A high performance hysteresis current control of a ......torque control components of the stator...

Turk J Elec Eng & Comp Sci

(2017) 25: 1 – 14

c⃝ TÜBİTAKdoi:10.3906/elk-1505-160

Turkish Journal of Electrical Engineering & Computer Sciences

http :// journa l s . tub i tak .gov . t r/e lektr ik/

Research Article

A high performance hysteresis current control of a permanent magnet

synchronous motor drive

Cosmas OGBUKA∗, Cajethan NWOSU, Marcel AGUDepartment of Electrical Engineering, University of Nigeria, Nsukka, Nigeria

Received: 19.05.2015 • Accepted/Published Online: 08.11.2015 • Final Version: 24.01.2017

Abstract: A high performance hysteresis current control of a permanent magnet synchronous motor (PMSM) drive

is developed in this paper. The core advantage of field orientation control (FOC) is utilized to separate the flux and

torque control components of the stator current of the PMSM. Specifically, the objectives of this work are to develop

and utilize the HCC algorithm for FOC of a complete closed-loop speed-controlled PMSM drive system, optimize the

control algorithm to obtain fast speed response while maintaining effective current and torque tracking, and examine the

hysteresis current control action clearly showing the inverter switching and the effects of hysteresis band selection. Being

a speed-controlled system, the suitability of the developed model with constant, step, and ramp reference speed inputs is

examined. The results obtained show that the developed model and algorithm based on hysteresis current control offer

effective current and torque in all scenarios tested.

Key words: Hysteresis current control, field orientation, permanent magnet synchronous motor, torque

1. Introduction

Since torque can be made proportional to current either in the stationary or rotor reference frames and control of

current gives control of speed and position, control of AC drives is exercised through current control. To achieve

high performance from servo drives, current control strategies are employed to ensure that the actual currents

flowing into the motor are as close as possible to the sinusoidal references using hysteresis current control (HCC).

When compared to other current control strategies, HCC offers a great advantage by eliminating feedback loop

compensation [1,2]. The problems of poor load transient response and regulator inaccuracy have, however,

consistently necessitated further research efforts to achieve optimal drive performances.

The permanent magnet synchronous motor (PMSM) has gained significant industrial importance, and

hence the choice of a PMSM for this study. For the same output power, the PMSM offers performance

enhancement over the conventional induction and synchronous motors in terms of power factor, efficiency,

power density, and torque-to-inertia ratio [3–5]. This justifies the recent concentration of research efforts on the

design, analysis, and control of the PMSM. PMSMs with rare-earth PMs are most popular in adjustable speed

drives, but the uncertainty in procuring such materials has necessitated several research efforts to utilize ferrite

magnets in place of permanent magnets where the ferrites are expected to have competitive power density and

efficiency compared to the rare-earth PMSMs for application in such areas as in electric vehicles and hybrid

electric vehicles [6–8].

∗Correspondence: [email protected]

1

OGBUKA et al./Turk J Elec Eng & Comp Sci

Current control of voltage source inverter-fed interior PMSMs has been surveyed and HCC is favored

due to its high precision and simplicity [9,10]. The trend in current control techniques for three-phase voltage

source inverters was surveyed in [1,11]. Specific improvements involving mostly predictive HCC, which offers

fixed switching frequencies, are equally researched. Predictive control presents several advantages that make it

suitable for the control of power converters and drives including the unique feature of having a variable band

[12–14].

In the present work, a high performance HCC of a PMSM drive, employing the core advantage of field

orientation, was developed and optimized to obtain fast speed response and effective current and torque tracking.

The developed model was tested using step and ramp reference speed inputs. MATLAB software was used for

the simulation.

2. Dynamic model of PMSM

The following simplifying assumptions were made to derive the dynamic model of the PMSM in the rotor

reference frame.

i. The stator windings are balanced with sinusoidally distributed magnetomotive force (mmf).

ii. The inductance versus rotor position is sinusoidal.

iii. The saturation and parameter changes are neglected

iv. The machine has no damping circuits [4].

