DESIGN AND IMPLEMENTATION OF A DIGITAL CONTROL SYSTEM FOR AN AXIAL FLUX SWITCHED RELUCTANCE MOTOR

Felipe Sass, José Andrés Santisteban and Eric Sanches

Universidade Federal Fluminense, Escola de Engenharia, Rua Passo da Pátria 156, São Domingos, Niterói, CEP 24210-240 jasantisteban@vm.uff.br

Abstract – Nowadays, besides the rapid growth of different areas like the mechanical and electrical ones, it is possible to identify a particular effort to develop new motors including new electrical drives and control systems. Additionally, these equipments are being designed to give them the maximum efficiency as the energy cost is continuously increasing. With this in mind, some results related to a particular switched reluctance motor, are presented. The airgap between its poles are distributed in such a way that they are parallel to the rotation axis. Such structure is little studied by researchers. On the other hand, in order to maintain a low ripple torque, a particular algorithm is proposed which consists in imposing motor currents with a special format. The implementation of this strategy was made using two microcontrollers, one to determine the position and speed of the rotor while the second impose the appropriated current to the motor windings. This strategy has been successfully tested to control the speed of the rotor in a simple feedback loop.

Keywords – Digital Control, Microcontroller, Switched

Reluctance Motor.

I. INTRODUCTION

Although induction machines are, at large, used in the industry, the research for efficient and robust machines continues. This purpose is even reinforced as the level of sophistication of electronic drivers is continuously improved [1, 2].

The operation principle of the Switched Reluctance Motor (SRM) with axial flux is equivalent to the SRM with radial flux. This can be explained using a rectangular piece of steel which after immersing it in a magnetic flux will be oriented in such a way that the equivalent airgap reluctance be the minimum [3]. In literature, many of the works are related to the radial flux SRM however few works are related to axial flux SRM. Some of them are about two stators axial flux SRM [4,5,6,7,8] but in this work the machine has only one stator.

In Fig. 1, the SRM prototype used in this work is shown. It has six stator poles and four rotor poles. Each pole has 250 coils of 24 AWG wires and covers forty degrees. As can be noted the airgap is parallel to the rotation axis. The core is made of steel 1020, supported with aluminum pieces. The motor was constructed with 1mm of airgap.

II. STRATEGY FOR TORQUE GENERATION

Fig. 2 depicts the totally misaligned situation between rotor(black) and stator(white) poles. From this figure, taking as a reference the angle θ measured clockwise from the middle of pole A in the stator, torque can be generated whenever exists misalignment with the nearest rotor pole forming an angle less then 45º (0.7854rad). In order to generate a clockwise angular displacement, negative values of θ will be considered.

Fig. 1. Prototype of axial flux SRM.

Fig. 2. Poles of rotor and stator totally misaligned.

In order to determine the torque, the principle of the differential of total magnetic energy (W) was considered (1).

TI)(LI21W ⋅θ⋅⋅= (1)

Where I is the current vector of all stator poles and L(θ ) is the inductance matrix of the motor. To obtain this matrix a series of experimental measures was done taking the pole A as the reference. In Fig. 3 are shown the results. Note that the self inductance is higher than any mutual inductance. As

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expected, there are regions where the differential of its terms are positive and other negative. From this observation it was concluded that the best strategy to generate torque consists in dividing the torque generation in three regions of operation:

;energizedE/BandD/A3045 D/A ⇒−<θ≤−

;energizedD/A1530 D/A ⇒−<θ≤− ;energizedF/CandD/A015 D/A ⇒<θ≤−

where A,B,C,D,E e F are the names of the stator poles as shown in Fig. 2.

INDUCTANCE LAA

0,00E+00

1,00E-02

2,00E-02

3,00E-02

4,00E-02

5,00E-02

6,00E-02

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(a)

INDUCTANCE LAB

0,00E+00

2,00E-03

4,00E-03

6,00E-03

8,00E-03

1,00E-02

1,20E-02

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(b)

INDUCTANCE LAC

0,00E+001,00E-03

2,00E-033,00E-03

4,00E-035,00E-03

6,00E-03

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(c)

INDUCTANCE LAD

0,00E+00

1,00E-03

2,00E-03

3,00E-03

4,00E-03

5,00E-03

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(d)

INDUCTANCE LAE

0,00E+001,00E-03

2,00E-033,00E-03

4,00E-035,00E-03

6,00E-03

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(e)

INDUCTANCE LAF

0,00E+002,00E-03

4,00E-036,00E-03

8,00E-031,00E-02

1,20E-02

-1,000 -0,500 0,000 0,500 1,000

Angle (rad)

Indu

ctan

ce (H

)

(f)

Fig. 3 Self and mutual inductances.

For each region, one torque equation can be evaluated. For

instance, considering windings A, B, D and E energized then (2) represents its torque equation.

