chapter 7 design and simulation of an anfis controller...
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CHAPTER 7
DESIGN AND SIMULATION OF AN ANFIS CONTROLLER
BASED DRIVE SYSTEM
This chapter presents the modeling and simulation of an adaptive
neuro-fuzzy inference strategy (ANFIS) to control one of the most
important parameters of the induction machine, viz., speed. IM’s are
non-linear machines having a complex and time-varying dynamics.
Some of the states are inaccessible during the operational stages and
also many of the states are not available for measurements; hence, it
is essential to design state observers.
The control of IMs is thus a challenging problem to be taken up in
the industries, especially in the control of speed in paper mills, etc.
Various advanced control techniques have been devised by various
researchers across the world, with some of them being based on
hybrid techniques. Some of them have already been explained in the
previous chapters.
These fuzzy-based controllers develop a control signal that yields
on the firing of the rule base, which is written on the previous
experiences, which is random in nature. Thus, the outcome of the
controller is also random and optimal results may not be obtained.
Selection of the proper membership functions and in turn selecting
the right rule base depending on the situation can be achieved by the
use of an ANFIS controller, which becomes an integrated method of
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approach for control purposes and yields excellent results, which is
the highlight of this chapter. In the designed ANFIS scheme, neural
network techniques are used to select a proper rule base, which is
achieved using the back-propagation algorithm. This integrated
approach improves the designed controller’s performance in many
ways in terms of cost-effectiveness and reliability.
The simulation results presented at the end of this chapter prove
that if the designed control is more effective, it has faster response
times or settling times. The sudden fluctuation or change in speed
and its effect on the various parameters of the dynamic system are
also considered further in this chapter. The designed controller not
only takes care of the sudden perturbations in speed, but also brings
back the parameters to the reference or the set value in a few
milliseconds, thus exhibiting the robustness in behavior. In other
words, the designed controller is robust to parametric variations. A
reasonable accuracy in the speed-control characteristics of the IM
could be observed using this robust control scheme.
7.1 INTRODUCTION
Artificial intelligence, ANN, Fuzzy Logic, hybrid networks, etc. have
been recognized as main tools to improve the performance of power
electronics-based drives in the industrial sectors. Currently, the
combination of this intelligent control with adaptiveness appears as
the most promising research area in the practical implementation and
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control of electrical drives [77]. A review of the research carried out by
various researchers [52]-[65] regarding the ANFIS control of AC
machines was discussed briefly in Chapter 2. The responses (speed)
had taken a long time to reach the set value. In the research work
presented in this chapter, an attempt is made to reduce the settling
time of the responses (speed) and make the response very fast by
designing an efficient controller using a hybrid type of ANFIS-based
control strategy taking into account some of the parameters
mentioned in the above papers.
An intelligently developed back-propagation algorithm could be
used for NN training for the proper selection of the rule base. Here, we
have formulated this complex control strategy for the speed control of
IM, which yielded excellent result compared to the other methods
mentioned in the literature survey.
7.2 ANFIS CONCEPT
ANN has strong learning capabilities at the numerical level. Fuzzy
logic has a good capability of interpretability and can also integrate
expert's knowledge. The hybridization of both paradigms yields the
capabilities of learning, good interpretation and incorporating prior
knowledge. ANN can be used to learn the membership values for fuzzy
systems, to construct IF-THEN rules, or to construct decision logic.
The true scheme of the two paradigms is a hybrid neural/fuzzy
system, which captures the merits of both the systems [89].
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This concept is made use of in developing the ANFIS controller in
this chapter. A neuro-fuzzy system has a neural-network architecture
constructed from fuzzy reasoning. Structured knowledge is codified as
fuzzy rules, while the adapting and learning capabilities of neural
networks are retained. Expert knowledge can increase learning speed
and estimation accuracy.
Fuzzy logic is one of the most successful applications in the control
engineering field, which can be used to control various parameters of
real-time systems. This logic combined with neural networks yields
very significant results. This merged technique of the learning power
of the NNs with the knowledge representation of FL has created a new
hybrid technique, called neuro-fuzzy networks [62]. This technique
gives a fairly good estimate of the speed and is robust to parameter
variation [58].
