2.3 Induction Machine Control

2.3.1 V/Hz Control

The open-loop Volts/Hz control was by far the most popular method to control

the machine speed, especially because of its simplicity. The method is based on the

control of the stator frequency. The objective is to control the machine speed while

keeping constant the magnitude of the stator flux. As a result, the machine retains its

torque/ampere capability at any speed. By neglecting the stator resistance drop, the stator

flux is kept constant if e

ss

Vω

λ = and the name of the method comes from this equation.

Early approaches assume that the rotor speed ωr is approximately equal to the

synchronous speed ωe (slip speed is neglected). For speed control, the speed reference ωr

is set and the stator voltage Vs is computed to maintain the desired stator flux. Integration

of the reference speed gives the angle of the stator voltage (θe). Finally, the space vector

described by Vs and θe is used as command voltage for the three-phase inverter that

powers the machine.

The approach can be improved by considering the effect of the non-zero stator

resistance and of the slip speed. To compensate for the stator resistance, a boost voltage

can be added to the stator voltage. This is especially useful at low speed since the stator

resistance absorbs the major amount of the stator voltage. The slip speed is also different

from zero. To compensate, the slip is estimated using model equations and is added in the

integration of the voltage angle. The control scheme is presented in Figure 2.6.

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IM

PI

Estimator

*rω

^

rω

*eω

*slω

- +

Inverter

*sV

Figure 2.6 V/Hz control scheme

A detailed discussion regarding the V/Hz method and other scalar control schemes can be

found in [2]. Generally, the method is very robust and works well even at very low stator

frequencies. The robustness of the method stems from the approach used in computation

of the voltage angle θe. A good-quality θe waveform (straight and undistorted) is obtained

and this results in smooth shaft motion without ripple torque or oscillations.

The major disadvantage of the V/Hz method is its sluggish dynamic response

since the method disregards the inherent machine coupling. A step change in the speed

command produces a slow torque response. During the transient, the magnitude of the

stator flux is not maintained (the magnitude decreases) and the machine’s torque response

is not sufficiently fast. In addition, there is some amount of under damping in the

machine’s flux and torque responses that increases at lower frequencies. In some

operating regions, the system may become unstable.

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2.3.2 Field-Oriented or Vector Control

The modern approach for induction machine control is based on vector or field-

oriented control. The invention of vector-control in early 1970’s brought a renaissance in

the high-performance control of ac drives. This is because, in spite of the coupled and

nonlinear machine model, the induction machine can be controlled similarly to a

separately excited dc machine.

In a dc machine, neglecting the armature reaction and saturation, the expression of

the torque is:

afe IKT λ= (2.38)

where K is a constant. The construction of a dc machine is such that the field flux λf is

proportional with the field current If and is orthogonal with the flux produced by the

armature current Ia. These two fluxes are kept orthogonal by the collector-brush

assembly. They are decoupled and stationary in space. This means that when torque is

controlled by controlling the current Ia, the field flux is not affected and vice-versa.

The induction machine exhibits the same behavior when viewed in the rotational

reference frame aligned with the rotor flux. The field current (id) and the torque current

(iq) appear as dc quantities in steady state and are orthogonal and decoupled. Therefore,

the flux and torque currents can be independently controlled to obtain torque production

in the same manner as in a dc machine. Accurate torque control has two prerequisites:

Accurate control of the currents id and iq with no steady-state error and desired

dynamics.

Accurate estimation of the rotor flux angle θe that allows transformation of the

variables from the stationary to the rotating reference frame.

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Generally, the first condition is easy to achieve. Traditional PI controllers are the most

common solution and they yield good experimental results; other types of controllers

have also been used (fuzzy-logic, sliding mode etc).

Estimation of the angle θe based on the equations of the model can be done in two

ways: by DFO or by IFO.

2.3.3 Direct Field Orientation (DFO)

This method computes the rotor flux angle based on the projections of the flux

vector on the stationary reference frame (Figure 2.7). The flux components and

are needed. Several model-based observers can be used to estimate them. The difficulties

of the method come from the various problems associated with implementation of the

observers (integration, dependency on machine parameters etc).

rαλ rβλ

d

α

β

q

θ

−

rλ

rαλ

rβλ

Figure 2.7 Principle of Direct Field Orientation (DFO)

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With the rotor fluxes known, the angle of the flux vector (also called rotor position) is

given by:

r

re

α

β

λ

λθ 1tan −= (2.39)

However, since sin and are really needed for the Park transformation, these can

be found directly by:

eθ eθcos

22sin

rr

re

βα

β

λλ

λθ

+= (2.40)

