The present invention relates to electric rotating machines and in
particular to a method for determining the position of the rotor of a synchronous
alternating-current permanent-magnet machine.

As is known, controlling a synchronous alternating-current permanent-magnet
machine requires knowing the position of the rotor, which can be determined by
means of a suitable sensor installed on the shaft of said machine.

However, when the presence of said sensor is impossible due to cost
reasons or other reasons, so-called sensorless algorithms are usually used which,
for example by using only current and voltage measurements on the machine, determine
the position of the rotor in each instant.

For speeds substantially different from zero, the use of methods based
on the counter-electromotive force of the synchronous machine allows good performance,
while at speeds close to zero or equal to zero, on isotropic synchronous machines
it is not possible to implement so-called sensorless algorithms, since the counter-electromotive
force of the motor is nil.

In this case it is possible to use any saturations of the machine,
i.e., if the inductance of the machine is a function of the position of the rotor
it is possible to use an algorithm of the sensorless type, but in this case it
is incorrect to define such a machine as isotropic.

Anisotropic synchronous machines, when supplied by impressed-voltage
inverters, due to the variability of the inductance according to the angle of
the rotor, impart an information content to the currents of the motor which is
independent of rotor speed and allows to deduce the position of the rotor at each
instant over time.

However, obtaining information on the position of the rotor from the
current of the motor can be extremely difficult.

The literature provides many methods, some of which are highly elaborate
and difficult to implement, to the point that they cannot be applied to ordinary
hardware platforms used for motor control applications, which do not have large
computational resources.

As an alternative, if instead of using mathematical algorithms one
uses so-called pre-calculated or pre-measured look-up tables of machine inductances
as a function of the position of the rotor of said machine (synchronous inductances),
said tables must be compiled with extreme accuracy, and this in turn is a significant
disadvantage, since extremely accurate tables are also very large and therefore
occupy considerable memory on the processor.

On the other hand, the advantage of these methods is that they allow
to obviate the problem of determining the angle 2&thetas;, since it is possible
to provide directly the angle &thetas;.

The aim of the present invention is to provide a method for determining
the position of the rotor of a synchronous alternating-current permanent-magnet
machine, which allows to determine the position of the rotor with calculations
that are simplified with respect to known types of method and therefore with reduced
computational resources.

Within the scope of this aim, an object of the present invention is
to provide a method for determining the position of the rotor of a synchronous
alternating-current permanent-magnet machine that allows to determine the sin(2&thetas;)
and cos(2&thetas;) parameters with &thetas; as the electrical angle.

Another object of the present invention is to provide a method for
determining the position of the rotor of a synchronous alternating-current permanent-magnet
machine that allows to obtain from sin(2&thetas;) and cos(2&thetas;) the pair sin(&thetas;)
and cos(&thetas;) that allows to univocally identify the position of the rotor
of the machine.

Another object of the present invention is to provide a method for
determining the position of the rotor of a synchronous alternating-current permanent-magnet
machine that is highly reliable, relatively simple to provide and at competitive
costs.

This aim and these and other objects that will become better apparent
hereinafter are achieved by a method for determining the position of the rotor
of a synchronous alternating-current permanent-magnet machine, characterized in
that it comprises the steps that consist in:

injecting in the machine a high-frequency voltage superimposed on the voltage
delivered by the machine control system;

measuring the current of the motor and extracting a current that is linked
to said injected voltage;

obtaining from said injected voltage and from said corresponding current the
electrical angle &thetas; suitable to identify the position of the rotor.

Further characteristics and advantages of the invention will become
better apparent from the detailed description of preferred embodiments according
to the present invention.

The method according to the invention, applied to a synchronous alternating-current
permanent-magnet machine, is as follows.

Considering a permanent-magnet anisotropic machine, the method entails
writing the equations of the machine in the reference system coupled to the stator
of said machine.

The equations of the machine are produced by a matrix of the inductances
of the machine, in which there is a fixed part and a part that depends on the electrical
angle of the machine.

Lind=Lfix+Lvar(&thetas;)

where

Ls2 := Lm2

Assuming the simplest case, in which the variation according to the
angle is sinusoidal, there is therefore a matrix of inductances that is determined
by a fixed part and by a part in which the inductances are linked sinusoidally
to the variation of the angle.

At this point it is necessary to define a Park matrix with fixed axes,
and the Park transform is applied to the equations mentioned above, written in
the reference system coupled to the stator of the machine, so as to describe said
equations according to axes α and β.

The Park transform therefore produces the matrix of inductances transformed
in the reference system α, β.

At this point a high-frequency voltage is injected into the motor
and, by applying the principle of overlapping effects, it is possible to ignore
the effect of the sinusoidal counter-electromotive force in the equations of the
machine with fixed axes.

For example, for a 50-Hz machine, the injected high-frequency voltage
can be a voltage at 800 Hz, with a switching frequency of 10 kHz, which overlaps
the voltage dispensed by the machine control system.

At this point the current of the motor is measured and the current
linked to the injected voltage is extracted by filtering.

