R Balamurugan FDP Electrical Drives and Control

1 R. Balamurugan - FDP on “Electrical Drives & Control,” DEEE, Anna Univ. of Tech. Coimbatore : 12th July, 2011

Faculty Development Programe on “Faculty Development Programe on “Faculty Development Programe on “Faculty Development Programe on “ELECTRICAL DRIVES AND CONTROLELECTRICAL DRIVES AND CONTROLELECTRICAL DRIVES AND CONTROLELECTRICAL DRIVES AND CONTROL””””

By

R. BALAMURUGAN Asst. Prof. – Electrical and Electronics Engineering

Anna University of Technology Coimbatore, Coimbatore

Anna University of Technology CoimbatoreAnna University of Technology CoimbatoreAnna University of Technology CoimbatoreAnna University of Technology Coimbatore

CoimbatoreCoimbatoreCoimbatoreCoimbatore

ELECTRICAL DRIVES CONTROLELECTRICAL DRIVES CONTROLELECTRICAL DRIVES CONTROLELECTRICAL DRIVES CONTROL

Date: 12Date: 12Date: 12Date: 12----07070707----2011 2011 2011 2011

Venue: Seminar Hall, School of Management Studies Venue: Seminar Hall, School of Management Studies Venue: Seminar Hall, School of Management Studies Venue: Seminar Hall, School of Management Studies

University Academic Campus University Academic Campus University Academic Campus University Academic Campus


1.1.1.1. IntroductionIntroductionIntroductionIntroduction

2.2.2.2. TypesTypesTypesTypes ofofofof DrivesDrivesDrivesDrives ControlControlControlControl

3.3.3.3. FieldFieldFieldField OrientedOrientedOrientedOriented ControlControlControlControl (FOC)(FOC)(FOC)(FOC)

4.4.4.4. DirectDirectDirectDirect TorqueTorqueTorqueTorque ControlControlControlControl (DTC)(DTC)(DTC)(DTC)

5.5.5.5. AdaptiveAdaptiveAdaptiveAdaptive ControlControlControlControl SchemesSchemesSchemesSchemes

Topics of DiscussionTopics of DiscussionTopics of DiscussionTopics of Discussion


Variable Frequency Drive SystemVariable Frequency Drive SystemVariable Frequency Drive SystemVariable Frequency Drive System

Figure: PWM VFD WaveformFigure: PWM VFD WaveformFigure: PWM VFD WaveformFigure: PWM VFD Waveform

Figure: VFD SystemFigure: VFD SystemFigure: VFD SystemFigure: VFD System


Possible Possible Possible Possible parameter parameter parameter parameter variations controlled variations controlled variations controlled variations controlled electrical drive systemselectrical drive systemselectrical drive systemselectrical drive systems,,,,

Change of winding electromagnetic time constant due to the temperature rise or material deterioration

Change of the mechanical time constant due to moment of inertia changes of the drive

Change of the flux value, in drive with the field weakening operation

Change of the drive system structure (e.g., due to the transition from continuous to discontinuous armature current in a rectifier-fed DC motor drive)


Variable Speed Electric DriveVariable Speed Electric DriveVariable Speed Electric DriveVariable Speed Electric Drive

Common features - Require information on instantaneous rotor position (speed), - Closed-loop control operation - Machine is supplied from a power electronic converter Applications Robotics Machine tools Elevators Rolling mills Paper mills Spindles Mine winders Electric traction Electric and hybrid electric vehicles, and the like.


Variable Speed Electric DriveVariable Speed Electric DriveVariable Speed Electric DriveVariable Speed Electric Drive

Figure : Schematic outlay of a high-performance variable speed electric drive


Variable Speed Electric Drive Variable Speed Electric Drive Variable Speed Electric Drive Variable Speed Electric Drive ---- OperationOperationOperationOperation

Electromagnetic torque of an electric machine - Product of the flux-producing current and torque-producing current - Control system has two parallel paths - Flux-producing current reference (as a constant) - Torque-producing current (the output of the torque controller)


Variable Speed Electric Drive Variable Speed Electric Drive Variable Speed Electric Drive Variable Speed Electric Drive ---- OperationOperationOperationOperation

- Torque controller is usually not present in high-performance drives - Torque-producing current reference can be obtained directly from the reference torque by means of a simple scaling (or the output of the speed controller can be made to be directly the torque-producing current reference