( ) ( )[ ] ( ) ( )[ ]

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂

+∂⋅⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛∂

+∂=

A

AAEAAB21

A

AADAAA21 θ

θLθLii2

θθLθL

iT

( ) ( )[ ]B

BADBAA22 θ

θLθLi∂

+∂+ (2)

where: i1 - Imposed current in A and D windings. i2 - Imposed current in B and E windings. LAA - Self inductance of pole A. LAB - Mutual inductance between A and B poles. LAD - Mutual inductance between A and D poles. LAE - Mutual inductance between A and E poles.

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It should be noted that in order to obtain a constant torque one appropriate set of currents must be imposed.

III. CURRENT WAVEFORMS

To preserve the coil isolation in each winding, the maximum value of current was limited to 3A. On the other hand, as our goal was to obtain a constant torque, this maximum should occur when only one couple of windings is being supplied, in this case A and D in the region where

)rad26,0(15)rad52,0(30 D/A −<θ≤−− . Thus, the torque in this region is equal to the first term in (2). One analysis on the differential term shows that the current should be maximum when θ is approximately -15º (-0.26rad), as seen in Fig. 4.

DERIVATIVE OF THE FIRST TERM IN (2)

0

0,01

0,02

0,03

0,04

0,05

0,06

-35 -30 -25 -20 -15 -10

ANGLE (DEGREES)

DER

IVA

TIVE

OF

THE

FIR

ST T

ERM

IN (

(N.m

/A²)

Fig.4 First derivative term in (2).

In the region where two pair of windings are supplied, one

reference of current begins with the maximum and follows a decreasing exponential trend (3). The other current is increased in such a way that torque be constant, taking into account (2).

44,15 θ+

−⋅= eII MAX (3)

These rules may be resumed as follows: DecreaseIandIncreaseI3045 E/BD/AD/A −−⇒−<θ≤− A3untilIncreaseI1530 D/AD/A −⇒−<θ≤− IncreaseIandDecreaseI015 F/CD/AD/A −−⇒<θ≤−

All the waveforms references are shown in Fig. 5.

Current x Angular Position

-0,50

0,51

1,52

2,53

3,5

Angle (Degrees)

Cur

rent

(A)

A/D C/F B/E

0-15-30 0-15-30-45 -45 -30

Fig. 5. Waveform references for winding currents.

It should be noted that waveforms in Fig. 5 were calculated for a maximum of 3A but with other value the net torque would be proportional. On the other hand, as we need to derive the inductances obtained experimentally, through a

polynomial approximation, it is possible to have some inaccuracies. In our approximation was used the continuity theorem [10]. To improve the references, one suggestion is to obtain the value of the inductances through computational modeling by finite elements method.

IV. SPEED CONTROL

In order to test our approach, this machine was initially tested without load. With the maximum current of 3A (Fig. 5) the final speed was 1600rpm. With this in mind, a simple feedback control was implemented to maintain the speed at 600rpm.

Fig. 6 depicts a simplified diagram of all the control system of this prototype. Each of them will be explained individually.

PROCESSING

COMPARATOR

REFERENCE CURRENT

CHANGE OF ANGLE

REAL CURRENT

ENCODER / OPTICAL SENSOR

TRIGGER SIGNALS

POWER CIRCUIT

CURRENT SENSOR

Fig. 6. Block Diagram of the control system.

A. The encoder and sensor From Fig. 5 may be observed that there is one particular

current for each angular position in order to have a constant torque. The real resolution is one degree. This was achieved with a disc containing 180 holes, attached to the rotor. One IR led and one phototransistor were used to generate angular information to the next block, the processing. Fig. 7 shows a detail of this arrange.

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Fig. 7. Optical sensor and aluminum disk with holes.

As the diameter of the holes is small (1mm), it was necessary to pre-process electronically the signal of sensor with operational amplifiers and a Schmidt trigger logic circuit, as shown in Fig. 8. The response of the optical sensor when the rotor is running at 600rpm is shown in Fig. 9.

SIGNAL INDICATING CHANGE OF ANGLE

74LS132+

U3LM324

+V

V615V

+VV5

-15V+VV4

-15V

+V

V315V

+

U2LM324

+V

V15V +

V

V25VU1

OPTOISO

R74.7k

R61k

R51k

R44.7k

R31k

R2330

R1330

Fig. 8. Circuit diagram of the optical sensor.

Fig. 9. TTL Digital output of the optical sensor.

As expected, 360 angular TTL changes are detected with this sensor.

B. The processing In this block the three current references are generated and

then sent to the comparator block. Each reference depends on two factors; the angular position and the actual speed. In Fig. 10 the internal details are shown. As seen, two microcontrollers were utilized. The microcontroller 1 implements the speed control while microcontroller 2 calculates the speed and its error.

