A Hybrid Sliding Mode Torque Controller for Switched Reluctance Motor
Yong Cheng
School of Electrical and Control Engineering, Xi’an University of Science and Technology，Xi’an，China
([email protected])
Abstract - In the paper, a new closed loop system was
proposed for torque controlling, which was based on sliding
mode control (SMC) in switched reluctant motor(SRM).
Analyzing direct instantaneous torque control method and
SRM, SMC was introduced in control algorithm with
detailed derivations. Relative outgoing phase torque
compensation algorithm was proposed. Finally, simulation
results indicate this method is validity of eliminating torque
ripple in SRM.
Keywords - torque ripple, direct instantaneous torque
control (DITC), hybrid sliding mode control(HSMC), torque
compensation
I. INTRODUCTION
Switched reluctance motor (SRM) has simple
structure and strong robust. It was widely used in different
fields. However, doubly salient structure[1] has made
strong nonlinear and torque ripple, which has effect SRM
usage. In terms of torque, many scholars has designed
different strategies to minimize torque ripple from
different theory[2][3].So scholars proposed modified
structure of SRM to reduce torque ripple. Another method
was controlling strategy. Current control, switching angle
and intelligent control were used in torque ripple
reducing. But this method has made progress limitedly.
Sliding Mode controller was a useful theory in nonlinear
system, which has been made great progress in pass
years[4-9]. In this fields, SMC(sliding mode controlling)
had unique advantage. SMC has robust controlling, which
need not accurate arithmetic modeling of nonlinear
system. In the paper, a hybrid SMC(HSMC) was used on
torque ripple reducing, which has been proposed to reduce
torque ripple at different stages. Controlling system has
been set up with torque close loop with DITC(direct
instantaneous torque control). By this method, torque was
reduced obviously in final simulation.
II. ANALYSIS OF HSMC
1) Controlling strategy on DITC: DITC was
generally acknowledged and effective method of torque
control, which took feedback torque as control variety.
DITC was used different instantaneous voltage to control
output torque in plus torque output area. Here, HSMC
was introduced to reduce torque ripple at single phase and
commutation region, which composed of SMC and
compensate algorithm of commutation region as figure 1.
In figure 1, phase (K-1) and phase K meant outgoing
phase and incoming phase. In single conductive driving,
asymmetry half-bridge circuit was typical circuits, which
has three states +1,0 and -1. In single conductive module,
there were single phase and two phases working. In the
switching region Z1, phase C and phase B were incoming
phase and outgoing phase. In commutation region,
incoming phase will go into single phase working stage
.Outgoing stage will turn off, which has larger current. In
figure3, a turn-off strategy was proposed at commutation
region. For continuity of SMC, incoming phase will work
on independently in single phase. So, it took main role at
commutation region, which meant increasing output
torque. Outgoing phase will step into turn-off. For
reducing torque ripple, outgoing phase took main role at
decreasing output torque state, which will corporate with
incoming phase. Figure 3 showed controlling strategy of
T   ,system need increased output
outgoing phase. If err
T  ,
torque，at which outgoing turn on at +1 state. If err
system need decreased output torque, at which outgoing
  Terr   ，incoming phase can
turn off at -1 state. If
output enough torque ,which meant outgoing deceased
slowly at freewheeling state.
commutation region
Incoming phase
Tref +
T
Terr
SMC
outgoing phase Compensation
algorithm
SMC
-
sensor
Driving
circuit
SRM
Single phase region
T(i, )

sensor
i
Fig.1. structure of control scheme
L
Commutation region
A
B
C
D
Z1
 Con  Boff
Single phase region
A
 (°)
 Don Coff
Aon  Doff
 Bon Aoff
Fig.2. Relation of induction and position angle
Sk-1
1
0
-1