- The torque and the torque-producing current - related through a constant. The control (when a high-performance control algorithm is applied)

- Control structure : Composed of cascaded controllers (typically of PID)


Fundamentals of Induction Motor (IM) TheoryFundamentals of Induction Motor (IM) TheoryFundamentals of Induction Motor (IM) TheoryFundamentals of Induction Motor (IM) Theory

Case 1: Case 1: Case 1: Case 1: VoltageVoltageVoltageVoltage----ControlledControlledControlledControlled IMIMIMIM RepresentedRepresentedRepresentedRepresented inininin aaaa StatorStatorStatorStator----FixedFixedFixedFixed SystemSystemSystemSystem ofofofof CoordinatesCoordinatesCoordinatesCoordinates ((((α,,,, β))))

Case 2: Case 2: Case 2: Case 2: CurrentCurrentCurrentCurrent----ControlledControlledControlledControlled IMIMIMIM RepresentedRepresentedRepresentedRepresented inininin SynchronousSynchronousSynchronousSynchronous CoordinatesCoordinatesCoordinatesCoordinates (d,(d,(d,(d, q)q)q)q)

FigureFigureFigureFigure:::: VectorVectorVectorVector diagramdiagramdiagramdiagram ofofofof InductionInductionInductionInduction MotorMotorMotorMotor (IM)(IM)(IM)(IM) inininin stationarystationarystationarystationary α − β

andandandand rotatingrotatingrotatingrotating dddd − qqqq coordinatescoordinatescoordinatescoordinates


Steady State CharacteristicsSteady State CharacteristicsSteady State CharacteristicsSteady State Characteristics

The The The The breakdown torque breakdown torque breakdown torque breakdown torque is is is is independent independent independent independent of the of the of the of the rotor resistancerotor resistancerotor resistancerotor resistance

The The The The breakdown slip frequency breakdown slip frequency breakdown slip frequency breakdown slip frequency is is is is proportional proportional proportional proportional to the to the to the to the rotor resistance rotor resistance rotor resistance rotor resistance

Under Under Under Under constant Us/constant Us/constant Us/constant Us/fsfsfsfs modemodemodemode, the , the , the , the breakdown torque breakdown torque breakdown torque breakdown torque remains remains remains remains constantconstantconstantconstant

The simplified The simplified The simplified The simplified KlossKlossKlossKloss formulaformulaformulaformula

where the breakdown torque iswhere the breakdown torque iswhere the breakdown torque iswhere the breakdown torque is


Steady State CharacteristicsSteady State CharacteristicsSteady State CharacteristicsSteady State Characteristics

Figure: Torque-slip frequency characteristic obtained from the Kloss formula


IM Control CharacteristicsIM Control CharacteristicsIM Control CharacteristicsIM Control Characteristics

Figure: Control characteristics of IM in constant and weakened flux regions

General Classification of IM control MethodsGeneral Classification of IM control MethodsGeneral Classification of IM control MethodsGeneral Classification of IM control Methods


Constant V/Hz control schemeConstant V/Hz control schemeConstant V/Hz control schemeConstant V/Hz control scheme


Constant V/Hz control schemeConstant V/Hz control schemeConstant V/Hz control schemeConstant V/Hz control scheme (dashed lines show version with limited slip frequency (dashed lines show version with limited slip frequency (dashed lines show version with limited slip frequency (dashed lines show version with limited slip frequency Ωslcslcslcslc and speed control)and speed control)and speed control)and speed control)



VectorVectorVectorVector controlcontrolcontrolcontrol (also(also(also(also calledcalledcalledcalled FieldFieldFieldField----OrientedOrientedOrientedOriented ControlControlControlControl,,,, FOC)FOC)FOC)FOC) isisisis oneoneoneone methodmethodmethodmethod usedusedusedused inininin

variablevariablevariablevariable frequencyfrequencyfrequencyfrequency drivesdrivesdrivesdrives totototo controlcontrolcontrolcontrol thethethethe torquetorquetorquetorque (and(and(and(and thusthusthusthus finallyfinallyfinallyfinally thethethethe speedspeedspeedspeed)))) ofofofof

threethreethreethree----phasephasephasephase ACACACAC electricelectricelectricelectric motorsmotorsmotorsmotors bybybyby controllingcontrollingcontrollingcontrolling thethethethe currentcurrentcurrentcurrent fedfedfedfed totototo thethethethe machinemachinemachinemachine....

