chapter 5 internal model control strategy 5.1...
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CHAPTER 5
INTERNAL MODEL CONTROL STRATEGY
5.1 INTRODUCTION
The Internal Model Control (IMC) based approach for PID controller
design can be used to control applications in industries. It is because,
for practical applications or an actual process in industries PID
controller algorithm is simple and robust to handle the model
inaccuracies and hence using IMC-PID tuning method [36], [37] a clear
trade-off between closed loop performance and robustness to model
inaccuracies is achieved with a single tuning parameter.
Also the IMC-PID controller allows good set-point tracking and gives
silky disturbance response especially for the process with a small time-
delay/time-constant ratio. But, for many process control applications,
disturbance rejection for the unstable processes is much more
important than set point tracking. Hence, controller design that
emphasizes disturbance rejection rather than set point tracking is an
important design problem that has to be taken into consideration.
In this thesis, optimum IMC filter to design an IMC controller for
better set-point tracking and disturbance rejection in a series power
quality controller is proposed. As the IMC approach is based on pole-
zero cancellation, methods which comprise IMC design principles result
in good set point responses. However, IMC results in a long settling
time for load disturbances for lag dominant processes which are not
desirable in the control industry. Usually, disturbances are categorized
as load disturbances, model uncertainties and noise. As the knowledge
about model uncertainties and noise is unknown, their impact is not
considered in thesis. The plant and model of actual process is
considered to same. Since all the IMC-PID [38], [39] approaches involve
some kind of model reduction techniques to convert the IMC controller
to the PID controller so approximation error usually occurs. This thesis
clearly illustrates an approach to obtain optimum filter structure to
IMC. Filter time constant plays a vital role to obtain better trade off
between robustness and disturbance rejection and stability.
Basically Internal Model Control (IMC) principle states that “Control
can be achieved if and only if the control system summarizes either
implicitly or explicitly, some representation of the process to be
controlled”. Internal stability and performance characteristics (correlate
to controller parameters) are the important aspects which makes it
more advantageous compared to classic feedback controller. The perfect
controller can be arrived if there is no model mismatch. If disturbance
rejection is not covered IMC gives sluggish response. The parameters of
IMC controller depend on the IMC filter time constant. Increase in the
filter time constant always reduces the overshoot to an acceptable limit,
but however reduces the disturbance rejection, desired noise
suppression capability. This study also proposes the procedural
method for selection of filter time constant.
The conceptual usefulness of the IMC lies in the fact that much
concern can be put on controller design rather than control system
stability provided that the process model is a perfect representation of a
stable process.
If there is a complete knowledge about the process being controlled,
perfect control can be achieved without feedback. Feedback control is
needed only when knowledge about the process is incomplete or
inaccurate. However, process-model mismatch is common. Process
model may not be invertible and the system is often affected by
unknown disturbances. Hence open loop control arrangement may not
be able to compensate for disturbances, model uncertainties and set
point tracking whereas an IMC is able to compensate for disturbances,
model uncertainties and set point tracking. IMC must be tuned to
assure the stability in model uncertainties cases.
5.2 IMC Strategy
An open loop control system is controlled directly, and only by an
input signal without the benefit of feedback. Open loop control systems
are not commonly used as closed loop control systems because of the
issue of accuracy. An open loop structure is shown in the fig 5.1.
Fig 5.1: Open loop structure of IMC
With controller ( )cG s , set to put control on the plant ( )pG s , then it is
clear from basic linear system theory that the output Y(s) can be
modeled as the product of the linear blocks as follows:
( ) ( ) ( ) ( )c pY s R s G s G s (5.1)
If we assume there exists model of the plant with transfer function
modeled as ( )pG s such that ( )pG s is an exact representation of the
process (plant), i.e. ( ) ( )p pG s G s , then set point tracking can be
achieved by designing a controller such that:
1( ) ( )c pG s G s (5.2)
This control performance characteristic is achieved without
feedback and highlights two important characteristic features of this
control modeling. These features are:
Feedback control can be theoretically achieved if complete
characteristic features of the process are known or easily
identifiable.
Feedback control is only necessary of knowledge about the
process is inaccurate or incomplete.
