PWM-based Instantaneous Current Profile

Tracknig Control for Torque Ripple Suppression in

Switched Reluctance Servomotors

H.Makino, T.Kosaka and N.Matsui M.Hirayama and M.Ohto

Dept. of Computer Science and Engineering Corporate Research & Development Center
Nagoya Institute of Technology Yaskawa Electric Corporation
Nagoya, Japan Kitakyusyu, Japan
makino@motion.elcom.nitech.ac.jp

Abstract— This paper proposes instantaneous current profile This paper presents PWM-based tracking control of instan-
tracking control for minimizing torque ripple of switched reluc- taneous current profile for torque ripple suppression of the
tance motors. Because of its unique principle of torque genera- developed four-phase SR servomotor. In the proposed ap-
tion different from conventional AC motors, instantaneous cur- proach, the controller determines the instantaneous current
rent profiling control is essential to regulate the torque with profile for a given torque command and rotor position, which
ripple minimized. In addition, since its conventional motor mod- minimizes torque ripple. Then, the controller calculates the
el in order to determine an adequate applied voltage reference is instantaneous applied voltage command which is determined
established not yet, a hysteresis current regulator is generally based on the voltage equation derived from non-linear magne-
employed, in which it is rather difficult to design switching fre-
tizing curve model. To achieve fast current tracking response,
quency of converter. In the proposed scheme, the controller can
the proposed controller predicts the flux linkage at next sam-
calculate the adequate applied voltage reference which can de-
termined based on the voltage equation derived from non-linear ple point and calculates the reference voltage being applied at
magnetizing curve model. The applied voltage reference is rea- next sampling interval based on the predicted flux linkage.
lized under conventional subharmonic PWM with a carrier fre- The instantaneous applied voltage reference is realized under
quency of 12 KHz and fixed DC-voltage of 283V. The experi- conventional subharmonic PWM with carrier frequency of 12
mental results using 400W test motor with 8/6 poles configura- KHz and fixed DC-voltage of 283V. Experimental studies
tion verify that the measured instantaneous current profiles well using the developed four-phase test motor show that the
follow the reference profiles. measured current waveforms can accurately track the instan-
taneous reference current profiles.
I. INTRODUCTION
II. SPECIFICATIONS OF TEST MOTOR
With the development in manufacturing industry, the
amount of servomotors used has increased for last decade. Figs. 1 and 2 shows a cross sectional view and a photo-
The most of servomotors of the day are a permanent magnet graph of test motor. In Fig. 1, the red colored dotted line indi-
(PM) servomotor using rare-earth magnet such as NdFeB. As cates series-connected winding of A-phase as an example.
well-known, however, the use of rare-earth magnet is bringing The major dimensions and specifications of the test motor
with it the risks such as cost elevation and under supply. In appear in Table 1. As mentioned earlier, the test motor, four-
order to avoid the risks, the authors have been developing phase 8/6-pole SR motor, has been designed for 400W servo
switched reluctance (SR) servomotor with four-phase 8/6-pole drive applications [1]. To achieve both the high efficiency
configuration as an alternative of PM servomotor [1]. The SR and high torque density without rare-earth permanent magnet,
servomotor developed has been intentionally designed so as to a short airgap length with 0.1mm has been employed in this
be comparable with 400W PM servomotor using the rare-earth machine design. Fig. 3 demonstrates the measured maximum
magnets in terms of the maximum torque capability in short- torque curve of the test motor. The test machine barely meets
time duty and motor efficiency more than 85% under frequent for the 300% torque requirement in short-time duty up to a
operating condition while keeping same motor size and similar few seconds under the given maximum current limitation
power supply restrictions. Whereas, another indispensable with 8 Amps. From this result, it seems reasonable to suppose
issue for servomotor drive applications is minimizing its tor- that the 300% torque requirement must be not satisfied if tor-
que ripple. que ripple minimization is considered in design process. Ta-
ble 2 summarizes losses and efficiency measurement results

978-1-4673-1792-4/13/$31.00 ©2013 IEEE 1055

 A
80.0mm 5
9.1mm
A
43.7mm 4
B D
7.9mm

Torque [Nm]
3
C 54.1mm C 14mm 53.9mm
2

D B necessary maximum torque curve

1
A
measured maximum torque curve
68.8mm 0
A 0 1000 2000 3000 4000 5000
Figure 1 Sectional view of test motor.
Speed [r/min]

Figure 3 Measured maximum torque curve of test motor.