7.2.1 The ANFIS Model
The architecture of the ANFIS model is a graphical representation
of the TS-FLC model. The general ANFIS control structure for the
control of any plant is presented in this section [63], [57]. The
functions of the various layers are given in the form of an algorithm as
described below. The structure contains the same components as .fis,
except for the NN block. The network structure is composed of a set of
units arranged into 5 interconnected network layers, viz., l1 to l5 as
shown in Fig. 7.5.
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Layer 1: This layer consists of input variables (membership
functions), viz., input 1 and input 2. Here, triangular or bell-shaped
MF can be used. This layer supplies the input values to the next layer,
where i=1 to n. In other words, layer 1 is the input layer with n nodes.
Layer 2: This layer (membership layer) checks the weights of each MF.
It receives the input values xi from the 1st layer and acts as MFs to
represent the fuzzy sets of the respective input variables.
Furthermore, it computes the membership values that specify the
degree to which the input value xi belongs to the fuzzy set, which acts
as the inputs to the next layer. Note that layer 2 has nK nodes, each
outputting the MF value of the ith antecedent of the jth rule given by
yij(2)=µAj
i x(i), where A is a matrix defining a partition of the space xi
and µAji(x(i)) is typically selected as a generalized bell MF defined by
the equation: µAji(x(i))= µ(xi,cj
i,aji,bj
i). Note that the parameters cji,aj
i,bji
in the above equation are referred to as the premise parameters.
Layer 3: This layer performs the pre-condition matching of the fuzzy
rules, i.e., they compute the activation level of each rule, the number
of layers being equal to the number of fuzzy rules. Each node of these
layers calculates the weights that are normalized. Layer 3 has K fuzzy
neurons with the product t-norm as the aggregation operator. Each
node corresponds to a rule and the output of the jth neuron
determines the degree of the fulfillment of the jth rule given by
)(1
)3(
i
i
j
n
ij xAy for j=1,………, K.
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Layer 4: This layer provides the output values y, resulting from the
inference of rules. Connections between the layers l3 and l4 are
weighted by the fuzzy singletons that represent another set of
parameters for the neuro-fuzzy network. Each neuron in layer 4
performs the normalization, and the outputs are called normalized
firing strengths, which are given by
(3)
(4)
(3)
1
j
j K
k
k
yy
y
for j=1,…..,K. (7.1)
Layer 5: This layer is called the output layer, which sums up all the
inputs coming from layer 4 and transforms the fuzzy classification
results into a crisp (binary). The output of each node in the layer can
be defined by )()4()5( xfyy jjj for j=1,……,K, where )(Xf j is given for the
jth node in layer 5. The outputs of layer 5 are summed up and the final
output of the network can be re-written as
K
j jj yy1
)4()5( . The ANFIS
structure is tuned automatically by least-square-estimation and the
back-propagation algorithm [89]. The algorithm shown above is used
in the next section to develop the ANFIS controller to control the
various parameters of the IM.
Learning of the ANFIS Model: In the ANFIS model, functions used at
all the nodes are differentiable; thus the BP algorithm can be used to
train the network. Each MF μAij is specified by a pre-defined shape
and its corresponding shape parameters. The shape parameters are
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adjusted by a BP learning algorithm using a sample set of size N (xt ,
yt). For non-linear modeling, the effectiveness of the model is
dependent on the MFs used. The TSK fuzzy rules are employed in the
ANFIS model as follows:
Ri : IF x is Ai, THEN
y=fi(x)= 1
1
( )k
i i i
i
i k
i i
i
A x f x
y
A x
(7.2)
where, ).,(),( 11 jixAjixAxA i
j
n
j
j
i
n
jii Accordingly, the error
measure at time t is defined by
y 21
( )2
t ttE y y
(7.3)
After the rule base is specified, the ANFIS adjusts only the MFs of
the antecedents and the consequent parameters. The BP algorithm
can be used to train both the premise and consequent parameters. A
more efficient procedure is to learn the premise parameters by the BP,
but to learn the linear consequent parameters ai,j by the RLS
(Recursive Least Square) method [89]. The learning rate η can be
adaptively adjusted by using a heuristic approach.
