Sensorless control of PMSM

Sensorless Control of PMSM for

Electric Vehicle Application

Author

Mohamed Hassan Abou El Ella

Supervisors:

Prof. Dr. Osama Mahgoub

Prof. Dr. Abdelatif El Shafei

Ass. Prof. Dr. Sherif Zaid

Cairo University, Egypt

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Contents

Introduction

Sensorless Control Techniques

PMSM Mathematical Modeling

Control basics of PMSM

Field Weakening Control of PMSM

Introduction to MRAS based estimators

MRAS speed Estimator for PMSM

ANFIS based MRAS speed estimator for PMSM

Conclusion

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Introduction

Introduction

Permanent Magnet Motors have received great attention in research in recent time due to:

High Power Density

High Efficiency

Maintenance free operation.

High reliability

High torque to inertia ratio

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Introduction Cont

Permanent Magnet Motor Types

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PMAC motor PMDC motor

Named as permanent magnet Synchronous motor PMSM.

Sinusoidal back EMF. Sinusoidal stator

current.

Named as brushless DC motor BLDC.

Trapezoidal back EMF. Square wave stator

currents.

Introduction Cont

PMSM Types

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Surface Mounted Interior Magnet

Magnets are mounted on the rotor Surface.

D, Q axis inductances are equal.

Zero reluctance torque

Magnets are buried inside the rotor

D, Q axis inductances are not equal.

Reluctance torque exists

Introduction Cont

PMSM Control Techniques Open Loop Control

Direct Torque Control

Vector Control

Sensorless Control

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Voltage Equations:

Where;

Cross section in the PMSM

PMSM Mathematical Modeling Cont

Voltage Equations in the frame

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Voltage Equation

Back EMF

Current Model

PMSM Mathematical Modeling Cont

Voltage Equations in the DQ frame

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Voltage Equation

Current Model

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Control Basic of PMSM

Control Basics of PMSM Control Techniques

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A. Open Loop Control:

Maximum torque is achieved by maintaining V/f ratio constant.

Valid for high speed values near to the base speed where the stator resistance voltage may be neglected.

The speed command should be from reference speed curve to avoid losing of synchronization.

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B. Direct Torque Control: The basic idea is to control the torque and flux linkage

by selecting the voltage space vectors properly using a pre-defined switching table.

The selection of the voltage vector is based on hysteresis controller for both the stator flux linkage and Torque.

Torque is controlled by changing angle between stator and rotor flux when stator flux is kept constant.

IPM

SPM

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B. Direct Torque Control: Block Diagram For the conventional DTC.

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B. Direct Torque Control: The Voltage vector is always maintained within a defined

hysteresis band according to values of and .

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C. Current Vector Control (FOC): The basic idea is to control the torque and flux linkage

independently by comparison of the motor currents and reference values in the rotor reference frame.

Reference values of the currents are obtained from Torque or Speed command.

Hysteresis or space vector based switching may be applied.

Torque is controlled by changing Iq while keeping Id constant.

IPM

SPM

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C. Current Vector Control: Feed back required data:

Stator Current is measured and transformed to the rotating DQ reference frame using Parks transformation.

Decoupling between Id and Iq for independent control for torque and flux is achieved by Feed Forward compensation.

Rotor position is obtained by the aid of hall effect sensors, resolvers and optical shaft encoders.

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C. Current Vector Control: Vector Control Block Diagram:

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D- Sensorless Control:

Position data is always required in PMSM vector control.

Position Sensors used may be: Resolvers

Hall Effect Sensors.

Shaft Encoders

D- Sensorless Control: Elimination of Sensors is recommended for the

following: Reduction of the overall drive cost Increasing the system reliability Reduction of system complexity.

All the previous mentioned reasons caused great motivation for research in the Sensorless control of PMSM

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Sensorless Control of PMSM Cont

Techniques Used in Sensorless Control:

1. Back EMF Estimation

Has great performance at high speed

Suffers at low speed and standstill due to low back EMF values.

Affected by the value of stator resistance.

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2. Saliency based methods

Depends on inductance variation due to saliency.

Shows great performance at low speed range and standstill.

Causes torque ripples at high speed ranges

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3. Extended Kalman Filters

Suffers from parameter sensitivity, complex computations

Requires initial conditions.

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4. Sliding Mode Observers

Great immunity against parameter variation.

Suffers from chattering problems

Requires great computational power.

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5. Model Reference Adaptive System (MRAS).