Based on these assumptions, the stator qd equation of the PMSM in the rotor reference frame is derived as:

[vrqs

vrds

]=

[Rs + Lqp ωrLd

−ωrLq Rs + Ldp

][irqs

irds

]+

[ωrλaf

0

]. (1)

The electromagnetic torque is obtained as:

Te =3

2

P

2[λaf + (Ld − Lq)irds]irqs. (2)

The rotor dynamic equations are:

Te = TL +Bωr + Jpωr (3)

and

θr =

∫ωrdt, (4)

where vrqs, vrds = q,d axis voltages, i

rqs, i

rds = q,d axis currents, Lq, Ld = q,d axis inductances, Rs= stator

resistances, λaf = stator resistances, ωr = angular rotor speed, P = number of motor poles, p= differential

operator, Te= electromagnetic torque, TL= load torque, B= rotor damping coefficient, and J = inertia

constant.

2


3. Field orientation control (FOC) of PMSM

Field orientation is used to decouple the stator current of the PMSM into equivalent flux and torque producing

current components for independent and precise control of torque and flux.

Considering the three-phase current as the input, the three phase currents are:

ias = is sin(ωrt+ δ), (5)

ibs = is sin(ωrt+ δ −2π

3), (6)

ics = is sin(ωrt+ δ +2π

3), (7)

where ωr is the electrical rotor speed and δ is the angle between the rotor field flux and stator current phasor,

known as the torque angle. The q- and d-ax-s stator currents in the rotor reference frame are obtained by

transformation as:

[irqs

irds

]=

2

3

[cosωrt cos(ωrt− 2π3 ) cos(ωrt+

2π3 )

sinωrt sin(ωrt− 2π3 ) sin(ωrt+2π3 )

]ias

ibs

ics

. (8)Substituting Eqs. (5), (6), and (7) into Eq. (8):

[irqs

irds

]=

[iT

if

]= is

[sin δ

cos δ

], (9)

where iT is the torque-producing component of the stator current and if is the flux-producing component of

the stator current.

As shown in Figure 1, the rotor flux linkage revolves at rotor speed ωr and is positioned away from a

stationary reference by rotor angle θr . The stator current phasor is at angle δ from the rotor flux linkages

phasor. FOC is achieved at δ = 90◦ , thereby rendering the stator flux current component zero.

if = irds = is cos δ = 0 (10)

Therefore:

Te =3

2

P

2λaf i

rqs. (11)

Since sin 90◦ = 1, irqs = is , therefore:

Te =3

2

P

2λaf is = Ktis, (12)

where Kt =32P2 λaf is the torque constant.

Under this condition, the PMSM behaves exactly as the separately excited DC motor as seen from the

torque expression of Eq. (12), where the torque is produced by the interaction of the rotor flux and the stator

current.

3


axisdfr

ds ii =

r

qsv

axisq

T

r

qs ii =

Stator Reference Frame

sv

r

dsv

si

r

s

r af

Figure 1. Phasor Diagram of FOC for PMSM.

4. Schematic of the speed-controlled drive system

The complete schematic of the speed-controlled PMSM drive system is shown in Figure 2. It consists of the

PMSM, speed and position feedback, PI speed controller, hysteresis current controller, and three-phase voltage

source inverter.

Signal

PMSM

3

Gating Reference

Stator Current

Estimator

Eq.( 8 )

Generation by

Hysteresis

Comparison VSI

Figure(

3 )

dcV

*r

dsi

L

bi ci

ci

2

P

6

1

g

g

v

to

v

r

qsi

0

s

1

e

e

af

P

22

3

1

1+s

K f

r

30

rN

Speed Sensor

*r

qsi

*

eT

Limiter

+

30

*

rN

PI Controller

s

KK ip +

Torque

*

r

Filter st1

Order Low Pass

bi ai

ai

*

ai

*

bi

*

ci

Figure 2. Complete schematic of the speed-controlled PMSM drive system.

4


All reference or command values are superscripted with an asterisk in the drive diagram. The rotor speed

sensed by the speed sensor is filtered by the 1st order low-pass filter to eliminate noise due to the speed sensor,

thereby attempting to make the rotor speed as pure as the reference speed. The speed error between the actual

rotor speed and its reference (ω∗r − ωr) is processed through the PI speed controller to nullify the steady-stateerror in speed. The output of the speed controller is the torque reference, which is restricted to an upper and

a lower limit by the torque limiter, thereby producing a realistic torque reference T ∗e .

