chapter 5 speed control of switched reluctance...
TRANSCRIPT
57
CHAPTER 5
SPEED CONTROL OF SWITCHED
RELUCTANCE MOTOR
The work presented in this chapter performs a comparison between
four types of controllers, namely fuzzy logic controller, fuzzy PI controller,
Particle Swarm Optimization (PSO) based tuning of Fuzzy PI controller and
the proposed hybrid PSODE based tuning of fuzzy PI controller, to control
the speed of three phase Switched Reluctance Motor (SRM). The main
objective is to obtain better performance of the system in stability, without
overshoot and minimum settling time in system response under the sudden
changes in speed of the motor. The performance comparison of all the
controllers is done based on their applicability, adaptability, simplicity and
controllability. The system is simulated using Matlab/ Simulink GUI
environment. In addition, an FPGA based hardware setup is also developed to
implement the above controllers for the speed control of SRM motor, shown
in Figure A 2.25. The results of the simulation and experimental setup are
discussed. Stability of the controllers is also discussed.
5.1 INTRODUCTION
The age of SRM is more than hundred and fifty years, but the
demand for SRM is increased only last few decades due to the tremendous
development in power electronic devices. The necessary requirements for
variable speed drives are achieved by modern power electronic components.
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In electrical drive market, SRM gets popularity due to low manufacturing cost
and reliable operation.
5.2 CONSTRUCTION AND OPERATION OF SRM
In switched reluctance motor, only the stator has windings and rotor
is constructed by steel lamination as poles. The rotor does not have any
conductor or permanent magnets. Based on this simple construction, the cost
of SRM is decreased and it can run at very high speeds due to absence of
conductor or magnet on the rotor. Laminated steel with excellent magnetic
permeability is used to construct the stator and rotor poles. Number of stator
poles should be greater than rotor poles to obtain the high starting torque.
Various configuration of SRM can be realized by various numbers of stator
poles, rotor poles and number of phases.
The operation of switched reluctance motor is based on very simple
concept. Torque on the rotor of switched reluctance motor is created by
variable reluctance in the air gap between rotor and stator. If the stator is
powered, reluctance torque is produced on the rotor towards minimum
reluctance. Variation in reluctance of the stator flux path to rotor depends on
the rotor position. For the clockwise rotation, the stator phases are excited
anti-clockwise with proper sequence. Flux density of SRM is higher at
aligned position due to low magnetic reluctance and low at unaligned position
due to higher magnetic reluctance. Switched reluctance motor can be
characterized by f
current. By increasing the stator phases, the torque ripples get reduced, but the
cost of the power electronics components will be highly increased. Similar to
other motors, the torque of SRM is limited by maximum allowed current and
the speed is limited by supply voltage.
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5.3 MATHEMATICAL MODEL OF SRM
Three sets of expressions are needed to obtain the mathematical
model of SRM, namely mechanical equation, electrical equation and angular
speed equation.
The mechanical equation describes the motion of the motor as,
e Ld 1 T B Tdt J
(5.1)
where,
Te - Torque developed by the motor
TL - Load torque
J - Moment of inertia
B - Damping or friction co-efficient
- Angular speed of motor
The electrical equations describes the electrical behavior of SRM,
given below
m
e ejj 1
T T (5.2)
Tej - Torque generated by the jth phase
ji
ej j0
T di (5.3)
where,
- Flux linkages
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The rotor position with respect to jth phase is described by,
j r2 ( j 1)N
m(5.4)
Nr- Number of rotor pole
m - Total phase numbers
- Rotor position with respect to starting Position
j - Rotor position with respect to the jth phase
5.4 BLOCK DIAGRAM FOR SPEED CONTROL OF SRM
The position of the rotor is sensed by the rotor sensor and converted
in terms of speed by its derivative. This output speed of the motor is
compared with the given reference speed of the motor. The error in speed and
change in speed error are given as the input to the controllers. The output
current of the controller is given as reference input to the current controller.
