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DCmotors and their representation

- The basic principle of a DC motor is the

production of a torque as a result of the flux

interaction between a field produced on the

STATOR (either produced by a permanent magnet, or

a field winding) and the current circulating in

the armature windings on the ROTOR.

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In order to produce a torque of constant sign,

the armature winding loops are connected to a set

of brushes which commutate the current

appropriately in each loop according to their

geometric position. The commutator is a

MECHANICAL RECTIFIER.

Basic Equations of a DC Machine

field winding

counter emf

armature voltage

electrical torque

developed power

Speed control

- For control problems, one assumes that the back

emfs magnetizing characteristic, E(If) is linear

Va Voltage Control If Field Control Ia

(with If fixed) Demand Torque

In practice, for speeds less than the base speed

(rated), the armature current and field currents

are maintained at fixed values (hence constant

torque operation), and the armature voltage

controls the speed. For speeds higher than the

base speed, the armature voltage is maintained at

rated value, and the field current is varied to

control the speed. However, this way the power

developed Pd is maintained constant. This mode is

referred to as field weakening operation.

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Case of Series Motor (or Universal Motor)

If and Ia are equal

Operating Modes of DC Motors

- Motoring
- The back emf E lt Va both Ia and If are positive.

The motor develops a torque to meet the load

torque

Dynamic Breaking

- The voltage source is removed, and the armature

is shorted. The kinetic energy stored in the

rotor of the motor is dissipated in the armature

resistance since the machine now works as a

generator.

Note here that theoretically, since the armature

voltage is proportional to the speed, the motor

would never stop... (windage

Regenerative Breaking

- The back emf E gt Va , the machine acts as a

generator, and the armature current flows towards

the source, hence energy stored in the machine

rotor is fed back to the source. Note however

that this will cause the machine to slow down

usually until EVa and then revert to mode 1.

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Plugging

- Plugging is when the field current is reversed,

hence the back emf changes sign, and the equation

of the machine becomes

a very high torque generated in the opposite

direction of rotation

Two Transistor control of regenerative operation

When the main switch opens, the armature current

I(a1) has to be dissipated through the

freewheeling diode.

Then if one closes switch T1, the machine behaves

as a generator with the energy stored in its

inertia. Therefore the armature current I(a2)will

start flowing and follows I(1).

After a certain time one opens the switch T1, and

the current I(a2) has to be redirected via diode

D2 back to the source with I(2).

- The chopping rate of switch T1 can be set in

order to control the average current (Ia2),

usually 1.5 times rated value. - This is possible only if the speed is fast enough

to provide terminal voltage. - When the emf E reaches ERa.I(rated), the switch

T1 remains closed for - maximum breaking possible with the given emf.

Four Quadrant Operation

CONTROL FEEDBACK LOOPS

- Assume that the source is a rectifier. We are

controlling the DC motor with the voltage control

of the armature (separate excitation).

The rectifier can be considered as a power

amplifier controlled by the firing angle ?. The

open loop system can be pictured as

- If one uses a tacho-generator to monitor the

speed a closed loop controller can be built

- The difference between input setting and the

feedback signal is the error signal. - However, with SCR drives, any change in motor

speed will immediately give rise to excessive

motor and thyristor currents. Hence a current

limiter must be added to the control loop. - This is obtained by a second feedback loop.

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Induction Motor Control

- Induction machines are the workhorse in

industry

The squirrel cage machine is of rugged

construction, low production cost, low

maintenance and environmental properties (for

example explosion proof). The advent of power

electronics have made it possible to match the

induction machine performance to that of DC

machines, in fact practically supplanting DC

machines in industries, since the price of a

single DC machine is much higher than the

equivalent induction machine with full control.

Adjustable Speed Drives are used in process

control for fans, compressors, pumps, blowers

etc... Servo drives are becoming more and more

common using very sophisticated control schemes,

for instance in computer peripherals, machine

tools and robotics applications. These are

usually lower power ratings though.

Example Centrifugal Pump

- The induction motor driving the centrifugal pump

will work at quasi constant speed

there is energy loss through the throttle

Setting the speed which will provide the desired

flow rate. Hence considerable energy savings. In

this case, the pump performance is

Induction Motor Principle

The simplified equivalent circuit is

It can be shown that the power developed by the

shaft is equal to the power that would be

dissipated in the equivalent resistance

Hence the POWER DEVELOPED in a 3 phase motor is

developed torque is

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STATOR VOLTAGE CONTROL

Constant Voltage Inverter Drive

Note that the source capacitor maintains a

constant voltage

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Constant Current Inverter Drive

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Speed Control with Rotor Resistance

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The only inconvenience here is of course the loss

of power in the external resistance. Automatic

control can be achieved by using a chopper in the

rotor circuit.