7.3 ANFIS CONTROLLER DESIGN
In the modeling and feedback control of any dynamical system, a
controller is a must for the plant as it takes care of all the
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disturbances and brings back the system to its original state in a
couple of second.
Fig. 7.1: Block diagram of the ANFIS control scheme
To start the design of the controller using the ANFIS scheme, first,
a mathematical model of the induction motor plant along with the
controller mathematical model is required, which can be further used
for simulation purposes.
The mathematical model of the plant is given by Eq. (3.56) in
Chapter 3 and it is a fourth-order mathematical model of size (4 4),
which is used here in the Simulink model. The basic structure of the
ANFIS coordination controller developed in this study to control the
speed of the IM. The block diagram of the developed controller is
shown in Fig. 7.1. Inputs to the ANFIS controller, i.e., the error and
the change in error, are modeled using Eqs. (7.4) and (7.5) as follows:
e(k) = ωref - ωr (7.4)
∆ e(k) = e(k) - e(k - 1) (7.5)
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where ωref is the reference speed, ωr is the actual rotor speed, e(k) is
the error and ∆e(k) is the change in error.
The fuzzification unit converts the crisp data into linguistic
variables, which is given as inputs to the rule-based block. The set of
49 rules is written on the basis of previous knowledge or experiences.
The rule-based block is connected to the neural network block. Back-
propagation algorithm is used for NN training in order to select the
proper set of rule base. For developing the control signal, training is a
very important step in the selection of the proper rule base. Once the
proper rules are selected and fired, the control signal required to
obtain the optimal outputs is generated.
The inputs are fuzzified using the fuzzy sets and are given as input
to the ANFIS controller. The rule base for the selection of proper rules
using the back-propagation algorithm is shown in Table 7.1.
Table 7.1: Rule base for controlling the speed of IM using ANFIS
e
∆e nb nm ns ze ps pm pb
nb nb nb nb nb nm ns ze
nm nb nb nm nm ns ze ps
ns nb nm ns ns ze ps pm
ze nb nm ns ze ps pm pb
ps nm ns ze ps ps pm pb
pm ns ze ps pm pm pb pb
pb ze ps pm pb pb pb pb
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The same rule base described in Table 5.1 in Chapter 5 (Section
5.2), which was used for Mamdani-based FLC and TS-based FLC for
decision-making purposes, is also used in this chapter for the
decision-making purposes to design the ANFIS controller. The same
49 rules have been used here for control purposes and are not shown
here for the sake of convenience.
The control decisions are made based on the fuzzified variables in
Table 7.1. The inference involves a set of rules for determining the
output decisions. As there are 2 input variables and 7 fuzzified
variables, the controller has a set of 49 rules for the ANFIS controller.
Out of these 49 rules, the proper rules are selected by training the
neural network with the help of back-propagation algorithm and these
selected rules are fired. Furthermore, it has to be converted into
numerical output. The output y is given as follows:
1 1
1 1
1
R Ri i i i
q q
i i
Ri
i
a x a x
y
(7.6)
This controlled output of the IM, i.e., y (here, it is the speed of the
IM), is the weighted average of the proper rule-based outputs, which
are selected by the back-propagation algorithm.
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ANFIS controller based system was developed using the various
toolboxes in Matlab /simulink. The various waveforms are observed
on the corresponding scopes after running the simulations. The
specifications of the SCIM used for simulation purposes were
described in Chapter 3 (table 3.1).
7.5 SIMULATION RESULTS AND DISCUSSIONS
The Simulink model of ANFIS controller is as in Fig.7.2. In order to
start the simulations, the 49 fuzzy rule set has to be invoked first from
the command window in the Matlab. Initially, the fuzzy file where the
rules are written with the incorporation of the T-S control strategy is
opened in the Matlab command window, after which the fuzzy editor
(FIS) dialogue box opens. The .fis file (sugenosevenrules2.fis) is
imported using the command window from the source and then
opened in the fuzzy editor dialog box using the file open command.
