A Review on Direct Torque Control of Induction Motorijntse.com/upload/14356478523. A Review on Direct Torque Control of Induction Motor.pdfelectromagnetic rotation and built the first

J. M. R. Malla et. al. / International Journal of New Technologies in Science and EngineeringVol. 1, Issue. 1, Jan. 2014, ISSN XXXX-XXXX

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A Review on Direct Torque Control ofInduction Motor

Jagan Mohana Rao Malla and Manti Mariya DasEmail: [email protected]

Abstract: At present, induction motors are the dominant drives in various industries. It is quitecumbersome to control an induction motor (IM) because of its poor dynamic response incomparison to the DC motor drives. The central theme of Vector Control (VC) is to decouplethe stator current of the IM into two orthogonal components and is to control these twocomponents individually so as to achieve an independent control of flux and torque of the IM.VC is still very complex to implement. Direct Torque Control (DTC) is an improvised VCmethod. With the DTC scheme employing a Voltage Source Inverter, it is possible to controldirectly the stator flux linkage and the electromagnetic torque by the optimum selection ofinverter switching vectors. The modeling of an IM drive employing DTC with application offuzzy is performed in this article, it is better to understand the DTC and its difficulties. Thereference voltage vector is then realized using a voltage vector modulator. Several variations ofDTC-SVM have been proposed and discussed in the literature. The work of this review paperis to study, evaluate and compare the various techniques of the DTC-SVM applied to theInduction Motor.

Keywords: Induction Motor Drive, Modeling of Induction Motor, Vector Control, Field OrientControl, Direct Torque Control, and Fuzzy Applications.

1. INTRODUCTIONThe history of electrical motors goes back as far as 1820, when Hans Christian Oersted

discovered the magnetic effect of an electric current. One year later, Michael Faraday discovered theelectromagnetic rotation and built the first primitive D.C. motor. Faraday went on to discoverelectromagnetic induction in 1831, but it was not until 1883 that Tesla invented the A.C.asynchronous motor [1]. Currently, the main types of electric motors are still the same, DC, ACasynchronous and synchronous, all based on Oested, Faraday and Tesla’s theories developed anddiscovered more than a hundred years ago.

An IM is a type of asynchronous AC motor where power is supplied to the rotating device bymeans of electromagnetic induction [2-5]. Induction motors are widely used, especially polyphaseinduction motors, which are frequently used in industrial drives. These facts are due to the inductionmotors advantages over the rest of the motors. Most of the industrial motor applications use ACinduction motors. The reasons for this include high robustness, reliability, low price and highefficiency [2-8].

2. PRINCIPLE OF OPERATION AND COMPARISON TO SYNCHRONOUS MOTORSA 3-phase power supply provides a rotating magnetic field in an IM. The basic difference

between an IM and a synchronous AC motor is that in the latter a current is supplied onto the rotor.This then creates a magnetic field which, through magnetic interaction, links to the rotating magneticfield in the stator which in turn causes the rotor to turn. It is called synchronous because at steadystate the speed of the rotor is the same as the speed of the rotating magnetic field in the stator. Byway of contrast, the IM does not have any direct supply onto the rotor; instead, a secondary current isinduced in the rotor [2, 9]. This changing magnetic field pattern can induce currents in the rotorconductors. These currents interact with the rotating magnetic field created by the stator and the rotorwill turn [10].



This difference between the speed of the rotor and speed of the rotating magnetic field in thestator is called slip. The three phase AC IM and is the most widely used machine. Because it ishaving the characteristic features Simple and rugged construction, Low cost and minimummaintenance, High reliability and sufficiently high efficiency, Needs no extra starting motor andneed not be synchronized, and an IM has basically two parts: Stator and Rotor [10].2.1. APPLICATIONS

A wide variety of induction motors are available and are currently in use throughout a rangeof industrial applications. Single phase induction motors are widely used, due to their simplicity,strength and high performance. They are used in household appliances, such as refrigerators, airconditioners, hermetic compressors, washing machines, pumps, fans, as well as in some industrialapplications. Before the days of power electronics, a limited speed control of IM was achieved byswitching the three-stator windings from delta connection to star connection, allowing the voltage atthe motor windings to be reduced [1-20].2.2. VARIABLE-FREQUENCY DRIVES (VFD)