This control performance as already said has been achieved without
feedback and assumed that the process model represent the process
exactly i.e. process model has all features of parent model. In real life
applications, however, process models have capabilities of mismatch
with the parent process; hence feedback control schemes are designed
to counteract the effects of this mismatching. A control scheme that
has gained popularity in process control has been formulated and
known as the Internal Model Control (IMC) scheme. This design is a
simple build up from the ideas implemented in the open loop model
strategy and has general structure as depicted by figure below
Fig 5.2: Schematic IMC structure without disturbance
Fig 5.3: Internal model control with disturbance
From the fig 5.3, description of blocks as follows:
Controller Gc(s)
Process Gp(s)
Internal model ( )pG s
Disturbance d(s)
The fig 5.3 shows the standard linear IMC scheme where the
process model ( )pG s plays an explicit role in the control structure. This
structure has some advantages over conventional feedback loop
structures. For the nominal case Gp(s) = ( )pG s , for instance, the
feedback is only affected by disturbance d(s) such that the system is
effectively open loop and hence no stability problems can arise. This
control structure also depicts that if the process Gp(s) is stable, which
is true for most industrial processes, the closed loop will be stable for
any stable controller Gc(s). Thus, the controller Gc(s) can simply be
designed as a feed-forward controller in the IMC scheme.
The manipulated input ( )U s is introduced to both the process and
its model. The process output ( )Y s is compared with the output of the
model resulting in
i.e. ˆ( ) ( ) ( ) ( ) ( )p pd s G s G s U s d s (5.3)
In the above equation, if ( ) 0d s , then ˆ( )d s is a measure of the
difference in behavior between the process and model and if
( ) ( )p pG s G s then ˆ( )d s will be unknown disturbance. Thus ˆ( )d s can be
used to improve the control and may be treated as the missing
information in the model ( )pG s . This can be achieved by sending an
error signal to the controller. The error signal incorporates the model
mismatch and disturbances and helps to achieve the set-point. The
resulting control signal is given by
ˆ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )c p p cU s R s d s G s R s G s G s U s d s G s (5.4)
( ) ( ) ( )( )
1 ( ) ( ) ( )
c
p p c
R s d s G sU s
G s G s G s
(5.5)
Since ( ) ( ) ( ) ( )pY s G s U s d s the closed loop transfer function for the
IMC scheme is therefore given by
( ) ( ) ( ) ( )( ) ( )
1 ( ) ( ) ( )
c p
p p c
R s d s G s G sY s d s
G s G s G s
(5.6)
From the above expressions, it can be concluded that if 1( ) ( )c pG s G s
and if 1( ) ( )p pG s G s , a set point tracking and disturbance rejection is
achieved. In some cases even if 1( ) ( )p pG s G s , perfect disturbance
rejection can still be achieved provided 1( ) ( )c pG s G s . Additionally,
minimal effects of process model mismatch improve the robustness.
Most of the discrepancies between process and model behavior occur at
the high frequency end of the systems frequency response. In general a
low pass filter is used to attenuate the effects of process-model
mismatch. Thus the internal model controller is usually designed as the
inverse of the process model in series with a low pass filter.
( ) ( ) ( )imc c fG s G s G s (5.7)
Excessive differential action is usually controlled by selecting the
order of the filter so as to make ( )imcG s proper. The resulting closed loop
equation is given by
( ) ( ) ( ) 1 ( ) ( ) ( )( ) ( )
1 ( ) ( ) ( )
imc p imc p
p p imc
G s G s R s G s G s d sY s d s
G s G s G s
(5.8)
In IMC scheme shown by fig 5.3, the Internal Model Control loop
calculates the difference between the outputs of the process and that of
Internal Model. This difference simply represents the effects of the
disturbances and uncertainties as well as that of a mismatch of the
model. Internal Model control devices have shown to have good
robustness properties against disturbances and model mismatch in the
case of linear model of the process. A control system is generally
required to regulate the controlled variables to reference commands
without steady state error against unknown and immeasurable
disturbance inputs. Control systems with this nature property are
called servomechanisms or servo systems. In servomechanism system
design, the internal model control principle plays an important role.
Hence the design of a robust servomechanism system with plant
uncertainty begins with three specifications as outline below:
Definition of the plant model and associated uncertainty.
Specification of inputs
Desired closed loop performance.
