Chapter 9 - second part

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9.11. FLUX OBSERVERS FOR DIRECT VECTOR CONTROL
WITH MOTION SENSORS
The motor stator or airgap flux space phasor
amplitude lma and its instantaneous position -
qerga - with respect to stator phase a axis
have to be computed on line, based on measured
motor voltages, currents and, when available,
rotor speed. The torque may be calculated from
flux and current space phasors and thus once the
flux is computed and stator currents measured,
the torque problem is solved. 9.11.1. Open loop
flux observers Open loop flux observers are
based on the voltage model or on the current
model. Voltage model makes use of stator voltage
equation in stator coordinates (from (9.32) with
w1 0) (9.95)
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From (9.37) with a Lm / Lr (9.96) Both
stator flux, , and rotor flux, , space
phasors, may thus, in principle, be calculated
based on and measured. The corresponding
signal flow diagram is shown in figure 9.29.
Figure 9.29. Voltage - model open loop flux
observer (stator coordinates)
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On the other hand the current model for the rotor
flux space phasor is based on rotor equation in
rotor coordinates (wb wr) (9.97) Two
coordinate transformations - one for current and
other for rotor flux - are required to produce
results in stator coordinates. This time the
observer works even at zero frequency but is very
sensitive to the detuning of parameters Lm and tr
due to temperature and magnetic saturation
variation. Besides, it requires a rotor speed or
position sensor. Parameter adaptation is a
solution. The corresponding signal flow diagram
is shown in figure 9.30.
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Figure 9.30. Current control open loop flux
observer More profitable, however, it seems to
use closed loop flux observers.
9.11.2. Closed loop flux observers
Figure 9.31. Close loop voltage and current model
rotor flux observer
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Many other flux observers have been proposed.
Among them, the third flux (voltage) harmonic
estimator 21 and Gopinath observer 22, model
reference adaptive and Kalman filter
observers. They all require notable on line
computation effort and knowledge of induction
motor parameters. Consequently they seem more
appropiate when used together with speed
observers for sensorless induction motor drives
as shown in the corresponding paragraph, to
follow after the next case study.
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9.12. INDIRECT VECTOR SYNCHRONOUS CURRENT CONTROL
WITH SPEED SENSOR - A CASE STUDY
The simulation results of a vector control system
with induction motor based on d.c. current
control - are now given. The simulation of this
drive is implemented in MATLAB - SIMULINK. The
motor model was integrated in two blocks, the
first represents the current and flux calculation
module in d - q axis (figure 9.32), the second
represents the torque, speed and position
computing module (figure 9.33). The motor used
for this simulation has the following parameters
Pn 1100W, Vnf 220V, 2p 4, rs 9.53W, rr
5.619W, Lsc 0.136H, Lr 0.505H, Lm 0.447H, J
0.0026kgfm2.
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Figure 9.32. The indirect vector current control
system
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Figure 9.33. The motor space phasor (d, q) model
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The following figures represent the speed,
torque, current and flux responses, for the
starting process and with load torque applied at
0.4s. The value of load torque is 4Nm.
Figure 9.34. Speed transient response
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Figure 9.35. Torque response
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Figure 9.36. Phase current waveform
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Figure 9.37. Stator flux amplitude
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Figure 9.38. Rotor flux amplitude
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• 9.13. FLUX AND SPEED OBSERVERS IN SENSORLESS
  DRIVES
• Sensorless drives are becoming predominant when
  only up to 100 to 1 speed control range is
  required even in fast torque response
  applications (1-5ms for step rated torque
  response).
• 9.13.1. Performance criteria
• To assess the performance of various flux and
  speed observers for sensorless drives the
  following performance criteria have become widely
  accepted
• steady state error
• torque response quickness
• low speed behaviour (speed range)
• sensitivity to noise and motor parameter
  detuning
• complexity versus performance.

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9.13.2. A classification of speed observers The
basic principles used for speed estimation
(observation) may be classified as A. Speed
estimators B. Model reference adaptive systems C.
Luenberger speed observers D. Kalman filters E.
Rotor slot ripple With the exception of rotor
slot ripple all the other methods imply the
presence of flux observers to calculate the motor
speed.
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9.13.3. Speed estimators Speed estimators are
in general based on the classical definition of
rotor speed (9.98) where w1 is the
rotor flux vector instantaneous speed and (Sw1)
is the rotor flux slip speed. w1 may be
calculated in stator coordinates based on the
formula (9.99) or (9.100)
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are to be determined from a flux
observer (see figure 9.32, for example). On the
other hand the slip frequency (Sw1), (9.23),
is (9.101) Notice that is
strongly dependent only on rotor resistance rr as
Lm / Lr is rather independent of magnetic
saturation. Still rotor resistance is to be
corrected if good precision at low speed is
required. This slip frequency value is valid both
for steady state and transients and thus is
estimated quickly to allow fast torque
response. Such speed estimators may work even at
20rpm although dynamic capacity of torque
disturbance rejection at low speeds is
limited. This seems to be a problem with most
speed observers.
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9.13.4. Model reference adaptive systems
(MRAS) MRASs are based on comparision of two
estimators. One of them does not include speed
and is called the reference model. The other,
which contains speed, is the adjustable model.
