Estimation of Rotor Position and Speed for

Sensorless DSP-based PMSM Drives

Lucio Ciabattoni, Massimo Grisostomi, Gianluca Ippoliti, Sauro Longhi

Abstract— In this paper a sensorless cascade control schemefor a Permanent Magnet Synchronous Motor (PMSM) drive isproposed. The rotor position and speed are obtained throughan Extended Kalman Filter (EKF). The proposed solution isexperimentally tested on a commercial PMSM drive equippedwith a control system based on a floating point Digital SignalProcessor (DSP).

I. INTRODUCTION

Permanent Magnet Synchronous Motors (PMSMs) have an

important role in motion control applications in the low and

medium power range (e.g. robotics and machine tool drives).

The desired features of PMSMs are fast dynamical response,

high torque to weight ratio, linear dependence of the torque

on one component of the current in a suitable reference frame

[1], [2]. To achieve fast four quadrant operation, smooth

starting and acceleration, the Field Oriented Control (FOC),

or vector control, is used in the design of the PMSM drive

[3]–[12]. Standard linear design methods for FOC consist

of a properly tuned cascate configuration of Proportional

Integral (PI) speed and current controllers. Therefore accu-

rate information regarding the motor parameters and load

conditions is necessary to guarantee good drive performance

in terms of precision, bandwidth and disturbance rejection

[13].

High performance control of PMSM drives also requires

the knowledge of the rotor shaft position and speed in order

to synchronize the phase excitation pulses to the rotor posi-

tion [14]–[16]. This implies the need for speed or position

sensors such as an encoder or a resolver attached to the

shaft of the motor. The demand of inexpensive and reliable

drives now pushes applied research toward the elimination of

mechanical sensors [17]–[20]. In fact, in most applications,

these sensors present several disadvantages, such as reduced

reliability, susceptibility to noise, additional cost and weight

and increased complexity of the drive system. The position

and velocity sensorless control of PMSM drive overcome

these difficulties. A comprehensive overview of methods

developed to obtain rotor position and angular speed from

measurements of electric quantities is reported in [21]–[23].

In this paper, an Extended Kalman Filter (EKF), which

is an optimal estimator for the states of dynamic nonlinear

systems with inherent robustness against parameters varia-

tions, is proposed for the motor rotor position and speed

The Authors are with the Dipartimento di Ingegne-ria Informatica, Gestionale e dell’Automazione, UniversitaPolitecnica delle Marche, Via Brecce Bianche, 60131Ancona, Italy {l.ciabattoni, m.grisostomi,gianluca.ippoliti, sauro.longhi}@univpm.it

estimation from measurements of electric quantities. With

advances in digital technology over the last several years,

adequate data processing capability is now available on cost-

effective DSP-based platforms and the EKF appears to be a

viable and computationally efficient candidate for the online

estimation of rotor position and speed of a PMSM [21], [24]–

[26]. Theoretical basis and digital implementation of the EKF

have been deeply investigated [16], [27]–[29] and a novel

procedure for the tuning of covariance matrices in EKF-

based PMSM drives has been presented in [23]. Application

examples, in which well-known pitfalls, such as the starting

from unknown rotor position and the filter matrices tuning

have been successfully fixed in [22].

Summing up, the features of the PI-based FOC technique

combined with the EKF-based rotor position and speed esti-

mator are exploited in this work to design the cascade control

architecture shown in Fig. 1 (the meaning of the signals

and blocks shown in Fig. 1 will be explained throughout

the paper). In this scheme, the external velocity PI-based

control loop, two internal current PI-based control loops and

the EKF-based rotor position and speed estimator can be

identified. The task is to make the speed error ω∗

r − ωr to

tend to zero as close as possible.

The paper is organized as follows. The nonlinear state

space model of the PMSM dynamics is presented in Section

II. The EKF algorithm is reported in Section III. Results on

experimental tests are reported in Section IV. The paper ends

with comments on the performance of the proposed solution.