Once the file is opened, the TS-fuzzy rules file gets activated.
Furthermore, the data is exported to the workspace and the
simulations are run for a specific period of time (say 3 second). The
fuzzy membership function editor is then obtained using the view
membership command from the menu bar.
The written TS-fuzzy rules also can be viewed from the rule view
command. The rule viewer for the 2 inputs and 1 output can be
observed pictorially. Now, after performing all the preliminary
operations, the simulations are run for a period of 3 second in Matlab
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7 with a set speed of 100 rad / second, i.e.,100 60
2
=955 rpm and
with a 2 N-m load torque. Once, the simulation is run, various
parameters such as speed, flux, torque, currents, slip, etc. get stored
in the workspace. After running the developed Simulink model, we get
the error, change in error and an intermediate parameter.
Fig. 7.3: ANFIS editor window
Fig. 7.4: ANFIS editor: Loading the data from the work space
These 3 parameters are stored in a variable in the command window.
The ‘anfis’ editor opened in the command window is shown in Fig 7.3.
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These variables, which are in the form of data in the workspace, are
loaded into the ‘anfis’ editor (Fig. 7.4).
Once the data file is loaded, the ‘anfis’ has to be trained by
selecting a back-propagation algorithm with a suitable number of
epochs. In our work, we have used the back-propagation algorithm
with a suitable number of epochs being used for training the rules.
This is done by selecting these 2 items in the ‘train window’ of the
‘anfis’ editor and training the neural network for proper selection of
the rule base. The trained data are further exported to the workspace
using the file-export command.
Fig. 7.5: ANFIS model with 2 inputs and 1 output showing the
ANN architecture
The developed ANFIS model structure with 2 input neurons and 1
output neuron along with 4 hidden layers (input membership
function, rule base, membership function and aggregated output) is
shown in Fig. 7.5. The training of the ANN by using the fuzzy rule
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base for the selection of the proper and optimal rule is taken care of
by the designed ANFIS controller. Note that 7 by 7 rules are used in
the hidden layers. Both neuron 1 and neuron 2 are connected to 7
fuzzy rules. The hidden layers contains 49-49 neurons to deal with
the problem (for selection of the proper rule base, because the rule
base is written randomly in fuzzy, the neural network selects the right
optimal rule base to fire).
The 2 input neurons, viz., the error and change in error, are given
as input to the 1st hidden layer of the ANN as shown in Fig. 7.5. This
1st hidden layer deals with various input membership functions. In
the 2nd and 3rd hidden layers, the set of 49 fuzzy rules is properly
identified by training and the sets of optimal rules are selected. These
sets of optimum rules are available at the 4th hidden layer. Out of the
49 rules, the optimal rules are fired here and the de-fuzzified output is
obtained as the output neuron. The de-fuzzified output is further used
to generate the firing pulse to be applied to the inverter bridge, which
is further used to control the speed of the IM drive.
After the simulation is run, the performance characteristics are
observed on the respective scopes. The response curves of flux, load,
torque, terminal voltage, speed, rotor angle, stator currents, slip, id, iq,
rotor currents ( and d-q ) v/s time, slip vs. speed for a set speed
of 100 rad/second (955 rpm) and with a 2 N-m load torque are
observed and are shown in Figs. 7.6 – 7.17, respectively.
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The simulation results in Fig. 7.6 show that the stator current does
not exhibit any overshoots or undershoots. The response curves takes
lesser time to settle and reach the desired value compared to the
results presented in [84], [76], and [90].
Fig. 7.6: Plot of speed vs. time
The simulation results showed that by using the neuro-fuzzy
(ANFIS) control, for the set speed of 100 rad/second and for the 49
rules, the speed reaches its desired set value at 0.3 second. This
shows the effectiveness of the designed neuro-fuzzy controller, which
tries to speed up the performance of the drive, thus showing faster
dynamism.
The motor speed increases like a linear curve up to the set speed of
955 rpm (100 rad/second) in 0.3 second as shown in Fig. 7.6.
