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.