The function of current controller is to compare the actual current and
reference current from the controller and give the firing pulse to the converter.
The input voltage of the motor is controlled by the firing angle of converter.
Figure 5.1 Block Diagram for Speed control of SRM
-
r + Fuzzy/Fuzzy PI
i HysteresisCurrentController
ConverterTriggeringCircuit
d/dt
Ia,ib,ic
SRM
PSO / PSODE
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5.5 WORK CARRIED OUT ON SRM
All the four controllers developed in this research are implemented
to control the speed of switched reluctance motor. The step-by-step procedure
for speed control of SRM is performed by following the steps discussed in
section 4.5 of this thesis. The SRM is fed by a three-phase asymmetrical
power converter having three legs, each of which consists of two IGBTs and
two free-wheeling diodes. The phase currents are independently controlled by
three hysteresis current controllers which generate the IGBTs drive signals by
comparing the measured currents with the references. The IGBTs switching
frequency is mainly determined by the hysteresis controllers. The output of
the FLC is the current, which is obtained from tuning of the membership
functions of the FLC by PSO and PSODE algorithms. The output of the FLC
is given to the hysteresis current controllers to generate the gate pulse and to
obtain the desired speed of the motor under various conditions.
5.6 ANALYZING THE PERFORMANCE OF CONTROLLERS
UNDER THE VARIOUS CONSTRAINTS
5.6.1 Varying Speed at No Load Conditions
In this section, the speed control of the SRM under the speed
variation with no load condition is described to analyze the system
performance of all the controllers. The response due to sudden change of
reference speed is illustrated in the graphs shown in Figures 5.2 and 5.3 for
various controllers. Performance analysis of the controllers due to sudden
change of speed reference is summarized in Table 5.1.
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Figure 5.2 Change in Speed under No-load Condition for Fuzzy and Fuzzy PI Controllers
Figure 5.3 Change in Speed under No-load Condition for PSO Fuzzy PI and PSODE Fuzzy PI Controllers
Time (sec)
Time (sec)
Spee
d (r
ads/s
ec)
Fuzzy
Fuzzy PI
Spee
d (r
ads/s
ec)
PSODE Fuzzy PI
PSO Fuzzy PI
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Table 5.1 Performance Analysis of SRM for Sudden Change in Speed at No Load Condition
No load condition Fuzzy Fuzzy PIPSO
Fuzzy PIPSO DEFuzzy PI
At ref speed 120 rads/sec
OS( %) - - - -
ts (sec) 0.042 0.024 0.024 0.020
Speed increased to 200 rads/sec
OS( %) - - - -
ts (sec) 0.028 0.022 0.016 0.010
Initially, this research focuses on the performance of the all the
controllers with no load condition at reference speed 120 rads/sec. From the
verification, the settling time of fuzzy logic controller is 0.042 seconds, the
fuzzy PI controller is 0.024 seconds, PSO based fuzzy PI controller is
0.024 seconds and PSODE based fuzzy PI controller is 0.020 seconds. When
the speed is increased to 200 rads/sec, the settling time of fuzzy logic
controller is 0.028 seconds, the fuzzy PI controller is 0.022 seconds, PSO
based fuzzy PI controller is 0.016 seconds and PSODE based fuzzy PI
controller is 0.010 seconds. From the above comparison, it is proved that
proposed PSODE based fuzzy PI controller performs better when compared to
the other controllers.
5.6.2 Varying Speed at Constant Load
To verify the validity of the proposed PSODE optimized fuzzy PI
controller, a sudden change in the reference speed at constant load is
introduced. From the response, the performances of the controllers are
summarized in Table 5.2 based on speed response parameters plotted in
Figures 5.4 and 5.5.