IMC theory provides a systematic approach in the synthesis of a
robust controller for systems with specified uncertainties. This brings
about two important advantages of applying IMC control scheme.
The closed loop stability can be choosing a stable IMC controller.
The closed loop performances are related directly to the controller
parameter, which makes on-line tuning of the IMC controller very
convenient.
Some important properties of IMC scheme
It provides time delay compensation
Reference signal tracking and disturbance rejection responses
can be shaped by a single filter
The controller gives offset free responses at the steady state.
5.3 SENSITIVITY AND COMPLIMENTARY SENSITIVITY
FUNCTIONS
Sensitivity function determines the performance and the
complimentary sensitivity function determines the robustness. The
sensitivity functions allow evaluating the controller behavior in relation
to the desired attenuation constraints. The gradient of output
sensitivity function determines the dynamic behavior of the system.
internal model control is the easiest way for PID tuning as it depends
on selection of only one variable compared to two (PI) or three
variables(RST).
If ( )s and ( )s represents the sensitivity function and
complimentary sensitivity functions, then
1 ( ) ( )( ) ( )( )
( ) ( ) ( ) 1 ( ) ( ) ( )
imc p
p p imc
G s G sE s Y ss
R s d s d s G s G s G s
(5.9)
If ( ) ( )p pG s G s then,
( ) 1 ( ) ( )imc ps G s G s (5.10)
( ) ( ) ( )imc ps G s G s (5.11)
Internal Model Control (IMC) Algorithm
Select the plant and obtain the transfer function of the
plant ( )pG s .
Chose the process model ( )pG s .
Factorize the process model into minimum phase and non-
minimum phase components. ( ) ( ) ( )p p pG s G s G s . This step
ensures that ( )q s is stable and causal. However ( )pG s contains
all Non-minimum Phase Elements (Noninvertible) in the plant
model. i.e. all right half plane (RHP) zeros and time delays. The
factor ( )pG s is Minimum Phase and invertible.
The controller ( )q s is chosen as inverse of minimum phase
component. 1( ) ( )pq s G s . If the process model contains only
components which cannot be factorized but is does show stability
with no right half poles (RHP) on the s-plane then the model is
considered invertible. If the process model contains only the non-
invertible components and with instability, the other improved
methods can be used because the IMC controller depends on the
stability and invertibility of the process model. The non-
invertibility of components may lead instability and realizability
problems when inverted.
If the controller q(s) is improper, then ( )q s is normally augmented
with the optimal controller to attenuate the effects of process-
model mismatching and remove the higher frequency part of the
noise in the system in order to meet robust specifications. The
robust compensator (filter) plays a pivotal role in the system as it
combats plant uncertainties in the system design so that the
designed control system can achieve the design objectives of
robust stability and robust performance. The filter transfer
function ( )f s is to make the controller stable, causal and proper.
The controller with filter is given by
1( )( )
1
p
n
G sq s
s
, (5.12)
Where n is the order of the filter and is the filter time
constant. The order of the filter is chosen such that ( )imcG s is
proper to prevent excessive differential control action. The filter
parameter in the design can be chosen as a rule of thumb; hence
the filter parameter values are often dictated by modeling errors,
as already stated that in the design, it remains only tunable
parameter. Usually from the eqn 5.12, the final form for the
closed loop transfer functions characterizing the system is
( ) 1 ( ) ( ) ( )ps q s f s G s (5.13)
( ) ( ) ( ) ( )ps q s f s G s (5.14)
Filter time constant shall be selected so as to obtain good closed
loop performance and disturbance rejection.
Internal model control parameter ( )
1 ( ) ( )imc
p
q sG
q s G s
Increasing increases the closed loop time constant and slows the
speed of the response; decreasing does the opposite. Usually the
choice of the filter parameter depends on the allowable noise
amplification by the controller and on modeling errors. Filter time
constant avoids the excessive noise amplification and accommodate
the modeling errors. To avoid excessive frequency gain of the controller
is not more than 20 times its low frequency gain. For controllers that
are ratios of polynomials, this criterion can be expressed as
( )20
(0)
q
q
(5.15)
Higher the value of , higher is the robustness of the control system.
