Wide Range Speed Control Based on Field Oriented ...

IRAQI JOURNAL OF APPLIED PHYSICS

Wide Range Speed Control Based on Field Oriented Control of

Ekhlas K. Hamza

Permanent Magnet Synchronous Motor This paper presents a wide speed range of a permanent magnet synchronous motor based on Field oriented control strategy. Rotor position estimation using model reference adaptive system method for interior permanent magnet Drive without using a mechanical

School of Applied Sciences,

sensor is illustrated considering the effects of cross-saturation between the d and q axes.

University of Technology,

The cross saturation between d and q axes has been calculated by finite-element analysis.

Baghdad, IRAQ

The inductance measurement regards the cross saturation which is used to obtain the suitable id - characteristics in base and flux weakening regions. The simulation results show that rotor position estimation error accuracy was improved. Various dynamic conditions have been investigated.

Keywords: Magnetic saturation, Rotor position estimation, Model reference adaptive system Received: 22 November 2013, Revised: 22 October 2013, Accepted: 22 December 2013

1. Introduction Interior Permanent Magnet Synchronous Motors (IPMSM) are used in many applications that require

2. Modeling of the PMSM The space-state equations can be written as:

pumps, actuators, and machine tools [1]. In these

x  Ax  BU  y  Cx

applications, the IPMSM drive systems are required

where

rapid

torque

response

and

high-performance

operation such as robotics, vehicle propulsion, heat

to

position

or

velocity

feedback.

In



most

applications, there is an optical shaft position

x i

encoder or resolver for position feedback signal. The objectives of sensorless drives control are: reduction of

hardware

mechanical

complexity robustness,

and

cost,

operation

increased in

machine inertia [2,3]. Therefore, FOC control of a pulse width modulation (PWM) inverter-fed motor drive is with

two

main

objectives:

C



T

sα

i

sβ

y  i sα i sβ

hostile

environments, higher reliability, and unaffected

proposed



(1)

,



U  V sα Vsβ





T

,

T

(2)

1 0 0 0 T 0 1 0 0

The Matlab/Simulink block diagram for the proposed system is shown in Fig. (1).

first,

achievement of an accurate and fast response of the flux and the torque, and second, reduction in the complexity of the control system. ISSN(Print) 1813-2065

ISSN(Online) 2309-1673

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IJAP, Vol. (9), No. (4), October 2013

q





ˆ r

iq



uq

V3(010)

ˆ

e jr

V4(011)

V2(110)

V0(000)

Uabc

Vsref φsref

ia

 jˆr

iq

e

ˆr

ˆ r

Model Reference Adaptive System

id

iq

ib

iα 

abc

eac ebc

iabc

MRAS



iq*

i id iq ud uq

U dc

V1(100)

V6(101)

ˆr

id



Es * ud'   ud 

K p  KI / s

S V P W M

V7(111)

V5(001)

u* id



id*

dq

MTPA i





SVPWM

u*

abc

*r



ud

id* 

IPM Motor

L

L 



uq'  

Kp  KI / s

ia ib ic IPMSM

uq*

Fig. (2) Forward compensation system model

Fig. (1) Matlab/Simulink block diagram

To illustrate the space vector pulse width modulation (SVPWM) strategy [5,6] Table 1, shows

3. Model Reference Adaptive System Model

the commutation strategy suggested by Takahashi, to

Model reference adaptive system (MRAS) based

control the stator flux and the electromagnetic torque.

rotor position estimation method is employed to

Fig.3 gives the partition of the complex plan in six

estimate rotor position and speed [4]. Fig.2 shows

angular sectors SI = 1… 6.

the forward voltage compensation model where the  

rotor position is estimated with MRAS that required in

transformation

process

needs

for

V3(010)

the

V2(110) V3(DF,AC)

V2(AF,AC)

V5(DF,DC)

V6(AF,DC)

compensation algorithm. To eliminate input ripples 3

from appearing at the output, it is important to

V4(011)

implement the feedforward voltage.

2 V0,7(000)

4

The voltage equations for IPM motor are as

7

5

V1(100)

 

1

6

Secteur 1

follows: V6(101)

V5(001)

 di d Ld  Ri d  u d'   dt   L di q  Ri  u ' q q q  dt 

Le code V6(1 0 1) signifie :  1 : interrupteur supérieur du 1er bras fermé;  0 : interrupteur supérieur du 2eme bras ouvert;  1 : interrupteur supérieur du 3eme bras fermé.