Vector ControlVector ControlVector ControlVector Control

PropertiesPropertiesPropertiesProperties

Speed or position measurement or some sort of estimation is needed

Torque and flux can be changed reasonably fast, in less than 5-10 milliseconds, by

changing the references

The step response has some overshoot if PI control is used

The switching frequency of the transistors is usually constant and set by the

modulator

The accuracy of the torque depends on the accuracy of the motor parameters

used in the control. Thus large errors due to for example rotor temperature

changes often are encountered.

Reasonable processor performance is required, typically the control algorithm

has to be calculated at least every millisecond.


Field Oriented ControlField Oriented ControlField Oriented ControlField Oriented Controll (l (l (l (FOC)FOC)FOC)FOC)

1. Principle of the FOC - An analogy to the mechanically commutated DC

brush motor

2. Owing to separate exciting and armature winding,

Flux - Controlled by exciting current

Torque - Controlled independently by adjusting the armature current

3. Flux and torque currents - Electrically and magnetically separated

4. The cage-rotor IM

- Only a three-phase winding in the stator

- Stator current vector (Is) - Used for both flux and torque control

5. Coupled Currents - Exciting and armature currents

(Not separated) in the stator current vector

- Cannot be controlled separately


Field Oriented ControlField Oriented ControlField Oriented ControlField Oriented Controll (l (l (l (FOC) Schemes FOC) Schemes FOC) Schemes FOC) Schemes

Direct FOCDirect FOCDirect FOCDirect FOC


Field Oriented ControlField Oriented ControlField Oriented ControlField Oriented Controll (l (l (l (FOC) Schemes FOC) Schemes FOC) Schemes FOC) Schemes

Indirect FOCIndirect FOCIndirect FOCIndirect FOC

Variants of FOC control schemes Variants of FOC control schemes Variants of FOC control schemes Variants of FOC control schemes

for fieldfor fieldfor fieldfor field----weakened operation: (a) Indirect FOC weakened operation: (a) Indirect FOC weakened operation: (a) Indirect FOC weakened operation: (a) Indirect FOC



Variants of FOC control schemes Variants of FOC control schemes Variants of FOC control schemes Variants of FOC control schemes

for fieldfor fieldfor fieldfor field----weakened operation: (b) direct FOCweakened operation: (b) direct FOCweakened operation: (b) direct FOCweakened operation: (b) direct FOC


TTTTrrrr ---- Adaption based on model reference adaptive system (MRAS)Adaption based on model reference adaptive system (MRAS)Adaption based on model reference adaptive system (MRAS)Adaption based on model reference adaptive system (MRAS)

Parameter Adaptation - The critical parameter - Rotor time constant (Tr)

ConditionsConditionsConditionsConditions ofofofof ChangeChangeChangeChange ::::

Under the influence of temperature changes of rotor resistance (Rr) and

Changes brought about by the saturation effect (Rotor inductance (Lr) )

The temperature changes of Rr - VeryVeryVeryVery slow,slow,slow,slow,

The changes of Lr - veryveryveryvery fast,fast,fast,fast,

( i.e., Case of speed reversal when the motor)


Variants of Variants of Variants of Variants of TTTTrrrr————Adaption AlgorithmsAdaption AlgorithmsAdaption AlgorithmsAdaption Algorithms


Block scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled S----FOC) FOC) FOC) FOC)

with optional outer torque control loop (dashed lines)with optional outer torque control loop (dashed lines)with optional outer torque control loop (dashed lines)with optional outer torque control loop (dashed lines)

Note: Note: Note: Note:

Natural field orientation(NFO)Natural field orientation(NFO)Natural field orientation(NFO)Natural field orientation(NFO)

---- Commercially available as Commercially available as Commercially available as Commercially available as

an ASICan ASICan ASICan ASIC


Block scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled SBlock scheme of NFO (Voltage Controlled S----FOC) FOC) FOC) FOC) with optional outer torque control loop (dashed lines)


Vector Vector Vector Vector control scheme for a multiphase machinecontrol scheme for a multiphase machinecontrol scheme for a multiphase machinecontrol scheme for a multiphase machine

Figure : Basic vector control scheme for a multiphase machine with CC in the stationary reference frame


Vector Vector Vector Vector control scheme for control scheme for control scheme for control scheme for PMSMPMSMPMSMPMSM