TABLE II. MEASURED LOSSES AND MOTOR EFFICIENCY

OF TEST MOTOR
Operating Copper Motor
Iron loss[W]
point loss[w] Efficiency[%]
1.27Nm
43.7 19.2 85.7
@3,000r/min
0.95Nm
31.6 16.6 86.9
@4,000r/min
0.76Nm
29.5 23.1 87
@5,000r/min

ia ~ d
θ∗ ω∗ T∗
APR ASR ATR SRM
Figure 2 External photograph of test motor.
θ ω va*~ d
TABLE I. DIMENSIONS AND SPECIFICATIONS OF TEST MOTOR s θ
Rated power [W] 400
Rated torque [N⋅m] 1.27
Rated speed [r/min] 3000 Figure 4 Block diagram of servo drive system.
Stator diameter [mm] 80
Stack length [mm] 40
iabcd Current Feedback
Shaft diameter [mm] 14
Air gap length [mm] 0.1 Torque Ripple
Grade of lamination steel 35H360
θ Minimizing
Current Swabcd
Regulator
Stator pole width [mm] 7.9 Control
Rotor pole width [mm] 9.1 B
A Sw i*
abcd

Stator pole height [mm] 7.35

Rotor pole height [mm] 5.1 ω0 ω T*
Stator yoke thickness [mm] 5.6
Rotor yoke thickness [mm] 14.85
A B High Swabcd
θo*， θc*，d*
Efficiency
No. of turns of windings [turn/pole] 185 ω
Winding resistance [Ω/phase] 5.2 θ Control Multi Pulse Drive

Fig. 5. Configuration of proposed adjustable torque regulator.

of the test motor at continuous rated operating points. The
test motor can achieve more than 85% of motor efficiency. tion regulator (ASR). In the ATR which is specially devel-
The motor efficiency of the designed SRM is as good as this oped, the proposed torque ripple minimizing control is em-
capacity of PM machine. ployed and works for only low speed range less than the thre-
shold speed ω0 which corresponds to 10% of the rated speed.
III. CONFIGURETION OF SERVO DRIVE SYSTEM It switches to high efficiency control through hysteresis com-
Figs. 4 and 5 show the block diagram of servo drive sys- parator with adequate speed band width when the speed ex-
tem and adjustable torque regulator (ATR), respectively. The ceeds ω0. From this point forward, the current profiling and
servo drive system has usual configuration and consists of the tracking control techniques employed in the proposed
ATR, adjustable speed regulator (ASR) and adjustable posi- ATR are explained.

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 IV. CURRENT PROFILING TECHNIQUE FOR TORQUE During the single phase excitation, only one phase generates
RIPPLE SUPPRESSION torque and the value of torque contour is stuck at 1. On the
other hand, in overlapping period, the shape of torque contour
A. Torque contour function
function between θ0 and θf0 is also a free parameter. Although
In order to achieve instantaneously flat torque, a control there are many possible choices of function to express the
approach based on instantaneous current profiling is well shape of torque contour function between θ0 and θf0, the fol-
known for SR motor drive. There are so many methods to lowing expression is employed in this study taking into ac-
create instantaneous current profile for each phase as a func-
count of reducing the maximum current and the necessary
tion of given rotor position, average torque reference and
applied voltage at the threshold speed.
motor speed [2]-[6]. Among them, a method to generate in-
stantaneous current profile via torque contour function [2] is
employed in this study. 1 ⎧⎪ ⎛⎜ θ − θ fo ⎞⎟ ⎫⎪
fTa (θ ) = ⎨cos π ⎟ + 1⎬ (4)
Fig. 6 depicts one possible selection of torque contour 2 ⎪⎩ ⎜⎝ θlap ⎠ ⎪⎭
function for a four-phase SR motor. The torque contour func-
tion fTx(θ) defines normalized generating torque profile in B. T-i-θ model based on the measured flux curve model
each phase as a function of rotor position and satisfies follow-
ing condition, In the proposed current profiling, torque-current-position
(T-i-θ) model is used. The process to build the T-i-θ model is
explained as following steps.
d