In microcontroller 2, changes of level are detected and then a register is continuously increased. At the same time the timer TMR0, from this microcontroller, is counting until a time base is reached. This time base was calculated as (1/6)s, which is approximately 0.1664s. As was mentioned, each change in level represents 1 angular degree. Thus, if only one change were detected in the time base, the rotor would be running at 1 rpm. After this processing, the speed error is calculated.

In order to implement the speed controller, it was necessary to find a model that relates the maximum current imposed on the motor and its speed. For this, applying as a reference Imax=1.79A, the motor speed goes to 600rpm, as shown in Fig. 11, which can be approximated as (4).

MULTIPLEXER 1 MULTIPLEXER 2 MULTIPLEXER 3

D/A CONVERTER 1D/A CONVERTER 2

DIGITAL REFERENCE PART 2(8 BITS)

DIGITAL REFERENCE PART 1(8 BITS)

MICROCONTROLLER 2:CALCULATES SPEED ERROR

CHANGE OF ANGLE

SPEED ERROR5 BITS

MULTIPLEXER (2 BITS)

MULTIPLEXER (2 BITS) MULTIPLEXER (2 BITS) MULTIPLEXER (2 BITS)

COIL REFERENCE 1 COIL REFERENCE 2 COIL REFERENCE 3

MICROCONTROLLER 1:REFERENCES GENERATOR

Fig. 10. Block diagram of the processing.

( )ate1k)t(f −−⋅= (4) From basic control theory it can be found that the transfer

function from the speed reference to the final speed results in (5):

( ) saska

ask

sksF

⋅+⋅=

+−=)( (5)

where, considering a 2% from the final value k=600 and a=0.25. Thus:

( ) s0,25s150)s(F

⋅+= (6)

Finally, as the maximum current was defined as 1,79A, then the transfer function G(s) that relates it with the speed is:

( )0,25s83,8)s(G+

= (7)

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Fig. 11. Experimental result: Speed vs time (Ver: 200rpm/div). The accuracy of this model was compared with the real

response. Fig. 12 shows the simulated result which is in accordance with Fig. 11.

Velocidade x Tempo

-

100,00

200,00

300,00

400,00

500,00

600,00

700,00

0 5 10 15 20 25 30 35 40 45

Tempo (s)

Vel

ocid

ade

(rpm

)

Fig. 12. Simulated result: Speed vs time. According to reference [11] a simple proportional

controller can be used. In this case the microcontroller 1 implements this work saving thirty one values of maximum current according to the error calculated with microcontroller 2. Additionally, this microcontroller saves a table of values which will be the current references for the windings associated to each maximum current, as shown in Fig. 13. These values are updated in each change of level of the optical sensor and sent to two D/A converters. With appropriated logic, microcontroller 1 manages the output of three analog multiplexers with the desired reference of currents. In Figs. 14 and 15 the references sent to D/A converters are shown individually. The multiplexing of these signals results on the desired references shown in Fig. 5.

This method was verified during starting, where initially one winding is energized with 3A in order to have the initial angle zero as the angle where two poles are aligned. Fig. 16 shows this process.

Current References x Angular Displacement

(0,50)-

0,501,001,502,002,503,003,50

-35 -30 -25 -20 -15 -10 -5 0Angular Displacement (Degrees)

Curr

ent R

efer

ence

s (A

)

Conversor D/A 1 Conversor D/A 2

Fig. 13. Current references vs angular displacement.

Fig. 14. Output of D/A converter 1 (Ver:1A/div).

Fig. 15. Output of D/A converter 2 (Ver:1A/div).

Fig. 16. Output of two multiplexers during starting (Ver:1A/div).

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C. The comparator Details of this block are shown in Fig. 17 and Fig. 18. It

consists of two buffers, one amplifier of error, one hysteresis comparator and an analog comparator (LM710).

A

Iref1

LM324

LM324

LM324

Ireal

LM324

R452.6k

R44150k

R434.7k

R424.7k

R412.6k

R404.7k

R394.7k

Fig. 17. Comparator circuit with hysteresis.

A B+LM710

R472.6k

R462.6k

-6V

+12V

Fig. 18. Comparator circuit with TTL output.

Additionally, in order to trigger the power circuit, a limiter

of switching frequency (20KHz) which consists of a timer and a simple flip flop type D were used.

D. The power circuit This block consists of three circuits in a Half Bridge

configuration [12] as shown in Fig. 19. In this figure, the terminals ´H´ and ´I´ are connected to each stator winding.

On the other hand, in order to serve as the interface with the comparator block, Fig. 20 shows the circuit used to trigger the Mosfet´s Q1 and Q2.

E

F

G

H I

+ V160V

C1100uF

D11N4004

D31N4004

D21N4004

Q1IRF630

Q2IRF630

Fig. 19. Power circuit.

