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Introduction

Scalar control

produces good steady state performancebut poor dynamic response.

This manifests itself in the deviation of airgap flux linkages from their set values.

This variation occurs in both magnitude

and phase.

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Introduction

Vector control (or field orientedcontrol)

offers more precise control comparedto scalar control.

used in high performance driveswhere oscillations in air gap flux

linkages are intolerable, e.g. roboticactuators, centrifuges, servos, etc.

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Introduction

Why does vector control provide superiordynamic performance compared to scalarcontrol ?

In scalar control there is an inherentcoupling effect because both torque andflux are functions of voltage or current

and frequency. This results in sluggishresponse and is prone to instabilitybecause of 5th order harmonics. Vectorcontrol decouples these effects.

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Torque Control of DC Motors

There is a close parallel between torquecontrol of a dc motor and vector control

of an ac motor. It is therefore useful toreview torque control of a dc motorbefore studying vector control of an acmotor.

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A dc motor has a stationary field structure(windings or permanent magnets) and arotating armature winding supplied by acommutator and brushes. The basicstructure and field flux and armature MMFare shown below:

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The field flux f(f) produced by fieldcurrent If is orthogonal to the armatureflux a (a) produced by the armature

current Ia. The developed torque Te can bewritten as:

Because the vectors are orthogonal, theyare decoupled, i.e. the field current onlycontrols the field flux and the armaturecurrent only controls the armature flux.

'

e t a f T K I I

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With vector control:

ids (induction motor) If(dc motor)

iqs

(induction motor) Ia(dc motor)

Thus torque is given by:

where is peak value of sinusoidalspace vector.

'

e t qs t ds qsrT K i K i i

r r

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This dc motor-like performance is onlypossible if iqs

* only controls iqs and doesnot affect the flux , i.e. iqs and ids are

orthogonal under all operating conditionsof the vector-controlled drive.

Thus, vector control should ensure the

correct orientation and equality of thecommand and actual currents.

r

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Equivalent Circuit of Induction

Motor

Since the rotor leakage inductance hasbeen neglected, the rotor flux = ,the air gap flux.

The stator current vector Is is the sum ofthe ids and iqs vectors. Thus, the statorcurrent magnitude, is related to ids and

iqs by:

r

m

sI

2 2s ds qsI i i

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Phasor Diagrams for Induction Motor

The steady state phasor (or vector)diagrams for an induction motor in thede-qe (synchronously rotating) referenceframe are shown below:

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Phasor Diagrams for Induction Motor

The rotor flux vector is alignedwith the de axis and the air gap voltageis aligned with the qe axis. The terminal

voltage Vs slightly leads the air gap voltagebecause of the voltage drop across thestator impedance. iqs contributes realpower across the air gap but ids only

contributes reactive power across the airgap.

( )r m

mV

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Phasor Diagrams for Induction

Motor

The first figure shows an increase in thetorque component of current iqs and thesecond figure shows an increase in the fluxcomponent of current, i

ds. Because of the

orthogonal orientation of these components,the torque and flux can be controlledindependently. However, it is necessary tomaintain these vector orientations under alloperating conditions.

How can we control the iqs and ids componentsof the stator current Is independently with the

desired orientation ?

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Principles of Vector Control

The basic conceptual implementation ofvector control is illustrated in the belowblock diagram:

Note: The inverter is omitted from this diagram.

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The motor phase currents, ia, ib and ic areconverted to ids

s and iqss in the stationary

reference frame. These are then

converted to the synchronously rotatingreference frame d-q currents, ids and iqs.

In the controller two inverse transforms

are performed:1) From the synchronous d-q to the

stationary d-q reference frame;

2) From d*-q* to a*, b*, c*.

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There are two approaches to vector control:

1) Direct field oriented current control

- here the rotation angle of the iqs

e vectorwith respect to the stator flux qr

s is beingdirectly determined (e.g. by measuring airgap flux)

2) Indirect field oriented current control- here the rotor angle is being measuredindirectly, such as by measuring slip speed.

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Direct Vector Control

In direct vector control the field angle iscalculated by using terminal voltages andcurrent or Hall sensors or flux sense

windings.

A block diagram of a direct vector controlmethod using a PWM voltage-fed inverteris shown on the next slide.

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A flux control loop is used to preciselycontrol the flux. Torque control is achievedthrough the current iqs

* which is generated

from the speed control loop (which includesa bipolar limiter that is not shown). Thetorque can be negative which will result in anegative phase orientation for iqs in the

phasor diagram.

How do we maintain idsand iqs orthogonality?This is explained in the next slide.

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Here the de-qe frame is rotating atsynchronous speed e with respect tothe stationary reference frame ds-qs, and

at any point in time, the angular positionof the de axis with respect to the ds axisis e (=et).

From this phasor diagram we can write:

andcoss

dr er sinsqr er

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These unit vector signals, when used inthe vector rotation block, cause ids to

maintain orientation along the de-axis andthe iqs orientation along the qe-axis.

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Summary of Salient Features of

Vector Control

A few of the salient features of vectorcontrol are:

The frequency e of the drive is not

controlled (as in scalar control). Themotor is self-controlled by using theunit vector to help control the frequencyand phase.

There is no concern about instabilitybecause limiting within the safe limitautomatically limits operation to thestable region.

sI

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Summary of Salient Features of

Vector Control

Transient response will be fastbecause torque control by iqs does notaffect flux.