Fig. 1. Block scheme of the proposed cascade controller (FOC)

II. MOTOR DYNAMICS

In the (d, q) reference frame, synchronously rotating with

the motor rotor, the electrical equations of motion of a

19th Mediterranean Conference on Control and AutomationAquis Corfu Holiday Palace, Corfu, GreeceJune 20-23, 2011

ThCT3.3

978-1-4577-0123-8/11/$26.00 ©2011 IEEE 1421

permanent-magnet synchronous motor can be written as [30],

[31]:

diddt

= −R

Lid + ωeiq +

1

Lud (1)

diqdt

= −R

Liq − ωeid −

1

Lλ0ωe +

1

Luq (2)

where id and iq are the d−axis and q−axis stator currents,

respectively; ud and uq are the d− axis and q− axis stator

voltages, respectively; R is the winding resistance and L =Ld = Lq is the winding inductance on axis d and q; λ0 is the

flux linkage of the permanent magnet and ωe is the electrical

angular speed of the motor rotor.

The electrical torque τe and the mechanical power P of

the motor are given by:

τe = Ktiq (3)

P = τeωr (4)

in which Kt = 32λ0Nr is the torque constant with Nr the

number of pole pairs and ωr is the mechanical angular speed

of the motor rotor. The developed torque of the motor is

proportional to the iq current because of the assumption that

there is no reluctance torque in the considered PMSM.

The mechanical motion equation of the motor is described

by:

Jdωr

dt+ Bωr = τe − τℓ (5)

dθr

dt= ωr (6)

where J is the mechanical inertia of the motor and load, Bis the coefficient of viscous friction, τℓ is the load torque

and θr denotes the mechanical angular position of the motor

rotor.

For the electrical angular position/speed and the mechan-

ical angular position/speed, the following relations hold:

ωe = Nrωr (7)

θe = Nrθr. (8)

III. ESTIMATION OF ROTOR POSITION AND

SPEED

The proposed EKF providing on line estimates of rotor

position and speed is derived in this section. Denote with

X(t) :=[

ωr(t) id(t) iq(t) ϑr(t)]

the motor state and

with U(t) :=[

ud(t) uq(t)]

the motor control input. The

motor nonlinear dynamic state space model can be written

in the compact form of the following stochastic differential

equation:

dX(t) = F (X(t), U(t))dt + dη(t), (9)

where F (X(t), U(t)) is obtained by (1), (2), (5), (6) and η(t)is a Wiener process such that E(dη(t)dη(t)T ) = Q(t)dt.Its weak mean square derivative dη(t)/dt is a white noise

process ∼ N(0, Q(t)) representing the model inaccuracies.

Assuming a constant sampling period ∆tk = T and denoting

tk+1 by (k +1)T , the following sampled nonlinear measure

equation can be associated to equation (9):

Z((k + 1)T ) = G(X((k + 1)T )) + v(kT ), (10)

where Z(kT ) is the vector containing measures of mo-

tor phase currents and v(kT ) is a white sequence ∼

N(0, R(kT )). The measure vector Z(kT ) is composed of

two elements, i.e. Z(kT ) = [z1(kT ) z2(kT )]T , where

z1(kT ) = id(kT ) + v1(kT ), z2(kT ) = iq(kT ) + v2(kT ).By definition of the measurement vector one has that the

output function G(X((k + 1)T )) has the following form:

G(X(kT )) =[

id(kT ) iq(kT )]T

= C(k)X(kT ) (11)

where

C(k) =

[

0 1 0 00 0 1 0

]

(12)

and v(kT ) = [v1(kT ) v2(kT )]T . Assume U(t) = U(kT )for t ∈ [kT, (k + 1)T ). To obtain an extended Kalman filter

with an effective state prediction equation in a simple form,

model (1) and (2) has been linearized about the current state

estimate x(kT, kT ) and the control input U((k − 1)T ) ap-

plied until the linearization instant. Subsequent discretization

with period T of the linearized model results in the following

EKF (where explicit dependence on T has been dropped for

simplicity of notation),

X(k + 1, k) = Ad(k)X(k, k) + L(k)U(k)

