion moving from the high speed region near to the rated value (-09 pu to 09 pu) In this case the speed follows a linear reference trajectory employing two seconds for the whole reversion The performance are satisfactorily in all the speed range including zero crossing

Finally Figure 16 shows the steady state performance at very low (3 Hz) operation the sine of the actual and estimated position appear as superimposed

VI CONCLUSIONS This paper presents an approach to speed sensorless

control of IPM motors based on an adaptive observer for high speed operation and a modified high frequency signal injection technique for standstilllow speed operation The mixed solution allows to merge the advantages of both methods ie safe standstill and start-up operation with

signal injection absence of not necessary losses and the availability of the full feeding voltage for fundamental operation with high speed observer The achieved results demonstrated the satisfactory performance of the proposed system which has been tested on a commercial prototype for city scooter application The use of some simple accuracy such as analog band pass filters to extract the injected current signals allows the implementation with low cost fixed point DSP equipped with 10 bits AD converter

Figure 14 Sampling and demodulation of the (d) error signal

Figure 15 Speed reversion from -09 to 09pu

Figure 16 Sine of the actual and estimated position

at low speed operation (3 Hz)

TABLE I MOTOR PARAMETERS

Ratedbase speed 3000 rpm

Ratedbase current 50 A rms

Rated power 18 kW

Pole pairs 2

Stator resistance 0023 mΩ

Direct inductance 02245 mH

Quadrature inductance 08115 mH

Back-EMF constant 705 mVrmsrpm (∆)Ii0 328 A Ii1 186 A

Average inductance (L) 0518 mH Inductance modulation (∆L) 029 mH

TABLE II INJECTIONCONTROLSYSTEM PARAMETERS

Voltage (Vsi) 611 Vrms

Frequency (fsi) 568 Hz

PWM period 220 us Speed of transition from low

to high speed observer 02 pu Speed where the signal

injection is removed 025 pu

DC bus voltage 48 V

APPENDIX SENSORLESS DRIVE SCHEME The sensorless drive scheme is presented in Figure 17

It refers to a fully-digital implementation employing fixed-point digital signal processor The field-oriented controller is based on a current-controlled voltage source inverter structure The current control loops are arranged in the two-phase synchronously rotating reference frame d-q aligned with the rotor magnet flux Proportional and integral regulators are used for both the current and speed control loops An adjacent-vector space vector pulse width modulator (AV-SVPWM) is used to apply the voltage commands

The adaptive observer estimates the rotor magnet flux angle rθ (needed for the field orientation) and the rotor speed feedback rω (used for the speed control loop) High frequency voltage signals are superimposed to the d-q voltage commands during low speed and standstill operation The resulting high frequency current components are processed by a heterodyning technique that produces an information on the rotor magnet position This signal is used to tune the adaptive observer in such critical operation conditions

2

dq

αβ

PMSM

αv

ia

dq

αβ

AV

SVPWMRiq

Rid

βv

qv

dv

qi

0=di

qi

di

αβ

ib

αi

βi

AD Interface

6

4

7

8

5

3

2rω

Rvel

1

rω

rθ

Signal injection

Signal Injection processing amp

Adaptive observer

10

ia ibαv

βv

Figure 17 Sensorless drive scheme

REFERENCES [1] F Parasiliti R Petrella and M Tursini ldquoSensorless Control of Buried

PM Synchronous Motorsrdquo in Proc of the Thirteenth Interactive Seminar Vol 2 pp147-168 Bressanone (Italy) March 18-20 2002 (in Italian)

[2] F Parasiliti R Petrella M Tursini ldquoSensorless Speed Control of Salient Rotor PM Synchronous Motor Based on High Frequency Signal Injection and Kalman Filterrdquo in Proc of the ISIE Conf CD ROM LrsquoAquila (Italy) July 2002

[3] F Parasiliti R Petrella and M Tursini ldquoSpeed Sensorless Control of an Interior PM Synchronous Motorrdquo Proc of the Thirty Seventh IEEE-IAS Annual Meeting CD ROM Pittsburgh October 13-17 2002

[4] N Bianchi S Bolognani M Zigliotto ldquoHigh-Performance PM Synchronous Motor Drive for an Electrical Scooterrdquo IEEE Trans Ind Applications Vol 37 No 5 pp 1348-1355 SeptemberOctober 2001

[5] PhK Sattler and K Staumlrker ldquoEstimation of speed and pole position of an inverter fed permanent excited synchronous machinerdquo in Proc of the EPE Conf pp 1207-1212 Aachen 1989

[6] LA Jones and JH Lang ldquoA state observer for the permanent magnet synchronous motorrdquo IEEE Trans Ind Electronics Vol 36 No 3 pp 374-382 August 1989

[7] F Parasiliti R Petrella and M Tursini ldquoSensorless speed control of a PM synchronous motor based on sliding mode observer and extended Kalman filterrdquo Proc of the Thirty Sixth IEEE-IAS Annual Meeting CD ROM Chicago September 30 October 4 2001

[8] S Bolognani R Oboe and M Zigliotto ldquoSensorless full-digital PMSM drive with EKF estimation of speed and rotor positionrdquo IEEE Trans on Industrial Electronics Vol 46 No 1 pp 184-191 February 1999

[9] N Matsui ldquoSensorless PM brushless dc motor drivesrdquo IEEE Trans on Industry Applications Vol 43 pp 300-308 April 1996

[10] MJ Corley and RD Lorenz ldquoRotor position and velocity estimation for a salientndashpole permanent magnet synchronous machine at standstill and high speedsrdquo IEEE Trans on Industry Applications Vol 34 No 4 pp 36-41 JulyAugust 1998

[11] M Shroedl ldquoSensorless control of AC machines at low speed and standstill based on the ldquoINFORMrdquo methodrdquo in Proc of the Industry Application Society Annual Meeting Vol 1 pp 270-277 1996

[12] A Consoli G Scarcella and A Testa ldquoSensorless control of PM synchronous motors at zero speedrdquo in Proc of the Industry Application Society Annual Meeting Vol 1 pp 270-277 1999

[13] A Bellini S Bifaretti and S Costantini ldquoIdentification of the mechanical parameters in high-performance drivesrdquo in Proc of the EPE Conf CD ROM Gratz 2001