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Figure 5.4 Change in Speed with Constant Load for Fuzzy and Fuzzy PI Controllers
Figure 5.5 Change in Speed with Constant load for PSO Fuzzy PI and PSODE Fuzzy PI Controllers
Time (sec)
Time (sec)
Spee
d (r
ads/s
ec)
Fuzzy
Fuzzy PI
Spee
d (r
ads/s
ec)
PSODE Fuzzy PI
PSO Fuzzy PI
65
Table 5.2 Performance Analysis of SRM for Sudden Change in Speed at Load Condition
At load condition Fuzzy Fuzzy PIPSO
Fuzzy PIPSO DEFuzzy PI
At ref speed 120 rads/sec
OS( %) - - - -ts (sec) 0.046 0.024 0.024 0.022
Speed increased to 200 rads/sec
OS( %) - - - -ts (sec) 0.026 0.02 0.016 0.012
From this investigation, the settling time of fuzzy logic controller is
0.046 seconds, the fuzzy PI controller is 0.024 seconds, PSO based fuzzy
PI controller is 0.024 seconds and PSODE based fuzzy PI controller is
0.022 seconds. When the speed is increased to 200 RPM, the settling time of
fuzzy logic controller is 0.026 seconds, the fuzzy PI controller is
0.02 seconds, PSO based fuzzy PI controller is 0.016 seconds and PSODE based
fuzzy PI controller is 0.012 seconds. From the above verification and comparison,
it is proved that the proposed PSODE based optimized Fuzzy PI controller
gives better performance in settling time when compared to the other controllers.
5.6.3 Varying Load at Constant Speed
In this criterion, a sudden disturbance is introduced in the load at
constant speed and then load is released. The speed of the motor is maintained
constant at this condition and the load is varied. Initially, no load is applied to
the motor. Hence, the motor attains the reference speed and remains same in
that speed. Obviously, when the load increases, the speed decreases. This
condition is obtained when the load is applied to the motor. Thus the decrease
in speed is indicated in Figures 5.6 and 5.7, when the load is changed from no
load to loaded condition and return to reference speed when load is released.
Based on the speed response, the results are summarized in Table 5.3.
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Figure 5.6 Change in Load with Constant Speed for Fuzzy and Fuzzy PI Controllers
Figure 5.7 Change in Load with Constant Speed for PSO Fuzzy PI and PSODE Fuzzy PI Controllers
Time (sec)
Time (sec)
Spee
d (r
ads/s
ec)
Fuzzy
Fuzzy PI
Spee
d (r
ads/s
ec)
PSODE Fuzzy PI
PSO Fuzzy PI
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Table 5.3 Performance Analysis of SRM for Sudden Change in Load with Constant Speed
At reference speed 120 rads/sec
Fuzzy Fuzzy PI PSO Fuzzy PI
PSO DE Fuzzy PI
At load
applied
OS (%) - - - -
ts (s) 0.012 0.01 0.01 0.01
At load released
OS (%) - - - -
ts (s) 0.012 0.01 0.01 0.01
From the above tabulation, in this criterion, the settling time of the
speed response of SRM for all the controllers is close to 0.01, while applying
the load and releasing the load. Speed of the SRM drops from the reference
speed when applying the load and attains the reference speed when the load is
released. In both the cases, settling time of speed response is 0.01 seconds in
all the controllers.
5.6.4 Varying Speed and Load Simultaneously
In this condition, simultaneous changes in both load and speed are
executed. Here, the motor with reference speed 1 and no load condition is
applied. This resembles first condition of the system. When the system
attains a steady state, the speed of the motor is changed along with the load.
Even though the speed of the motor is changed, there will be slight decrease
in speed due to increase in load.
Performance analysis of the simulation for this investigation is
summarized in Table 5.4, based on the speed response graph of the motor,
shown in Figures 5.8 and 5.9.