∑f Tx (θ ) = 1 (1) 1) The first step ― Modeling of the measured magnetizing

x=a
curves: Fig. 7 shows the measured magnetizing curves of A-
phase in test motor which is the relationship among the flux
where, the subscript x represents a name of phase. In Fig. 6,
linkage λ, the winding current i and the rotor position θ. The
θlap is an overlapping conduction period for consecutive two
magnetizing curve for every rotor position is modeled as a
phases. When a certain torque reference T* is given and in-
polynomial expression using the curve fitting and given in,
stantaneous torque can be generated properly according to
torque contour function, resultant total torque has no pulsa- nmax
tion and is given in, λ (i ) θ =θ = ∑ Ln θ =θ ⋅ i n . (5)
x x
n =1
d
Ttotal (θ ) = T * × ∑ fTx (θ ) =T * (2)
x =a
To model the magnetizing curves with enough accuracy, the
highest current order nmax is selected as 20. The correspond-
The torque contour function is designed by two main free ing spatial coefficient distribution of each current order is
parameters. One is θlap and the other is θf0 which is the start modeled by Discrete Fourier Transform (DFT) and given in,
angle of single phase excitation. Assuming the symmetric
kmax
motor construction, the phase deference between one phase Ln (θ ) = ∑ Lnk cos( kαθ ) . (6)
and the adjacent phase is 15deg and therefore, the other pa- k =0

rameters of the torque contour function, θ0, θfc and θc become

dependent parameters on θlap and θf0 as following manner. In (6), symbol “α” denotes the number of rotor poles and the
highest order of Fourier cosine series kmax is set to 9 consider-
θ 0 = θ f 0 − θlap , θ fc = θ0 − 15D ,θ c = θ f 0 − 15D (3) ing the sampling theorem. Consequently, the magnetizing
curves model λ-i-θ is obtained as a function of current and
rotor position as following fashion.

Rotor position (deg. )

fTaA(θ ) fTb (θ )
B CfTc (θ )
0.3 Aligned
Torque contour function

Flux linkage λ (Wb )

d
position
DfTd (θ ) ∑total
x=a
f (θ )
Tx
60deg
1.2 0.2
1 every 5/3deg
0.8
0.6
0.4 0.1 Unaligned
0.2 Position
0
0 θ o θ fo θ fc θ c 60
30deg
0
Rotor position (deg) θlap θlap 0 2 4 6 8

Figure 6 Torque contour function. Winding current (A)

Figure 7 Measured magnetizing curves of test motor.

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 nmax
Finally, a certain x-phase instantaneous current reference ix*
λ (i,θ ) = ∑ Ln (θ ) ⋅ i n (7) at the detected position θd can be calculated by substituting
n =1
computation result of (11) into (10) as in,
2) The second stage ― Calculating model of i-T-θ charac-
teristics from the magnetizing curves model: The magnetic mmax

co-energy can be calculated from the area surrounded by the ( ) ∑ K (θ ) ⋅τ

ix* τ x* (θ d ) , θ d = m d
*
x (θ d ) m (12)
m =1
magnetizing curve and current axis and is derived as,

i
D. Motoring and regenerating torque control
Wm ' = ∫ λ (i,θ )di (8)
0 The motoring and regenerating torque control of SR motor
is discussed in this section. The instantaneous current profiling
The instantaneous torque can be calculated from the rate of based on (12) generates motoring (positive) torque. Fig. 9 de-
change of the magnetic co-energy at constant current. picts A-phase instantaneous current profiles for motoring and
regenerating torque control. As can be seen in the figure, the
∂Wm '
relationship between two current profiles is symmetrical about
τ (i , θ ) = (9) the unaligned rotor position. Therefore, each-phase instanta-
∂θ i =const
neous current profile for regenerating torque control is calcu-
lated using the same coefficients for the motoring torque con-
Substituting (7) and (8) into (9), the model of T-θ-i characte- trol in (12) and given in,
ristic, the relationship among the torque T, the rotor position θ
and the current i of test motor, is obtained as shown in Fig. 8. mmax
Based on the model of T-θ-i characteristic, i-T-θ model is ob- ( )
ix* τ x* (θ d ) , θ d = ∑ K m ( 60 − θ d ) ⋅ τ x* (θ d )
m
(13)
tained as following expression. m =1