+D(k), (13)

P (k + 1, k) = Ad(k)P (k, k)ATd (k)

+Qd(k), (14)

K(k + 1) = P (k + 1, k)CT (k + 1)

[C(k + 1)P (k + 1, k)CT (k + 1) + R(k + 1)]−1,(15)

X(k + 1, k + 1) = X(k + 1, k) + K(k + 1)

[Z(k + 1) − G(X(k + 1, k))], (16)

P (k + 1, k + 1) = [I − K(k + 1)C(k + 1)]

P (k + 1, k), (17)

where

Ad(k) = eA(k)T≃ I + A(k)T

=

1 −BJ

T 0

iq(k, k)T 1 −RL

T

−

(

λ0

L+ id(k, k)

)

T −Nrωr(k, k)T

1 0Kt

JT 0

Nrωr(k, k)T 01 −

RL

T 00 0

(18)

A(k) :=[

∂F (X(t),U(t))∂X(t)

]

X(t)=X(k,k)U(t)=U(k−1)

(19)

L(k) =

0 0TL

00 T

L

0 0

(20)

978-1-4577-0123-8/11/$26.00 ©2011 IEEE 1422

D(k) = T D(k) =

−τℓTJ

−iq(k, k)Nrωr(k, k)T

id(k, k)Nrωr(k, k)T0

(21)

D(k) := F(

X(k, k), U(k − 1))

−A(k)X(k, k) − L(k)U(k − 1) (22)

Qd(k) = σ2η(k)Q(k). (23)

For the sake of brevity, the elements of the matrix Q(k)have not been reported. The form of Qd(k) expressed by

(23) derives by the hypothesis that Q(τ) = σ2η(k)I4, τ ∈

[kT, (k + 1)T ). This simplification assumption has been in-

troduced to obtain a Qd(k) which is completely known up to

the unknown multiplicative scaling factor σ2η(k). Moreover,

the covariance matrix R(k) is assumed to have the following

diagonal form:

R(k) = diag[σ2v,1(k), σ2

v,2(k)]. (24)

This means that no correlation is assumed between the

measurement errors introduced by the sensors. As R(k)is diagonal, the components of Z(k) may be processed

one by one by reducing the inversion of the 2 × 2 matrix

in (15) to the 2 inversions of scalars [32], thus saving

much computation time. The sequential processing of each

component z1(k), z2(k) must be performed in a period of

time (typically the sampling period) such that no significant

change occurs in the state estimate and in its covariance

matrix due to dynamics (9) [32].

The EKF can be implemented once estimates of Qd(k)and R(k) are available. As stated in [21], to reduce the

computational effort for a real time implementation of the

EKF an acceptable approximation is to use a diagonal

covariance matrix Qd(k).

IV. EXPERIMENTAL IMPLEMENTATION

The proposed PI-based FOC and EKF-based rotor po-

sition and speed estimator have been implemented on the

Technosoft MCK28335-Pro DSP motion control kit [33],

available in the Robotics Laboratory at Dipartimento di

Ingegneria Informatica, Gestionale e dell’Automazione of

the Universita Politecnica delle Marche. The experimental

setup is shown in Fig. 2. It is a combination of hardware

and software and includes a DSP-based controller board, a

power module, a PMSM equipped with a 500-line quadrature

encoder (4 is the multiplication ratio of the position resolu-

tion done in the encoder interface) and a software platform

to develop motion control applications. All communication

between PC and DSP board is done through the RS-232interface using a real-time serial communication monitor

resident in the DSP flash.

In this section, the drive structure, the experimental setup

and the results are discussed.