Furthermore, it can also be observed that using the ANFIS control, the
system stabilizes in a less time compared to the other methods.
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Fig. 7.7: Plot of flux vs. time
From the variation of flux with time as shown in Fig. 7.7, it can be
observed that when the motor speed increases (during the transient
period); more stator current is required to develop the requisite flux in
the air gap. Hence, the flux also starts increasing during the transient
period (0 to 0.3 second) exponentially. Once, the motor attains the set
rated speed, the flux required to develop the torque almost remains
constant after >0.3 second. Once the flux in the air gap remains
constant, the variation of the load torque and speed will not disturb
the flux curve. Hence, the IM will operate at a constant flux. The
is with time is shown in Fig. 7.8.
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It can be clearly observed from this figure, that at lower speeds, the
slip is more, and hence the flux required to develop the suitable
torque is also more. Moreover, the torque required to reach the set
speed is also more. Hence, the magnitude of the stator currents will
also be more during the transient periods (starting periods) of the
induction motor. When the speed reaches the set value from zero, the
speed at 0.3 second, it requires a nominal stator current to drive the
IM system.
Torque characteristics for a reference speed of 100 rad/second
(955 rpm) are shown in Fig. 7.9. From this figure, we can conclude
that when the motor operates at lower speeds, the slip is more. Hence,
the machine requires more torque to attain the set speed. Once the
machine reaches the set speed of 955 rpm, the average torque of the
machine becomes nearly zero after 0.3 second, which is justified from
the torque simulation result shown in Fig. 7.9. The terminal voltage of
the IM is shown in Figs. 7.10 (a) and (b), respectively.
Fig. 7.9: Plot of torque vs. time
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(a) Plot of voltage vs. time (normal)
(b) Plot of voltage vs. time (normal and zoomed) between t=0.984s
to 1.033s
Fig. 7.10: Plot of voltage vs. time (normal and zoomed)
Fig. 7.11 shows the variation of slip vs. time characteristics for a
speed of 100 rad/second (955 rpm). From this simulation result, we
infer that the IM attains the set reference speed of 955 rpm in 0.3
second using the ANFIS (neuro-fuzzy) controller. At that instant, the
slip being s
s
N N
N
=1800 955
1800
=0.46 can be verified from the result
shown. Note that the slip decreases from 1.0 to 0.46 linearly in a time
span of just 0.3 second.
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Fig. 7.11: Plot of slip vs. time
The slip-speed characteristics are shown in Fig. 7.12. When the
speed is varied from 0 to the rated speed, the slip decreases, i.e., the
slip is inversely proportional to the speed, which is a characteristic of
IM. When the speed is zero, the slip is 100% whereas the IM operates
close to the rated speed (180 rad/second), the slip is very low. The
plots of the direct axes id and i q and quadrature axes currents iq
versus time are shown in Figs. 7.13 and 7.14. From these figures, it
can be inferred that the machine reaches the set reference speed of
955 rpm at a time interval of 0.3 second.
Fig. 7.12: Plot of speed vs. slip
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Fig. 7.13: Plot of direct axis id v/s time
The variation of rotor currents ir-abc with time is shown in Fig. 7.15.
It can be inferred that at lower speeds, the slip is more, and hence the
flux required to develop the suitable torque is also more. Moreover,
the torque required to reach the set speed is also more. Hence, the
magnitude of the rotor currents will also be more during the transient
periods (starting periods) of the induction motor.
Fig. 7.14: Plot of rotor current iq v/s time
Whe
currents decrease exponentially up to 0.3 second; thereafter it
ir-abc are transformed to the
direct axes and quadrature axes currents using the d–q
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transformation techniques; the variation of the transformed currents
with time is shown in Fig. 7.16. Here, only two phases d and q axes of
the currents can be observed in the characteristic curve. In this case,
also, once the motor achieves the set speed at 0.3 second, it requires a
nominal current to drive the IM system.