(3)

where R and Ld, Lq are stator resistance and d-q

Fig. (3) Partition of the complex plan in six angular sectors S I = 1 … 6

inductances, respectively. The d-q axis voltages are:

ud'  K p (id*  id )  K (id*  id )dt  i  ' u  K p (iq*  iq )  K  (iq*  iq )dt  i  q

Table (1) Selection table for direct torque control

(4)

ΔΨs

ΔCe

S1

S2

S3

S4

S5

S6

1

1

V2

V3

V4

V5

V6

V1

0

V7

V0

V7

V0

V7

V0

-1

V6

V1

V2

V3

V4

V5

1

V3

V4

V5

V6

V1

V2

0

V0

V7

V0

V7

V0

V7

-1

V5

V6

V1

V2

V3

V4

To avoid the variation of the controlled currents, a saturation signal has been used.

ud*  Es   Liq  ud'   * '  uq   Lid  uq

0

(5)

To explain the system of speed regulation, the saturation of the manipulated variable can involve a phenomenon of racing of the integral action during

22

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IRAQI JOURNAL OF APPLIED PHYSICS

the great variations (starting of the machine), which is likely to deteriorate the performances of the overcome this phenomenon, a solution consists in correcting the integral action according to the

Lq(mH)

system or even to destabilize it completely. To

Lq vs. iq

0.2 0.18 0.16 0.14

diagram shown in Fig. 4.

0.12

Feedforward compensation is used in d and q

0

100

200 iq(A)

anti windup PI regulators to enhance the dynamic system performance.

300

400

(b) Fig. (5) d and q inductances calculations with finite element analysis It is cleared that magnetic circuit is subject to saturation as the current increses. Fig.5-b observed that when the current iq is increased, the inductance Lq is decresed. Whereas when the current id is increased then the inductance Ld is maintained constant as shown in Fig.5-a.

Fig. (4) Structure of the anti-windup PI system 5. Simulation Results 4. Cross Saturation Effect

In Fig. 6 the simulation results for the extended

In order to consider the saturation effect therefore the d and q inductances are calculated based on saturation effects. Magnetic saturation effects such as cross-coupling and permanent

EMF voltage is present, estimated rotor position

ˆr

respectively. The estimated rotor position

follows the voltage.

magnet demagnetization can introduce large errors on the rotor position estimation [7, 8], therefor It is thus important to correctly model the magnetic saturation effects, which is usually done through d-q

ea (5v/div)

magnetizing curves. The d-q inductance calculations are obtained using finite element analysis via Maxwell software. The Ld variation with respect to

 (rad/s)

id is shown in Fig.5-a, while the Lq variation with respect to iq is shown in Fig. (5b). time (5ms/div)

Ld(mH)

Fig. (6) Simulation results: Estimated rotor position

Ld vs. id

0.078

and extended EMF

0.076 0.074

From the simulation results shown in Fig. 7, it

0.072 0.07 -250

can be observed that: -200

-150 -100 id(A)

-50

0

Fig.7-a, when the

(a)

ISSN(Print) 1813-2065

Without consider saturation effect as shown in

ISSN(Online) 2309-1673

id*

=4A、

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iq*

=0A，then changes

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23

IJAP, Vol. (9), No. (4), October 2013

load to

id* =8A and iq* =0A

the flux and speed tracking are good and error convergence is guaranteed. However an anti-windup

Consider saturation effect as shown in Fig.7-b,

PI regulator has been used to replace the classical PI

id* =6A and iq* =0A，then changes load to

controller in the speed control. In conclusion, it

when the

seems that the anti-windup PI controller outperforms the classical PI controller in speed control of high

id* =6A、 iq* =-5A

performance FOC motor drive. Simulation results demonstrate a good performance and robustness. Reference

id (5A/div)

[1] A. Parviainen, J. Pyrhönen and M. Niemela, “Axial

Flux

Interior

Permanent

Magnet

Synchronous Motor With Sinusoidally Shaped Magnets”, ISEF 2001, 10th Inter. Symp. on

iq (5A/div)

Electromag. Fields in Electrical Eng. Cracow, Poland, September 20-22, 2001. time (5ms/div)

[2] L. Gao et al., Electric. Mach. and Sys. (ICEMS),

(a)

October 2010, 931-936. [3] M. Mengoni et al., IEEE Trans. on Power Electronics, 27(1) (2012) 307.

id (5A/div)

[4] B.M.F. Bushofa and A.H.A. Azab, “Simulating Discrete Time Model Reference Adaptive Control System with Great Initial Error”, World Academy of iq (5A/div)

Science, Engineering and Technology (2010) 71. [5] J. Singh et al., Inter. J. of Rev. in Computing, 9 (2012) 9. time (5ms/div)

(b) Fig. (7)

id* , iq* currents (a) without consider

saturation effect, (b) consider saturation effect

[6] P. Guglielmi et al., IEEE Trans. on Industry Appl., 49(1) (2013) 31. [7] N. Bianchi, S. Bolognani and A. Faggion, “Predicted and measured errors in estimating rotor position by signal injection for salient-pole PM synchronous motors”, in IEEE Inter. Electric

6. Conclusions

Machines and Drives Conf., 2009, 1565–1572.

This paper presented a sensorless FOC on of

[8] A.K. Jebai et al., “Estimation of Saturation of

MRAS improves the system performance. The

Permanent-Magnet Synchronous Motors Through an

magnetic saturation effect is considered hence the d

Energy-Based Model”, Electric Machines & Drives

and q inductances calculations are obtained using the

Conf. (IEMDC), 2011 IEEE Inter., Niagara Falls,

finite element analysis. Simulation results reveal that

Canada (2011).

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