Fig 5.4: closed loop diagram with IMC controller
5.4 THEORETICAL DESIGN
The plant can be written as
2 7
2 2 2 2 7
1/ 1.66*10( )
2 ( / ) 1 / 333.33 1.66*10
n
n n
LCG s
s s s R L s LC s s
Substituting the filter values in the equation and from the
equation, the values of damping factor and natural frequency are
0.04 and 4082.4 rad/sec
Since the plant contains poles on the left hand plane, the system
is a minimum phase system. Hence 2
1/( )
( / ) 1/p
LCG s
s R L s LC
2
1 ( / ) 1/( ) ( )
1/p
s R L s LCq s G s
LC
, From the equation, it is evident
that q(s) is improper and needs to be proper for realization, so
with adding the filter
1 2( ) ( / ) 1/( )
1 (1/ )* 1
p
n n
G s s R L s LCq s
s LC s
becomes
proper. Considering the order of the filter same as the plant (n=2)
and λ as 0.001 based on equation
2 7
2
333.33_1.667*10( )
(0.01) 0.02 1
sq s
s
(5.16)
2 7
2
( ) 6( 333.33 1.667*10 )( )
1 ( ) ( ) 0.02imc
p
q s s sG s
q s G s s s
Table 5.1: Test parameters
Parameters Values
Suuply Voltage 11kV
Filter Capacitance 20µF
Filter Inductance 3mH
Filter resistance 1
IMC filter time constant 0.001
Load power factor 45deg lagging
The simulink diagram and results are shown in figs 5.5-5.6. Step input
is given to the system with magnitude of 10 at 1sec.
Fig 5.5: Simulink diagram for IMC controller without disturbance
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
Time (secs)
magn
itu
de
Fig 5.6: IMC control with step input without disturbance
To test the performance of the proposed controller, a step disturbance
is added at the output in the test system. The simulink diagram of the
test system with disturbance is depicted in fig 5.7. The corresponding
result is depicted in fig 5.8 which clearly indicates the effectiveness of
the proposed controller in mitigating the disturbance. The output is
nearly same as the input reference signal tracking nature of the
controller in the presence of the disturbance. The transient parameters
for the step response with internal model controller are
Rise time =0.000348secs
Settling time = 0.000589
Peak overshoot = 1.55*10-13%
Peak time = 0.016secs.
Fig 5.7: IMC Design: Step Input disturbance at the output of plant
0 1 2 3 4 5 6 7 8 9 100
2
4
6
8
10
12
Time (secs)
magn
itu
de
Fig 5.8: Step response of IMC control disturbance at the output
The transient parameters namely rise time, settling time and peak
overshoot depends on the filter time constant. The lower is the filter
time constant, lower is the rise time and peak overshoot. Moreover the
robustness in terms of stability is affected by the filter time constant.
Smaller filter time constant leads to more robust system but decreases
the disturbance rejection capability. Hence an optimum value of filter
time constant is very much required.
Particle Swarm Optimization for obtaining Filter Time constant
[40]
1. Randomly initialized position and velocity of the particles: Xi(0)
and Vi(0)
2. Evaluate the fitness function for the particle iX .
3. Position of the particle becomes particle’s best ( bestp ) and global
best ( bestg ).
4. for i = 1 to number of particles
5. Evaluate the fitness:= fi , 1
1if
error
6. For each particle, compare the particle’s value with bestp . If the
current value is better than the bestp value, than set this value as
the bestp and current particle’s position, iX as ip
7. Identify the particle that has the best fitness value. The value of
its fitness function is identified as bestg and its position as gp .
8. Update the position and velocities of all particles
9. ( ) ( 1) ( )i i iX t X t v t and
10. 1 1 2 2( ) ( 1) . ( ( 1) . ( ( 1)i i i i g iv t v t rand p X t rand p X t
11. Adapt velocity of the particle using equations (1);
12. Update the position of the particle;
13. increase i
14. Repeat steps 2-5 until a stopping criterion is met (either
maximum number of iterations or sufficiently good fitness
value)
The output sensitivity function provides the measure of dynamic
behavior of the system. The dynamic behavior is quantified by modulus
margin and delay margin; measure for robustness of modeling
uncertainties.