Figure : Vector control of a PMSM with surface-mounted magnets in the base

speed region (K1 = Pψm)


FieldFieldFieldField----Oriented Control of Oriented Control of Oriented Control of Oriented Control of

Multiphase Synchronous Multiphase Synchronous Multiphase Synchronous Multiphase Synchronous Reluctance MachinesReluctance MachinesReluctance MachinesReluctance Machines

Figure: FOC of a multiphase Syn-Rel using CC in the stationary reference frame




Figure: Basic form of an RFOC scheme for a multiphase induction machine, with CC in the stationary reference frame (base speed region only)




Figure: Indirect RFOC scheme for operation of an induction machine in the base speed region (p = Laplace operator; 1/p = integrator)


IRFOC scheme with compensation of magnetizing flux IRFOC scheme with compensation of magnetizing flux IRFOC scheme with compensation of magnetizing flux IRFOC scheme with compensation of magnetizing flux

dededede----saturation saturation saturation saturation for operationfor operationfor operationfor operation

Figure: IRFOC scheme with compensation of magnetizing flux de-saturation for operation in both base speed and field weakening region. Inverse magnetizing curve of the machine is embedded in the controller as ananalytical function in per unit form.


Direct Torque Control (DTC)Direct Torque Control (DTC)Direct Torque Control (DTC)Direct Torque Control (DTC)

In the FOC strategy, the torque is controlled by the stator current component (Isq), in accordance with equation

where δ is the torque angle between the rotor flux vector and the stator current vector

This makes the current-controlled PWM inverter very convenient for the implementation of the R-FOC scheme (Figure shown below) and torque is controlled by adjusting the stator current vector.

FigureFigureFigureFigure:::: InverterInverterInverterInverter outputoutputoutputoutput voltagevoltagevoltagevoltage

representedrepresentedrepresentedrepresented asasasas spacespacespacespace vectorsvectorsvectorsvectors



In the case of voltage source PWM inverter–fed IM drives, Both the stator current and the torque are used as the control components

FigureFigureFigureFigure:::: VectorVectorVectorVector diagramdiagramdiagramdiagram ofofofof inductioninductioninductioninduction motormotormotormotor inininin statorstatorstatorstator----fixedfixedfixedfixed coordinatescoordinatescoordinatescoordinates α––––β



FigureFigureFigureFigure:::: InverterInverterInverterInverter outputoutputoutputoutput voltagevoltagevoltagevoltage representedrepresentedrepresentedrepresented asasasas spacespacespacespace vectorsvectorsvectorsvectors

where

Eight voltage vectors (correspond to possible inverter states) – Equation shown

above

Six active vectors, U1–U6, and two zero vectors, U0 and U7



The stator flux vector can directly be adjusted by the inverter voltage vector

In six-step operation,

Inverter output voltage constitutes a cyclic and symmetric sequence of active vectors

The stator flux moves with constant speed along a hexagonal path (Figure : a).

The introduction of zero vectors stops the flux, but does not change its path.

In Sinusoidal PWM operation,

The inverter output voltage constitutes a suitable sequence of two active and zero vectors and the stator flux moves along a track resembling a circle (Figure: b).

Figure : a Figure : b


Magnified part of the flux vector trajectoryMagnified part of the flux vector trajectoryMagnified part of the flux vector trajectoryMagnified part of the flux vector trajectory

Figure:

Forming of the stator flux trajectory by selection of appropriate voltage vectors

sequence


Magnified part of the flux vector trajectoryMagnified part of the flux vector trajectoryMagnified part of the flux vector trajectoryMagnified part of the flux vector trajectory

In any case, the rotor flux rotates continuously at the actual synchronous speed along a near-circular path, since it is smoothed by the rotor circuit filtering action.

In the view of torque production, Relative motion of the two vectors

- Forms the torque angle δΨ (that determines the instantaneous motor torque)

The cyclic switching of active and zero vectors – Control of Motor torque

Field-weakening region,

No zero vectors

Torque control - Via a fast change of the torque angle, δΨ, by advancing (to increase the torque) or

retarding (to reduce it) the phase of the stator flux vector


Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)

The generic DTC scheme - Two hysteresis controllers

The stator flux controller - The time duration of the active voltage vectors,

(imposes) (move the stator flux along the commanded trajectory)

The torque controller - The time duration of the zero voltage vectors,

(determines) (The motor torque in the defined-by-hysteresis tolerance band)

At every sampling time - The voltage vector selection block chooses

- The inverter switching state (SA, SB, SC),

- which reduces the instantaneous flux and torque errors.


Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)Generic Direct Torque Control (DTC)

Figure: Block scheme of switching table based direct torque control (ST-DTC) method.


Characteristics features of Generic Direct Torque Control (DTC)Characteristics features of Generic Direct Torque Control (DTC)Characteristics features of Generic Direct Torque Control (DTC)Characteristics features of Generic Direct Torque Control (DTC)

Nearly sinusoidal stator flux and current waveforms Harmonic content (Determination)

- By the flux- and torque-controller hysteresis bands, HΨ and HM Excellent torque dynamics Flux and torque hysteresis bands (Determination) - Inverter switching frequency, (which varies with the synchronous speed and load conditions)


Sectors in the classical STSectors in the classical STSectors in the classical STSectors in the classical ST----DTC methodDTC methodDTC methodDTC method



Figure: Selection of the optimum voltage vectors for the stator flux vector

located in sector 1.



TABLE : Optimum Switching Table of Classical DTC


DSC DSC DSC DSC –––– Block DiagramBlock DiagramBlock DiagramBlock Diagram


DSC AlgorithmDSC AlgorithmDSC AlgorithmDSC Algorithm

Based on

the command stator flux, Ψsc, and

the actual phase components, ΨsA, ΨsB, and ΨsC,

the flux comparators generate

digital variables, dA, dB, and dC,

which correspond to active voltage vectors (U1–U6).

The hysteresis torque controller

- Generates signal dm,

-which determines zero states.

In the constant flux region, the control algorithm is as follows:


DSC DSC DSC DSC –––– Characteristics Characteristics Characteristics Characteristics

Non-sinusoidal stator flux and current waveforms that, with the exception of

the harmonics, are identical for both PWM and the six-step operation

The stator flux vector moves along a hexagonal path also under the PWM

operation

No voltage supply reserve is necessary and the inverter capability is fully

utilized.

The inverter switching frequency is lower than in the ST-DTC scheme, because

PWM is not of sinusoidal type as it turns out by comparing the voltage

patterns

Excellent torque dynamics in constant and weakening field regions.


DTCDTCDTCDTC----SVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with Closed----Loop Torque ControlLoop Torque ControlLoop Torque ControlLoop Torque Control

For torque regulation -> PI controller is applied

An increment in the torque angle, ΔδΨ

Produced by the output of PI controller (Figure 21.31).

Assuming that rotor and flux magnitudes are approximately equal,

the torque is controlled only by changing the torque angle, δΨ.

Figure: Vector diagram for DTC-SVC control scheme


DTCDTCDTCDTC----SVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with Closed----Loop Torque ControlLoop Torque ControlLoop Torque ControlLoop Torque Control

Figure: DTC-SVM scheme with closed-loop torque control


DTCDTCDTCDTC----SVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with Closed----Loop Torque and Flux ControlLoop Torque and Flux ControlLoop Torque and Flux ControlLoop Torque and Flux Control

The output of the PI flux and torque controllers is k interpreted as the

reference stator voltage components, Usdc and Usqc, in S-FOC (d − q).

DC voltage commands – Transformed into

Stationary coordinates (α − β), and

Commanded values, Usαc and Usβc,

- Delivered to the SVM block

DTCDTCDTCDTC----SVMSVMSVMSVM SchemeSchemeSchemeScheme withwithwithwith ClosedClosedClosedClosed----LoopLoopLoopLoop TorqueTorqueTorqueTorque ControlControlControlControl

DTCDTCDTCDTC----SVMSVMSVMSVM SchemeSchemeSchemeScheme withwithwithwith ClosedClosedClosedClosed----LoopLoopLoopLoop TorqueTorqueTorqueTorque andandandand FluxFluxFluxFlux ControlControlControlControl –––– LessLessLessLess SensitiveSensitiveSensitiveSensitive

Commanded voltage vector is generated by flux and torque controllers


DTCDTCDTCDTC----SVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with ClosedSVM Scheme with Closed----Loop Torque and Flux ControlLoop Torque and Flux ControlLoop Torque and Flux ControlLoop Torque and Flux Control

Figure: DTC-SVM scheme operated in stator flux Cartesian coordinates d–q.


