Sensorless PM Brushless Drives

The University of SheffieldElectrical Machines & Drives Research Group

IEEE UK Chapter Seminar 15 December 2003

Sensorless PM Brushless Drives

Prof. D. Howe and Prof. Z. Q. Zhu


Outline

• Review of sensorless techniques

• Zero-crossing detection of back-emf waveform

• 3rd back-emf detection

• Flux observer

• Rotor saliency

• Extended Kalman filter

• Design of high-speed (>100krpm) BLDC motor for sensorless operation

• Vector control

• Flux weakening control

• Direct torque control


Sensorless Techniques

Why sensorless?• Reduced component count

• Improved reliability

• Eliminates mechanical/hysteresis problems of discrete sensors

Key consideration:• Simple algorithm

• Accurate rotor position estimates to dynamic load disturbances

• Robust to parameter variations



• Brushless DC:

- Back-emf zero crossing detection

- Third harmonic voltage detection

- Freewheel diode approach

- ...

• Brushless AC

- Flux/position observer

- Inductance variation

- Kalman filter

- …



• Sensitive to parameter variation• Poor performance at low speed• Initial position not identifiable• May not work at zero speed

Existing problems

Rotor saliency based approaches

• Operational at zero & low speed• Rotor saliency required

Key issues: - two zeros

• Zero crossing of back-emf waveform for BLDC• Zero speed for both BLDC & BLAC


Typical Sensored Brushless Drive System

Position sensors

Speed controller-

-Speed demand

Currentfeedback

3 ∅BLACmachine

DClink

3 ∅Inverter

DSP

Speed estimator

Switching logic

Currentcontroller


Typical Sensorless Brushless Drive System

3 ∅PM

machineNo sensor

Measurements from motorterminals

Switching logic

Currentcontroller

Speed controller-

-Speed demand

Currentfeedback

Rotor Position& Speed estimator

DSP

DClink

3 ∅Inverter

Sensorless controller


(1) Detection of Zero-Crossing of Back-EMF Waveform

0 30 60 90 120 150 180 210 240 270 300 330 360

phase voltageemf

detection point

Diode conduction angle

ideal current waveform

current waveform

• Most common technique for sensorless operation of brushless DC motors • Appropriate switching devices commutated 30oelec. after detection of zero-

crossing of back-emf waveform when phase is unexcited• Conduction angle of free-wheeling diodes must <30oelec.

- may be problem at high speed or high load condition- not suitable for flux-weakening operation

• Starting and low speed operation problems (due to absence of emf)


Detection of zero-crossing of back-emf waveform

Example:

Time (0.1ms/div)

Cur

rent

(0.5

A/d

iv)

Vol

tage

(50V

/div

)

Phase CurrentPhase Voltage

Measured @120krpm

Various commercial ICs, e.g.- Micro-linear 4425/4426/4428

Sensorless PWM motor controller

Mode of operation:• Initial alignment• Synchronous open-loop run-up• Sensorless close-loop


Design of 120krpm high-speed motor for sensorless operationOptimal design: within same space envelope, maximum efficiency,

diode conducting duration significantly <30oelec.

Motor A Motor B• Longer stator core• Fewer turns/coil• Shorter end winding• More iron, less copper• Relatively high unbalanced magnetic pull.

• Shorter stator core• More turns/coil• Longer end winding• Less iron, more copper• Lower unbalanced magnetic pull


Design of 120krpm high-speed motor for sensorless operation

Motor A

• Sinusoidal back-emf waveform

Motor B

• High conduction angle, almost continuous current waveform• Low diode conduction angle


Design of 120krpm high-speed motor for sensorless operation

Motor A Motor B• Suitable for sensorless control • Unsuitable for sensorless control

Phase terminal voltage

Line terminal voltage

Phase terminal voltage

Line terminal voltage

emf

emfemf

emf

Zero-crossing

Zero-crossing

No zero-crossing

No zero-crossing


Sensorless high-speed PM brushless motors

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007

Time (s)

Cur

rent

(A)

MeasuredPredicted

Sensorless control board

Inverter connectionboard

Heat sink

Current waveforms on no-load, 125,000rpm


Pros & cons of back-emf zero-crossing detection

Simple, fast, commercial IC chips available

Cases in which zero-crossing of back emf is not detectable:

• BLDC - High speed operation (high reactance)