DMCD28x-Pro�

MSK28335 board

PM50 power module�

MBE300.E.500 PMSM�

Fig. 2. Experimental setup

A. Drive Structure

Control design methods performed in the (d, q) coor-

dinates are called field-oriented control which consists of

controlling the stator currents represented by a vector (vector

control). This approach uses a state transformation after

which the decoupling and linearization tasks can be per-

formed [14]. In particular, FOC-based schemes exploit the

fact that in the (d, q) rotating reference frame the torque and

the flux dynamics are linear and decoupled and independent

torque and flux control loops can be implemented. PI con-

trollers are commonly used in both loops in order to produce

the ‘d’ and ‘q’ voltage vector components, affecting the

flux and torque dynamics, respectively. Recently, high-speed

Digital Signal Processor (DSP) has become very common

in electric drive systems and FOC has been implemented

in many drive systems of AC machines. The field-oriented

control scheme of Fig. 1 is based on the measure of two

phase currents (ia and ib). The EKF-based estimator is

designed to estimate the rotor position and speed from

measurements of electric quantities. The measured phase

currents, ia and ib, are transformed, based on the rotor

position information and the Park coordinate transformation,

into the rotor frame direct and quadrature components, idand iq. The inverse Park coordinate transformation is used

for the computation of the three-phase voltage references, u∗

a,

u∗

b and u∗

c , applied to the inverter starting from the values of

voltage references computed by the current controllers in the

(d, q) reference frame, i.e. ud and uq. Thus, 6 PWM outputs

of the DSP controller are directly driven by the implemented

control algorithm, based on these reference voltages.

The motion control uses a cascate control structure with

inner loops for the current control and an outer loop for

the speed control (see Fig. 1). Standard PI controllers have

been designed for each control loop following the directions

reported in the user manual of the MCK28335-Pro kit

[33]. In particular, the current control is performed by two

identical PI regulators that have been designed and tuned to

get a bandwidth of 400 Hz. Similarly, the parameters of the

PI speed regulator has been set considering a bandwidth of 40Hz. PI constants are related to both the system parameters

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and the required bandwidth; the proportional gain and the

integral action factor are 0.0001 and 0.9618, respectively,

for the two current controllers and 171.2532 and 31.4921,

respectively, for the speed controller.

In the proposed solution the reference (i∗d) of the direct

current component is set to zero (see Fig. 1). This case

corresponds to the motion of the motor in the normal

speed range, without considering possible field weakening

operations [30].

The sampling frequency is selected as 1 kHz for the

velocity control loop and 10 kHz for the current control

loops.

As proposed in [21], Fig. 1 shows that the EKF is fed with

the reference voltages ud and uq instead of the measured

ones. In fact, taking into account saturation phenomena in

the current controller implementation, it is possible to use

the voltage references instead of the actual voltages because

of the inverter switching period is small with respect to the

electrical time constant of the motor [21].

The initial values for the matrices Qd(·), R(·) and P (·, ·)have been chosen with a trial-and-error procedure to get the

best tradeoff between filter stability and convergence time

[21], [34]. Such matrices are reported in the following:

Qd(0) =

14 0 0 00 7.2 · 10−4 0 00 0 7.2 · 10−4 00 0 0 0.1

(25)

R(0) =

[

3.35 · 10−4 00 3.35 · 10−4

]

(26)

P (0, 0) =

10 0 0 00 0.04 0 00 0 0.04 00 0 0 1

. (27)