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Figure 5.8 Change in Speed and Load for Fuzzy and Fuzzy PI Controllers
Figure 5.9 Change in Speed and Load for PSO Fuzzy PI and PSODE Fuzzy PI Controllers
Time (sec)
Time (sec)
Spee
d (r
ads/s
ec)
Fuzzy
Fuzzy PI
Spee
d (r
ads/s
ec)
PSODE Fuzzy PI
PSO Fuzzy PI
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Table 5.4 Performance Analysis of SRM for Changes in Speed and Load Simultaneously
Fuzzy Fuzzy PI PSO Fuzzy PI
PSO DEFuzzy PI
Suddenchange 1
OS( %) - - - -
ts (sec) 0.044 0.024 0.024 0.020
Suddenchange 2
OS( %) - - - -
ts (sec) 0.03 0.02 0.018 0.015
Under the sudden change one, settling time of speed response is
0.044 seconds with FLC, 0.024 seconds with fuzzy PI, 0.024 seconds with
PSO Fuzzy PI and 0.020 seconds with PSODE fuzzy PI.
Under the sudden change two, settling time of speed response is
0.03 seconds with FLC, 0.02 seconds with fuzzy PI, 0.018 seconds with PSO
Fuzzy PI and 0.015 seconds with PSODE fuzzy PI. From the performance
comparison of the controllers, the PSODE gives better results compared to the
other controllers.
5.7 MOTOR PARAMETERS
Stator resistance (R) - 0.05 Ohms
Movement of inertia (J) - 0.05 kg-m2
Friction Co-efficient (B) - 0.02 N-M-S
Number of stator poles (Ns) - 6
Number of rotor poles (Nr) - 4
70T
able
5.5
Com
para
tive
Ana
lysis
of s
ettli
ng ti
me
(in se
cond
s) o
f all
the
cont
rolle
rs u
nder
all
four
con
ditio
ns fo
r sp
eed
cont
rol o
f SR
mot
or
S–
Sim
ulat
ion
H–
Har
dwar
e
Con
ditio
nsPI
Fuzz
yFu
zzy
PIPS
OFu
zzy
PIPS
O D
EFu
zzy
PIS
HS
HS
HS
HS
H
Cha
nge
inSp
eed
unde
r No
Load
500
Rpm
to
1000
Rpm
1.
21.
81.
11.
610.
81.
20.
650.
80.
460.
72
1000
Rpm
to
2000
Rpm
1.
21.
91.
11.
60.
80.
80.
60.
80.
50.
72
Cha
nge
inSp
eed
unde
r C
onsta
nt L
oad
500
Rpm
to
1000
Rpm
1.
42
1.3
1.63
0.9
11
0.72
0.5
0.61
1000
Rpm
to
2000
Rpm
1.
412.
11.
21.
851
10.
650.
720.
50.
64
Cha
nge
in L
oad
unde
r Con
stan
t Sp
eed
At l
oad
appl
ied
1.4
21.
391
0.9
0.86
1.1
0.52
0.61
0.3
At l
oad
rele
ased
0.5
2.2
1.38
10.
30.
860.
60.
520.
050.
3
Cha
nge
in b
oth
Spee
d an
d Lo
ad
Sim
ulta
neou
sly
Sudd
enC
hang
e 1
1.2
21.
11.
30.
821
0.63
0.74
0.46
0.58
Sudd
enC
hang
e 2
0.9
21.
011.
30.
90.
80.
630.
740.
460.
58
71
5.8 WORK CARRIED OUT ON SR MOTOR WITH MODIFIED
PARAMETERS
All the work mentioned in the section 5.5 is carried out in both
simulation and experimental setup for the system with new parameters, given
below:
Stator resistance (R) - 2.4 Ohms
Movement of inertia (J) - 0.0013 kg-m2
Friction Co-efficient (B) - 0.0183 N-M-S
Number of stator poles (Ns) - 6
Number of rotor poles (Nr) - 4
Maximum inductance - 40mH
Maximum inductance - 7mH
The performance of the controllers under the various operating
conditions for the speed control of SR motor is tabulated in Table 5.5, based
on the simulation and experimental setup results, shown in Figures A 2.1 to A
2.20 of Appendix 2 (x-axis represents Time in seconds, y-axis represents
Speed in rpm). Channel 1 represents reference speed and Channel 2 represents
actual speed.