A VFD can easily start a motor at a lower frequency than the AC line, as well as a lowervoltage, so that the motor starts with full rated torque and with no inrush of current. The rotorcircuit's impedance increases with slip frequency, which is equal to supply frequency for a stationaryrotor, so running at a lower frequency actually increases torque [21-23]. Industries have manyapplications, where variable operating speed is a prime requirement. Principal benefits of variablespeed drives in industrial applications are that they allow the drive speed and torque to be adjusted tosuit the process requirements. In many applications, operating the plant at a reduced speed when fulloutput is not needed produces a further important benefit: energy savings and reduced cost [21].Whereas infinitely variable speed drives with good performances for DC motors already existed.These drives not only permitted the operation in four quadrants but also covered a wide power range.Moreover, they had a good efficiency, and with a suitable control even a good dynamic response. Itsmain drawback was the compulsory requirement of brushes [10].

The various methods of speed control of squirrel cage IM through semiconductor devices aregiven in [2, 9-20] as under: Scalar control, Vector control (Field-Oriented Control, FOC), DirectTorque Control (DTC) and DTC with SVM & Fuzzy based control. These controllers are depends onhow inverters can be controlled, mostly multilevel inverters are using in industries due to theiradvantages [21-45].

Scalar controllers: Despite the fact that “Voltage-Frequency” (V/F) is the simplest controller, itis the most widespread, being in the majority of the industrial applications [2]. It is known as a scalarcontrol and acts by imposing a constant relation between voltage and frequency, so as to give nearlyconstant flux over wide range of speed variation [9]. More over Constant voltage/hertz control keepsthe stator flux linkage constant in steady state without maintaining decoupling between the flux andtorque [2]. However, this controller does not achieve a good accuracy in both speed and torqueresponses, mainly due to the fact that the stator flux and torque are not directly controlled. Eventhough, as long as the parameters are identified, the accuracy in the speed can be 2% (expect in avery low speed), and the dynamic response can be approximately around 50ms [2, 9].

Vector controllers: In 1971, Blaschke propose a scheme which aims as the control of an IMlike a separately excited dc motor, called field oriented control, VC, or Trans vector control [46-48].In this scheme the IM analyzed from a synchronously rotating reference frame where all fundamentalvariables appears to be dc ones. The torque and flux component of currents are identified andcontrolled independently to achieve good dynamic response [46, 47]. The most widespreadcontrollers of this type are the ones that use vector transform such as either Park or Ku. Howeverthere is a necessity of transforming the variables in the synchronously rotating reference frame tostator reference frame to affect the control of actual currents/voltages [47]. Additionally thetransformation also needs the approximate flux vector angle, where is either calculated slip angle ormeasured rotor angle as indirect VC or by estimating the flux angle directly by employing a flux



observer as in direct VC [47]. Its accuracy can reach values such as 0.5% regarding the speed and2% regarding the torque, even when at standstill. The main disadvantages are the huge computationalcapability required and the compulsory good identification of the motor parameters.

Recently advanced control strategies for PWM inverter fed IM drives have been developedbased on the space vector approach, where the IM can be directly and independently controlledwithout any co-ordination transformation [48]. One of the emerging methods in this perspective isthe direct torque and flux control (DTFC). In DTFC, the motor torque and the flux are calculatedfrom the primary variables, and they are controlled directly and independently by selecting optimuminverter switch modes [2-52]. This control results in quick torque response in the transient operationand improvement in the steady state efficiency [14]. Its main characteristic is the good performance,obtaining results as good as the classical vector control but with several advantages based on itssimpler structure and control diagram.

