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Rotor angle error correction
The effects of rotor angle errors and the correction methods for optimized control of
permanent magnet machines are critical factors in electric powertrain development
Due to their outstanding
power density, permanent
magnet synchronous machines play
a prominent role in highly integrated
applications such as hybrid vehicle
powertrains. Accurate knowledge
of the rotor angle is necessary to
achieve optimal utilization and
reliable motor operation.
Potential errors in the
measurement of the rotor angle
can be split between time-varying
(gaining error between resolver
signals) and time-constant
(misalignment of the rotor’s zero
position against the angle sensor).
Time-varying errors cause a torque
ripple that results in increasing
noise, less comfort and lower
efficiency. Time-constant errors
result in lower torque accuracy,
which critically affects functional
aspects such as ESP, torque
vectoring and lower efficiency.
The intensity of this issue can be
illustrated in the rotating synchronous
d/q frame of the PM. In extreme
cases where the error of the
electrical angle is 90°, an intended
pure torque producing q-current is
turned into a field-only producing
d-current. Thus, no torque is
produced at all.
Torque deviation for q-currents
is proportional to cos(İ) and
d-currents is proportional to sin(İ),
where İ is the misalignment angle.
Consequently, the torque deviation
is extremely sensitive against the
operating range of the PM. At high
q-currents, torque deviation due to
an angle error is small (such as an
İ = 2° results in a 0.04% torque
deviation). At high d-currents the
deviation is larger (3.5%).
Due to the automotive industry’s
significant redundancy and safety
requirements, the use of a rotor
angular position sensor is practically
mandatory. But what are the effects
Left: The torque of PM machines
Center: PM machine voltage model
Below: PM machines are playing a
greater role in EV development
of errors introduced during serial
production and errors due to the
overall tolerance chain on the angle?
Mechanical tolerances of rotor
manufacturing and assembly of the
position sensor have an effect on
the angle. The corresponding
electrical angle deviation is equal to
the mechanical deviation multiplied
by the number of permanent
magnet pole pairs. For example, a
mechanical tolerance of 1° of an
eight-pole machine results in an
electrical angle error of 4° and ~7%
torque deviation. Therefore, it is
imperative to add an automated
calibration of the angular offset at
the end of line. Several calibration
methods are available, including
magnetic alignment of the rotor with
DC current; evaluation of the voltage
162 // July 2013 // Electric & Hybrid Vehicle Technology International
equation
of the d/q
system on
the running
motor; and analysis of
the current response of
injected test signals.
The issue is further complicated
as the offset between the position
signal and the rotor is affected by the
tolerances of the sensor itself and
the signal processing. Temperature
drift, aging and signal delays may
also cause a varying error. The
influence of factors such as the
propagation time or frequency
dependence can be easily
determined through simple
formulae in the control software.
To fully compensate the effect of
the remaining factors, an offset
auto-tracking function is necessary
during normal operation. This may
be accomplished via several
methods. One potential software
approach is through an observer
module, which calculates a control
loop based on the known system
parameters in parallel with the real
control path and derives the
correction angle from the
differences. Another method is
based on calculating the electric
angle from the current and voltage
values in accordance with the EMF
method, or by integrating the phase
voltage with a flux estimator model.
Although real-time
calculation of the rotor
angle increases the
processor load,
it substantially
improves the
control
performance,
especially at
high speeds.
This method
also helps to
reduce the cost of the
entire position sensor system.
Instead of a high-precision resolver,
a more cost-efficient hall sensor
configuration could be integrated
for monitoring purposes only. For
precise torque control the
calculated angular value is used.
n at Hofer
Volker Hartman
Powertrain
9335-500
T. +49 931 35
[email protected]
E. volker.hartm
m.de
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