Full-order stator flux observer Based Sensorless Vector Controlled Induction Motor Drives Applying

Full-order stator flux observer Based Sensorless Vector Controlled Induction Motor Drives Applying Particle Swarm Optimization Algorithm

Yung-Chang Luo1* Chen-Lung

Tsai1 Wen-Cheng

Pu1 Cheng-Tao

Tsai 1

1Department of Electrical Engineering

National Chin-Yi University of Technology

Taichung, Taiwan

luoyc@https://www.sodocs.net/doc/a015936746.html,.tw aa3706177@https://www.sodocs.net/doc/a015936746.html, puo@https://www.sodocs.net/doc/a015936746.html,.tw cttsai@https://www.sodocs.net/doc/a015936746.html,.tw

*Correspon

d ing

Author

Abstract—A speed estimation approach of vector-controlled induction motor drive based on flux observer that applying particle swarm optimization (PSO) algorithm is presented. The proposed estimation speed scheme using full-order stator flux observer has the advantage of simple structure and facile implementation. The observer gain matrix of the full-order flux observer is designed applying the particle swarm optimization algorithm which acquired exact gain parameters rapidly. Simulation and experimental results confirms the effectiveness of the proposed approach. Keywords-sensorless vector control; flux observer; PSO

I.I NTRODUCTION

Ind uction motor (IM) d rives ad opting vector control method possesses superior torque-current ratio, which utilizes appropriate coordinate transformation and then the complicate mathematical mo el of an IM can be converted similarity as a DC motor that field and armature voltage can be independently controlled [1]. However, the implementation of vector controlled IM d rive requires rotor-shaft position sensor such as encod er to d etect the rotor speed. This position sensor, nevertheless, reduces the d rive d epen d ability an d is not suitable for hostile environment. Consequently, the sensorless vector control approaches that apply flux observer to estimate rotor speed metho d s have been generally use d to replace the conventional vector-controlled IM drives [2, 3].

The implementation of the full-ord er flux observers require to adjust the observer gain matrix and the observer gain matrix has numerous gain parameters for vector-controlle d IM d rive, consequently, the conventional optimal gain matrix is acquired applying try-and-error or the experiences of professional. PSO algorithm is one of optimum control method s which has the possession of rapid convergence and low operational cost, which is suitable for variation cond itions [4]. Hence, the observer gain matrix regulation applying PSO algorithm for the full-order flux observer of the sensorless vector-controlled IM drive is developed in this paper.

II.S TATOR FIELD VECTOR CONTROL INDUCTION

MOTOR DRIVE

The vector state equations are expressed ad opting the stator current and flux of an IM in the synchronous reference coordinate frame to be given by [5]

e

s

e

s

r

r

e

s

sl

r

s

e

s

v

L

j

L

i

j

L

R

i p

r

r

r

r

σ

σ

σ

λ

ω

τ

ω

στ

1

1

1

1+

???

?

???

?

?

+

???

?

???

?

+

+

?

= (1)

e

s

e

e

s s

e

s

j

i R

pλ

ω

λ

r

r

r

?

?

= (2)

where e

qs

e

ds

e

s

jv

v

v+

=

r and e

qs

e

ds

e

s

ji

i

i+

=

r

are the stator voltage

and current, respectively, e

qs

e

ds

e

s

jλ

λ

λ+

=

r

is the stator flux,

s

R and r R are the stator and rotor resistance, respectively,

s

L and r L are the stator and rotor inductance, respectively,

m

L is the mutual ind uctance, r

r

r

R

L

=

τis the rotor time

constant, )

(

12

r

s

m

L

L

?

=

σis the leakage in d uctance

coefficient,

s

L

Lσ

σ

=is the stator leakage inductance, eω is

speed of the synchronous reference coordinate frame,

r

ω

is the electric speed of the rotor,

r

e

sl

ω

ω

ω?

=is the slip

speed, and dt

d

p=is the d ifferential operator. The

developed electromagnetic torque of an IM is obtained as

)

(

4

3e

qs

e

ds

e

ds

e

qs

e

i

i

P

Tλ

λ?

= (3) where P is the pole number of the motor. The

mechanical equation of the motor is

e

L

rm

m

rm

m

T

T

B

p

J=

+

+ω

ω (4)

where

m

J is the inertia of the motor, m B is the viscous

friction coefficient,

L

T is the load torque, and rmω is the

mechanical speed of the motor rotor-shaft. The speed of

the motor rotor-shaft can also be expressed as

r

rm Pω

ω2

= (5) Und er the stator field vector control cond ition, set

0=

e

qs

λin (2), the d-axis stator flux can be derived as

e

qs

r

sl

r

e

ds

e

ds

s

r

r i

s

i

L

s

s

)

1(

)

1(

)

1(

τσ

ω

τσ

λ

τσ

τ

+

?

=

+

+ (6)

where s is the Laplace operator.