• BLDC - High load

• BLDC - Flux-weakening operation

• BLAC - Brushless ac operation

Current is continuous or almost continuous

Alternative sensorless technique is required


(2) 3rd Harmonic Back-EMF Detection

rmsn Eeu θ3sin33 −=≈

crmKreKre t∆⋅+= − ωθθ )1()(usn uxn

3 ways of detecting e3in literature:

usn, uhn, uhs


Features of 3rd harmonic back-EMF detection

• 3rd harmonic back-EMF can be extracted from voltage

• Only voltage usn is suitable for extracting 3rd harmonic back EMF in both BLDC and BLAC drives

• Independent of motor operation mode

• Applicable to both BLDC and BLAC operations

• Open-loop starting & close-loop operation as conventional back-emf detection

• Most suitable for high-speed application

• Example: 18 slots, 6 poles, surface-mounted magnet rotor, overlapping winding, 1 slot pitch skew


Detection of 3rd harmonic back-EMF - Voltage usn


BLDC operation with/without commutation advance

Low speed 320rpm, 4.62Nm; without advanced commutation, θad =0o

High speed 1950rpm, 0.25Nm; with advanced commutation, θad =45o


BLDC operation with/without commutation advance

0

1

2

3

4

5

0 500 1000 1500 2000Speed (rpm)

Toq

ue (N

m)

0

10

20

30

40

50

Opt

imal

ang

le (e

lec-

deg.

)

with optimal commutation advance optimal commutation

anglewithout commutation advance


BLAC operation with/without flux-weakening control

High speed 2010rpm, 0.27Nm; with flux-weakening control

Low speed 320rpm, 4.63Nm; without flux-weakening control


BLAC operation with/without flux-weakening control

0

1

2

3

4

5

0 500 1000 1500 2000Speed (rpm)

Toqu

e (N

m)

0

20

40

60

80

100

Opt

imal

ang

le (e

lec-

deg.

)

with optimal flux-weakening

optimal angle

without flux-weakening


Restriction of 3rd harmonics back-emf detection

)( 3333333 skdpwm kkkBkBE ⋅⋅⋅⋅=⋅⋅∝ ωωAbsented Em3

B3=0 - Sinusoidal shaped magnet, 120oelec. pole arc magnet, Halbach magnetised motor

kp3=0 - Conventional 3 slot / 2 pole BLDC (120oelec. coil pitch)

Reduced Em3

kd3 → 0 - Distributed winding

ksk3 → 0 - Skewed winding/magnet

Low speed, as conventional back-EMF based technique


(3) Based on rotor saliency

Method 1:

• Inject high frequency signal into motor terminals

• AC current component resulting from injected signal ii ∼ sin(2∆θ)sin(ωit)≈ 2∆θsin(ωit)

• ∆θ =instantaneous difference between estimated rotor position and actual rotor position

• ∆θ fed into observer that updates velocity and position to force error to zero

Method 2:

• Current variation from hysteresis current PWM controller

• Inductance ∼ 1/(∆I/∆t)

• ∆I=current variation over ∆t

• ∆t=current rise or decay time

• Rotor position obtained from variation of winding inductance

∆t

∆I

dtdiL

dtdiLV

/1

∝

=

• Applicable to PM motors with rotor saliency (interior and inset magnet rotors)

• Winding inductance is rotor position dependent


(4) Flux observer and rotor position estimation

• Suitable for brushless ac machines• Based on machine model• Influenced by parameter variations due to temperature & saturation• Speed obtained from differentiation of estimated rotor position• Filtering necessary

1. Voltage and current vectors - measured:

2. Stator flux-linkage vector - observed:

3. Excitation flux-linkage vector - observed:

4. Rotor position - calculated:

)0(0

)( st

s dtIRU Ψ+⋅−=Ψ ∫ &&&&

ILssf &&& −Ψ=Ψ

α

β

ψ

ψ=θ

f

festr arctan._

IU && ,


High pass filter to eliminate influence of DC offset on flux observer

)0(0

)( st

s dtIRU Ψ+⋅−=Ψ ∫ &&&&Stator flux-linkage vector

time

Flux locus without high pass filter Flux locus with high pass filter


Low pass filter on observed excitation flux-linkage vector

Rotor position

- calculated from observed excitation flux-linkage vector

α

β

ψ

ψ=θ

f

festr arctan._

With low pass filter:

Smooth locus of flux-linkage vector.Reduced ripple in estimated position.Time delay in position estimation.High frequency position error still exists, causes ripple in estimated speed.