DTC is said to be one of the future ways of controlling the IM in four quadrants. In DTC it ispossible to control directly the stator flux and the torque by selecting the appropriate inverter state[46, 54]. DTC main features are direct control of flux and torque, indirect control of stator currentsand voltages, approximately sinusoidal stator fluxes and stator currents, and High dynamicperformance even at stand still [53, 54]. DTC have several advantages like, Decoupled control oftorque and flux, Absence of co-ordinate transforms, Absence of voltage modular block, Absence ofmechanical transducers, Current regulator, PWM pulse generation, PI control of flux and torque andco-ordinate transformation is not required, Very simple control scheme and low computational time,and Reduced parameter sensitivity and Very good dynamic properties as well as other controllerssuch as PID for motor flux and torque, and Minimal torque response time even better than the VCs[53, 54]. However, some disadvantages are also present such as: Possible problems during starting,Requirement of torque and flux estimators, implying the consequent parameters identification, andInherent torque and stator flux ripple [53-54]. Although, some disadvantages are: High torque ripplesand current distortions, Low switching frequency of transistors with relation to computation time,Constant error between reference and real torque [3]. After this, comparison of variable speed drivesis given. The aim being to find even simpler methods of speed control for induction machines onemethod, which is popular at the moment, is DTC.

Initially the theory of induction machine model is given. The understanding of this model ismandatory to understand both the control strategies (i.e. FOC and DTC). DTC drives utilizinghysteresis comparators suffer from high torque ripple and variable switching frequency. Straightlyspeaking, Major drawback of Classical DTC is high torque & flux ripples. The most commonsolution to this problem is to use fuzzy applications with Space Vector Modulation (SVM) or usingmultilevel inverter [2, 3]. In this Paper the author briefly explained about two-fuzzy controller alongwith the SVM technique is applied to two level inverter. Before going to DTC, first we study aboutthe mathematical background of DTC.

3. INDUCTION MOTOR MATHEMATICAL MODELThe steady-state model and equivalent circuit are useful for studying the performance of

machine in steady state. This implies that all electrical transients are neglected during load changesand stator frequency variations. The dynamic model of IM is derived by using a two-phase motor indirect and quadrature axes [55]. This approach is desirable because of the conceptual simplicityobtained with the two sets of the windings, one on the stator and the other on the rotor. Theequivalence between the three-phase and two-phase machine models is derived from the simpleobservation. The concept of power invariance is introduced [2, 3, 8]. The reference frames arechosen to arbitrary and particular cases such as stationary, rotor, and synchronous reference frames,are simple instances of the general case. The space-phasor model is derived from the dynamic modelin direct and quadrature axes [55].3.1 DYNAMIC d-q MODEL



The assumptions are made to derive the dynamic model as uniform air gap, balanced rotor andstator windings, with sinusoidal distributed mmf, inductance vs. rotor position in sinusoidal, andSaturation and parameter changes are neglected. The dynamic performance of an AC machine issomewhat complex because the three-phase rotor windings move with respect to the three-phasestator windings as shown in Fig 1(a). Basically, it can be looked on as a transformer with a movingsecondary, where the coupling coefficients between the stator and rotor phases change continuouslywith the change of rotor position correspond to rotor direct and quadrature axes [2-4, 7, 8]. Notethat a three-phase machine can be represented by an equivalent two-phase machine as shown in Fig1(b), where ds ~ qs correspond to stator direct and quadrature axes, and d r ~q r is corresponding torotor.

Fig 1: (a) Coupling effect in three-phase stator and rotor windings of motor; (b) Equivalent two-phasemachine.

Although it is somewhat simple, the problem of time-varying parameters still remains. R.H.Park, in the 1920s, proposed a new theory of electric machine analysis to solve this problem.Essentially, he transformed or referred, the stator variables to a synchronously rotating referenceframe fixed in the rotor [56]. With such a transformation (called Park’s transformation), he showedthat all the time-varying inductances that occur due to an electric circuit in relative motion andelectric circuits with varying magnetic reluctances can be eliminated [3,7]. Later, in the 1930s, H. C.Stanley showed that time- varying inductances in the voltage equations of an induction machine dueto electric circuits in relative motion can be eliminated by transforming the rotor variables tovariables associated with fictitious stationary windings. Later, G. Kron proposed a transformation ofboth stator and rotor variables to a synchronously rotating reference frame that moves with therotating magnetic field. D. S. Brereton proposed a transformation of stator variables to a rotatingreference frame that is fixed on the rotor. In fact, it was shown later by Krause and Thomas that time-varying inductances can be eliminated by referring the stator and rotor variables to a commonreference frame which may rotate at any speed.3.2. AXES TRANSFORMATION