Great dynamic performance

High immunity against parameter variations.

We Will discuss the MRAS based Sensorless Control in this literature

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Control Basics of PMSM Regions Of Operation

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n

T

Constant Torque MTPA

Below base speed the operation is in the Constant torque With the voltage and power increasing as the speed increases.


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n

nb

P T

Constant Torque MTPA

Constant Power

FW

Above the rated Speed Voltage is limited to its maximum value and the operation is in the constant Power speed range with flux weakening.

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Phasor Diagram

Below Rated Speed

Phasor Diagram

Above Rated Speed

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Control Basics of PMSM Voltage constraint

All PMSM operation should be within the specified voltage and current limits.

The voltage constraint: From the voltage equations of the motors.

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Ellipse Equation Centre at (-m/Ld,0)

The voltage constraint: Referring the voltage constraint equation to the id and iq

axis

Id

Iq

-m/Ld

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The voltage constraint: For Surface Mounted Motors. Ld=Lq=Ls Voltage constraint will be equation of a circle.

Id

Iq

-m/Ls

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The current constraint: Equation of a circle with radius Ismax

Id

Iq

Ismax

Current Constraint

Voltage Constraint

Control Basics of PMSM Current constraint

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Control Basics of PMSM Voltage and Current constraint

PMSM are divided into two main types from the constraints point of View

Type I:

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4-10

-8

-6

-4

-2

0

2

4

6

8

10

iq(A

)

id (A)

Voltage limit circles

w1

w2

w3

w4

Voltage Limit Circle

current

Limit

Circle

Extending Speed is Limited by Current

Constraint

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Control Basics of PMSM Voltage and Current constraint

PMSM are divided into two main types from the constraints point of View

Type II:

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4-10

-8

-6

-4

-2

0

2

4

6

8

10

iq(A

)

id (A)

Voltage / Current limit circles

w1

w2

w3

Voltage Limit Circle

current

Limit

Circle

w4

w5

Speed Can be increased to infinity

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Control Basics of PMSM Control Regions

1. Maximum Torque Per Ampere (MTPA) Current Control:

Applied when speed

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1. Maximum Torque Per Ampere (MTPA) Current Control:

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4-10

-8

-6

-4

-2

0

2

4

6

8

10

voltage limit

circle

iq(A

)

id (A)

Voltage / current limit circles

current

limit

circle

MTPA trajectory

W1

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2. Flux Weakening Control: Applied at speed > b. Flux weakening can be achieved by applying negative armature

reaction by (Id ve). Voltage is limited to its rated value. Current vector should be maintained within its limit Relation between Id and Iq during FW control

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2. Flux Weakening Control: For Type I motor

-16 -14 -12 -10 -8 -6 -4 -2 0 2 4-10

-8

-6

-4

-2

0

2

4

6

8

10

voltage limit

circle

iq(A

)

id (A)


current

limit

circle

W1

W2

MTPA trajectoryFW trajectory

W3

W4

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2. Flux Weakening Control: For Type II motor

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

voltage limit

circle

iq(A

)

id (A)


Current

limit

CircleW4

W2

W3

MTPA

FW

LVMTW1

0

A

B

C

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2. Flux Weakening Control: Region 1: MTPA will be applied where Region 2: FW will be applied where Region 3 (For type2 motors only): , LVMT will be applied where

Motor Used in this Thesis a Type Motor

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Field Weakening Control Of PMSM

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Field Weakening Control

The main aim in FW control is selection of a proper Id value that meets the motor constraints Id reference Value is calculated from the torque demand of the speed loop.

+-

r*

PI +-

FW +-

PI

PI

Vq* V

V

Space

Vector

PWM

d-q

-

PMSM

Motor

d-q

abc

Iq

Iq*

Id* Vd*

Id

Vabc

Iabc

Position / Speed sensor

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Reference Id is affected by the transient response in torque demand and the motor speed.

The proposed trajectory depends on setting a

predefined value depending on the desired speed

The optimum current trajectory at a certain speed is calculated from the voltage and current constraints

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The Graph representing this trajectory

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

iq(A

)

id (A)


Voltage Limit

B

Te 3

Te 2

Te 1

A

Current Limit

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The Offline Reference values of Id is

-1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

iq(A)

id (

A)

Id reference values

id

1200 RPM

1100 RPM

1300 RPM

1400 RPM

1500 RPM

1600 RPM

1700 RPM

1800 RPM

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A look up table will be used containing the reference Id value according to each speed demand.

