U.S. patent application number 10/316734 was filed with the patent office on 2003-07-31 for method for estimating the position and speed of an actuator body in an electromagnetic actuator for controlling the valve of an engine.
This patent application is currently assigned to MAGNETI MARELLI POWERTRAIN S.p.A.. Invention is credited to Marchi, Marco, Morselli, Michele, Panciroli, Marco.
Application Number | 20030140875 10/316734 |
Document ID | / |
Family ID | 11439743 |
Filed Date | 2003-07-31 |
United States Patent
Application |
20030140875 |
Kind Code |
A1 |
Panciroli, Marco ; et
al. |
July 31, 2003 |
Method for estimating the position and speed of an actuator body in
an electromagnetic actuator for controlling the valve of an
engine
Abstract
Method for estimating the position and the speed of an actuator
body in an electromagnetic actuator for controlling a valve of an
engine, according to which, starting from a known value for the
position and a first moment, a value is calculated at the first
moment of the magnetic flux passing through a magnetic circuit
constituted by an electromagnet and by the actuator body, the value
for the speed at the first moment is estimated as a function of the
magnetic flux and the position at the first moment, and the value
is calculated at a second moment following the first moment and
separated from said first moment by an interval of time determined
by adding to the value of the position at the first moment the
product of the speed at the first moment for the interval of
time.
Inventors: |
Panciroli, Marco; (Ravenna,
IT) ; Morselli, Michele; (Bologna, IT) ;
Marchi, Marco; (Bologna, IT) |
Correspondence
Address: |
CHAPMAN AND CUTLER
111 WEST MONROE STREET
CHICAGO
IL
60603
US
|
Assignee: |
MAGNETI MARELLI POWERTRAIN
S.p.A.
Torino
IT
|
Family ID: |
11439743 |
Appl. No.: |
10/316734 |
Filed: |
December 11, 2002 |
Current U.S.
Class: |
123/90.11 |
Current CPC
Class: |
F02D 2200/063 20130101;
F02D 41/20 20130101; F02D 2041/2055 20130101; F02D 13/0253
20130101; F01L 2009/2109 20210101; F01L 2800/00 20130101; H01F
7/1844 20130101; F02D 2041/2058 20130101; F02D 2041/001 20130101;
F01L 9/20 20210101; F01L 2009/2136 20210101; F02D 2041/2034
20130101; Y02T 10/12 20130101; F02D 2041/2079 20130101 |
Class at
Publication: |
123/90.11 |
International
Class: |
F01L 009/04 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 14, 2001 |
IT |
BO2001A000760 |
Claims
1. Method for estimating the position (x) and the speed (v) of an
actuator body (4) in an electromagnetic actuator (1) for
controlling a valve (2) of an engine; the actuator body (4) being
made at least partly of ferromagnetic material and being displaced
towards at least one electromagnet (8) through the effect of the
force of magnetic attraction generated by said electromagnet (8);
the method being characterised by the fact that starting from a
known value of the position (x) and a first moment (T1), a value is
calculated at the first moment (T1) of the magnetic flux (p)
passing through a magnetic circuit (18) constituted by the
electromagnet (8) and by the actuator body (4), the value of the
speed (v) at the first moment (T1) is estimated as a function of
the magnetic flux (.phi.) and the position (x) at the first moment
(T1), and the value is calculated at a second moment (T2) following
the first moment (T1) and separated from said first moment (T1) by
an interval of time (dt) determined by adding to the value of the
position (x) at the first moment (T1) the product of the speed (v)
at the first moment (T1) for the interval of time (dt).
2. Method according to claim 1, in which said electromagnet (8)
defines, together with said actuator body (4), a magnetic circuit
(18) influenced by a magnetic flux (.phi.) produced by a coil (17)
through which an electric current (i) passes; said magnetic circuit
(18) having a total reluctance (R), which is assumed to be composed
of the sum of a first reluctance (R.sub.0) arising from an air gap
(19) in the magnetic circuit (18) and a second reluctance
(R.sub.fe) arising from the part of the magnetic circuit (18) made
of ferromagnetic material (4, 16); the first reluctance (R.sub.0)
depending on the structural properties of the magnetic circuit (18)
and on the value of the position (x), while the second reluctance
(R.sub.fe) depending on the structural properties of the magnetic
circuit (18) and on the value of the magnetic flux (.phi.) passing
through the magnetic circuit (18).