B. Experimental Setup

Experiments have been carried out on the Technosoft

MBE.300.E500 PMSM. The motor catalog electric and me-

chanical parameters are given in Table I. The Technosoft

PM50 power module includes a 3-phase inverter, the pro-

tection circuits and the measurement circuits for the DC-

bus voltage and the motor currents. The 3-phase inverter

uses MOSFET transistors with switching frequency up to

50 kHz. The PM50 interface includes 6 PWM command

inputs (TTL/CMOS compatible) through which the control

unit can drive each transistor of the inverter. The PM50electrical specifications are given in Table II. The control

unit is the Technosoft MSK28335 board based on the high

performance Texas Instruments DelfinoTM TMS320F28335Digital Signal Controller (DSC) [35]. The three-phase volt-

age commands are generated using the PWM unit of the

DSP. The PWM outputs are applied to the 6 transistors of

the power inverter, based on sinusoidal reference values for

the motor phase voltage, as generates after computation in

(d, q) rotor coordinates frame at the output of the current

controllers, and transformation to stator coordinates frame

by the inverse Park transformation (see Fig. 1). The DSP

TABLE I

TECHNOSOFT MBE.300.E500 PMSM PARAMETERS [33].

Coil dependent parameters

Phase-phase resistance ohm 8.61Phase-phase inductance mH 07.13

Back-EMF constant V/1000 rpm 3.86Torque constant mNm/A 36.8

Pole pairs – 1

Dynamic parameters

Rated voltage V 36Max. voltage V 58

No-load current mA 73.2No-load speed rpm 9170

Max. cont. current (at 5000 rpm) mA 913Max. cont. torque (at 5000 rpm) mNm 30

Max. permissible speed rpm 15000Peak torque (stall) mNm 154

Mechanical parameters

Rotor inertia Kgm2· 10−7 11

Mechanical time constant ms 7

TABLE II

TECHNOSOFT PM50 POWER MODULE ELECTRICAL SPECIFICATIONS

[33].

Param. Cond. Min. Typ. Max. Units

DC Input Power

Mot. supply – 9 – 36 V

Mot. supply cur. – – – 2.1 Arms

Mot. supply cur. – – – 6.33 Apeak

Output Power

Voltage set by external 0 – 36 Vrms

PWM control

Nom. Mot. Power Vin = 36V , – – 75 W

fpwm = 20kHz,

TA = 40◦CNom. Mot. Cur. TA = 40◦C – – 1.7 Arms

PWM frequency – 0.1 20 100 kHz

has a 150 MIPS, 32 bit single-precision floating-point DSP

core and operates at a 150MHz frequency. The MSK28335board is equipped also with 128-kWords 0-wait state exter-

nal RAM, 2 channels of 12-bit accuracy D/A outputs, 16channels of 12-bit accuracy and 80 ns conversion time A/D

inputs, RS-232, CAN-bus and JTAG interfaces.

The motor phase current measurement scheme of the

MCK28335 kit is based on shunts mounted on each lower

leg of the inverter. The voltage drop on a shunt is amplified

and sent to the TMS320F28335 A/D channels. This current

measurement scheme, simple and cost-effective from the

hardware point of view, requires some special care from

the software implementation. The A/D conversions have to

be synchronized with the PWM command of the inverter

transistors, for a proper measurement of the currents on each

phase of the motor. In fact a ripple in the motor currents

exists and its value is relative to the motor parameters (elec-

trical time constant), PWM frequency, and current controller

bandwidth. Consequently, due to this inherent current ripple,

in order to get the closest measured value of the current,

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the measurements have been performed at the middle of the

PWM period [33].

The MCK28335-Pro kit includes the DMCD28x-Pro, the

Technosoft software platform, which allows the development

of motor control applications. The code is developed in C

language using a modular approach providing flexibility for

further system integration.

C. Experimental Results

A sample of the performed speed-tracking experiments is

shown in Fig. 3. In this figure, the performance produced

by the proposed PI-based FOC equipped with the EKF-

based rotor position and speed estimator is illustrated for the

motor following a reference trajectory given by a trapezoidal

velocity profile.

A comparison with the performance of a PI-based FOC

equipped with a conventional backward-difference method

for speed estimation, using sampled position measurements

provided by a digital incremental encoder, has been also

made.