The reference value represents the average of each curve The trajectory is described by the following figure

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

iq(A

)

id (A)


Voltage Limit

Te 3

Te 2

Te 1

Current Limit

A

A'

BB'

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A smooth transition will take place after transient response to the optimum value of the current.

The transition will only take place if : Id(Optimum) < Id (LUT) This is done to increase the efficiency of the motor. For the case of: Id(optimum) > Id (LUT) No transition will take place which will only require a

small increase in the DC bus voltage The proposed trajectory will result in greater efficiency

of operation and better dynamic response

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Graphical Representation of Proposed Trajectory

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

-3

-2

-1

0

1

2

3

iq(A

)

id (A)


Current Limit

Voltage

Limit BB'

AA'

C C' Te

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Graphical Representation of Proposed Trajectory

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

-3

-2

-1

0

1

2

3

iq(A

)

id (A)


Current Limit

Voltage

Limit BB'

A'

C C' Te

A

1200 RPM

1500 RPM

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Field Weakening Control * < base

MTPA

Yes

No

Vs < Vsm

Yes

No

Id*(LUT)

|| *- || < error

Get Id** (iq*)

No

Yes

Id** (iq*) < Id*(LUT)

FW id**(iq*)

Yes

No

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Field Weakening Control Simulation Results

Case I : Speed Demand of 1200 , 1500 , 1800 RPM Tl = 0.5 NM

0 5 10 15-5

-4

-3

-2

-1

0

1

2

time (Sec)

id V

s.

id*

(A

)

Actual Vs Desired Id

id

id*

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0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

Id /

Iq

(A

)

Id and Iq

id

iq

0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

sta

tor

Cu

rre

nts

(A

)

Ia and Ib

ia

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0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

IS

(A)

Magnitude of current vector

IS

0 5 10 150

10

20

30

40

50

60

70

80

90

100

time (Sec)

Vs

(V)

Magnitude of Voltage vector

Vs

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Case II : Speed Demand of 1200 , 1500 , 1800 RPM Tl = 2 NM

0 5 10 150

500

1000

1500

2000

2500

time (Sec)

nsp

vs.

nfb

(R

PM

)

Actual Vs Desired Speed

Sp

Fb

0 5 10 15-5

-4

-3

-2

-1

0

1

2

time (Sec)

id V

s.

id*

(A

)


id

id*

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0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

Id /

Iq

(A

)

Id and Iq

id

iq

0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

sta

tor

Cu

rre

nts

(A

)

Ia and Ib

ia

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0 5 10 15-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

IS

(A)

Magnitude of current vector

IS

0 5 10 150

10

20

30

40

50

60

70

80

90

100

time (Sec)

Vs

(V)

Magnitude of Voltage vector

Vs

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Case III : Speed Demand of 1200 , 1500 , 1800 RPM Tl = 0.5 NM and 2 NM Comparing two techniques

0 5 10 150

500

1000

1500

2000

2500

time (Sec)

nsp

vs.

nfb

(R

PM

)


Sp

Fb

0 5 10 150

500

1000

1500

2000

2500

time (Sec)

nsp

vs.

nfb

(R

PM

)


Desired

LUT

direct

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Field Weakening Control Experimental Results

Case I : Speed Demand of 500, 800, 1200 , 1500 RPM Tl = 2 NM

0 2 4 6 8 10 12 14 160

500

1000

1500

2000

2500

time (Sec)

nsp

vs.

nfb

(R

PM

)


Sp

Fb

0 2 4 6 8 10 12 14 16-5

-4

-3

-2

-1

0

1

2

time (Sec)

id V

s.

id*

(A

)


id

id*

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7.5 8 8.5 9 9.5

-2.4

-2.2

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

time (Sec)

id V

s.

id*

(A

)


id

id*

11.5 12 12.5 13 13.5

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

time (Sec)

id V

s.

id*

(A

)


id

id*

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0 2 4 6 8 10 12 14 16-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

Iq*

vs.

Iq

(A)

Actual vs. Desired Iq

iq

iq*

0 2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

9

10

time (sec)

Is

(A)

Current Vector Is

Is

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Case I : Comparing Two Techniques

8 9 10 11 12 13 14 15

-200

0

200

400

600

800

1000

1200

1400

1600

1800

time (Sec)

nsp

vs.

nfb

(R

PM

)


Sp

FW with transition

FW without Transition

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MRAS Based Estimators

MRAS based Estimators MRAS is based on the comparison of two

models: The reference Model Adjustable Model Each Model Has its input

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Reference Model

Adjustable Model In 2

In 1

MRAS based Estimators

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Reference Model

Adjustable Model error

The error between the two model is processed to a certain adaptation mechanism

The output of the adaptation mechanism is used to tune the adjustable model.