Fig. 20. Mosfet driver.

E. The current sensor In this work a commercial sensor based on the Hall effect

was utilized. This one was set in such a way that 1V of output was equivalent to 1A circulating for the stator winding. Fig. 21 shows a photo of this sensor.

Fig. 21. Hall effect current sensor.

V. EXPERIMENTAL RESULTS

As commented before, this prototype was initially tested without load. Using the same DC link, three tests were realized. First, the motor was submitted to voltage steps, being that stator windings were supplied in sequence. With this strategy the speed of the motor was 1200rpm. Second, the motor was supplied following the new strategy, supplying currents as described in item III, the speed of the motor was 1600 rpm. It should be noted that mechanical vibrations were reduced indicating the reduction of torque harmonics.

In Fig. 22 one reference of current and the respective real current using the second strategy can be observed (Vertical scale: 1A/div. for both channels).

Fig. 22. Reference current (CH2) and real current (CH1).

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The final test consisted in testing the new approach in a

closed loop control. The reference speed was set at 600 rpm. At this speed one perturbation was applied during 0.5s. As expected, the controller attempts to maintain the speed around 600rpm in such a way that the current in each winding is raised until the maximum of 3A (Fig, 23. Vertical scale: Ch1-1A/div.; Ch2-600rpm/div.).

Fig. 23. Perturbation response of the speed controller. CH1: Phase current; CH2: Motor speed.

VI. CONCLUSION

A digital control system was designed and implemented for an axial flux switched reluctance motor. Different from the large number of works in literature, the motor under study has only one stator and a rotor.

Through experimental tests the motor model was obtained. The adopted strategy of control consists on impose appropriated currents in order to maintain the net torque free of harmonics. Experimental results show the effectiveness of this approach.

The use of two microcontrollers to implement the digital control system was verified as an appropriated technique.

With respect to the internal model of this motor, the authors believe that numerical simulations through finite elements method might improve the accuracy of the reference currents for each stator winding.

ACKNOWLEDGEMENT

The authors would like to thank the support of FAPERJ.

REFERENCES

[1] L. O. A. P. Henriques, Implementação de estratégia de minimização de oscilações de torque e remoção de sensor de posição para um acionamento de relutância variável usando técnica neuro-fuzzy. Rio de Janeiro, 2004. 156 f. Tese (Doutorado em Engenharia Elétrica) – Coordenação dos Programas de Pós-Graduação de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro. 2004.

[2] V. R. Bernardelli, D. A. Andrade, A. W. Fleury, L. C. Gomes, W. J. Carvalho, D. P. Carvalho, C. A. Bissochi Junior, “Proposta de Estratégia para Melhoria do Perfil de Conjugado de Motores a Relutância Variável”, in Anais do XVII Congresso Brasileiro de Automática, 2008.

[3] D. A. Andrade, H. Paula, J. L. Domingos, T. T. Borges, M. A. A. Freitas, “Motores a Relutância Chaveados: Uma Opção Potencial para Acionamentos Elétricos”, Revista Eletricidade Moderna, vol. XXXII, no. 361, pp. 136-149, 2004.

[4] M. Abouzeid, The use of an axial field-switched reluctance generator driven by wind energy. Renewable Energy. Vol 6, No 5-6, p. 619-622. 1995.

[5] R. Krishnan, M. Abouzeid, X. Mang, A design procedure for axial field switched reluctance motors. In Conf. Rec. of the IEEE IAS Ann. Mtg., Seattle, Washington, vol. 1, pp. 241-246, October 1990.

[6] S. H. MAO, M. C. TSAI, A novel switched reluctance motor with c-core stators. IEEE Transactions on Magnetics. Vol 41, No 12, December 2005, p4413-4420.

[7] D. Pulle, I. R. Petersen, A unified approach to switched reluctance drive modeling: application to an axial flux (SRAF) motor. Power Electronics Specialists Conference, 1998. PESC 98 Record. 29th Annual IEEE Volume 2, 17-22 May 1998 Page(s):1681 - 1686.

[8] M. A. Zaid, M. El-Attar, M. Mousa, Analysis and performance of axial field switched reluctance generator. International Electric Machines and Drives Conference, 1999. p 141-143. Seattle.

[9] R. Krishnan, Switched reluctance motor drives: modeling, simulation, analysis, design and applications. Boca Raton: CRC Press, 2001. 432 p.

[10] A. Howard, Cálculo um novo horizonte, Vol. I, São Paulo, Ed- Bookman, 6ª Ed., 2004.

[11] K. Ogata, Engenharia de controle moderno, Pearson, Prentice Hall, 4ª Ed., São Paulo, 2003.

[12] N. Mohan, T. M. Undeland, W. P. Robbins, Power Electronics: converters, applications, and design, John Wiley & Sons, 2nd Edition, New York, USA, 1995.

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