The torque reference T ∗e is divided by the motor torque constant Kt =32P2 λaf to produce the reference

quadrature axis current ir∗qs . To achieve vector control by field orientation, the reference direct axis current

ir∗ds = 0. The ir∗ds and i

r∗qs are passed through the inverse Park transform block to produce the stator abc phase

current references i∗a , i∗b , and i

∗c . Electrical rotor position θe feedback realized by integrating the electrical

rotor speed ωe is required in order to generate the phase current references as shown in Eq. (13).

i∗a = ir∗qs cos θe + i

r∗ds sin θe

i∗b = ir∗qs cos(θe − 2π3 ) + i

r∗ds sin(θe − 2π3 )

i∗c = ir∗qs cos(θe +

2π3 ) + i

r∗ds sin(θe +

2π3 )

(13)

The parameter ∆ is the hysteresis band that moderates ir∗qs as shown in Figure 2. HCC is achieved through the

generation of gating signals by the appropriate firing of the power semiconductor switches S1 to S6 of Figure

3 using the control logic detailed below.

1S

3S 5S

4S 6S 2S

av

bv

cv

2

dcV

2

dcV

a b c N

ai

bi

ci

1D

4D

3D

6D

5D

6D

Figure 3. Power circuit of three-phase inverter.

if ia < i∗a −∆i∗qs OR ( ia > i∗a −∆i∗qs AND ia < i∗a +∆i∗qs AND diadt > 0 )

vg1 = 1;

vg4 = 0

else vg1 = 0 ; vg4 = 1

end

if ib < i∗b −∆i∗qs OR ( ib > i∗b −∆i∗qs AND ib < i∗b +∆i∗qs AND

dibdt > 0 )

vg3 = 1;

vg6 = 0

else vg3 = 0 ; vg6 = 1

end

if ic < i∗c −∆i∗qs OR ( ic > i∗c −∆i∗qs AND ic < i∗c +∆i∗qs AND dicdt > 0 )

vg5 = 1;

vg2 = 0

else vg5 = 0 ; vg2 = 1

end

5


Using phase ‘a’ as a case study, the HCC allows the actual value of ia to track the reference current i∗a

to exceed it or be less than it by ∆ir∗qs , thereby giving maximum and minimum values of ia as i∗a +∆i

r∗qs and

i∗a −∆ir∗qs , respectively. The hysteresis current controller attempts to force the actual motor currents to trackthe reference values at all times. The phase current to the motor is limited by inductor L of value 5 mH.

The drive performance is influenced by the hysteresis window, which determines the extent to which the

actual phase currents track the reference values. The narrower the hysteresis window, the more effectively the

phase currents tract their respective references and the less the pulsation in torque. The reverse is the case if

the hysteresis window is made wide.

5. Motor and control parameters

The complete drive system is simulated for the motor rated as follows: rated torque, speed, and power = 26

Nm, 3000 rpm, and 11 Hp; stator phase resistance Rs (Ω) = 0.11; stator quadrature axis inductance Lq (H)

= 0.00097; stator direct axis inductance Ld (H) = 0.00097; flux linkage established by magnet (Wb) = 0.1119;

inertia constant J (kgm2) = 0.0016; viscous frictional constant B = 0.0002024; Vdc = 600 V; number of poles =

8. To obtain the best possible performance, a tuning method was employed to obtain the optimal proportional

and integral gain values. The procedure is to lower the proportional and integral gain values and gradually tune

them up until the best possible performance is achieved. This is the practice in industry. The optimal control

variables are: proportional gain = 5, integral gain = 100, 1st order low-pass filter time constant = 1.6e-3 s,

torque limiter upper lower = 30 Nm/–30 Nm.

6. Hysteresis current control action and the inverter switching

The selected hysteresis band, delta ∆, is 0.05 except when specified as 0.025 for the purpose of comparison. A

reference speed of 200 rpm is set to achieve steady state at about 0.02 s.

The gating signals, vg1 to vg6 , for the six switches of the inverter are shown in Figure 4. The comple-

mentary switching between switches (S1 and S4), (S3 and S6), and (S5 and S2) are seen in gating signals vg1

and vg4 , vg3 and vg6 , and vg5 and vg2 , respectively. The variation in the switch-on and switch-off time of each

of the inverter switches highlights the pulse width modulation nature of the HCC techniques. Figure 5 shows

the inverter phase to phase voltage vab for phase ‘a’ and phase ‘b’.

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg1

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg2

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg3

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg4

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg5

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg6

Time [s]

Figure 4. Inverter gating signals.

6


0.1396 0.1396 0.1396 0.1396 0.1396 0.1396 0.1397

–600

–400

–200

0

200

400

600

Inve

rter

Pha

se to

Pha

se V

olta

ge, [

V]

Time [s]

Figure 5. Inverter phase ‘a’ to phase ‘b’ voltage vab .