Essentially, the injected high-frequency voltage can be broken down
into the two components along the axes α and β. The equations of the
injected voltage contain the derivative with respect to time of the flux

vα := R&peseta;iα + p&phis;α

vβ := R&peseta;iβ + p&phis;β

with respect to the axes α and β, respectively, and therefore by integrating
these equations one obtains the fluxes along the axes α and β, which
are given by the product of the matrix of inductances along the axes α and
β and the current, along the axes α and β, linked to the injected
voltage

&phis;αβ=Lind_{αβ} *i_{αβ}

A system of two equations in the unknowns sin(2&thetas;) and cos(2&thetas;)
is thus obtained.

The determinant of the matrix

which is constituted by the product of the inductances of the machine, along the
axes α and β, and the injected current along the axes α and β,
linked to the injected voltage, is constantly negative and nonzero if the injected
current is not nil.

The system of equations described above therefore allows to obtain
sin(2&thetas;) and cos(2&thetas;).

At this point, the problem is to obtain sin(&thetas;) from sin(2&thetas;)
and cos(&thetas;) from cos(2&thetas;).

The filtering step performed to measure the current of the motor and
thus extract the current linked to the injected voltage can be obtained by implementing
a hardware or software filter that is suitable to obtain only the currents produced
by the injection of high-frequency voltage, without thereby altering their information
content, eliminating the components at the frequency of the fundamental and those
derived from high-frequency pulse width modulation.

For example, it is possible to use second-order bandpass filters
implemented analogically or digitally in the processor.

It is noted that when the rotor is locked (i.e., the frequency of
the fundamental is zero), filtering is practically useless and the results are
highly valid.

Therefore, the method described above allows to determine the initial
position of the motor, minus a 180° angle, and also allows to control the machine
when the rotor is locked (torque control with locked rotor).

Once sin(20) and cos(20) have been determined, there are two possible
solutions for sin(&thetas;) and cos(0). This means that the position of the rotor
is known in terms of orientation, but its orientation is not known, i.e., the magnetic
north and south of the rotor are not known.

In order to define the direction of the position of the rotor, when
the machine starts it is sufficient to inject a very small voltage for a very short
time in the direction of the axis α, thus obtaining a small movement of the
rotor, and then observe the change in position; the north of the rotor tends to
align with the axis α, and therefore the variation of sin(2&thetas;) and
cos(2&thetas;) that is observed allows to define the direction of the rotor position.
From that moment onward, at each step k of the observation algorithm, one chooses
from the two possible solutions for sin(&thetas;) and cos(&thetas;) the solution
that is closest to the one found in the preceding step, i.e., k-1, while the other
solution is spaced by an angle &thetas; which is equal to approximately 180°.

In greater detail, assuming that one has two mutually different values
of the angle &thetas;, and assuming that the correct solution of the equations
is the first value, for example the north pole is close to the axis α, at
45°, if a positive voltage is applied along the α axis, the cosine of the
angle increases, while the sine decreases, because the north pole tends to align
with the axis α. If instead the solution is the second one found (i.e., the
south pole is close to the axis α, at 45°, and therefore the north pole is
at 225°), the cosine of the angle is seen to decrease, while the sine increases
because the south pole tends to move away from the axis α.

In practice it has been found that the method according to the invention
allows to determine the position of the rotor of a permanent-magnet anisotropic
alternating-current machine without using a position sensor for said rotor.

The method according to the invention, moreover, can be implemented
with computational resources that are commonly available in ordinary hardware platforms
used for motor control.

Furthermore, the method for determining the electrical angle &thetas;,
starting from the sine and cosine of the angle 2&thetas;, obtained by means of
the method according to the invention, is performed without resorting to pre-calculated
tables of machine inductances as a function of rotor position and by using solving
algorithms that are extremely simple with respect to known solutions.

Anspruch[en]

A method for determining the position of the rotor of a synchronous alternating-current
permanent-magnet machine, characterized in that
it comprises the steps that
consist in:

injecting in the machine a high-frequency voltage superimposed on the voltage
delivered by the machine control system;

measuring the current of the motor and extracting a current that is linked
to said injected voltage;

obtaining from said injected voltage and from said corresponding current the
electrical angle &thetas; suitable to identify the position of the rotor.

The method according to claim 1, wherein said step that consists in obtaining
said electric angle &thetas; comprises the steps that consist in:

determining fluxes of said machine as a function of inductances of said machine,
of the electrical angle of said rotor, and of the current linked to said injected
voltage.

The method according to claim 2, wherein said step that consists in obtaining
said electrical angle &thetas; of said rotor comprises the steps that consist in:

obtaining the sine and cosine of twice the electrical angle of said machine,
and extracting from said sine and cosine values the sine and cosine value of the
electrical angle &thetas; of said machine.

The method according to claim 1, wherein said step that consists in obtaining
said electrical angle of said rotor starting from the sine and cosine of twice
said electrical angle comprises the steps that consist in:

when said machine starts, injecting a low-value voltage for a short time in
the direction of one of the reference axes of said machine, in order to obtain
a minimum movement of said rotor;

observing the change in position of the rotor and determining, from the variation
of the sine and cosine of twice the electrical angle, the direction of the position
of the rotor.