Low pass filter on observed excitation flux-linkage vectorFlux locus Estimated and measured rotor position

0

1000

2000

3000

4000

0 0.01 0.02 0.03 0.04 0.05

Time (s)

Rot

or p

ositi

on (p

ulse

s)

-200

-100

0

100

200

Erro

r of e

stim

ated

pos

ition

(pul

ses)

actual positionestimated positionestimation error

0

1000

2000

3000

4000

0 0.01 0.02 0.03 0.04 0.05

Time (s)

Rot

or p

ositi

on (p

ulse

s)-200

-100

0

100

200

Erro

r of e

stim

ated

pos

ition

(pul

ses)

actual positionestimated positionestimation error

Without low pass flux-filter

α-axis (0.05Wb/div)

β-ax

is (0

.05W

b/di

v)

• High frequency ripple exists in flux locus

• Large position error exists

With low pass flux-filter

α-axis (0.05Wb/div)

β-ax

is (0

.05W

b/di

v)

• Smooth flux locus

• Significant phase shift exists


Speed estimation 1 - Differential of estimated rotor position

ttdtd errractrestrestr

p ∆

θ∆−θ∆=

∆

θ∆≈

θ=ω ._._._._

† _est.: estimated value; _act.: actual value; _err.: error.

∆t small, ∆θr_act. small comparable to error ∆θr_err.

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)

estimated speedactual speed

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)


Comparison of Estimated and Actual Speeds

Sensorless operationSensored operationError in estimated position causes ripple in estimated speed.System maybe unstable if estimated speed used as feed-back.


Speed estimation 2 - Average speed estimation

)()( ._t

LPFLPF estrpd ∆

θ∆=ω=ω † LPF: low pass filter.

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)


0

1000

2000

3000

4000

Time (0.5s/div)

Spee

d (r

pm)

estimated speedactual speedestimated speedactual speed

time delay

Sensorless operationSensored operation


Accurate estimation during steady-state operation.Time delay in estimated speed during transient operation.System maybe unstable if estimated speed used as feed-back.


Speed estimation 3 - from induced EMF & excitation flux-linkage

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)


no time delay

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)


Sensored operation Sensorless operation


No time delay in estimated speed.System stable if estimated speed used as feed-back.Estimation error even during steady-state operation.

dsf

qsqqe iL

piLRiu+Ψ

⋅−−=ω( )

+ω+⋅+=

Ψω=

mdsqsqq

fm

EiLpiLRiu

E

f

qqe

RiuΨ

−≈ω


Speed estimation 4 - Improved estimation (combined 2 & 3)

.. 1

1)(

111

comddifd

dededh

TsTs

TsTs

TsTs

Ts

ω+ω=+

ω+ω=

+ω−ω+ω=

+ω+

+ω=ω

† ωdif.: difference of estimations 2. & 3.; ωcom: compensation.Accurate speed estimation during steady-state (s 0, ωh ωd).Fast dynamic response to speed changes (s ∞, ωh ωe).System stable if estimated speed used as feed-back.


Comparison of estimated and actual speedsSensored operation Sensorless operation

-500

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5Time (s)

Spee

d (r

pm)

actual speed

estimated speed

speed differencespeed compensation

no time delay

0

1000

2000

3000

4000

0 1 2 3 4 5Time (s)

Spee

d (r

pm)


Accurate speed estimation during steady-state (s 0, ωh ωd).Fast dynamic response to speed changes (s ∞, ωh ωe).System stable if estimated speed used as feed-back.


(5) Based on Extended Kalman FilterEKF - An optimal recursive estimation algorithm for nonlinear systems

Applications - High-accuracy estimates of non-linear system

• State variables (current, speed from measured terminal variables and machine model)

• Model parameters (influence of temperature on resistance and back-emf, or saturation)

• Eliminating measurement noise (combined state observer & filtering functions)

Pros and cons

Pros

• Non-linear system

Cons:

• Computation requirement

• Parameter sensitivity

• Initial conditions (particularly noise behaviour)


Extended Kalman filter (only for illustration)

Non-linear discrete models with white noise )())(),(()1( kwkukxfkx +=+)())(()( kvkxhky +=

I. Prediction stage - calculates states at time (k+1) from those at time k

(a) State estimation neglecting noise

(b) Estimation of an error covariance matrix

II. Correction stage (filtering stage) - corrects estimation process in recursive manner based on deviation of estimated values from measured values

(c) Computation of a Kalman filter gain

(d) Update of an error covariance matrix

(e) State estimation

))(),/(ˆ()/1(ˆ kukkxfkkx =+

QkkkPkkkP T +ΓΓ=+ )()/()()/1(

[ ] 1)()/1()()()/1()1( −+∆+∆∆+=+ RkkkPkkkkPkK TT

[ ] )/1()()1()1/1( kkPkkKIkkP +∆+−=++

[ ]))/1(ˆ()1()1()/1(ˆ)1/1(ˆ kkxhkykKkkxkkx +−++++=++


Extended Kalman filter (only for illustration)Linearization is required at each sampling interval

=

))(),((......