In ord er to attain the linear control of the stator flux

loop, d efine the d-axis stator flux fee d-forwar d

compensation as

e

qs

r

sl

r

e

dq

i

s

i

)

1(τσ

ω

τσ

+

= (7) Then the decoupled d-axis stator flux is given by

e

ds

r

s

r

e

ds

i

s

L

s

)

1(

)

1(

τ

τσ

λ

+

+

= (8)

2016 International Symposium on Computer, Consumer and Control

The d eveloped electromagnetic torque of an IM und er

vector control condition is acquired as

e

ds e qs e i P T λ4

3= (9) Furthermore, setting 0=e qs λ

in (1), the d -axis and q-axis stator voltage equations are given by

e

ds e ds e ds s v p i R =+λ (10)

e qs e ds e e qs s v i R =+λω (11)

Inspecting (11), the linear control can be obtained by efining the fee -forwar compensation as e ds e λωto eliminate the coupling term. Hence, the voltage command of the d-axis and q-axis stator current loops are acquired as, respectively e ds e ds v v ′=*

(12)

e ds e e qs e qs v v λω+=′

*

(13) where e ds

v ′ and e qs v ′are the output of the d -axis and q-axis stator current controller, respectively.

III. F ULL -ORDER STATOR FLUX OBSERVER DESING

USING PSO ALGORITEM

In the two-axis stationary reference coord inate frame

(0=e ω), accord ing to (1) and (2), the full-ord er stator

flux observer can be defined as )?(01??0?11?1??s s s s s s σs s s s s r r σr r σs s s s s i i G v i R ωj τL ωj στL R i p r r r r r r r ?+??????????+?????????????????

????????????????????+?=????????λλ(14) where G is the observer gain matrix.

The proposed flux observer based sensorless stator field

vector controlled IM d rive is shown in Fig. 1, in which the speed error between the rotor speed command *

r ω and the estimated rotor speed r ω

? is cond ucted by the stator field vector controlled IM d rive to trigger the voltage

source inverter to con uct IM, then the ifference between the estimated stator current s s i ?r (deriving from the

full-ord er stator flux estimator ) and the measured stator

current s s i r is mod ulated by the observer gain matrix G to acquire the estimated rotor speed.

Owing to PSO algorithm is suitable for noise, time-varying and irregular application. Hence, the observer gain matrix of the full-order stator flux observer is designed applying PSO algorithm

PSO algorithm observer gain design PSO algorithm is devised to simulate social behaviour [6], which applying the iteratively procedure improve candidate solution (called particles) to attain the

prescribed quality. Owing to the conventional PSO algorithm has a disadvantage of local solution convergence, there are some modified PSO algorithms to be presented such as constriction factors method, tracking dynamic system method, and inertia weight method [7].

On account of the inertia weight method promotes the search capability of the optimum solution during the initial computation stage and to improve the convergence

quality during the latter computation stage. Hence, this PSO algorithm is adopted in this paper. The inertia weight

method of PSO algorithm applying the concept of progressive deceleration, in which the particles are allocated quick searching velocity for larger region during the initial computation stage, until the iterations are

progressive increase, the searching velocity are

progressive decrease to improve convergence effect. The

iteration formula of the position and velocity are, respectively, )

( )()()1(21i best i best i i x G Rand C x P Rand C k V w k V ?××+?××+×=+ (15) )1()()1(++=+k V k x k x i i i (1

6) where )(k V i and )(k x i are the velocity and position of the particle, respectively, best P and best G

are the optimum solution position of the individual particle and swarm

particles, respectively, w is the weighting factor, 1C and 2C are the learning factors, and Rand is the uniform distribution random variable over [0,1].

In (15), the first item stands for the improvement effect of convergence, the second item stands for the cognition-only model of the particle, and the third item stands for

the social-only model of the particles. The displacement and velocity of each particle are limited to the bounds between maximum and minimum. If the updated

displacement and velocity of the particle exceed the bounds, then the updated displacement and velocity of the particle are settled the maximum and minimum. The two-dimension search of velocity and position of the particles is shown in Fig. 2. The computation procedures of the

inertia weight method of PSO algorithm is shown in Fig. 3, which includes allocating the initial position and velocity of the particle, computation adaptation value, update the optimal values of the individual particle and the swarm particles, and evaluated the desired precision.

Figure 2 the 2-dimensions search of velocity and position of the particles.

best

P

best

G

Figure 3 computation procedure of the inertia weight method based PSO algorithm

IV.S IMULATION AND EXPERIMENTAL The block diagram of the proposed full-order flux observer based sensorless vector controlled IM drive with PSO algorithm observer gain matrix design is shown in Fig. 4, which includes PSO algorithm observer gain matrix design, speed controller, flux controller, q-axis and d-axis stator current controllers, d-axis stator flux decouple, q-axis stator voltage decouple, coordinate transformation. In this system, the proportion-integral (PI) type controllers for the speed control loop, flux control loop, d-axis, and q-axis stator current control loops are designed by the root-locus methods. The observer gain matrix of the full-order stator flux observer is designed using PSO algorithm.