Consider a symmetrical three-phase induction machine with stationary as-bs-cs axes at 2π/3-angle apart, as shown in Fig 2. Our goal is to transform the three-phase stationary reference frame(as-bs -cs) variables into two-phase stationary reference frame (ds~qs) variables and then transformthese to synchronously rotating reference frame (de ~ qe), and vice-versa [3, 56]. Assume that the de

–

qe. Axes are oriented at angle, as shown in Fig 2. The voltages and can be resolved intoas-bs-cs components and can be represented in the matrix form as

= (1)

r

sdsV s

qsV

cs

bs

as

VVV

1)120sin()120cos(1)120sin()120cos(1sincos

00

00

sos

sds

sqs

VVV



The corresponding inverse relation is.

= (2)

Where is added as the zero sequence component, which may or may not be present. Thecurrent and flux linkages can be transformed by similar equations. It is convenient to set = 0, sothat the qs axis is aligned with the as-axis, the transformation relations can be simplified by ignoringzero sequence. Fig 3 shows the synchronously rotating de- q e, which rotates at synchronous speed

with respect to the ds-qs axes and the angle the two-phase de- qs windings aretransformed into the hypothetical windings mounted on the de-qe axes [3]. The voltages on the ds-qs

axes can be converted (or resolved) into the de-qe frame as follows:(3)

(4)For convenience, the superscript e has been dropped from now on from the synchronously

rotating frame parameters. Again, resolving the rotating frame parameters into a stationary frame, therelations are.

(5)

(6)The qe -de components can also be combined into a vector form:

(7)

Or inversely(8)

Note that the vector magnitudes in stationary and rotating frames are equal, that is,

(9)

Fig 2. Stationary frame a~b~c to ds~qs axes transformation.

sos

sds

sqs

VVV

32

5.05.05.0)120sin()120sin(sin)120cos()120cos(cos

00

00

cs

bs

as

VVV

sosV

e .tee

es

dses

qsqs VVV sincos

es

dses

qsds VVV cossin

edseqss

qs VVV sincos

edseqss

ds VVV cossin

ee jjsds

sqs

es

dses

qses

dses

qsdsqse

qds

eVejVV

VVjVVjVVV

)(

)cossin()sincos(

ejdsqs

sds

sqs ejVVjVVV )(

22ˆdsqsm VVVV



In Equation (7), eje is defined as the inverse vector rotator that converts ds -qs variables intode - qe variables. The vector V and its components projected on rotating and stationary axes areshown in Fig 3. The as-bs-cs variables can also be expressed in vector form. And also:

(10)

Where a=e j 2∏ / 3. The parameters a and a2 can be interpreted as unit vectors. Similartransformations can be made for rotor circuit variables also [3, 8, 17].3.3. SYNCHRONOUSLY ROTATING REFERENCE FRAME - DYNAMIC MODEL.

For the two-phase machine shown in Fig 3, we need to represent both ds -qs and dr – qr circuitsand their variables in a synchronously rotating de -qe frame. We can write the following stator circuitequations:

(11)

sds

sdss

sds dt

dIRV (12)

Where and are q- axis and d-axis stator flux linkages, respectively. When theseequations are converted to de -qe frame, the following equations can be written:

(13)

qsedsdssds dtdIRV (14)

Fig.3: (a) Stationary frame ds - qs to rotating frame de - qe ; (b) Flux and current vectors de - qe.

If the rotor is not moving, that is, , the rotor equations for a doubly fed wound-rotormachine will be similar to Equations (13) - (14):

csbsas

csbscsbsas

sds

sqs

VaaVV

VVjVVV

jVVV

2

32

31

31

31

31

32

sqs

sqss

sqs dt

dIRV

sqs

sds

dseqsqssqs dtdIRV

0r



(15)

qredrdrrdr dtdiRV (16)

The rotor actually moves at speed r , the d - q axes fixed on the rotor move at a speed e - rrelative to the synchronously rotating frame. Therefore, rotor equations should be modified as.