Fig. 7.15: Plot of rotor current ir abc v/s time
Fig. 7.16: Plot of rotor current irdq v/s time
7.6 JUSTIFICATION OF ROBUSTNESS ISSUES IN SPEED
CONTROL
A significant contribution of the developed controller in the work
presented in this chapter is that, the designed controller can also be
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used for variable speed. When the system is in operation (when the
simulations are going on), due to sudden changes in set speed (say,
the set speed immediately changed from 100 rad/second
100 60955
2
rpm to140 rad/second
140 601337
2
rpm or anything
else and then suddenly decrease the speed back to normal), with the
incorporation of the designed controller in loop with the plant, the
system comes back to stability within a few millisecond (ms).
The simulation results due to the parametric variations of speed
from 100 to 140 rad/second and then back to normal are shown in
Figs. 7.17-7.25, respectively. It is clearly observed that the dynamic
performance of the system is quite improved, and also insensitive to
parametric variations with the incorporation of the ANFIS-based
control scheme. Furthermore, it can be also concluded that although
some motor parameters are non-linear, it appears linear in nature.
Fig. 7.17: Speed curve for variation in speed from 100–140 r/s
and back
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Note that when the speed is varied from 100 to 140 rad/second at
say t =0.75 second, the motor takes very less time (only 0.26 second)
to reach the new set speed point (140 rad/second) to become stable.
Again when the IM runs at 140 rad/second, the speed suddenly varies
from 140 to 100 rad/second at say t =1.6 second, and the motor again
takes very less time (only 0.45 second) to reach the new set speed
point (100 rad/second) to become stable as shown in Fig. 7.17. From
this, it can be observed that the speed of the IM is robust (insensitive)
to sudden changes in speed, which is because of the ANFIS controller.
This speed characteristic curve shows that even when there is a
sudden change in speed, the controller takes very less time to reach
stability. The stator current does not exhibit any overshoots or
undershoots. The motor speed increases similar to a linear curve up
to the set speed of 955 rpm in 0.3 second. The torque vs. time for
variation in speed from 100 to 140 rad/second and back to 100
rad/second is shown in Fig. 7.18. It can be seen that when the speed
of the IM increases from 0 to the set value (100 rad/second), the
torque required to reach the set speed is high.
After the motor reaches the set speed of 100 rad/second, the
average torque required to run the motor at the set speed of 100
rad/second will be zero (average of upper and lower half
characteristics of the torque during the rated speed). The motor
reaches the rated speed in just 0.3 second. Now, if the speed is
suddenly increased from 100 to 140 rad/second, the torque
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requirement also increases between the period from t =0.75 second to
1.01 second.
Fig. 7.18: Torque characteristic for variation in speed
After the motor reaches the new set speed of 140 rad/second, the
average torque required to run the motor at the new set speed of 140
rad/second will be zero between the period from t =1.01 second to 1.6
second. Now, if the speed is suddenly decreased from 140 to 100
rad/second, the torque requirement is less between the period from t
=2.1 second to 3.0 second. After the motor reaches the original set
speed of 100 rad/second, the average torque required to run the
motor at the original set speed of 100 rad/second will be zero from t
=2.1 second onwards. From Fig. 7.18, we can conclude that when the
motor operates at lower speeds, the slip is more. Hence, the machine
requires more torque to attain the set speed.
Once the machine reaches the set speed of 955 rpm, the average
torque of the machine becomes nearly zero, which is justified from the
is-abc with time
for the variation in speed from 100 to 140 rad/second and back to
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normal is shown in Fig. 7.19. There is a change in the stator current
variation during the change in speed from one value to another during
the time interval from t =0.75 to 1 second and from t =1.6 to 2.1
second.
Fig. 7.19: Stator current characteristics for variation in speed
Once the stable point is reached, the stator current becomes
normal. This figure clearly shows that at lower speeds, the slip is
more, and the flux required to develop the suitable torque is also
more.
The torque required to reach the set speed is also more. Hence, the
magnitude of the stator currents will also be more during the
transient periods (starting periods) of the induction motor. When the
exponentially as shown in Fig. 7.19. Once it attains the set speed at
0.3 second, it requires a nominal stator current to drive the IM
system.
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One observation that can be made in the flux characteristics
during the change in speed is that, during speed variation, the flux
varies slightly only during the time interval at which the speed
variation occurs. The flux characteristics are shown in Fig. 7.20.