In 2

In 1

Adaptation Mechanism

MRAS based Estimators Cont

The adaptation mechanism results in minimizing the error between both models

At minimum error both models will be the same

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Reference Model

Adjustable Model

error

In 2

In 1

Adaptation Mechanism

=

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MRAS based on Popov Theory

Speed Estimators

MRAS based Speed Estimator Block Diagram

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Reference Mode (PMSM Motor)

Adjustable Model (Current Model)

Vq

Vd

+ -

Adaption Mechanism

For Hybrid Learning

+ -

Id

ed

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MRAS based Speed Estimator Current Model

Current Model in

DQ Frame

where

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MRAS based Speed Estimator Current Model

Replacing Actual Values with the estimated values, the adjustable model used is

Adjustable Model

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MRAS based Speed Estimator Adaptation Mechanism

The generalized error equation is

where

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MRAS based Speed Estimator Adaptation Mechanism

According to Popov hyperstability Theory the following conditions should be satisfied:

Positive Definite

From these two conditions the speed can be calculated from the following Equation

Position

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MRAS based Speed Estimator Simulation Results

+-

r*

PI +-

FW +-

PI

PI

Vq* V

V

Space

Vector

PWM

d-q

-

PMSM

Motor

d-q

abc

Adjustable

Model

Vd

Vq

Iq

+-

Iq*

Id* Vd*

Id

Vabc

Iabc

r

r

id

iq

+-

r

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

100

200

300

400

500

600

700

800

900

1000

time (Sec)

ns

p v

s.

nfb

(R

PM

)

Desire, Actual, Estimated Speed (RPM)

Sp

Fb

Estimate

Case I: speed demand (100-800) RPM, Tl=(1-2-0.5 )NM , Nominal Parameters

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20

-15

-10

-5

0

5

10

15

20

time (Sec)

err

or(

RP

M)

speed error

error

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Case I: speed demand (100-800) RPM, Tl=(1-2-0.5 )NM , Nominal Parameters

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

8

Time (Sec)

Th

eta

m

(Ra

d)

Actual vs. Estimated position

Act

Est

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

-4

-3

-2

-1

0

1

2

3

4

5

time (Sec)

Id /

Iq

(A

)

Id and Iq

id

iq

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Case II: speed demand (300-800-1200-1500-1800) RPM, Tl=(2 )NM , Nominal

Parameters

0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

1400

1600

1800

2000

time (Sec)

nsp

vs.

nfb

(R

PM

)

Desired, Actual, Estimated Speed (RPM)

Sp

Fb

Estimate

0 1 2 3 4 5 6 7 8 9 10-20

-15

-10

-5

0

5

10

15

20

time (Sec)

err

or(

RP

M)

speed error

error

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Case II: speed demand (300-800-1200-1500-1800) RPM, Tl=(2 )NM , Nominal

Parameters

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

Time (Sec)

Th

etam

(R

ad)


Act

Est

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Case III: speed demand (300-800-1200) RPM, Tl=(2 )NM , 30% increase inductance

0 1 2 3 4 5 60

200

400

600

800

1000

1200

1400

1600

1800

2000

time (Sec)

nsp

vs.

nfb

(R

PM

)

Desired, Actual, Estimated Speed (RPM)

Sp

Fb

Estimate

0 1 2 3 4 5 6-20

-15

-10

-5

0

5

10

15

20

time (Sec)

err

or(

RP

M)

speed error

error

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Case III: speed demand (300-800-1200) RPM, Tl=(2 )NM , 30% increase inductance

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

Time (Sec)

Th

eta

m (R

ad

)


Act

Est

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MRAS based Speed Estimator Experimental Results

Case I: speed demand (500-1200-1500) RPM, Tl=(2 )NM, Nominal parameters

1 2 3 4 5 6 7 8 9 10 11 120

200

400

600

800

1000

1200

1400

1600

1800

2000

time (Sec)

Sp

ee

d

(RP

M)

Actual Vs. Estimated Speed

Act speed

Estimated Speed

1 2 3 4 5 6 7 8 9 10 11 12-200

-150

-100

-50

0

50

100

150

200

time (Sec)