Vector control allows for speed controlin all four quadrants (withoutadditional control elements) sincenegative torque is directly taken careof in vector control.

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Flux Vector Estimation

The air gap flux can be directly measured ina machine using specially fitted search coilsor Hall effect sensors. However, the drift inthe integrator with a search coil isproblematic at very low frequencies. Halleffect sensors tend to be temperature-

sensitive and fragile.

An alternative approach is to measure theterminal voltage and phase currents of themachine and use these to estimate the flux.These techniques are discussed on pp. 363-

368 of the Bose text.

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Indirect Vector Control

Indirect vector control is similar to directvector control except the unit vectorsignals (cose and sine) are generated in

a feedforward manner.

The phasor diagram on the next slide can

be used to explain the basic concept ofindirect vector control.

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The ds-qs axes are fixed on the stator andthe dr-qr axes are fixed on the rotor. Thede-qe axes are rotating at synchronous

speed and so there is a slip differencebetween the rotor speed and thesynchronous speed given by:

Since, , we can write:

e r sl

e edt

e r sl

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In order to ensure decoupling between thestator flux and the torque, the torquecomponent of the current, iqs, should be

aligned with the qe axis and the stator fluxcomponent of current, ids, should be alignedwith the de axis.

We can use the de-axis and qe-axisequivalent circuits of the motor (shown onthe next slide) to derive controlexpressions.

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The rotor circuit equations may be written as:

( ) 0dr r dr e r qr d

R i

dt

( ) 0qr

r qr e r dr

dR i

dt

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The rotor flux linkage equations may bewritten as:

These equations may be rewritten as:

dr r dr m dsL i L i

qr r qr m qsL i L i

1 mdr dr ds

r r

Li iL L

1 mqr qr qs

r r

Li i

L L

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Combining these with the earlier equationsallows us to eliminate the rotor currentswhich cannot be directly obtained. The

resulting equations are:

where .

0dr mrdr r ds sl qr

r r

d LRR i

dt L L

0qr mr

qr r qs sl dr

r r

d LRR i

dt L L

sl e r

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For decoupling control the total rotor fluxneeds to be aligned with the de-axis and sowe want: qr=0 => dqr/dt =0

If we now substitute into the previousequations, we get:

and

where has been substituted for dr .

r

r rm dsr

r

dLL i

R dt

m rsl qs

rr

L Ri

L

r

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For implementing the indirect vector controlstrategy, we need to take these equationsinto consideration as well as the equation:

Note:

A constant rotor flux results in the equation:

so that the rotor flux is directly proportional

to ids in steady state.

m dsrL i

e r sl

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An implementation of indirect vector controlfor 4-quadrant operation is shown below:

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Features of this implementation:

Diode rectifier front-end with a PWMinverter with a dynamic brake in the dc

link. Hysteresis-band current control.

Speed control loop generates the torquecomponent of current, iqs

*.

Constant rotor flux is maintained by usingthe desired ids

*.

The slip frequency sl* is generated from

the desired iqs*

.

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If iqs*

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Harmonic content of hysteresis-bandcurrent control is not optimum. Also,at higher speeds the current controller

will saturate in part of the cyclebecause of the high back emf.

Synchronous current control can be

used to overcome these problems. SeeBose text, pp. 372-374 for details.

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A dc motor-like electromechanical modelcan be derived for an ideal vector-controlled drive using the followingequations:

32 2

me qsr

r

LPT iL

r rm dsr

r

dLL i

R dt

2 re L

dT T J

P dt

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A transfer function block diagram isshown below:

Note: The torque Te responds instantlybut the flux has first order delay (with

time constant =Lr/Rr).

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The physical principle of vector control canbe explained more clearly with the help ofthe below de-qeequivalent circuits:

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Since ids and iqs are being controlled, we canideally ignore the stator-side parameters.With qr=0 under all conditions, the emf

source on the rotor side de-circuitslqr=0.This means that in steady state ids flows onlythrough the magnetizing inductance, Lm, butin the transient case, is shared by the rotor

circuit whose time constant = Llr/Rr.

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In the qe-circuit when torque is controlled byiqs the emfsldr changes instantaneously(because ). Since qr=0, this

emf causes a current (Lm/Lr)iqs to flowthrough the rotor resistor Rr. If Llr isneglected and flux is constant, ids is seento only flow through Lm and iqs only flows

through the rotor side, as desired.

/sl dr m r qs rL R i L

r

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A serious issue with respect to indirectvector control is that ofslip gaindetuning. This is due primarily tovariation in rotor resistance. This effect isillustrated below where Rr=actual rotorresistance and

= estimated rotor resistance.rR

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Continuous on-line tuning of Ks is verycomplex and computationally intensive.However, two methods, one based on

extended Kalman filtering (EKF) forparameter estimation and a second onebased on a model referencing adaptivecontroller (MRAC) approach are good

options. The EKF method will beconsidered later when studyingsensorless vector control but the MRACmethod is described next.

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Suppose we decide to use torque as themodel parameter X. Thus,

Substituting Lmids* for gives:

The actual torque can be estimated from thestator frame variables using the equation:

* * *3

2 2

me qsr

r

LPX T i

L

r

2* * * *3

2 2

me ds qs

r

LPX T i i

L

3

2 2

s s s s

e ds qs qs ds

P

X T i i

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Note: Lm and Lr parameter variationsaffect the estimation accuracy of X*

and at low speeds, the statorresistance Rs affects the estimationaccuracy of X.

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