3. Method according to claim 2, in which the value for said first
reluctance (R.sub.0) and the value for said position (x) are
connected by the following equation:
R.sub.0(x(t))=K.sub.1[1-e.sup.-k.sup..sub.2.sup.x-
(t)+k.sub.3.multidot.x(t)]+K.sub.0in which R.sub.0 is said first
reluctance (R.sub.0), x(t) is said position (x) and K.sub.0,
K.sub.1, K.sub.2, K.sub.3 are four constants.
4. Method according to claim 2, in which the relationship between
the speed (v), the magnetic flux (.phi.) and the position (x) is
supplied by the following equation: 6 i ( t ) t = R 0 ( x ( t ) ) x
x ( t ) t ( t ) + R 0 ( x ( t ) ) ( t ) t + H fe ( ( t ) ) ( t ) t
x ( t ) t = i ( t ) t - R 0 ( x ( t ) ) ( t ) t - H fe ( ( t ) ) (
t ) t R 0 ( x ( t ) ) x ( t ) in which i is the electric current
(i) circulating within the coil (17), R.sub.0 is said first
reluctance (R.sub.0), x is the position (x) of the actuator body
(4), .phi. is the magnetic flux (.phi.) and H.sub.fe is the
quantity of ampere-turns acted on by the iron part (4, 16) of the
magnetic circuit (18).
5. Method according to claim 1, in which the value of the magnetic
flux (.phi.) is estimated by measuring the value assumed from some
electric parameters (i, v; va) of an electric circuit (17; 22)
coupled to the magnetic circuit (18), calculating the time
derivative of the magnetic flux (.phi.) as a linear combination of
the values of the electrical parameters (i, v; va), and integrating
in time the derivative of the magnetic flux (.phi.).
6. Method according to claim 5, in which the current (i)
circulating through a coil (17) of the electromagnet (8) and the
voltage (v) applied to the terminals of said coil (17) are
measured; the time derivative of the magnetic flux (.phi.) and the
magnetic flux (.phi.) itself being calculated by applying the
following formulae: 7 ( t ) t = v ( t ) - RES i ( t ) ( T ) = 0 T (
v ( t ) - RES i ( t ) ) t + ( 0 ) in which .phi. is the magnetic
flux (.phi.), v is the voltage (v) applied to the terminals of the
coil (17), RES is the resistance of the coil (17) and i is the
current (i) circulating through the coil (17).
7. Method according to claim 6, in which the voltage (v.sub.aux) at
the terminals of an auxiliary turn (22) coupled to the magnetic
circuit (18) and concatenating the magnetic flux (.phi.) is
measured; the auxiliary turn (22) being substantially open
electrically; and the time derivative of the magnetic flux (.phi.)
and the magnetic flux (.phi.) itself being calculated by applying
the following formulae: 8 ( t ) t = v aus ( t ) ( T ) = 0 T v aus (
t ) t + ( 0 ) in which .phi. is the magnetic flux (.phi.) and
v.sub.aux is the voltage (v.sub.aux) present at the terminals of
the auxiliary turn (22).
Description
[0001] The present invention relates to a method for estimating the
position and speed of an actuator body in an electromagnetic
actuator for controlling a valve of an engine.
BACKGROUND OF THE INVENTION
[0002] As is known, experiments are currently being conducted on
internal combustion engines of the type described in Italian patent
application BO99A000443 filed on 4, Aug. 1999, in which the intake
and exhaust valves are set in motion by electromagnetic actuators.
Such electromagnetic actuators have undoubted advantages, in that
they make it possible to control each valve according to a law
optimised for each operating condition of the engine, whereas
traditional mechanical actuators (typically camshafts) require the
definition of a valve lift profile that represents an acceptable
compromise for all possible operating conditions of the engine.
[0003] An electromagnetic actuator for a valve of an internal
combustion engine of the type described above normally comprises at
least one electromagnet capable of displacing an actuator body made
of ferromagnetic material and mechanically connected to the stem of
the respective valve. In order to apply a particular law of motion
to the valve, a control unit drives the electromagnet with a
time-variable current in order to displace the actuator body in a
suitable manner.
[0004] From experimental testing it has been observed that, in
order to achieve relatively high precision in controlling the valve
it is necessary to have feedback control of the position of the
actuator body; it is therefore necessary to have an accurate--and
substantially real-time--reading of the position of said actuator
body at any time. In order to achieve high performance levels from
the feedback control it is furthermore preferable also to have an
accurate--and substantially real-time--reading of the speed of the
actuator body at any time.