mmax
i (T ,θ ) = ∑K
m =1
m (θ ) ⋅ T m (10) V. CURRENT TRACKING CONTROL BASED ON PWM
A. Advantage of PWM based current tracking control
where, the coefficients Km(θ) are tabled and stored in memory The reference current profile i* with respect to a given
space for every 0.09 mech. degrees according to the position torque command T* and a detected rotor position θd for mini-
sensor resolution. In consideration of online processing time, mizing torque ripple is computed online based on i-T-θ model
the highest torque order mmax is set to 10 in this study. of the test motor. To make the actual instantaneous current
follow the reference current profile at a certain rotor position,
C. i-T-θ model based online computation of instatanoues one of well-known technique is the use of hysteresis current
current profile regulator. However, the hysteresis band control depends on a
For the given torque command T* and the detected posi- level of DC-bus voltage as well as switching frequency. For
tion θd, the instantaneous torque command τx*(θd) to be the purpose of current profile tracking control with the mini-
charged to a certain x-phase can be determined via the torque mum current ripple and delay, the proposed current control
contour function and given in, implements PWM based voltage control under fixed switching
frequency and DC-bus voltage. Fig. 10 illustrates the calcula-
tion and execution diagram of applied voltage with respect to
τ x* (θ d ) = T * × fTx (θ d ) (11) the sampling intervals under PWM control. Here, the all equa-
tions proposed in this section are executed the sampling inter-
val from “n” to “n+1”. Fig. 11 shows the block diagram of

6.0
Torque (Nm)

i =8.1 A 9
5.0
Motoring
4.0 6 Regenerating
Idealized inductance
3.0
every 0.3 A
Current (A)

3
2.0
1.0 0
0.0 i =0.0 A

30 35 40 45 50 55 60 -3
Rotor position (deg. ) 0 10 20 30 40 50 60
Rotor position (deg)
Figure 8 T-θ-i characteristics calculated from the measured magnetizing
curves model of test motor. Figure 9 Instantaneous current profiles at motoring and regenerating con-
trol

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proposed current regulator. Symbol “x” denotes again the computation, the controller only calculates (7) on the condi-
name of phase. Based on the torque contour function, x-phase tion that the highest current order is limited by 4. This num-
torque reference is determined from the total reference torque ber is selected by trial and error taking modeling error and
T*[n+2] and the estimated rotor position θest[n+2] and given in, memory capacity into consideration. As s result, the flux lin-
kage at the sampling point “n” is calculated as a function of
the detected phase current i[n] and the detected rotor position
τ x*[n + 2] = T *[n + 2] × fTx (θest [n + 2]) (14)
θ[n] as given in,
where, the reason for description “n+2” is that the reference is ML
achieved at the sampling point “n+2”. The estimated rotor λx [n] = ∑ Lm (θ d [n]) ⋅ ix [n]m . (19)
position θest[n+2] is calculated by extrapolation using the m =1

detected velocity “ω[n]” and the sampling interval TS as fol-

lowing manner. Secondly, the controller calculates the flux linkage at the
sampling point “n+1”. Another expression to calculate the
flux linkage is well-known and given in,
θ est [ n + 2] = θ d [ n] + 2ω[ n]Ts (16)
*
ix [n + 1] + ix [n]
From (12), the current reference is calculated as, λx [n + 1] = λx [n] + (vx*[n] − R )Ts (20)
2

(
ix*[n + 2] = ix* τ x*[n + 2],θ est [n + 2] . ) (17) The change of flux linkage between “n” and “n+1” is esti-
mated by the voltage reference vx*[n].
Thirdly, the controller computes the voltage reference be-
A certain phase of the applied voltage equation of SR mo-
tween the sampling interval “n+1” and “n+2”. Using (19),
tor in the discrete from is expressed as,
the reference of flux linkage at the sampling point “n+2” is
given in,
* * *
* ix [n + 2] + ix [n + 1] λx [n + 2] − λx [n + 1]
vx [n + 1] = R + (18) ML
2 TS λx*[n + 2] = ∑ Lm (θ est [n + 2]) ⋅ ix*[n + 2]m . (21)
m =1

According to the above equation, the controller needs to es-

timate the change of flux linkage between “n+1” and “n+2” By substituting (20) and (21) into (18), finally, we can obtain
in order to calculate the necessary voltage. To achieve the the applied voltage reference vx*[n+1] during the sampling
calculation, firstly, the controller computes the flux linkage at interval from “n” to “n+1”.
the sampling point “n”. Online computations based on (6) and
(7) require a lot of time. To suppress the computation time, VI. EXPERIMENTAL RESULTS
we calculated (6) off-line and stored the resultant distribution A. Experimental setup
of coefficients in memory every 0.09 deg. As the on-line Fig.12 shows the configuration of experimental setup. The
position sensor attached is an incremental encoder of
1,000ppr. PE-Expert III employing DSP executes all pro-
Calculation Execution ix*[n + 2] posed control algorithm and generates PWM gate signals to
the converter for test motor. Rectifying three-phase AC 200V
input, DC-bus voltage is supplied to the drive circuit. A servo
motor is connected with test motor as load machine with
v *x = v *x [n + 1]