The error between the two is used to derive an
adaption model that produces the estimated speed
for the adjustable model. To eliminate the
stator resistance influence, the airgap reactive
power qm 25 is the output of both
models (9.102) (9.103) The
rotor flux magnetization current equation in
stator coordinates is ((9.15) with w1
0) (9.104)
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Now the speed adaptation mechanism
is (9.105) The signal flow diagram of
the MRAS obtained is shown in figure 9.39.
Figure 9.39. MRAS speed estimator based on airgap
reactive power error
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The effect of the rotor time constant tr
variation persists and influences the speed
estimation. However if the speed estimator is
used in conjunction with indirect vector current
control at least rotor field orientation is
maintained as the same (wrong!) tr enters also
the slip frequency calculator. The MRAS speed
estimator does not contain integrals and thus
works even at zero stator frequency (d.c.
braking) (figure 9.40.a) and does not depend on
stator resistance rs. It works even at 20rpm
(figure 9.40.b) 25.
Figure 9.40. a.) Zero frequency b.) low speed
operation of MRAS speed estimator
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9.13.5. Luenberger speed observers First the
stator current and the rotor flux are calculated
through a full order Luenberger observer based on
stator and rotor equations in stator
coordinates (9.106) with
(9.107) The full order Luenberger
observer writes (9.110) The matrix G
is chosen such that the observer is
stable. (9.111)
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The speed estimator is based on rotor flux
and estimators (9.113) In essence
the speed estimator is based on some kind of
torque error. If the rotor resistance rr has to
be estimated an additional high reference current
ida is added to the reference flux current ids.
Then the rotor resistance may be estimated 26
as (9.114)
Remarkable results have been obtained this way
with minimum speed down to 30rpm. The idea of an
additional high frequency (10 times rated
frequency) flux current may be used to determine
both the rotor speed and rotor time constant tr
27. Extended Kalman filters for speed and flux
observers 28 also claim speed estimation at 20
- 25rpm though they require considerable on line
computation time.
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9.13.6. Rotor slots ripple speed estimators The
rotor slots ripple speed estimators are based on
the fact that the rotor slotting openings cause
stator voltage and current harmonics ws1,2
related to rotor speed , the number of rotor
slot Nr and synchronous speed
(9.115) Band pass filters centered on
the rotor slot harmonics are used to
separate and thus calculate from
(9.115). Various other methods have been proposed
to obtain and improve the transient
performance. The response tends to be rather slow
and thus the method, though immune to machine
parameters, is mostly favorable for wide speed
range but for low dynamics (medium - high powers)
applications 27. For more details on
sensorless control refer to 30.
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9.14. DIRECT TORQUE AND FLUX CONTROL (DTFC) DTFC
is a commercial abbreviation for the so called
direct self control proposed initially 32 - 33
for induction motors fed from PWM voltage source
inverters and later generalized as torque vector
control (TVC) in 4 for all a.c. motor drives
with voltage or current source inverters. In
fact, based on the stator flux vector amplitude
and torque errors sign and relative value and the
position of the stator flux vector in one of the
6 (12) sectors of a period, a certain voltage
vector (or a combination of voltage vectors) is
directly applied to the inverter with a certain
average timing. To sense the stator flux space
phasor and torque errors we need to estimate the
respective variables. So all types of flux
(torque) estimators or speed observers good for
direct vector control are also good for DTFC. The
basic configurations for direct vector control
and DTFC are shown on figure 9.41.
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Figure 9.41. a.) Direct vector current control
b.) DTFC control As seen from figure 9.41 DTFC
is a kind of direct vector d.c. (synchronous)
current control.
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9.14.1. DTFC principle Though figure 9.41
uncovers the principle of DTFC, finding how the
T.O.S. is generated is the way to a succesful
operation. Selection of the appropiate voltage
vector in the inverter is based on stator
equation in stator coordinates (9.117) B
y integration (9.118) In essence the
torque error eT may be cancelled by stator flux
acceleration or deceleration. To reduce the flux
errors, the flux trajectories will be driven
along appropriate voltage vectors (9.118) that
increase or decrease the flux amplitude.
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Figure 9.42. a.) Stator flux space phasor
trajectory b.) Selecting the adequate voltage
vector in the first sector (-300 to 300)
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The complete table of optimal switching, TOS, is
shown in table 9.2. Table 9.2. Basic voltage
vector selection for DTFC
As expected the torque response is quick (as in
vector control) but it is also rotor resistance
independent above 1 - 2Hz (figure 9.43) 2.
Figure 9.43. TVC torque response
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9.15. DTFC SENSORLESS A CASE STUDY
The simulation results of a direct torque and
flux control drive system for induction motors
are presented. The example was implemented in
MATLAB - SIMULINK. The motor model was integrated
in two blocks, first represents the current and
flux calculation module in d - q axis, the second
represents the torque, speed and position
computing module (figure 9.44).
Figure 9.44.The DTFC system
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Figure 9.45. The I.M. model
The motor used for this simulation has the
following parameters Pn 1100W, Unf 220V, 2p
4, rs 9.53W, rr 5.619W, Lsc 0.136H, Lr
0.505H, Lm 0.447H, J 0.0026kgfm2.
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Figure 9.46. Speed and torque estimators
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Figure 9.47. Speed transient response (measured
and estimated)
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Figure 9.48. Phase current waveform (steady state)
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Figure 9.49. Torque response (measured and
estimated)
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Figure 9.50. Stator flux amplitude
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Figure 9.51. Rotor flux amplitude