In particular, the PI-based FOC equipped with the EKF-

based rotor position and speed estimator (Fig. 3(a) - black

continuous line) shows a better tracking performance with

respect to the PI-based FOC equipped with the encoder and

the backward-difference based speed estimator (Fig. 3(a)

- blue dashed line). The speed-tracking error is reported

in Fig. 3(b); in particular the black continuous line is the

tracking error for the PI-based FOC with the EKF-based rotor

position and speed estimator and the blue dashed line is the

tracking error for the PI-based FOC with the encoder and

the backward-difference based speed estimator.

In Fig. 3(c), the EKF-based estimated rotor position (black

continuous line) is compared with the encoder-based mea-

sured one (blue dashed line); the estimated position shows

good correspondence to the measured rotor position. The

index IAE, i.e. the integral of the absolute value of the speed-

tracking error and of the error between the estimated and

the measured rotor position, is used to summarize the above

experimental result and also the performance obtained con-

sidering a reference trajectory given by a sinusoidal velocity

profile (see Table III). Experimental tests at low speed have

TABLE III

PERFORMANCE COMPARISON AT HIGH SPEED.

157 rad/s EKF-speed backward-difference EKF-position

Trapezoidal 0.6185 1.0100 0.2651Sinusoidal 1.2297 2.1900 0.2374

been also performed with trapezoidal and sinusoidal velocity

profiles. In particular velocities of 78.5 rad/s and 31.4 rad/shave been considered; results have been summarized in

Table IV. The reported index IAE shows an appreciable

improvement of the proposed solution with the EKF-based

rotor position and speed estimator with respect to the PI-

based FOC equipped with the encoder and the standard

backward-difference method for speed estimation.

TABLE IV

PERFORMANCE COMPARISON AT LOW SPEED.

78.5 rad/s EKF-speed backward-difference EKF-position

Trapezoidal 0.2904 0.3670 0.6797Sinusoidal 0.4556 0.7810 0.3355

31.4 rad/s EKF-speed backward-difference EKF-position

Trapezoidal 0.2165 0.2440 0.5974Sinusoidal 0.2995 0.3950 0.1496

V. CONCLUDING REMARKS

This paper proposed a DSP-based algorithm for the ac-

curate rotor position and speed estimation of a PMSM

from measurements of electric quantities. The approach is

based on a linearized Kalman filter and the estimated rotor

position and speed are used for the control of the PMSM.

Experiments on a commercial PMSM drive reported in the

paper confirmed that high performance of the rotor position

and speed estimation algorithm are really obtainable in a

wide range of experimental situations.

REFERENCES

[1] Z. Xu and M. F. Rahma, “Direct torque and flux regulation of an ipmsynchronous motor drive using variable structure control approach,”IEEE Transactions on Power Electronics, vol. 22, no. 6, pp. 2487–2498, Nov. 2007.

[2] K.-K. Shyu, C.-K. Lai, Y.-W. Tsai, and D.-I. Yang, “A newly robustcontroller design for the position control of permanent-magnet syn-chronous motor,” IEEE Transactions on Industrial Electronics, vol. 49,no. 3, pp. 558–565, Jun. 2002.

[3] F. J. Lin, “Real-time IP position controller design with torque feedfor-ward control for PM synchronous motor,” IEEE Trans. Ind. Electron.,vol. 44, pp. 398–407, 1997.

[4] F. J. Lin, R. F. Fung, and Y. C. Wang, “Sliding mode and fuzzy controlof toggle mechanism using PM synchronous servomotor drive,” Proc.

of IEE Control Theory Applicat., vol. 144, no. 5, pp. 393–402, 1997.[5] F. J. Lin and S. L. Chiu, “Robust PM synchronous motor servo

drive with variable-structure model-output-following control,” Proc.

IEE Elect. Power Applicat., vol. 144, no. 5, pp. 317–324, 1997.[6] F. J. Lin and Y. S. Lin, “A robust PM synchronous motor drive

with adaptive uncertainty observer,” IEEE Trans. Energy Conversion,vol. 14, pp. 989–995, Dec. 1999.