))(),(())(),((

))(),(( 2

1

kukxf

kukxfkukxf

kukxf

N

If

Jacobian matrices are given by:

)/(ˆ)(21

2

2

2

1

2

1

2

1

1

1

...............

...

...

)(

kkxkxN

NNN

N

N

xf

xf

xf

xf

xf

xf

xf

xf

xf

k

=

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=Γ)/(ˆ)(

)())(),(()(

kkxkxi kxkukxfk

=∂

∂=Γ

)/1(ˆ)()()(()(

kkxkxi kxkxhk

+=∂∂

=∆


Surface-mounted PM motor (only for illustration)

−−−

+−−

++−

=

ω

ωθθλ

θωλ

θωλ

θω

αβ

ββ

αα

β

α

JTn

JDii

Jn

Lu

Li

LR

Lu

Li

LR

ii

dtd

Lpmp

ss

m

s

s

ss

m

s

s

)sincos(23

cos

sin

2

I&

β

αa,

d

sΨ&

fΨ&

αψ f

βψ f

rθ

qILs &

V

+−−

++−

=

ω

θωλ

θωλ

θω

ββ

αα

β

α

0

cos

sin

ss

m

s

s

ss

m

s

s

Lu

Li

LR

Lu

Li

LR

ii

dtd

Decoupled electrical and mechanical equations


Salient-pole PM motor (only for illustration)

+

−=

β

α

β

α

θωθωθωθω

ii

LRLLLR

uu

s

s

2sin22cos22cos22sin2

22

22

−

++

β

α

θθθθ

ii

LLLLLL

&

&

2cos2sin2sin2cos

202

220

−+

θθ

ωλcossin

m

++++−+−−−−

−=

β

α

β

α

θωθθωωθθωωθθωθ

ii

LLLRLRLLLLRLLLLRLLLRLR

LLii

sss

sss

2sin22cos2cos222sin2cos222sin2sin22cos1

022002222

022220220

22

20

&

&

−

−+

+−−−

−−

θθωλ

θθθθ

β

α

cossin

2cos2sin2sin2cos1

20202

22022

20 LLu

uLLL

LLLLL

m

where

2

2

2

0

qd

qd

LLL

LLL

−=

+=

θ

θθ

αβ

β

α

2sin

2cos2cos

2

20

20

LL

LLLLLL

=

−=+= where, Ld = d axis inductance

Lq = q axis inductance


Comments on application to PM brushless machines

In addition to the state observer, such as position and speed

It can be used to estimate:

• Stator resistance and/or emf, for high temperature applications

• Winding inductances, for better modeling of magnetic saturation

• Load torque and/or rotor inertia, to improve dynamic speed control

• It is still far too complicated to implement the full-order EKF observer

• Hence, the reduced-order EKF is most desirable


(6) Example - Sensorles DTC based on simplified EKF

dtdiRu s

sssψ

+=Stator voltage equation:

Stator flux linkage vector obtained from measured stator voltages and currents:

dtiRu ssss )(∫ −=ψ

This equation can be expressed in stationary reference frame:dtRiu sss )(∫ −= αααψ

)(23

αββ ψψ ssssa iipT −=

22βα ψψψ ss +=

dtRiu sss )(∫ −= βββψ

Magnitude of stator flux linkage:

Electromagnetic toque equation:


Control strategy of DTC

Block diagram of DTC for PM BLAC drive


Sensorless DTC

• Conventional approach:

s

ksks

Tdtd )1()( −−

≈=θθθω

β

α

ψψ

θs

ss arctan=

dtdiRu s

sssψ

+=

dtiRu ssss )(∫ −=ψ

dtRiu sss )(∫ −= αααψ

dtRiu sss )(∫ −= βββψ

This equation can be expressed in stationary reference frame:

Stator voltage equation:

Stator flux linkage vector obtained from measured stator voltages and currents:

From DTC

Estimated stator flux position

Estimated speed Need filters


Sensorless DTC based on simplified EKF

u(k)=0Output variables

=

α

β

ψψ

s

s

kyky

)()(

2

1 Input variables

+

=

)()(

)(sin)(cos

)()(

2

1

2

1

kvkv

kk

kyky

θθFor brushless ac drives,

fundamentals of fluxes are sinusoidal

)()()1( kwkFxkx +=+)())(()( kvkxhky +=

=

10011001 sT

F

=

)(sin)(cos

))((kk

kxhθθ

Tr wx ]',,[ ωθ=

−⋅

=

θθθθˆˆˆˆ

000

3

2

1

cossinsincos

kkk

K

where k1, k2, and k3 are tuning parameters, and can be pre-computed from simulations, by using, for example, the Matlab DLQE command for Kalman estimator design of discrete-time systems