The gating signals, vg1 and vg4, for the complementary switches in the first leg of the inverter S1 and

S4 are shown in Figure 6 using phase ‘a’ to highlight the hysteresis property for a narrow time band (0.282 to

0.284 s) for the purpose of clarity. It can be seen that the two switches conduct alternately as earlier explained.

The phase ‘a’ current ia tracts the upper boundary i∗a +∆i

r∗qs (increasing) when switch S1 is conducting and

tracts the lower boundary i∗a−∆ir∗qs (decreasing) when switch S4 is conducting. The HCC action, which makesthe phase ‘a’ current ia track its reference i

∗a , is seen as ia moves between i

∗a +∆i

r∗qs and i

∗a −∆ir∗qs as switches

S1 and S4 conduct alternately.

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.284–25

–20

–15

Cur

rent

+/–

Del

ta i

ian*ian*+Delta iian*–Delta iian

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg1

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg4

Time [s]

Figure 6. Phase ‘a’ hysteresis current with S1 and S4 gating signals.

Figures 7, 8, and 9 show the HCC property for phase ‘a’, phase ‘b’, and phase ‘c’, respectively. The 120◦

phase shift between the phases is observed in the plots since the plots are made within the same time band.

Figures 10 and 11 compare the switching speed of the inverter switches S1 and S4 in the inverter first

leg as the hysteresis band is varied. It can be seen that the switching speed decreases as the hysteresis band is

increased. As a result, the best phase current ia tracking of the reference current i∗a is when the hysteresis band

is narrowest (i.e. delta ∆ = 0.025). Similarly, the wider the hysteresis band, the poorer the quality of phase

current tracking and vice versa, as can be seen in Figures 12, 13, and 14. The smaller the hysteresis band, the

more closely the phase currents represent sine waves. Small hysteresis bands, however, imply a high switching

7


frequency, which is a practical limitation on the power device’s switching capability. Increased switching also

implies increased inverter losses.

0.282 0.283 0.284 0.285 0.286 0.287 0.288 0.289–25

–20

–15

–10

–5

0

Phas

e a

Cur

rent

, Ref

eren

ce C

urre

nt +

/–D

elta

i

ia*ia*+Delta iia*–Delta iia

Time [s]

Figure 7. Phase ‘a’ hysteresis current.

0.282 0.283 0.284 0.285 0.286 0.287 0.288 0.289

–35

–30

–25

–20

–15

–10

ibn*

ibn*+Delta i

ibn*–Delta i

ibn

Time [s]

Phase b

Current,

Reference

Current

+/– Delta i

Figure 8. Phase ‘b’ hysteresis current.

0.282 0.283 0.284 0.285 0.286 0.287 0.288 0.28925

30

35

40

45

50

Time [s]

Phase c Current, Reference Current +/-Delta i

icn*icn*+Delta iicn*-Delta iicn

Figure 9. Phase ‘c’ hysteresis current.

7. Drive performance under various speed references

The motor is simulated for speed references obtainable in practical drive scenarios. All the simulations are at

the rated load torque (26 Nm) to examine the response at full load. The case study reference speed inputs

8


are examined as follows, showing the speed (reference/actual), phase current (reference/actual), and torque

(reference, electromagnetic, and load)

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.284–25

–20

–15

Cu

rren

t +

/–D

elta

i

ia*ia*+Delta iia*–Delta iia

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg

1

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg

4

Time [s]

Figure 10. Phase ‘a’ hysteresis current with gating signals at delta = 0.025.

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.284

–25

–20

–15

Cu

rren

t +

/–D

elta

i

ian*ian*+Delta iian*–Delta iian

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.284

0

0.5

1

vg1

0.282 0.2822 0.2824 0.2826 0.2828 0.283 0.2832 0.2834 0.2836 0.2838 0.2840

0.5

1

vg4

Time [s]

Figure 11. Phase ‘a’ hysteresis current with gating signals at delta = 0.05.

0 0.05 0.1 0.15 0.2 0.25 0.3

–40

–30

–20

–10

0

10

20

30

40

50

Ph

ase

a R

efer

ence

Cu

rren

t ia

*

Time [s]

Figure 12. Phase ‘a’ current reference i∗a .

