Adaptive signal amplitude for high frequency signal

injection based sensor less PMSM drives

Ravikumar Setty .A and Shashank Wekhande Avant Garde Solutions Pvt Ltd,

(Consultant to Allegro Micro Systems, USA)

Mumbai,India.

Kishore Chatterjee Electrical Engg Department,

IIT Bombay,

Mumbai,India.

Abstract— High frequency signal injection based sensor less

techniques are well proven and reliable techniques to estimate

rotor position from low speed to stand still. However these

techniques distort motor currents, which introduce torque ripple

and acoustic noise. Lower signal injection amplitude reduces

torque ripple but increases position estimation error, so correct

signal injection amplitude is required for satisfactory drive

performance. More over signal injection amplitude required in

transients is higher than steady state conditions. In this work

signal amplitude is adaptively increased during transients based

on rate of change of load and reduced back to original value

under steady state. This work reports implementation details and

simulation results of adaptive signal injection based sensor less

control. Simulation results shows reduction in torque ripple

Keywords— Sensor less control; High frequency signal

injection; torque ripple; acoustic noise and adaptive signal

injection.

NOMENCLATURE

PMBL Permanent Magnet Brush Less

R Stator winding resistance / Phase

L Stator winding inductance / Phase

Ld, Lq Stator inductance of direct and quadrature

axis components

αβ Stator orthogonal coordinate system

dq Rotor orthogonal coordinate system

dq' Magnetic Saliency axis on rotor side.

A 3 phase to 2 phase transformation matrix

(Clark Transformation)

B αβ to dq transformation matrix

(Park transformation)

T Transpose

vc, ic High frequency voltage and high

frequency current response

Lc High frequency stator inductance vector

VDC DC Supply Voltage to Inverter

Ia,Ib,Ic Currents through Phase a, b and c

respectively

Iab1 Iαβ rotated with injected frequency and

filtered.

θr or λdq’ Rotor Magnetic saliency Position angle

reference to rotor orthogonal system.

I. INTRODUCTION

Permanent Magnet Brushless (PMBL) Motors are

increasingly used in high performance applications. This is

because PMBL motor has many features, like high efficiency,

compactness, high torque to inertia ratio and good dynamic

response. High frequency signal injection based sensor less

control techniques are widely accepted due to their robustness

at low speed to standstill. According to the type of signal

injected these are classified into rotating injection [1]-[3] and

pulsating [4]-[6] injection. In all these methods high frequency

signal is super imposed on fundamental excitation and

resulting high frequency current response is demodulated to

extract rotor position information. These high frequency

signals super imposed on fundamental components distort the

phase currents and introduce torque ripple and acoustic noise.

The amplitude and frequency of the injected signal to be

chosen carefully to ensure that undesirable torque ripples can

be minimized. The amplitude of the injected signal will be

small thus making it particularly susceptible to interference

from nonlinear distortion effects [7], [8], but results in reduced

position estimation, signal injection amplitude cannot be

reduced below certain threshold level. If this level is

optimized to steady state conditions, which is not enough in

transient condition as the high frequency current response

distorts and reduces the signal to noise ratio. [9] Uses

oversampling approach and [10] uses delta-sigma AD

conversion techniques to improve the signal to noise ration

and allows to minimize the signal amplitude, doesn’t indicate

drive performance during transient conditions.

This work studies the requirements of signal amplitude

under steady state and transient conditions. Lower signal

injection amplitude results in increased estimated position

error and higher signal injection amplitude results in torque

pulsations and audible noise. To trade off between torque

pulsations and position error optimum amplitude of signal

injection is necessary. Current work proposed adaptive signal

amplitude based sensor less control to reduce the torque ripple

and acoustic noise. Which is then verified using simulations.

II. ADAPTIVE SIGNAL INJECTION BASED SENSOR LESS

CONTROL

This technique is based on an injection of an adaptive

high frequency signal on top of the fundamental signal. Signal

amplitude is dynamically adjusted based on load transient so

resulting on optimum signal amplitude compared to

conventional signal injection methods. Fig.1 shows the block

diagram of the rotating HF voltage injection principle and

Fig.2 shows the adaptive signal injection principle.

This work deals with the position estimation using

rotating signal injection in αβ -reference frame. An adjustable

amplitude voltage vector rotating with a high frequency (500

to 2.5 kHz) is superimposed to the fundamental voltage vector.

The injected high frequency voltage vector vcαβ is defined by

(1). A rotating HF current vector arises superimposed on to the

fundamental current vector. The high frequency current

response is filtered with band pass filter from the measured

machine currents and then demodulated to extract the rotor

position. The same measured phase currents are used as

feedback for the fundamental component current controllers

after the injected HF currents are filtered with a low or band

stop filter.