To confirm the effectiveness of the proposed full-order stator flux observer based sensorless vector controlled IM drive applying PSO algorithm observer gain matrix design, a 3-phase, 220V, 0.75kW, -connected, standard squirrel-cage IM is used, which serves as the controlled plant for experimentation. In a running cycle, the speed command is designed as follow: forward direction acceleration from 0

t= to 1

t=sec; forward direction steady-state operation during 2

t

1≤

≤ sec; forward direction braking operation to reach zero speed in the interval 3

t

2≤

≤sec; reverse direction acceleration from 3

t= to 4

t= sec; reverse direction steady-state operation during 5

t

4≤

≤ sec; reverse direction braking operation to reach zero speed in the interval 6

t

5≤

≤ sec.

The simulated and measured responses are shown in Figs. 5-8. Each figure contains four responses: the estimated shaft speed and actual shaft speed, the stator current, the electromagnetic torque, and the stator flux linkage locus. The simulated and measured responses with 2 N-m load for reversible speed commands ±1800 rpm and ±300 rpm are shown in Figs. 5-6, and 7-8, respectively.

controlled IM drive applying PSO algorithm design strategy.

036912

Time(sec)

(a)

-2000

-1000

1000

2000

S

p

e

e

d

(

r

/

m

i

n

)

036912

Time(sec)

(b)

2

4

6

I

s

(

A

)

036912

Time(sec)

(c)

-6.0

-3.0

0.0

3.0

6.0

T

e

(

N

-

m

)

-0.40.00.4

Flux_ds

(d)

-0.4

0.0

0.4

F

l

u

x

_

q

s

Figure 5 Simulated responses of the full-order stator flux observer rotor-shaft speed on line estimation sensorless vector controlled IM dive applying PSO algorithm observer gain matrix design strategy w ith loading 2 N-m at reversible steady-state speed command 1800 rpm.

(a)command (red line) and estimated (dotted line) rotor-shaft speed,

(b)stator current, (c)estimated electromagnetic torque, (d)stator flux locus (s

qs

λvs.s

ds

λ).

3

6912Time(sec)

(a)

-2000

-100001000

2000

S p e e d (r /m i n )

03

6912

Time(sec)

(b)

2

4

I s (A )

3

6

9

12

Time(sec)

(c)

-4.0

-2.00.02.0

4.0

T e (N -m )

-0.4

0.00.4

Flux_ds (d)

-0.4

0.0

0.4

F l u x _q s

Figure 6 Measured responses of the full-order stator flux observer rotor-shaft speed on line estimation sensorless vector controlled IM dive applying PSO algorithm observer gain matrix design strategy w ith loading 2 N-m at reversible steady-state speed command 1800 rpm. (a)command (red line) and estimated (dotted line) rotor-shaft speed, (b)stator current, (c)estimated electromagnetic torque, (d)stator flux locus (s qs

λvs.s ds λ). 0

3

6912Time(sec)

(a)

-400

-2000200400

S p e e d (r /m i n )

03

6912

Time(sec)

(b)

123

4I s (A )0

3

6

9

12

Time(sec)

(c)

-4.0

-2.00.02.04.0

T e (N -m )

-0.4

0.00.4

Flux_ds (d)

-0.4

0.0

0.4

F l u x _q s

Figure 7 Simulated responses of the full-order stator flux observer rotor-shaft speed on line estimation sensorless vector controlled IM dive applying PSO algorithm observer gain matrix design strategy w ith loading 2 N-m at reversible steady-state speed command 300 rpm. (a)command (red line) and estimated (dotted line) rotor-shaft speed, (b)stator current, (c)estimated electromagnetic torque, (d)stator flux locus (s qs

λvs.s ds λ). 0

3

6

9

12

Time(sec)

(a)

-400

-2000200400

S p e e d (r /m i n )

03

6912

Time(sec)

(b)

123

4I s (A )

3

6

9

12

Time(sec)

(c)

-6.0

-4.0-2.00.02.0

4.0T e (N -m )

-0.4

0.00.4

Flux_ds (d)

-0.4

0.0

0.4

F l u x _q s

Figure 8 Measured responses of the full-order stator flux observer rotor-shaft speed on line estimation sensorless vector controlled IM dive applying PSO algorithm observer gain matrix design strategy w ith loading 2 N-m at reversible steady-state speed command 300 rpm. (a)command (red line) and estimated (dotted line) rotor-shaft speed,

(b)stator current, (c)estimated electromagnetic torque, (d)stator flux locus (s qs

λvs.s ds λ). Based on the simulated and experimental results for different operational speeds as shown in Figs. 5-8, the proposed full-order stator flux observer rotor-shaft speed on line estimation sensorless vector controlled IM dive apply ing PSO algorithm observer gain matrix design strategy has shown that desired performance can be acquired.

V. C ONCLUSIONS

A full-order stator flux observer rotor-shaft speed on-line estimation apply ing PSO algorithm observer gain matrix design strategy has been proposed to control a sensorless vector controlled IM drive. The proposed estimation speed scheme using the full-order stator flux observer has the advantage of simple structure and facile implementation. The observer gain matrix of the full-order flux observer is designed appl ing the PSO algorithm which acquired exact gain parameters rapidly. The simulation and experimental responses at different reversible steady -state speed commands (±1800 rpm and ± 300 rpm) confirm the effectiveness of the proposed approach.

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