[7] M. Ghribi and H. Le-Huy, “Optimal control and variable structurecombination using a permanent-magnet synchronous motor,” in Conf.

Rec. IEEE-IAS Annu. Meeting, vol. 1, Denver, CO, Oct. 1994, pp.408–415.

[8] M. Rashed, P. MacConnell, A. Stronach, and P. Acarnley, “Sensorlessindirect-rotor-field-orientation speed control of a permanent-magnetsynchronous motor with stator-resistance estimation,” IEEE Transac-

tions on Industrial Electronics, vol. 54, no. 3, pp. 1664 –1675, june2007.

[9] K. Gulez, A. Adam, and H. Pastaci, “Torque ripple and emi noiseminimization in pmsm using active filter topology and field-orientedcontrol,” IEEE Transactions on Industrial Electronics, vol. 55, no. 1,pp. 251 –257, jan. 2008.

[10] P. Mattavelli, L. Tubiana, and M. Zigliotto, “Torque-ripple reduction inpm synchronous motor drives using repetitive current control,” IEEE

Transactions on Power Electronics, vol. 20, no. 6, pp. 1423 – 1431,nov. 2005.

[11] S. Chi, Z. Zhang, and L. Xu, “Sliding-mode sensorless control ofdirect-drive pm synchronous motors for washing machine applica-tions,” IEEE Transactions on Industry Applications, vol. 45, no. 2,pp. 582 –590, march-april 2009.

[12] A. Pisano, A. Davila, L. Fridman, and E. Usai, “Cascade controlof PM DC drives via second-order sliding-mode technique,” IEEE

Transactions on Industrial Electronics, vol. 55, no. 11, pp. 3846–3854,Nov. 2008.

978-1-4577-0123-8/11/$26.00 ©2011 IEEE 1425

[13] W. Leonhard, Control of Electric Drives. London, U.K.: Springer-Verlag, 1990.

[14] P. Vas, Vector control of AC machines. London, U.K.: Oxford Univ.Press, 1990.

[15] G. Bartolini, A. Damiano, G. Gatto, I. Marongiu, A. Pisano, andE. Usai, “Robust speed and torque estimation in electrical drivesby second order sliding modes,” IEEE Trans. Control Syst. Technol.,vol. 11, no. 1, pp. 84–90, Jan. 2003.

[16] M. Boussak, “Implementation and experimental investigation of sen-sorless speed control with initial rotor position estimation for interiorpermanent magnet synchronous motor drive,” IEEE Transactions on

Power Electronics, vol. 20, no. 6, pp. 1413 – 1422, nov. 2005.[17] R. Wu and G. Slemon, “A permanent magnet motor drive without a

shaft sensor,” IEEE Transactions on Industry Applications, vol. 27,no. 5, pp. 1005–1011, Oct. 1991.

[18] P. Schmidt and A. Wijenayake, “Sensorless control of a permanentmagnet synchronous machine down to near zero speed applied toposition motion control,” in Industry Applications Conference, 1996.

Thirty-First IAS Annual Meeting, IAS ’96., Conference Record of the

1996 IEEE, vol. 1, Oct. 1996, pp. 21–28 vol.1.[19] M. Corley and R. Lorenz, “Rotor position and velocity estimation

for a permanent magnet synchronous machine at standstill and highspeeds,” in Industry Applications Conference, 1996. Thirty-First IAS

Annual Meeting, IAS ’96., Conference Record of the 1996 IEEE, vol. 1,Oct. 1996, pp. 36–41 vol.1.