������������� � ��� �

(1)

HF current response to the injected HF voltage vc and

modulated high frequency inductance vector Lcαβ is given by

������������ � ������ ���� � dt

(2)

�i�αi�β� �� ������∆!�� "�# $L� & �∆��' ( cos,2λ./′0" �∆��' ( sin,2λ./′0"�∆��' ( sin,2λ./′0" L� 2 �∆��' ( cos,2λ./′0"3 (

� �v�αv�β" (3)

�i�αi�β� �� ������∆!�� "�# $L� & �∆��' ( cos,2λ./′0" �∆��' ( sin,2λ./′0"�∆��' ( sin,2λ./′0" L� 2 �∆��' ( cos,2λ./′0"3 (

5 � � sin67�892cos67�89� (4)

From (3) it can be seen that the resulting HF current

contains two rotating vector components. One component is

rotating with the injected voltage frequency in the same

direction and one rotating at (- ωc+2λdq') in the opposite

direction to the injected HF voltage. The icp term is also

referred to as positive sequence and the icn term as the negative

sequence component.

Fig.1 High Frequency Signal Injection based Sensor less vector control

Block Diagram

Fig.2 Adaptive signal Injection

������������ � ,i�:�6� ��;/'90+=i�> ��,� ��'λ?@′�;/'0A

(5)

Where i�: � B �����∆!�� "�5 � ; i�> � ∆!�������∆!�� "�

5 �

(6) ��������������� � �,i�:�6� ��;/'90 & =i�> ��,� ��'λ?@′�;/'0A" * �6� �9

(7)

Current signal contains rotor position information,

but all theses current signals at the injection frequency are

hidden in the stronger fundamental stator current component

and the switching harmonics. Many methods have been

proposed for the demodulation of the rotor position signals

from the measured stator currents. This work uses heterodyne

demodulation technique to extract rotor position information.

Heterodyning demodulation detects modulated signal by

multiplying it with an intermediate signal between the carrier

signal and the signal which needs to be transmitted. The error

signal ε of the observer can be given as function of the αβ HF

current components or the positive and negative sequence

currents icp and icn as shown below. Which is fed to PI

controller to track this error to zero , which ensures estimated

position is same as actual rotor position.

ε � i�:sin,27�8 2 2λ./′e0 & i�>sin,2λ./′ 2 2λ./′e0 (8)

III. SIMULATION RESULTS

First sensorless vector control system based on fixed high

frequency signal injection is developed using

MATLAB/Simulink TM

.The machine parameters used in the

simulation are as follows: Ld=16mH, Lq=20mH , 4 poles on

rotor and VDC =300V. Important parameters concerned to

sensorless drive are shown in Fig.3. and Fig.4.

Fig.3 Sensor less vector control drive using high frequency signal

injection .

Fig.4 Speed , Torque and Phase currents at fixed signal injection

amplitude

Fig.5. and Fig.6. shows the sensor less drive performance

when signal amplitude changed from 50V to 35V and 50V to

30V respectively. In both these cases system is stable.

Harmonics resulting from transients corrupt the, current

response used in rotor position estimation, so the signal

required under transient to be higher than steady state.

Fig.5 Iab1,Theta when Signal amplitude changed from 50V to 35V

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-50

0

50

HF S

ignal

(V)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-5

0

5

10

To

rqu

e(N

-m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-10

-5

0

5

10

Ia,I

b,I

c

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-10

-5

0

5

10

15

Ialp

ha,

Ibet

a

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-4

-2

0

2

4

6

8

10

To

rqu

e(N

-m)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-200

0

200

400

600

800

1000

1200

Sp

eed

(RP

M)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-10

-5

0

5

10

15

Ia,I

b,I

c

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-10

-5

0

5

10

15

Ialp

ha,

Ibet

a

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-50

0

50

HF

Sig

nal

(V)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Iab

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

4

6

8

Th

eta(

Rad

)

FFT results Fig.7 and Fig.8 compare the THD with

50V and 30V signal injection amplitude and with 30V signal

amplitude THD is lower.

Fig.6 Iab1, Theta when Signal amplitude changed from 50V to 30V

Fig.7 THD with 50V signal injection amplitude

Fig.8. Reduced THD with 30V signal injection amplitude

IV. CONCLUSIONS

Signal injection technique results in torque

pulsations, which causes audible noise. Optimum

signal injection amplitude is necessary to keep the

torque pulsations at minimum, without increasing

estimated position error. Signal injection amplitude

required under transients is higher than steady state

conditions. This work also proposed adaptive

amplitude signal injection to reduce torque ripple ,

and is verified using MATLAB/Simulink

simulations.

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-50

0

50

HF

Sig

nal

(V)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Iab

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

4

6

8

Th

eta(

Rad

)

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