(17)

(18)

The de -qe dynamic model equivalent circuits that satisfy Equations (13), (14) and (17), (18). Aspecial advantage of the de -qe dynamic model of the machine is that all the sinusoidal variables instationary frame appear as dc quantities in synchronous frame. The flux linkage expressions in termsof the currents can be written from Fig 3(b) as follows:

(19)

)( qrqsmqrlrqr iiLiL (20)

)( qrqsmqm iiL (21)

)( drdsmdslsds iiLiL (22))( drdsmdrlrdr iiLiL (23)

)( drdsmdm iiL (24)Combining the above expressions with Equations (13), (14), (17) and (18), the electrical

transient model in terms of voltages and currents can be given in matrix form as

(25).

Where S is Laplace operator. For a cage motor, Vrq=Vdr= 0. If the speed is consideredconstant. Then, knowing the inputs Vsq, Vsd and , the currents iqs, ids, iqr and idr can be solved fromEquation (25). If the machine is fed by current source, iqs, ids and are independent. Then thedependent variables Vsq,Vsd, iqr and idr can be solved from Equation (25). The speed in Equation(25) cannot normally be treated as a constant. It can be related to the torques as

(26)

Where TL = load torque, J = rotor inertia, and = mechanical speed. Often, for compactrepresentation, the machine model and equivalent circuits are expressed in complex form [3].Multiplying Equation (14) by –j and adding with Equation (13) gives.

(27)

Or (28)

Similarly, the rotor equations (17)-(18) can be combined to represent

qdrreqdrqdrrqdr jdtdiRV )( (29)

dreqrqrrqr dtdiRV

drreqrqrrqr dtdiRV )(

qrredrdrrdr dtdiRV )(

)( qrqsmqslsqs iiLiL

dr

qr

ds

qs

rrrremmre

rrerrmrem

mmessse

memsess

dr

qr

ds

qs

iiii

SLRLSLLLSLRLSL

SLLSLRLLSLLSLR

VVVV

)()()()(

r

e

e

r

dtdJ

PT

dtdJTT r

Lm

Le 2

m

)()()( dsqsedsqsdsqssdsqs jjjdtdjiiRjVV

qdsreqdsqdssqds jdtdiRV )(



Where Vqdr=0. Therefore, the steady-state equations can be derived as(30)

(31)

If the parameter Rm is neglected. We know that

sin22

3rme IPT

(32)

From Equation (32), the torque can be generally expressed in the vector form as

(33)

drqmqrdme IiPT

223

(34)

Some other torque expressions can be derived easily as follows:

dsqmqsdme IiPT

223

(35)

dsqsqsdse IiPT

223

(36)

)(22

3qrdsdrqsme iiiiLPT

(37)

)(22

3drqrqrdre IiPT

(38)

Equations (25), (26), and (37) give the complete model of the electro-mechanical dynamics ofan IM in synchronous frame. Fig 4 shows the block diagram of the machine model along with inputvoltage & output current transformation [2, 8] and resolving variables into dqe components.Renewable energy based water supply system is one of the application [57-74]. In irrigation anddrinking water supply, mostly we are using induction motors; hence study of control of inductionmotor is necessary.

sesss jIRV

rerr jI

SR

0

rme IxPT

223



Fig 4. Synchronously rotating frame machine models with input voltage and output current transformations.4. CONTROL METHODS

Stator flux linkage is estimated by integrating the stator voltages. Torque is estimated as a crossproduct of estimated stator flux linkage vector and measured motor current vector [75, 76]. Theestimated flux magnitude and torque are then compared with their reference values. If either theestimated flux or torque deviates from the reference more than allowed tolerance, the GTO of thevariable frequency drive are turned off and on in such a way that the flux and torque will return intheir tolerance bands as fast as possible. Thus DTC is one form of the hysteresis or bang-bangcontrol. This control method implies the properties of the control: Torque and flux can be changedvery fast by changing the references, The step response has no overshoot, No coordinate transformsare needed, all calculations are done in stationary coordinate system, No separate modulator isneeded, the hysteresis control defines the switch control signals directly [3, 75, 76], and There are noPI current controllers. Thus no tuning of the PI is required.