From the variation of flux with time, it can be observed that when the
motor speed increases (during the transient period); more stator
current is required to develop the requisite flux in the air gap.
Fig. 7.20: Flux characteristics for variation in speed
Hence, the flux also starts increasing during the transient period (0
to 0.3 second) exponentially. Once the motor attains the set rated
speed, the flux required to develop the torque almost remains
constant at 0.9 wbs after ≥0.3 second. Once the saturation of the flux
takes place in the air gap, the variation of the load torque and speed
will not disturb the flux curve. Hence, the IM will operate at a
constant flux.
The plots of the direct axis current id and quadrature axis current
iq versus time are shown in Figs. 7.21 and 7.22, respectively. From
145
these figures, it can be inferred that the machine reaches the set
reference speed of 955 rpm at a time interval of 0.3 second initially.
When there is a variation in speed (either increase or decrease), the
current also changes approximately during that transition period, i.e.,
t =0.75 to 1 second and from t =1.6 to 2.1 second. It can be inferred
that at lower speeds, the slip is more, and hence the flux required to
develop the suitable torque is also more.
Fig. 7.21: Direct axes current characteristics for variation in
speed
Moreover, the torque required to reach the set speed is also more.
Hence, the magnitude of the rotor currents will also be more during
the transient periods (starting periods) of the IM. When the speed
exponentially and finally reach a steady-state value.
ir-abc are transformed to the direct axes and
quadrature axes currents using the (d and q) transformation
techniques and the variation of the transformed currents with time is
146
shown in Figs. 7.21 and 7.22 ir-
abc with time is shown in Fig. 7.23
Fig. 7.22: Quadrature axes current characteristics for variation in
speed
Fig. 7.23: 3 Φ rotor current characteristics for variation in speed
Furthermore, the combined curve of the 2-phase rotor currents in
the d-q plane is shown in Fig. 7.24. Here, only two phases (d and q
axes) of the currents can be observed in the characteristic curve. In
this case, also, once the motor achieves the set speed at 0.3 second, it
requires a nominal current to drive the IM system. When there is a
variation in speed (either increase or decrease), the current also
147
changes approximately during that transition period, i.e., from t =0.75
to 1 second and from t =1.6 to 2.1 second.
Fig. 7.24: Rotor current: 2 phase characteristics for variation in
speed
Fig. 7.25: Plot of load torque v/s. time
The load torque is set at a constant value of 2 N-m throughout the
process of simulation at the time of change in speed, which can be
seen in Fig. 7.25. The performance of the developed method in this
chapter also demonstrates the effectiveness of the sudden variation of
speed from clockwise to anticlockwise rotation (-50 rad/second to +50
rad/second with specific amount of time) to obtain stability (which is
shown in Fig. 7.26). The simulation results demonstrate the good
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damping performance of the designed robust controller despite speed
fluctuations.
Fig. 7.26: Plot of variation of speed with time for clockwise and
anticlockwise rotation of IM
7.7 SUMMARY
A novel and systematic method of achieving robust speed control of
an IM system using SVPWM technique for voltage source inverter by
means of adaptive neuro-fuzzy inference system has been investigated
in this chapter. The SVPWM is used to control the firing angle of the
inverter. This, in turn, controls the speed of the IM. The Simulink
model was developed in Matlab 7. Due to the incorporation of the
ANFIS controller, it was observed that the motor reaches the set speed
very quickly in a shorter period of time, i.e., only 0.3 second to reach
the set speed (100 rad/second).
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One of the main advantages of the ANFIS scheme is that, it is
computationally efficient, increases the dynamic performance and
provides good stabilization when there is a sudden fluctuation in one
of the system parameters, say speed of the IM. This shows the
excellent response of the proposed control scheme as it has the
learning capability using the neural networks.
The ANFIS systems handling more complex parameters, which
demonstrates the effectiveness of the sudden variation of speed
(because of parametric variation) from the normal value and its effects
on the various parameters (such as slip, current, torque, etc.) to
obtain the stability.