22cos

rr

re

βα

α

λλ

λθ

+= (2.41)

2.3.4 Indirect Field Orientation (IFO)

An alternative approach to obtain the rotor flux angle is by Indirect Field

Orientation (IFO). The method is based on Equation (2.36). The right-hand side terms in

(2.36) are the rotor electrical speed and the slip speed. Their integration provides the

desired angle. For accurate estimation, the method requires correct values for both the

rotor speed and the rotor time constant. Also, the integration can produce incorrect rotor

angle estimates if the initial condition is not properly chosen. Generally, IFO works best

for drives that use a speed sensor to measure the rotor speed (sensored drives). In

sensorless drives, the speed information is not available by direct measurement and it

must be estimated. The accuracy of the angle produced by IFO depends heavily on the

speed estimate.

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Many speed estimators are available, however, steady-state errors, floating of the

machine parameters, estimation delay due to low pass filtering are common problems that

influence the speed estimation bandwidth and accuracy. An incorrect speed estimate can

generally be acceptable for speed feedback but has severe effects on the drive stability

and performance if the transformation angle is found by IFO.

Various topics regarding sensorless control are presented in the subsequent

chapters. The basic IM control scheme used in this research is shown in Figure 2.8.

3-PhaseInverter

IM

PWM

*αV

*βV

*aV*

bV

*cV

αβ

αβ

αβ

abc

abc

abcT

dcV

dq

dq

*dV

*qV

PI

PI

Speed and Flux

Estimator

dcVabcT

aibi

- -

-

PI

mL1*

rλ*di

*qi

*rω

rω

rω

rαλ

rβλr

r

α

β

λλ1tan −

αβ

θ

θ

di

qi

αi

βi

+

+

compdqV

Figure 2.8 Block diagram of sensorless DFO induction motor control

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The control scheme presented has the following characteristics:

PI controllers are used to regulate the currents and the speed.

The angle θe is computed using (2.39) for convenience of computations.

Various flux and speed estimators have been used and they are not specifically

shown in the control scheme. Details will be presented in the subsequent chapters.

For easy implementation, the flux magnitude λr is not regulated directly. Instead,

the desired flux level is obtained by setting the reference d-axis current. The

approach significantly simplifies the software and is equivalent to flux regulation

as long as the magnetizing inductance Lm does not saturate.

Note the block that adds two compensation voltages to the outputs of the current

controllers. Generally, these are used in order to completely decouple the

dynamics of the d and q-axis currents. Their expressions are:

+−=

r

qmqrps

compd

iLinLV

ληωσ

2

(2.42)

++=

r

dqmdrprrps

compq

iiLinnLV

ληωλωβσ (2.43)

The addition of the two decoupling voltages is not mandatory. For the motor

under study, it was found through simulation that the addition of the terms in

(2.42)-(2.43) may not significantly improve the dynamics. The calculation of the

above terms is computationally intensive and requires both the speed and the

magnitude of the rotor flux. In the work related to Chapters 4 and 5, the

compensation voltages have been omitted.

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2.4 Experimental Setup

The experimental setup used in this research consists of the following:

Dayton model 2N863M 3-phase induction motor. The motor plate data and rated

parameters are presented in Table 1.

Rating ¼ hp Pole # 4

Speed 1725 rpm Voltage 220 V

Rs 10.98 Ω

Lls,Llr 0.0149 H

Lm 0.297 H

Rr 5.572 Ω

Table 1 Rated parameters of Dayton motor model 2N863M

Spectrum Digital DMC 1500 3-phase inverter. The rated values for the inverter

are: 350V dc bus maximum value; 5 A continuous current; 10 A peak current.

Current sensor interface: this current acquisition board was built in the laboratory.

The board has 2 LEM current sensors model HY 5-P (maximum peak current: 5

A) and two differential op-amp structures to allow signal interfacing with the DSP

board.

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Spectrum Digital TMS 320F2407-PGEA Evaluation Module. This is the

controller board of the setup. It contains the Texas Instruments 16 bit, fixed-point

Digital Signal Processor as well as analog interfaces and emulator port. The board

has a digital to analog converter (D/A) with 4 channels that has been used to

display the waveforms of interest.

A block diagram of the experimental setup is shown in Figure 2.9.

Spectrum Digital3-PhaseInverter

Dayton 2N863M

D/A

LEM a

LEM b

Spectrum DigitalTMS320F2407

Evaluation Board

PWMSignals

AnalogSignalsVdc,ia,ib

DigitalScope

Currents ia,ib

350 V (max)

5 V 12 V

Figure 2.9 Block diagram of the experimental setup

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