Bode Diagram
Frequency (rad/sec)
100
101
102
103
104
0
45
90
Ph
ase (deg)
-40
-30
-20
-10
0
10
Magn
itu
de (dB
)
Fig 5.9: Bode plot for output sensitivity function with IMC
The fig 5.9 illustrates the step response of output sensitivity
function. The transient parameters are:
Rise time = 0.000336secs
Peak time = 0secs
The peak magnitude of the output sensitivity function is observed to be
1.23db. This peak magnitude clearly indicates the robustness
capability of IMC controller.
Bode Diagram
Frequency (rad/sec)
102
103
104
105
106
107
108
109
1010
-180
-135
-90
-45
0
Ph
ase
(d
eg
)
-200
-150
-100
-50
0
Ma
gn
itu
de
(d
B)
Fig 5.10: Bode plot of closed loop system with IMC
The fig 5.10 represents the bode plot of the closed loop system.
Compared to open loop system stability are observed to be increased.
Gain margin: inf
Phase margin: 180
Gain margin indicates that there is a large scope of adding a gain at
phase crossover frequency to bring the system to verge of instability.
Phase margin indicates that the maximum of 180˚ angle can be added
to the system at the gain crossover frequency to bring the system to
verge of instability. Since both gain margin and phase margin are large,
system is more robust to the disturbances. Since the stability margins
are increased the system may be treated as more robust to
disturbances.
5.5 SIMULATION RESULTS
The test system is described briefly in chapter 3. The test system
includes distribution system with medium voltage level. Voltage sag
and interruption are considered as the power quality issues. These
disturbances are created in the test system by varying the fault
resistances. The fault resistance for voltage sag is 0.66Ω and for voltage
interruption is 0.001Ω. The DVR is modeled with Internal Model
Control (IMC) for the generation of control angle δ. This control angle δ
is used for generation of reference signal. The various case studies are
presented in the thesis to verify the performance of the controller. The
first case study includes distribution system employing DVR feeding to
RL load. DVR operates only during the period of voltage sag and
interruption. Voltage sag is mitigated with IMC based DVR. The fig 5.11
depicts the load voltage with IMC controller in DVR. It can be seen very
clearly that DVR is able to maintain the load voltage at 98%. The tame
taken by the DVR to respond to voltage sag is less than 4ms. The
corresponding Total Harmonic Distortion (THD) of load voltage is
observed to be 1.60%. The THD is measured for the fault duration only
comprising of 22 cycles.
Case 1: Voltage sag mitigation with IMC based DVR
0 0.2 0.4 0.6 0.8 1-1
0
1
Vca(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Vb(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Time
Vc(V
)
Fig 5.11: Load voltage with IMC controller compensating voltage sag
0 0.2 0.4 0.6 0.8 1-1
0
1Selected signal: 55.34 cycles. FFT window (in red): 22 cycles
Time (s)
0 1 2 3 4 5 6 7 8 9 100
5
10
15
Harmonic order
Fundamental (50Hz) = 0.9351 , THD= 1.60%
Mag (%
of
Fu
ndam
en
tal)
Fig 5.12: Total harmonic distortion of load voltage with IMC
Case 2: DVR with rectifier load for mitigation of voltage sag
The second case study refers to test system involving distribution
system feeding to a rectifier load. The non-linearity nature of the
rectifier load distorts the load voltage waveform. The voltage sag is
created as described in the first case study. The performance of the
controller is verified by incorporating it in DVR, used for mitigating
voltage sag. The fig 5.13 represents the load voltage waveform with DVR
conducting during the period of voltage sag. The recovery time for
restoration of load voltage to normal is less than 4ms. It is very clearly
evident that the injected voltage by DVR is free from harmonics. The
Total Harmonic Distortion (THD) is found to be 2.02% which is within
the standards.