Figure 10 Calculation and execution timings of applied voltage. Test motor

Proposed
Z −1 v *x [n + 1] i x [ n + 1] i x [n]
+ R + −1 drive
SRM Z
+ 2 + circuit
ix*[n + 2] −1
v x** [ n] Z i x [ n − 1]
Z −1
+ − R + +
Vdc = 283[V ] Encoder
1 / Ts
2 Gate signals 1000ppr

Δλ x [ n] Ts DSP Controller PE-Expert III

λ*x [n + 2]
+ − + + λ x [n]
λ (i, θ ) λ (i, θ )
λˆx [n + 1]
θ est [ n + 2] θ [n] Ref. Torque T*

Figure 11 Block diagram of applied voltage reference computation. Figure 12 Experimental system.

1059
speed control. Subharmonic PWM is used, in which the ca-
5
reer frequency is set to 12 kHz. The sampling frequency of
4 Reference A-phase
the proposed controller is also 12 kHz.
3 B-phase C-phase
B. Measured instantaneous current profile 2 D-phase

Current (A)
1
Fig. 13 demonstrates comparisons between the reference
0
and the measured current profiles under the proposed control.
In the figure, the operating conditions are set to (a) motoring, -1

(b) regenerating and (c) step change motoring to regenerating -2

with the rated torque of 1.27 N⋅m under the threshold speed -3

300 r/min. It can be seen from the figure that the measured -4

current waveforms are in phase with the reference current -5

5ms/div
profiles on all conditions. It is verified that the proposed cur- (a) Motoring
rent controller achieves accurate and fast instantaneous cur-
rent tracking response. 5
4 Reference A-phase
VII. CONCLUSION 3 B-phase C-phase
This paper has presented PWM-based instantaneous cur- 2 D-phase
rent profile tracking control for torque ripple minimization of Current (A)
1
SR servomotor. The proposed current regulator calculates the 0
necessary applied voltage based on the voltage equation with -1
feed-forward of the flux linkage to compensate the PWM -2
delay. Experimental results have verified that the proposed -3
current regulator has worked effectively to track the instanta- -4
neous current profiles. -5
5ms/div
REFERENCES (b) Regenerating
[1] T. Kosaka, A. Kume, T. Shikayama and N. Mtasui: “Development of
5
High Torque Density and Efficiency Switched Reluctance Motor with
0.1mm Short airgap”, Proc. of 12th European Conference on Power 4
Electronics and Applications (EPE2007), No.834, 2007. 3
[2] I. Husain and M. Ehsani: “Torque Ripple Minimization in Switched 2
Reluctance Motor Drives by PWM Current Control”, IEEE Trans. on
Current (A)

1
PE, Vol.11, No.1, Jan/Feb, 1996.
[3] S. Mir, M. E. Elbuluk and I. Husain: “Torque-Ripple Mi-nimization in 0
Switched Reluctance Motors Using Adaptive Fuzzy Control”, IEEE -1
Trans. on IA, Vol.35, No.2, pp.461- 468, Mar/Apr, 1999. -2 Reference A-phase
[4] N. J. Nagel and R. D. Lorenz: “Rotating Vector Methods for Smooth -3 B-phase C-phase
Torque Control of a Switched Reluctance Motor Drive”, IEEE Trans.
-4 D-phase
on IA, Vol.36, No.2, pp.540-548, Mar/Apr, 2000.
[5] K. M Rahman, S. Gopalakrishnan, B. Fahimi, A. V. Raja-rathnam and -5
5ms/div
M. Ehasani: “Optimized Torque Control of Switched Reluctance Motor
at all Operational Regimes Us-ing Neural Network”, IEEE Trans. on (c) Step change from motoring to regenerating
IA, Vol.37, No.3, pp.904-913, May/June, 2001.
[6] Z. Lin, D. S. Reay, B. W. Williams and X. He: “Torque Ripple Reduc- Figure 13 Comparisons between the reference and the measured current
tion in Switched Reluctance Motor Drives Using B-Spline Neural profiles under the proposed control.
Networks”, IEEE Trans. on IA, Vol.42, No.6, pp.1445-1453, Nov/Dec,
2006.

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