Terr
Fig.3. scheme of torque compensation
2) SMC: Consider the following dynamical system
as:
 x1  x2

 x2  f ( x)  b( x)u
(1)
where x  [ x1
x2 ]T is the state vector, u is the
system control input and f(x) and b(x) are nonlinear
functions. Now, consider a given desired
trajectory x1d (t ) and the error e(t )  x1 (t )  x1d (t ) . SM
control forces the system, after a reaching phase, to the
following sliding line:
s ( x)  e   e
between VDC and -VDC , voltage can be adjusted by duty
cycle of PWM.
However, equivalent control can easily produce
chatter close to boundary. So switching control was
selected by error , which was different value within error
bands or not to minimize chatter in SMC.
Terr

Terr  
 VDC

u
Terr  
sgn(T ) V
err
DC

(2)
where x2 d (t )  x1d (t ) and the sliding constant  is
strictly positive. At steady state the system follows the
desired trajectory once s=0. Hence, a suitable control
action is to be designed for the system to hit the sliding
surface (2). We select the Lyapunov function:
1
V  s2
(3)
2
with control making it meeting:
1 d 2
V
S 0
2 dt
According to high dynamic performance and direct
instantaneous torque control, switch function was defined
as:
S  Terr  Tref  T
(4)
(12)
III. SIMULATION RESULTS
In simulation, Matlab7.6.0 was used as simulating
software for SRM 8/6 research, at which turn-on and turnoff angles were set as 6° and 27°. For details of research,
waveform were focused on A, B and C phases. The
control system was designed with DITC structure[10]. So
sampling torque was derived from table of T ( , i) , in
which angle and current signal were captured from
simulating module in MATLAB.
4
Total
总 torque
转 矩
Torque
C 相 in
转phase
矩 C
Torque
A 相 in
转phase
矩 A
Torque
B 相in转phase
矩 B
3.5
3
转T矩/ N . m

di
 1
 d
(
) (u  iR 
)
(10)
dt
i
 dt
From functions above, there was：
T d T 1 
 d
ueq  (
)( ) (
)  iR 
(11)
 dt i
i
 dt
Equivalent voltage ueq were influenced by current
and derivation between flux , current and angle. In
controlling, saturation of voltage was VDC .If ueq was
2.5
2
1.5
1
Supposing
d
Tref  0 , there was：
dt
d
T (Tref  T )  0
dt
0.5
0
0.2
0.21
0.22
0.23
0.24
0.25
time间 / s
时
Fig.4. torque and current curve at refered torque changing
When speed was 600r/m , there was
    0.1N.m. So output torque has these waveforms as
figure below.
7.4
7.2
转矩
/N.m
T/N.m
where Terr was error of torque, Tref was reference
torque, T is feedback torque. And the control was:
u  U 0 sgn( S )
(5)
All u must meet :
1 d 2
S 0
(6)
2 dt
From equation (5), there was :
d

(7)
 dt (Tref  T )  (Tref  T )  0


7
6.8
(8)
6.6
0.4
0.42
0.44
0.46
0.48
0.5
时间/s
Time/s
0.52
0.54
0.56
0.58
0.6
Fig.5. torque curve at steady state under hybrid SMC
Torque was function with current and angle, so:
T i T 
T (i, ) 

i t  t
With prime voltage function , there was
(9)
7.4
转矩
/N.m
T/N.m
7.2
7
6.8
6.6
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
时间/s
Time/s
Fig.6. torque curve at steady state under switching type SMC
From figures above, HSMC can limit torque error
between error bands. HSMC has performed better than
switching SMC, because HSMC has designed algorithm
for output torque, especially in commutation region.
In results, there were two testing parts, which were
changing at desired torque changing and details of torque.
In first part, there was     0.05N.m, and desired
torque was changed from 3N.m to 1N.m. System has
perfect dynamic performance.
V. CONCLUSION
A new torque control base SMC was proposed in the
paper. With detailed derivation, HSMC was proposed,
which was also proved to be convergent and steady.
Simulating results showed HSMC were valid in SRD to
reduce torque ripple.
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