0 0.2 0.4 0.6 0.8 1-1
0
1
Va(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Time
Vc(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Vb(V
)
Fig 5.13: load voltage after compensation of voltage sag In utility system with
rectifier load
0 0.2 0.4 0.6 0.8 1-1
0
1Selected signal: 51.94 cycles. FFT window (in red): 22 cycles
Time (s)
0 2 4 6 8 100
5
10
15
Harmonic order
Fundamental (50Hz) = 0.94 , THD= 2.02%
Mag (%
of
Fu
ndam
en
tal)
Fig 5.14: Total harmonic distortion of load voltage
Case 3: Mitigation of voltage interruption with IMC based DVR
0 0.2 0.4 0.6 0.8 1 1.2 1.4-1
0
1
Va(V
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4-1
0
1
Vb(V
)
0 0.2 0.4 0.6 0.8 1 1.2 1.4-1
0
1
Time
Vc(V
)
Fig 5.15: Load voltage with IMC
0 0.2 0.4 0.6 0.8 1 1.2 1.4-1
0
1
Selected signal: 70 cycles. FFT window (in red): 30 cycles
Time (s)
0 1 2 3 4 5 6 7 8 9 100
20
40
60
Harmonic order
Fundamental (50Hz) = 0.71 , THD= 3.81%
Mag (%
of
Fu
ndam
en
tal)
Fig 5.16: Total Harmonic Distortion of load voltage
Third case study illustrates the robustness of the controller in
mitigating the voltage interruption in a distribution system feeding RL
Load. DVR with closed loop control can mitigate the voltage fluctuation
upto 50% only. Research work involves open loop control to increase
the capability of DVR in mitigating deeper voltage fluctuations like
interruptions. In this case study, DVR is fed from independent DC
voltage source and the magnitude of DC voltage required to mitigate the
voltage interruption gives the measure of robustness of IMC controller.
The fig 5.15 shows the load voltage waveform with IMC controller based
DVR injecting voltage during the period of interruption. Since, the DVR
has to inject a large voltage, a small delay is observed at the time of
switching on of DVR. This delay is due to slow response of filter and
PWM controller for large voltage error. The corresponding THD is
observed to be 4.67% as shown in the fig 5.16
Case 4: DVR with rectifier load for mitigation of voltage
interruption
0 0.2 0.4 0.6 0.8 1-1
0
1V
a(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Vb(V
)
0 0.2 0.4 0.6 0.8 1-1
0
1
Time
Vc(V
)
Fig 5.17: Load voltage with rectifier load
0 0.2 0.4 0.6 0.8 1 1.2-1
0
1
Selected signal: 65.12 cycles. FFT window (in red): 25 cycles
Time (s)
0 2 4 6 8 100
20
40
60
Harmonic order
Fundamental (50Hz) = 0.7017 , THD= 4.67%
Mag (%
of
Fu
ndam
en
tal)
Fig 5.18: Total harmonic distortion of load voltage
Fourth case study illustrates the performance of the IMC controller
in generating switching pulses for the multilevel inverter which injects
the missing voltage at the load end. The rectifier load is considered in
this case study. The figs 5.17 & 5.18 represent the load voltage and
THD at the load side. To inject missing voltage of 11kV, DC voltage
magnitude of 1.8kV is sufficient with IMC controller. This DC voltage
magnitude indicates effectiveness of IMC controller in rejecting the
disturbance and reducing the stress on PWM controller. However, the
PWM controller and filter introduced a small delay which is very clearly
seen in the fig 5.17. The THD is observed to be 4.67%.
5.6 SUMMARY
The IMC is process model dependant method i.e the control is
possible only when there is no mismatch between the plant and
process model. Hence, the selection of process model is very
important in IMC based controller design.
IMC technique involves the pole cancellation process and
selection of filter time constant. The algorithm for IMC based
controller is described in this chapter with mathematical
calculations of the proposed controller.
The selection of only one variable (filter time constant) makes the
design of controller very easy. However, a balance is required
between the good voltage regulation and disturbance rejection in
selection of filter time constant.
Particle swarm optimization technique is described for the
selection of filter time constant. The proposed controller is a
feedback controller with only one degree of freedom.
IMC based controller is able to reject the disturbance to some
extent but not completely. Hence, IMC is able to reduce the DC
voltage magnitude to 2kV for mitigation of voltage sag of 20%.
However, two degree of freedom is required to process the input
and output signals effectively. Four case studies are presented to
validate the performance of IMC based controller in DVR for
mitigation of voltage sag and interruption with RL and rectifier
loads.
Finally, IMC based controller is better than PI controller but still
unable to reduce the DC voltage magnitude effectively. The
controller is effective in reducing the Total Harmonic Distortion
(THD) and mitigation voltage sag and interruption at the utility
end.