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DCmotors and their representation


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 ... – PowerPoint PPT presentation

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Title: DCmotors and their representation

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
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

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

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 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
  • 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

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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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.
  • 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
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.
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.
  • 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 )
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