State variables

State-space model

Kalman filter gain can now be significantly simplified and is given by


Sensorless DTC based on simplified EKF

• Simplified extended Kalman filter (EKF) based sensorless DTC:

=

α

β

ψψ

s

s

kyky

)()(

2

1Recursive Algorithm:

)(ˆsin)()(ˆcos)()( 12 kkykkyk θθε −=

)]()(ˆ)(ˆ[)1(ˆ1 kkkTkk rs εωθθ ++=+

)()(')(ˆ)1(ˆ 2 kkkwkk rr εωω ++=+

)()(')1(' 3 kkkwkw ε+=+


Phase current and stator flux linkage

-3.75

-2.5

-1.25

0

1.25

2.5

3.75

0 0.02 0.04 0.06 0.08Time (ms)

Cur

rent

(A)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

-0.15 -0.1 -0.05 0 0.05 0.1 0.15alfa (Wb)

beta

(Wb)

(a) Phase current (simulation)Time (20ms/div)

Cur

rnet

(1.2

5A/d

iv)

(c) Phase current (experiment)

alfa (0.05wb/div)

beta

(0.

05w

b/di

v)

(d) Locus of stator flux linkage (experiment)(b) Locus of stator flux linkage (simulation)


Comparison of measured and estimated speed

Time (1s/div)

Spee

d (1

000r

pm/d

iv)

E stimatedM easured

(a) Using encoder for feedback, estimated speed derived from stator flux-linkage

without speed filter

Time (1s/div)

Spee

d (1

000r

pm/d

iv)

E stim atedM easured

(b) Using estimated speed for feedback, speed derived from stator flux-linkage with speed filter

With delay

Tim e (1s/div)Sp

eed

(100

0rpm

/div

)

E stim atedM easured

(c) Using estimated speed for feedback, speed derived from stator flux-linkage by simplified EKF

No delay


Comparison of measured and estimated rotor position

Time (10ms/div)

Posi

tion

(100

0 pl

uses

/div

)

Erro

r (10

0 pl

uses

/div

)

MeasuredEstimatedError

Time (10ms/div)

Posi

tion

(100

0 pl

uses

/div

)

Erro

r (10

0 pl

uses

/div

)

MeasuredEstimatedError

(a) Estimated directly from stator flux-linkage

(b) Estimated by using simplified EKF


Acknowledgment

Dr Jason EDE

Dr Jian Xin SHEN

Mr Yan Feng SHI

Mr Yong LIU


Speed and electromagnetic torque

0

500

1000

1500

2000

2500

3000

3500

4000

0 1 2 3 4 5 6 7 8Time (s )

Measured speedSpeed reference

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

1.2

1.4

0 1 2 3 4 5 6 7 8Time (s )

Est imated to rq ueTorq ue reference

(a) Speed (simulation)

(b) Electromagnetic torque (simulation)

Time (1s /d iv)

Measured sp eedSp eed reference

(c) Speed (experiment)

Time (1s /d iv)

Es t imated To rq ueTo rq ue reference

(d) Electromagnetic torque (experiment)


Comparison of measured and estimated rotor position

Tim e (10m s/div)

Posi

tion

(100

0 pl

uses

/div

)

Erro

r (10

0 pl

uses

/div

)

M easuredEstim atedError

Tim e (10m s/div)

Posi

tion

(100

0 pl

uses

/div

)

Erro

r (10

0 pl

uses

/div

)

M easuredEstim atedError

(a) Estimated directly from stator flux-linkage

)3

2(

rs

s

pTL

arctgψψ

δ =

δθθ −= sr

)(23

αββ ψψ ssssa iipT −=

)](2sin)()sin(2[43

δψδψψ

dqsqrqd

s LLLLL

pT −−=

for a surface-mounted permanent magnet BLAC motor, Ld=Lq=Ls

The stator flux-linkage position is converted to the rotor position by subtracting the load angle, δ, that is

)sin(2

3δψ

ψr

s

s

Lp

=

Thus,

Since the electromagnetic torque can be estimated as:

• Position estimation:

(b) Estimated by using simplified EKF

Documents

Sensorless PM Brushless Drives