Kramer Drive

Frequency Control of the Drive

- Intuitively one can see that the rotor will

rotate at speed slightly lower than the stator

frequency (slip), hence a speed control is

achieved when the stator frequency is changed.

If we want to have both speed control and still

maintain a high torque, the maximum torque at

base speed (synchronous rated) is given by

This is equivalent to the DC machine. Tmax-base

remains constant. In this region the control is

done by the Voltage, maintaining the flux at its

maximum. Then the region called the field

weakening as for the DC machine. In order to

maintain the flux constant, the ratio V/f must be

maintained constant. However, due to losses in

the machine, at low speeds, one must have a boost

voltage at low speeds to compensate for losses.

VECTOR CONTROL of INDUCTION MOTORS

- The production of torque in a d.c. or cage

induction motor is a function of the position or

vector relationship in space of the air-gap

magnetic flux to the rotor current. The flux and

armature current are always ideally positioned by

virtue of the switching action of the commutator

hence control of the armature current gives

immediate control of the torque, a feature which

makes both the steady state and transient control

of the torque in a d.c. motor relatively easy.

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The torque developed is related to the in-phase

component of I2 shown as Iq, and the flux is

related to the current Im modified by the

reactive component of I2 to give the component

shown as Id.

The object of vector control, sometimes referred

to as field orientation control, is to

separately control the magnitude of the two

components Id and Iq, such that the flux is

proportional to Id and the torque is proportional

to Iq. This is referred to as DECOUPLING the

control (we need 2 degrees of freedom).

In the d.c. motor the flux is stationary, with

the armature current fixed in space by the

commutator action, but in the induction motor

both the flux and rotor currents rotate together.

We have only 1 degree of freedom in the 3 phase

source currents.

The instantaneous values of the three-phase

currents in the stator determine the angle of the

flux in space and that of the rotor current, so

we must have a shaft encoder (2nd degree of

freedom) which measures the rotor angular

mechanical position relative to the instantaneous

stator currents.

To implement vector control the motor parameters

must be known and values put into a highly

complex set of mathematical equations developed

from generalized machine theory.

The basic tools used in calculations is the use

of Parkers Model which allows to transform a 3

phase rotating vector system into a 2 phase

rotating vector system (which is the same as of a

DC machine with a direct in line with the flux,

and quadrature axis perpendicular to it).

The phase command currents () are triggering the

inverter to produce the real line currents

(a,b,c). An acquisition system must sample the

line currents, filter and condition these

quantities and presents them to an ABC to DQ

transformation block. The calculated (c) direct

and quadrature quantities must now be positioned

in such a way that the direct axis aligns with

the stator axis. Hence the block which computes

this alignment must also receive the absolute

position of the rotor using the rotor angle q. We

now obtain the (D-Q) components aligned with the

real rotor position, and feed this into the Model

Block.

The components (DQ) have to be realigned to the

stator axis (e), and fed to an inverse

transformation module which calculates the line

control vector currents (ABC) feeding the

inverter, and the loop is closed.

The main difficulty here is that the stator frame

reference is used in calculations of the model,

and that I(ds) must be aligned with the rotor

flux. However this rotor flux depends upon the

SLIP, and of course varies in time (this is why

it is called Asynchronous!). The trick in the

method is to establish the rotor flux axis at

each sample.

INDIRECT VECTOR CONTROL

The flux vectors are computed from the terminal

quantities of the motor (stator currents,

voltages and measured air gap flux). It uses the

motor slip frequency to compute the desired flux

vector. The amount of DECOUPLING is dependant

upon the motor parameters in the indirect method.

Without a good knowledge of the motor parameters

an ideal decoupling is not possible.

DIRECT VECTOR CONTROL

- determine directly the air gap flux by

measurement, and from there derive the rotor flux

and stator flux linkages.

excellent low-speed performance

Indirect Vector Control (indirect field oriented

control) or IFOC

- In this method the feedback uses the rotor slip.

The first equation tries to make sure that we

have a constant flux (magnitude of ),

while controls the torque.

The speed is integrated in order to obtain the

position and hence obtain the unit vectors for

the transformation

If the motor parameters change during operating

conditions, the model is not accurate and the

model predictions will not align exactly the

rotor flux with the direct axis, and the control

is not adequately decoupled.

(Indirect field oriented control )