However, by controlling the width of the tolerance bands the average switching frequency canbe kept roughly at its reference value [2, 3]. This also keeps the current and torque ripple small. Thusthe torque and current ripple are of the same magnitude than with vector controlled drives with thesame switching frequency. Due to the hysteresis control the switching process is random by nature.Synchronization to rotating machine is straightforward due to the fast control; just make the torquereference zero and start the inverter [2, 3, 75, 76]. The flux will be identified by the first currentpulse. Typically the control algorithm has to be performed with 10 - 30 microseconds or shorterintervals because of the simplicity of the algorithm.

The DTC method performs very well even without speed sensors [3]. However, the fluxestimation is usually based on the integration of the motor phase voltages [75, 76]. Due to theinevitable errors in the voltage measurement and stator resistance estimate the integrals tend tobecome erroneous at low speed. Thus it is not possible to control the motor if the output frequency ofthe variable frequency drive is zero. However, by careful design of the control system it is possible tohave the minimum frequency in the range 0.5 Hz to 1 Hz that is enough to make possible to start anIM with full torque from a standstill situation. A reversal of the rotation direction is possible too if



the speed is passing through the zero range rapidly enough to prevent excessive flux estimatedeviation [77, 78]. If continuous operation at low speeds including zero frequency operation isrequired, a position sensor can be added to the DTC system [77-79].

Fig 5: Block diagram of the induction motor drive system based on DTC scheme.4.1. VIEW OF DIRECT TORQUE CONTROL

In principle the DTC method selects one of the six nonzero and two zero voltage vectors of theinverter on the basis of the instantaneous errors in torque and stator flux magnitude [13, 76]. In spiteof its simplicity, DTC allows good torque control in both steady and transient state. Its maincharacteristic is the good performance, obtaining results as good as the classical vector control. Fig 5.Shows the Block diagram of the IM drive system based on DTC scheme [3, 75, 76]. DTC methodstill required further research in order to improve the motor’s performance, as well as achieve abetter behavior regarding environment compatibility (Electro Magnetic Interference and Energy),that is desired nowadays for all industrial applications.4.2 CLASSICAL DIRECT TORQUE CONTROL

Classic DTC makes use of hysteresis comparators with torque and stator flux magnitude errorsas inputs to decide which stator voltage vector is applied to motor terminals. The complex plane isdivided in six sectors, and a switching table is designed to obtain the required vector based on thehysteresis comparators outputs [3, 4]. Due to fast time constants of stator dynamics it is very difficultto keep machine torque between the hysteresis bands. This can do either by increasing the samplingfrequency as in, thus increasing switching frequency, commutation losses and computationrequirements, or using multilevel converters. The use of hysteresis comparators in classic DTCimplementations give rise to variable switching frequency (VSF), which depends on rotor speed,load, sample frequency, etc. VSF may excite resonant dynamics in the load and hence constitute aserious drawback of DTC.

Generally there are two methods to reduce the torque and flux ripple for the DTC drives. Oneis multi level inverter; the other is space vector modulation (SVM) [77, 78]. In the first method, thecost and the complexity will be increased, in the second method, the torque ripple and flux ripple canbe reduced, however the switch frequency still changes. In the next section a fuzzy approach is givento reduce torque ripple [8]. This goal is achieved by the fuzzy controller which determinates thedesired amplitude of torque hysteresis band.4.3 TORQUE EXPRESSIONS WITH STATOR AND ROTOR FLUXES

The torque expression for induction machine can be expressed in vector form as,

223

sse IPT

(39)

Where sds

sqss j and

sds

sqss jiiI . In this equation, sI is to be replaced by rotor

flux r . In the complex form, s and r can be expressed as function of currents as,

rmsss ILIL (40)



smrrr ILIL (41)From equations 39, 40 and 41:

srsr

me LL

LPT '223

(42)

That is, the magnitude torque is

sin22

3' srsr

me LL

LPT

(43)