7.1. Step reference speed input (1500 rpm to 3000 rpm to –1000 rpm)

The motor is started at a reference speed input of 1500 rpm at full load stress as shown in Figure 15. At 0.15 s,

the speed reference is stepped up to 3000 rpm, which is the rated speed. At 0.35 s, a negative speed command

9


of –1000 rpm is issued. It is observed that the rotor speed would, after brief transients, catch up and remain

at the reference speed in each case of speed change. Figures 16 and 17 respectively show the reference phase

currents and the actual phase currents. The phase currents responded to two step speed changes. Figure 18,

using phase ‘a’ for illustration, shows that the switching frequency increased by 100% as reference speed was

stepped from 1500 rpm to 3000 rpm. The actual phase currents effectively track the references. Of specific

interest is the nature of phase inversion (reversal) from a-b-c to c-b-a that occurs as speed changes from 3000

rpm to –1000 rpm. The expanded view is shown in Figure 19.

0 0.05 0.1 0.15 0.2 0.25 0.3–50

–40

–30

–20

–10

0

10

20

30

40

50

Phas

e a C

urre

nt ia

with

Delt

a=0.0

25

Time [s]

Figure 13. Phase ‘a’ current ia with delta = 0.025.

0 0.05 0.1 0.15 0.2 0.25 0.3

–50

–40

–30

–20

–10

0

10

20

30

40

50

Ph

ase

a C

urr

ent

ian

wit

h D

elta

=0.

05

Time [s]

Figure 14. Phase ‘a’ current ia with delta = 0.05.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5–2000

–1000

0

1000

2000

3000

4000

Time [s]

Ref

eren

ece

and

Act

ual S

peed

[rpm

]

Ref Speed NrrefActual Speed Nr

Figure 15. Reference and actual rotor speed for step speed input.

As shown in Figure 20, during starting, reference torque and the electromagnetic torque equal the

maximum set torque capability. This ensures that the rotor runs up in the shortest possible time. As soon

as the rotor speed catches up with the reference, the electromagnetic torque and the torque reference settle at

10


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

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Ref

eren

ce P

has

e C

urr

ents

[A]

ian*

ibn*

icn*

Figure 16. Reference phase currents for step speed input.

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

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Act

ual

Ph

ase

Cu

rren

ts[A

]

iaibic

Figure 17. Actual phase currents for step speed input.

0.12 0.14 0.16 0.18 0.2 0.22 0.24–50

–40

–30

–20

–10

0

10

20

30

40

50

Act

ual

Ph

ase

'A' C

urr

ents

[A]

Time [s]

3000 rpm1500 rpm

Figure 18. Phase ‘A’ current (expanded).

0.345 0.35 0.355 0.36 0.365 0.37

–50

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Act

ual

Ph

ase

Cu

rren

ts[A

]

ia

ib

ic

icibia ic

ib ia

Figure 19. Current phase reversal for step speed input (expanded).

the load torque and the rotor cruises at 1500 rpm. At time 0.15 s when speed is stepped up to 3000 rpm, the

reference torque again attains the maximum possible torque of 30 Nm. At the instant of step speed change

11


from 3000 rpm to –1000 rpm at 0.35 s, the reference torque attains the minimum value of -30 Nm. As soon as

stability is achieved after each case of speed change, the reference torque is restored to 26 Nm, which is the full

load torque.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5–40

–30

–20

–10

0

10

20

30

40

Time [s]

To

rqu

es, T

e,T

ref

and

Tl [

N.m

]

TeTref

Tl

Figure 20. Te , Tref , and load torque Tl for step speed input.

7.2. Ramp reference speed input (0 rpm to 500 rpm to –500 rpm to 0 rpm)

The reference speed input is a ramp rising from zero to a positive input value of 500 rpm and falling back

to a negative input value of –500 rpm and then to zero. A combined plot of the reference speed input and

actual rotor speed is shown in Figure 21. As can be seen, ramping provides a gradual speed transition, thereby

enabling the actual rotor speed to trace the path of the reference speed input very closely.

0 0.05 0.1 0.15 0.2 0.25 0.3

–600

–400

–200

0

200

400

600

Time [s]

Ref

eren

ece

and

Act

ual S

peed

[rpm

]

Ref Speed Nrref

Actual Speed Nr

Figure 21. Reference and actual rotor speed for RAMP speed input.

Just as in the case of step speed input, phase sequence reversal also occurs at the instant of speed change

from positive to negative, as seen in Figures 22 and 23. A comparison of Figures 19 and 24, however, shows that

excellent dynamic stability is obtained during phase reversal in the case of ramp input. Ramp input provides

smooth speed transition.