[0005] In electromagnetic actuators of the type described above,
the position of the actuator body is read by a laser sensor, which
is, however, expensive, delicate and difficult to calibrate and is
therefore unsuitable for use in mass production. Furthermore, the
speed of the actuator body is estimated in a time-derivation
operation on the position of said actuator body at any time.
However, such an operation supplies a relatively inaccurate result
in that it tends to amplify the noise present when measuring the
position of the actuator body.
SUMMARY OF THE INVENTION
[0006] The aim of the present invention is to provide a method for
estimating the position and speed of an actuator body in an
electromagnetic actuator for controlling a valve of an engine,
which does not have the drawbacks described and, in particular, is
easy and economical to operate.
[0007] According to the present invention a method is provided for
estimating the position and speed of an actuator body in an
electromagnetic actuator for controlling a valve of an engine as
claimed in claim 1.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] The present invention will now be described with reference
to the attached drawings, which illustrate a few non-exhaustive
embodiments thereof, in which:
[0009] FIG. 1 is a diagrammatic view, in side elevation and in
partial section, of a valve of an engine and of a corresponding
electromagnetic actuator operating according to the method that is
the subject-matter of the present invention;
[0010] FIG. 2 is a diagrammatic view of a control unit for the
device in FIG. 1;
[0011] FIG. 3 illustrates diagrammatically a part of the control
unit of FIG. 2; and
[0012] FIG. 4 illustrates a circuit diagram of a detail of FIG.
3.
DETAILED DESCRIPTION OF THE INVENTION
[0013] In FIG. 1 an electromagnetic actuator 1 (of the type
described in Italian patent application BO99A000443 filed on 4,
Aug. 1999) is indicated as a whole by the reference number 1,
coupled to an intake or exhaust valve 2 of an internal combustion
engine of a known type for displacing said valve 2 along a
longitudinal axis 3 of the valve between a closed position (known
and not illustrated) and a maximally open position (known and not
illustrated).
[0014] The electromagnetic actuator 1 comprises a swinging arm 4
made at least partly of ferromagnetic material, which has a first
end hinged to a support 5 so as to be able to oscillate about an
axis 6 of rotation perpendicular to the longitudinal axis 3 of the
valve 2, and a second end connected by a connector 7 to an upper
end of the valve 2. The electromagnetic actuator 1 also comprises
two electromagnets 8 carried in a fixed position by the support 5
so as to be arranged on opposite sides of the swinging arm 4, and a
spring 9 coupled to the valve 2 and capable of holding the swinging
arm 4 in an intermediate position (illustrated in FIG. 1) in which
said swinging arm 4 is equidistant from the pole pieces 10 of the
two electromagnets 8.
[0015] In use, the electromagnets 8 are controlled by a control
unit 11 so as to exert alternately or simultaneously a force of
attraction of magnetic origin on the swinging arm 4 in order to
make it rotate about the axis 6 of rotation, thereby displacing the
valve 2 along the respective longitudinal axis 3 and between the
aforementioned maximally open and closed positions (not
illustrated). In particular, the valve 2 is in the aforementioned
closed position (not illustrated) when the swinging arm 4 is
abutting against the upper electromagnet 8, is in the
aforementioned maximally open position (not illustrated) when the
swinging arm 4 is abutting against the lower electromagnet 8, and
is in a partly open position when the two electromagnets 8 both
have power shut off and the swinging arm 4 is in the aforementioned
intermediate position (illustrated in FIG. 1) by the effect of the
force exerted by the spring 9.
[0016] The control unit 11 provides feedback control, in a
substantially known manner, for the position of the swinging arm 4,
i.e. the position of the valve 2, on the basis of the conditioning
of engine function. In particular, according to the illustration in
FIG. 2, the control unit 11 comprises a reference generation block
12, a calculation block 13, a driving block 14 capable of supplying
the electromagnets 8 with time-variable current, and an estimation
block 15 capable of estimating--substantially in real time--the
position x(t) and, where necessary, the speed v(t) of the swinging
arm 4.
[0017] In use, the reference generation block 12 receives as inputs
a plurality of parameters indicating the operating conditions of
the engine (for example the load, the engine speed, the position of
the throttle body, the angular position of the drive shaft, the
temperature of the coolant) and supplies the calculation block 13
with a target value x.sub.R(t) (i.e. a desired value) for the
position of the swinging arm 4 (and therefore the valve 2).