SummarySummarySummarySummary

Scalar control is based on the IM equations at steady-state operating points

and is typically implemented in open-loop schemes keeping constant V/Hz.

However, such a scheme applied to a multivariable, coupled system like the

IM cannot perform decoupling between inputs and outputs, resulting in

problems of independent control of outputs, for example, torque and flux.

To achieve decoupling in high-performance IM drives, vector control, also

known as field oriented control as well as direct torque control, has been

developed. The FOC and DTC are now de facto standard, in highly dynamic IM

industrial drives.



The R-FOC is easily implemented in combination with a current-controlled

PWM inverter.

For a good low-speed operation performance, indirect R-FOC with a

speed/position sensor is recommended. This scheme, however, is sensitive

to changes of the rotor time constant, which has to be adapted online.

DTC has a very fast torque response, a very simple structure, does not

require a shaft motion sensor, and is less sensitive to IM parameter changes

as in FOC.

For a speed-sensorless operation, the DTC or the direct R-FOC scheme can be

advised..



To reduce torque ripple and fix the inverter switching frequency, the SVM has

been introduced into the DTC structure, resulting in a new scheme known as

DTC-SVM.

Basically, this is S-FOC without current control loops. However, the DTC-SVM

scheme combines advantages and eliminates disadvantages of classical DTC

and FOC schemes.

Therefore, it is an excellent solution for general-purpose IM (also PMSM)

drives.


Overview of Main IM Control Strategies Overview of Main IM Control Strategies Overview of Main IM Control Strategies Overview of Main IM Control Strategies

((((in in in in Low and Medium Low and Medium Low and Medium Low and Medium Power)Power)Power)Power)


Digital Digital Digital Digital control of a multiphase SPMSM drivecontrol of a multiphase SPMSM drivecontrol of a multiphase SPMSM drivecontrol of a multiphase SPMSM drive

Figure: Fully digital control of a multiphase SPMSM drive with CC in rotational reference frame.


The The The The three three three three classes of adaptive classes of adaptive classes of adaptive classes of adaptive control control control control systemssystemssystemssystems

Gain scheduling systems (GS)

Self-tuning regulators (STR)

Model reference adaptive systems (MRAS)

Figure: Block diagram of a system with gain scheduling.


Adaptive Adaptive Adaptive Adaptive control control control control systemssystemssystemssystems

Figure : Block diagram of a system with an MRAS

Figure : Block diagram of STR


Fuzzy Logic (FL) ControllerFuzzy Logic (FL) ControllerFuzzy Logic (FL) ControllerFuzzy Logic (FL) Controller

Figure: Structure Figure: Structure Figure: Structure Figure: Structure of adaptive speed control loop of adaptive speed control loop of adaptive speed control loop of adaptive speed control loop forforforfor

sensorlesssensorlesssensorlesssensorless DC drive with DC drive with DC drive with DC drive with FL FL FL FL controllercontrollercontrollercontroller


Figure: The internal structure of the FL controller

Figure: Membership functions

Figure: The rule base.

Fuzzy Logic (FL) ControllerFuzzy Logic (FL) ControllerFuzzy Logic (FL) ControllerFuzzy Logic (FL) Controller


REFERENCESREFERENCESREFERENCESREFERENCES

1. Bogdan M. Wilamowski J. david Irwin, The Industrial Electronics Handbook - Power

electronics and motor drives Edited by, Second Edition, CRC Press, 2011 by Taylor

and Francis Group, LLC.

2. Austin Hughes, Electric Motors and Drives - Fundamentals, Types and Applications,

Third edition, Newnes , published by Elsevier Ltd., 2006.

3. Bimal K. Bose, Modern Power Electronics and AC Drives, Prentice Hall PTR, 2002.

4. Bimal K. Bose, Power Electronics and Motor Drives-Advances and Trends, Academic

Press, Elseveir Group, 2006.

5. R. Krishnan, Electric Motor Drives: Modeling, Analysis and Control, Prentice Hall

Inc., 2002.

6. www.wikipedia.com

7. www.google.com


THANKS FOR YOUR KIND ATTENTIONTHANKS FOR YOUR KIND ATTENTIONTHANKS FOR YOUR KIND ATTENTIONTHANKS FOR YOUR KIND ATTENTION

R Balamurugan FDP Electrical Drives and Control

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