0 0.05 0.1 0.15 0.2 0.25 0.3

–50

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Refe

ren

ce P

hase

Cu

rren

ts[A

]

ia*

ib*

ic*

Figure 22. Reference phase currents for RAMP speed input.

12


0 0.05 0.1 0.15 0.2 0.25 0.3

–50

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Act

ual P

hase

Cur

rent

s[A

]

ia

ib

ic

Figure 23. Actual phase currents for RAMP speed input.

0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2

–50

–40

–30

–20

–10

0

10

20

30

40

50

Time [s]

Act

ual

Ph

ase

Cu

rren

ts[A

]

iaia ib ic ib ic

Figure 24. Current phase reversal for RAMP speed input (expanded).

Unlike in the step input where the reference torque takes its minimum value at the instant of speed

reversal, thereby momentarily forcing the electromagnetic torque to a negative extreme, the torque-speed profile

during speed ramping as shown in Figure 25 is positive due to the gradual speed transition. Electromagnetic

torque and its reference are equal to the load torque at steady state.

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15

20

25

30

35

Time [s]

Torq

ues,

Te,T

ref a

nd T

l [N

.m]

TeTrefTl

Figure 25. Te , Tref , and load torque Tl for RAMP speed input.

8. Conclusion

This paper has successfully achieved a high performance HCC of a PMSM drive. The core advantage of vector

control by FOC has been used in this work to effectively convert the PMSM performance-wise into an equivalent

separately excited DC motor by decoupling the stator current into torque and flux, producing components for

independent control of torque and flux.

13


A complete closed-loop control system employing an outer PI speed controller and an inner hysteresis

current controller was implemented to realize this speed-controlled drive. Since torque can be made proportional

to current either in the stationary or rotor reference frames and effective control of current gives effective control

of torque, speed, and position, the HCC strategy has been used to ensure that the actual motor phase currents

tracked their respective sinusoidal references.

The HCC algorithm was developed and employed for the logical firing of the power semiconductor switches

of the inverter. Optimization of the control algorithm yielded very fast speed response under full load stress,

with the motor attaining a steady state at 0.01 s with minimal torque pulsation at steady state.

Effective tracking in current and torque was achieved, confirming that the control variables are optimal

for a wide range of PMSM ratings both for the step and ramp reference speed inputs.

References

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[4] Pillay P, Krishnan R. Control characteristics and speed controller design for a high performance permanent magnet

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magnets. Electr Eng Jpn 2014; 187: 42-50.

[8] Morimoto S, Ooi S, Inoue Y, Sanada M. Experimental evaluation of a rare-earth-free PMASynRM with ferrite

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14

http://dx.doi.org/10.1109/41.720325http://dx.doi.org/10.1109/41.720325http://dx.doi.org/10.1109/ICCCI.2012.6158897http://dx.doi.org/10.1109/ICCCI.2012.6158897http://dx.doi.org/10.1109/ICCCI.2012.6158897http://dx.doi.org/10.1109/28.25541http://dx.doi.org/10.1109/28.25541http://dx.doi.org/10.1109/63.53152http://dx.doi.org/10.1109/63.53152http://dx.doi.org/10.1109/TIA.2013.2294999http://dx.doi.org/10.1109/TIA.2013.2294999http://dx.doi.org/10.1002/eej.22362http://dx.doi.org/10.1002/eej.22362http://dx.doi.org/10.1109/TIE.2013.2289856http://dx.doi.org/10.1109/TIE.2013.2289856http://dx.doi.org/10.1049/iet-epa.2009.0022http://dx.doi.org/10.1049/iet-epa.2009.0022http://dx.doi.org/10.1109/TIE.2008.2007480http://dx.doi.org/10.1109/TIE.2008.2007480http://dx.doi.org/10.1109/TIE.2006.888802http://dx.doi.org/10.1109/TIE.2006.888802http://dx.doi.org/10.1109/63.641494http://dx.doi.org/10.1109/63.641494http://dx.doi.org/10.1109/TPEL.2002.807131http://dx.doi.org/10.1109/TPEL.2002.807131

IntroductionDynamic model of PMSMField orientation control (FOC) of PMSMSchematic of the speed-controlled drive systemMotor and control parametersHysteresis current control action and the inverter switchingDrive performance under various speed referencesStep reference speed input (1500 rpm to 3000 rpm to –1000 rpm)Ramp reference speed input (0 rpm to 500 rpm to –500 rpm to 0 rpm)

Conclusion

A high performance hysteresis current control of a ......torque control components of the stator...

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