Where γ is the angle between the fluxes, indicating the vectors s , r , and sI for positivedeveloped torque. If the rotor flux remains constant and stator flux is changed incrementally by statorvoltage sV as shown and the corresponding change of γ angle is , the incremental torque eTexpression is given as

sin22

3'

ssr

sr

me LL

LPT (44)

4.4 CONTROL STRATEGY OF DTCBlock diagram of the IM drive system based on DTC scheme is shown in Fig 6. The speed

control loop and the flux program as a function of speed are shown as usual and will not be

discussed. The command stator flux *ˆ s and torque*

eT magnitudes are compared with the respectiveestimated values and the errors are processed through hysteresis-band controllers, as shown [2]. Theflux loop controller has two levels of digital output according to the following relations:

for1 HBEH (45)

HBEH for1 (46)

Where HB2 = total hysteresis-band width controller. The circular trajectory of the command

flux vector*ˆ s with the hysteresis band rotates in an anti-clockwise direction as shown in Fig 7. The

actual stator flux s is constrained within the hysteresis band and it tracks the command flux in azigzag path. The torque control loop has three levels of digital output, which have the followingrelations [2]:

TeTeTe HBEH for1 (47)

TeTeTe HBEH for1 (48)for0 TeTeTeTe HBEHBH (49)



Fig 6: In principle the DTC method selects one of the six nonzero and two zero voltage

Fig 7: Inverter voltage vectors and corresponding stator flux variation in time Δt.

Figure 8: Direct torque and flux control block diagram.



The feedback flux and torque are calculated from the machine terminal voltages and currents.The signal computation block also calculates the sector number S(k) in which the flux vector s lies.There are six sectors (each /3 angle wide), as in Fig 7(a). The voltage vector table block in Fig 8receives the input signals ,, TeHH and S(k)and generates the appropriate control voltage vector(switching states) for the inverter by lookup table, which is shown in table 1 (the vector sign isdeleted) [2, 3]. The inverter voltage vector and a typical s are shown in Fig 7(b). Neglecting thestator resistance of the machine, we can write.

)( ss dtdV (50)

Or. tVss (51)

Which means that s can be changed incrementally by applying stator voltage sV for timeincrement Δt. The flux increment vector corresponding to each of six inverter voltage vectors isshown in Fig 7. The flux in machine is initially established to at zero frequency (dc) along the

trajectory OA shown in Figure 7. With the rated flux, the command torque is applied and the*

svector starts rotating [2, 3].

Table1: Switching table of inverter voltage vectors.HΨ HTe S(1) S(2) S(3) S(4) S(5) S(6)

1

1 V2 V3 V4 V5 V6 V1

0 V0 V7 V0 V7 V0 V7

-1 V6 V1 V2 V3 V4 V5

-1

1 V3 V4 V5 V6 V1 V2

0 V7 V0 V7 V0 V7 V0

-1 V5 V6 V1 V2 V3 V4

Table2: Flux and Torque variations due to applied voltage vector in.

Voltage vector V1 V2 V3 V4 V5 V6 V0 or V7

Ψs 0

Te

Table 1 applies the selected voltage vector, which essentially affects both the torque and fluxsimultaneously [2, 3]. The flux trajectory segments AB, BC, CD and DE by the respective voltagevectors 4343 and,,, VVVV are shown in Figure 7(a). The total and incremental torque due to sare explained in Fig 7(b). Note that the stator flux vector changes quickly by, but the r change is



very sluggish due to large time constant Tr. Since r is more filtered, it moves uniformly at

frequency ωe, whereas s movement is jerky. The average speed of both, however, remains thesame in the steady-state condition. Table2 summarizes the flux and torque change (magnitude anddirection) for applying the voltage vectors for the location of s shown in Fig 7(b) [2, 3]. The flux

can be increased by the 621 and,, VVV vectors, whereas it can be decreased by the 543 and,, VVVvectors [2]. Similarly, torque is increased by the 432 and,, VVV Vectors, but decreased by the

651 and,, VVV vectors. The zero vectors (V0 or V7) short-circuit the machine terminals and keepthe flux and torque unaltered. Due to finite resistance (Rs) drop, the torque and flux will slightlydecrease during the short-circuit condition.