Sp

ee

d E

rro

r (

RP

M)

Speed Error

Speed Error

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ANFIS based MRAS Speed Estimators

ANFIS based MRAS Speed Estimator

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Reference Mode (PMSM Motor)

Adjustable Model (Current Model)

Vq

Vd

+ -

ANFIS Adaption

Mechanism

For Hybrid Learning

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ANFIS Architecture

ANFIS Introduction

ANFIS is Adaptive Neuro Fuzzy Inference System Advantages: Combines advantages of both

1. Artificial Neural Network (ANN) Learning ability

2. Fuzzy Logic Controllers Linguistic representation

Can handle the non linearities of a system such as the PMSM

Have high convergence rate due to hybrid learning algorithm

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ANFIS Architecture

ANFIS consists of 5 network layer with two inputs DQ currents and one Output, electrical angular speed.

Layer 1 (Fuzzification layer):

Each node is an adaptive node.

Node is square represented.

Three membership functions are assigned to each input.

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ANFIS Architecture Cont


The mathematical formula for each node is

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Member Ship Functions



Parameters of this layer are called Premise parameters .

Premise parameters will be tuned through back propagation technique

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Layer 1


Layer 2 ( Multiplication layer):

Multiplies the incoming signals.

Each node is circle represented symbolized with .

Mathematical formula

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Layer 1 Layer 2


Layer 3 ( Normalization layer):

Calculates the normalized firing strength of each rule

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Layer 1

Layer 2

Layer 3


Layer 4 Consists of adaptive nodes Multiplies the normalized firing strength with

the Input Parameters are known as consequent

parameters. Consequent parameters will be tuned by

Recursive Least Square Estimate(RLS)

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Layer 1

Layer 2

Layer 3

Layer 4


Layer 5 ( output layer)

Calculates the overall output of the system.

The output r is used to tune the adjustable model.

The mathematical formula is

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Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

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ANFIS Training Algorithm

ANFIS Training Algorithm

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Hybrid Learning Algorithm

Premise Parameter

Back Propagation

Consequent Parameter

RLS

ANFIS Training Algorithm Cont

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Back Propagation Method

The error used will be the quadrature current error

The updating formula will be

ANFIS Training Algorithm Cont

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100

RLS Method

The updating formula will be

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Simulation Results

Simulation Results

Simulation is carried out by Matlab/Simulink

A simple FOC is used to control the speed of the PMSM

The drive system used will be

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102

Simulation Results Cont

Case 1: Speed variation at No Load and nominal parameters

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103

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-500

0

500

1000

1500

2000

time (Sec)

Est

imate

d v

s. A

ctu

al

speed

(R

PM

)

Act

Est


Case 1: Speed variation at No Load at nominal parameters

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104

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

time (Sec)

Est

imate

d v

s. A

ctu

al

po

siti

on

Rad

Act

Est

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

0

200

400

600

800

1000

time (Sec)

Sp

eed

Err

or

(RP

M)

speed error


Case 2: Speed variation at with load and nominal parameters

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105

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

0

200

400

600

800

1000

1200

1400

1600

1800

time (Sec)

Est

imate

d v

s. A

ctu

al

speed

(R

PM

)

Act

Est


Case 2: Speed variation at with load and nominal parameters

6/3/2014

106

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

time (Sec)

Est

imate

d v

s. A

ctu

al

po

siti

on

Rad

Act

Est

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

0

200

400

600

800

1000

time (Sec)

Sp

eed

Err

or

(RP

M)

speed error


Case 3: Speed variation with 20% resistance increase , with and without torque.

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107

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

200

400

600

800

1000

1200

1400

1600

1800

2000

time (Sec)

Est

imate

d v

s. A

ctu

al

speed

(R

PM

)

Act

Est


Case 4: Speed variation with 20% resistance and inductance increase , with constant torque.

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108

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-500

0

500

1000

1500

2000

time (Sec)

Est

imate

d v

s. A

ctu

al

speed

(R

PM

)

Act

Est


Case 4: Speed variation with 20% resistance and inductance increase , with constant torque.

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109

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

time (Sec)

Est

imate

d v

s. A

ctu

al

po

siti

on

Rad

Act

Est

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

0

200

400

600

800

1000

time (Sec)

Sp

eed

Err

or

(RP

M)

speed error

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110

Thank You

Questions

Sensorless control of PMSM

Documents