[20] J. Solsona, M. Valla, and C. Muravchik, “A nonlinear reduced orderobserver for permanent magnet synchronous motors,” IEEE Transac-

tions on Industrial Electronics, vol. 43, no. 4, pp. 492–497, Aug. 1996.[21] S. Bolognani, R. Oboe, and M. Zigliotto, “Sensorless full-digital

pmsm drive with ekf estimation of speed and rotor position,” IEEE

Transactions on Industrial Electronics, vol. 46, no. 1, pp. 184 –191,feb. 1999.

[22] S. Bolognani, M. Zigliotto, and M. Zordan, “Extended-range pmsmsensorless speed drive based on stochastic filtering,” IEEE Transac-

tions on Power Electronics, vol. 16, no. 1, pp. 110 –117, Jan. 2001.[23] S. Bolognani, L. Tubiana, and M. Zigliotto, “Extended kalman filter

tuning in sensorless pmsm drives,” IEEE Transactions on Industry

Applications, vol. 39, no. 6, pp. 1741 – 1747, nov. 2003.[24] R. Dhaouadi and N. Mohan, “Application of stochastic filtering to

a permanent magnet synchronous motor-drive system without electro-mechanical sensors,” in Proc. Int. Conf. Electrical Machines, ICEM90,1990, pp. 1225–1230.

[25] R. Dhaouadi, N. Mohan, and L. Norum, “Design and implementationof an extended kalman filter for the state estimation of a permanentmagnet synchronous motor,” IEEE Transactions on Power Electronics,vol. 6, no. 3, pp. 491 –497, July 1991.

[26] P. Vas, Parameter Estimation, Condition Monitoring, and Diagnosis

of Electrical Machines. Oxford, U.K.: Oxford Science, 1993.[27] M. Barut, S. Bogosyan, and M. Gokasan, “Speed-sensorless estimation

for induction motors using extended kalman filters,” IEEE Transac-

tions on Industrial Electronics, vol. 54, no. 1, pp. 272 –280, feb. 2007.[28] Y. Liu, Z. Q. Zhu, and D. Howe, “Instantaneous torque estimation

in sensorless direct-torque-controlled brushless dc motors,” IEEE

Transactions on Industry Applications, vol. 42, no. 5, pp. 1275 –1283,sept. 2006.

[29] S. Bolognani, L. Tubiana, and M. Zigliotto, “Ekf-based sensorlessipm synchronous motor drive for flux-weakening applications,” IEEE

Transactions on Industry Applications, vol. 39, no. 3, pp. 768–775,June 2003.

[30] J. Shi and Y. Lu, “Field-weakening operation of cylindrical permanent-magnet motors,” in Proc. IEEE International Conference on Control

Applications, Dearborn, MI, sep. 1996, pp. 864–869.[31] V. I. Utkin, J. Guldner, and J. Shi, Sliding mode control in electrome-

chanical systems, ser. Systems and Control. Florida, USA: CRC PressLLC, 1999.

[32] A. Jazwinsky, Stochastic processes and filtering theory. New-York,USA: Academic Press, 1970.

[33] (2009) Technosoft s.a. [Online]. Available: http://www.technosoftmotion.com/

[34] H.-G. Yeh, “Real-time implementation of a narrow-band kalmanfilter with a floating-point processor dsp32,” IEEE Transactions on

Industrial Electronics, vol. 37, no. 1, pp. 13–18, Feb. 1990.[35] (2009) Texas instruments incorporated. [Online]. Available: http:

//www.ti.com/

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Fig. 3. Trapezoidal velocity profile. (a) PI-based FOC with the EKF-based rotor position and speed estimator (black continuous line), PI-basedFOC with the encoder and the backward-difference based speed estimator(blue dashed line) and reference velocity (red dotted line, almost completelysuperimposed by the black and blue lines) (b) Speed error: PI-based FOCwith the EKF-based rotor position and speed estimator (black continuousline) and PI-based FOC with the encoder and the backward-difference basedspeed estimator (blue dashed line) (c) EKF-based estimated rotor position(black continuous line) and encoder-based measured rotor position (bluedashed line).

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