Consider for example, an operation in sector S(2) as shown in Fig 7(a), where at point B, the

flux is too high and the torque is too low; that is, 1H and 1TeH . From table 1, voltage

V4 is applied to the inverter, which will generate the trajectory BC. At point C, 1H and

1TeH and this will generate the V3 vector from the table. The drive can easily operate in thefour quadrants, and speed loop and field-weakening control can be added, if desired [80]. The torqueresponse of the drive is claimed to be comparable with that of a vector-controlled drive [2].

5. FUZZY APPLICATIONSoft computing techniques can apply for nonlinear system [80-83]. A fuzzy controller is

introduced to allow the performance of DTC scheme in terms of flux and torque ripple to beimproved [84-87]. The speed regulators are conventional PI controllers (CPIC), which requiresprecise math model of the system and appropriate value of PI constants to achieve high performancedrive. Therefore, unexpected change in load conditions or environmental factors would produceovershoot, oscillation of the motor speed, oscillation of the torque, long settling time and causesdeterioration of drive performance [84-87].

The selected voltage vector is applied for the entire switching period, and thus allowselectromagnetic torque and stator flux to vary for the whole switching period. This causes hightorque and flux ripples. To overcome these problems in DTC, two fuzzy controllers are widelyanalyzed in literature [2, 3]. Those are:

1. Fuzzy PI Controller (FPIC) to achieve precision speed control.2. Fuzzy Logic Duty Ratio Control (FLDRC) to minimize torque & flux ripple.When Fuzzy Logic is used for the on-line tuning of the PI controller, it receives scaled values

of the speed error and change of speed error. Its output is updating in the PI controller gains based ona set of rules to maintain excellent control performance even in the presence of parameter variationand drive non-linearity [87]. Block diagram of the method with close-loop torque and flux control instator flux coordinate system is presented in Fig 9. The output of the PI flux and torque controllerscan be interpreted as the reference stator voltage components Vsx, Vsy are the stator flux orientedcoordinates (x − y). Design of Fuzzy Logic Controller is depend on Selection of input variables,Selection of output variable, Number of fuzzy controllers, Selection of Membership functions andSelection of defuzzification. Here, we had taken two fuzzy controllers for torque and flux, triangularmembership and centroid defuzzification.

FPIC does dynamically adjusts the gains kP and kI to ensure the stability of system over widetorque-speed range, Swift speed response, Less overshoot and, Extremely small steady state errors.

FLDRC does Minimizes torque & flux ripples effectively, increased efficiency, Low acousticnoise, Operates at a lower switching frequency compared to the existing methods, and Reducescomputation burden.



By using these two fuzzy controllers we achieve good speed and torque responses. Afteroutputs of these fuzzy controllers (after defuzzification) we generate Vsx and Vsy, again convertedthis X-Y coordinate components to α-β components. By using this values generate 6 pulses with thehelp of Space Vector Modulation.).

InductionMotor

Vα

Vβ

Flux, Torque andθ estimator

PIController

Fuzzy

Fuzzy

Ψ*

Ψ

T*

T

ω*

ω

Inverter

Vdc

θ

VdcIαIβ

ωr

ABC to αβ

x-yto

α-β

Vsx

Vsy

SVM

Fig: 9. Two fuzzy based DTC-SVM model

CONCLUSIONSThe paper has presented a DTC drive with fuzzy controller. This controller determinates the

desired amplitude of torque hysteresis band. The main advantage is the improvement of torque andflux ripple characteristics at any speed region; this provides an opportunity for motor operation underminimum switching loss and noise.

The two-fuzzy based DTC-SVM-IMD system, thereby dramatically reducing the torque ripple.A fuzzy controller seems to be a reasonable choice to evaluate the amplitude of torque hysteresisband according to the torque ripple level. Fuzzy-PI Controller to achieve precision speed control andFuzzy Logic Duty Ratio Control is used to minimize torque & flux ripple. When Fuzzy Logic is usedfor the on-line tuning of the PI controller, it receives scaled values of the speed error and change ofspeed error.

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