From the observation, the proposed PSODE fuzzy PI controller
gives better settling time at all the operating conditions than all other
controllers in both simulation and hardware results.
5.8.1 Stability Analysis
The stability analysis is performed as follows for the SR motor. The
settling time and peak time of the all the responses are obtained for all the
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controllers under the four conditions. From the settling time and the peak
time, the damping ratio and natural frequency of the system are calculated.
From the values of damping ratio and natural frequency, the transfer function
and the poles of the response are derived. With the help of the location poles,
the stability of the system is obtained by using the root locus method. From
the observations and calculations, the system is stable for all the conditions
mentioned in this chapter for all the controllers. These observations are
verified by taking the criteria of varying speed with constant load as example
for stability analysis. The settling time and peak time of the response of all the
controllers are tabulated in Table 5.6. With help of this, the values of natural
frequency and damping ratio are derived. By using the second order standard
formulae, the transfer function of the system is derived the stability of the
system is analyzed by root locus method.
Table 5.6 Stability Analysis of controllers for the speed control of SRMotor under varying speed at constant load
S.No. Controllers
Settlingtime in seconds
Peaktime in seconds
Naturalfrequency
n
DampingRatio Transfer Function Stability
Analysis
1 Fuzzy 1.63 1.63 2.7 0.939.78.4
39.72 ss
Stable
2 Fuzzy PI 1 1 5.08 0.7885.258
85.252 ss
Stable
3 PSO FuzzyPI 0.72 0.72 7.06 0.79
501150
2 ssStable
4 PSODEFuzzy PI 0.61 0.61 8.34 0.79
5.6912.135.69
2 ssStable
73
34.879.0
13.555.613.555.6
13.555.61
13.561.0
1
55.661.044
sec61.0sec61.0
2
1
2
2
n
nn
pn
sn
p
s
jsjs
jpolesjpoles
T
T
sTsT
5.8.2 Sample Calculations
(5.5)
(5.6)
(5.7)
Transfer function of the system at this instant is 5.6912.13
5.692 ss
From the above calculation, the two poles of the system are derived
from the settling time and peak time. It is observed that the system is stable at
this instant because two poles of the system are located in left half of the S
Plane. The graphs obtained for the transfer functions to analyze the stability
are displayed in Figures A 2.21 to A 2.24 of Appendix 2.
5.8.3 Operating Range
All the controllers performed smoothly for all the ranges of speed
within the rated speed. For all the ranges of load, the speed of the motor can
be controlled effectively without overshoot, by all the controllers. The range
of settling time is differed based on the algorithms. The settling times of the
controllers are already compared and the values are illustrated in the Table
5.5.
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If the gain value in the transfer function is equal to one, the system
is stable. While increasing the gain value from 1 to 10, the system is stable
with small oscillatory response. While increasing the gain value from 11 to
15, the system becomes oscillatory, but finally settles down. Thus the stability
of the system is decreased. While further increasing the gain value above 15,
the system’s state becomes unstable from stable.
All the four controllers developed and reported in this thesis have
good adaptability and strong robustness than the conventional PI controller.
5.9 CONCLUSION
A PSODE-based fuzzy PI controller for the speed controller system
has been successfully developed to control the speed of a SR motor. Also,
FPGA based experimental setup has been developed to control the speed of
the motor. A comparative analysis of the simulation and hardware results has
been done for the fuzzy, fuzzy PI, PSO fuzzy PI, PSODE fuzzy PI and
conventional PI controller. It has been found that the speed regulation by the
proposed PSODE-Fuzzy PI controller is superior to the other controllers.