MAGNETIC FLUX LINKAGE ESTIMATION AND CONTROL FOR A
RELUCTANCE ACTUATOR
Darya Amin-Shahidi, Ian MacKenzie, and David L. Trumper
Mechanical Engineering Department
Massachusetts Institute of Technology
Cambridge, MA
INTRODUCTION
This abstract presents a method for estimating
the flux linkage in a reluctance actuator by using
both a sense coil measurement and current
measurement. A complimentary filter pair is
used to combine the two measurements into one
signal used for feedback control.
FLUX SENSING METHODS
A variable reluctance actuator generates force
on a mover through a magnetic flux density
normal to the actuator pole face. One method
for accurately controlling the force is to measure
this magnetic flux and close a feedback loop on
this signal. A simple and elegant way to
measure the flux linkage is to use a sensing coil:
the voltage across the coil leads is proportional
to the rate of change of the flux linked by the coil
[1]. This method has high-bandwidth capability
because it linearizes magnetic hysteresis and
eddy current effects. Its primary drawback is
that the measured signal (flux rate of change)
must be integrated to get the desired variable
(flux). Therefore, there is no true DC signal.
filter. The low-pass filter signal is then fed into a
look-up table (L(x)) that estimates the flux based
on the current and operating gap. This lookup
table is generated experimentally by using the
flux sensing coil to measure the inductance (flux
linkage divided by current) at different gaps.
The two resulting signals are then summed to
provide a flux estimate for feedback control that
is accurate at both low and high frequencies.
The current in a reluctance actuator is related to
the magnetic flux density in the operating gap
through Ampere’s Law and Gauss’s Law [2].
Thus, measuring current provides a means for
estimating the actuator force as well, including
the force at DC. However, this relationship
degrades at higher frequencies owing to the
effect of eddy currents, so it only remains a good
estimate at lower frequencies.
FIGURE 1:
Complimentary filter pair for
estimating flux linkage
FLUX ESTIMATION AN CONTROL
In this research, we combined the two methods:
the sense coil provides an accurate feedback
signal at higher frequencies, while the current
measurement provides an accurate feedback
signal at lower frequencies. FIGURE 1 shows a
complimentary filter structure used for combining
the two signals. The sense coil measurement is
passed through a high-pass filter and then
integrated.
The current sense resistor
measurement is first passed through a low-pass
One drawback of the flux estimation scheme is
that magnetic hysteresis is unaccounted for in
the low frequency measurement. Research is
currently being undertaken to incorporate a
hysteresis model in the low frequency
measurement to improve the accuracy.
This estimation scheme was tested on two
reluctance actuators that each included a sense
coil measurement, a current sense resistor
measurement, and a gap measurement. A
crossover frequency of 1 kHz was achieved.
REFERENCES
[1] Haus H, Melcher J. Electromagnetic Fields
and Energy.
Englewood Cliffs, New
Jersey: Prentice Hall. 1989.
[2] Zahn, M. Electromangetic Field Theory: a
problem solving approach. Malabar, FL:
Krieger, 1987.