[0018] On the basis of the target value x.sub.R(t) for the position
of the swinging arm 4 and on the basis of the estimated value x(t)
of the position of the swinging arm 4 received from the estimation
block 15, the calculation block 13 prepares and sends to the
driving block 14 a control signal z(t) for driving the
electromagnets 8. In a preferred embodiment, the calculation block
13 prepares the control signal z(t) also on the basis of an
estimated value v(t) for the speed of the swinging arm 4 received
from the estimation block 15.
[0019] According another embodiment, not illustrated, the reference
generation block 12 supplies the calculation block 13 with either a
target value x.sub.R(t) for the position of the swinging arm 4, or
a target valve x.sub.R(t) for the speed of the swinging arm 4.
[0020] As illustrated in FIG. 3, the driving block 14 supplies
power to the two electromagnets 8, each of which is composed of a
respective magnetic core 16 coupled to a corresponding coil 17, for
displacing the swinging arm 4 on the basis of the commands received
from the calculation block 13. The estimation block 15 reads the
values, as shown in detail below, either from the driving block 14,
or from the two electromagnets 8, in order to calculate an
estimated value x(t) for the position and an estimated value v(t)
for the speed of the swinging arm 4.
[0021] The swinging arm 4 is arranged between the pole pieces 10 of
the two electromagnets 8, which are carried by the support 5 in a
fixed position and at a fixed distance D from one another, and
therefore the estimated value x(t) of the position of the swinging
arm 4 can be obtained directly with a simple operation of algebraic
addition from an estimated value d(t) of the distance between a
given point on the swinging arm 4 and a corresponding point on the
one of the two electromagnets 8. By analogy, the estimated value
v(t) for the speed of the swinging arm 4 can be obtained directly
from an estimated value for the speed existing between a given
point on the swinging arm 4 and a corresponding point on one of the
two electromagnets 8.
[0022] In order to calculate the value x(t) the estimation block 15
calculates the two estimated values d.sub.1(t), d.sub.2(t) for the
distance between a given point on the swinging arm 4 and a
corresponding point on one of the two electromagnets 8; from the
two estimated values d.sub.1(t), d.sub.2(t), the estimation block
15 obtains two values x.sub.1(t), x.sub.2(t), which generally
differ from one another because of measuring errors and noise.
According to a preferred embodiment, the estimation block 15 takes
an average of the two values x.sub.1(t), x.sub.2(t), weighted if
necessary on the basis of the accuracy attributed to each value
x(t). By analogy, in order to calculate the value v(t) the
estimation block 15 calculates the two estimated values for speed
existing between a given point on the swinging arm 4 and a
corresponding point on one of the two electromagnets 8; from the
two estimated values for speed, the estimation block 15 obtains two
values v.sub.1(t), v.sub.2(t), which generally differ from one
another because of measuring errors and noise. According to a
preferred embodiment, the estimation block 15 takes an average of
the two values v.sub.1(t), v.sub.2(t), weighted if necessary on the
basis of the accuracy attributed to each value v(t).
[0023] With particular reference to FIG. 4, which illustrates a
single electromagnet 8, a description is given below of the method
used by the estimation block 15 for calculating an estimated value
d(t) for the distance between a given point on the swinging arm 4
and a corresponding point on the electromagnet 8, and for
calculating an estimated value for the speed existing between a
given point on the swinging arm 4 and a corresponding point on the
electromagnet 8.
[0024] In use, when the driving block 14 applies a voltage v(t)
variable over time to the terminals of the coil 17 of the
electromagnet 8, a current i(t) passes through said coil 17,
consequently generating a flux .phi.(t) over a magnetic circuit 18
coupled to the coil 17. In particular, the magnetic circuit 18
coupled to the coil 17 is composed of the core 16 of ferromagnetic
material of the electromagnet 8, the swinging arm 4 made of
ferromagnetic material and the air gap 19 existing between the core
16 and the swinging arm 4.
[0025] The magnetic circuit 18 has a total reluctance R defined by
the sum of the reluctance of iron R.sub.fe and the reluctance of
the air gap R.sub.0; the value for the flux .phi.(t) circulating
over the magnetic circuit 18 is connected to the value of the
current i(t) circulating within the coil 17 by the following
relationship (in which N is the number of turns in the coil
17):
N*i(t)=R*.phi.(t)
R=R.sub.fe+R.sub.0
[0026] In general the value for total reluctance R depends both on
the position x(t) of the swinging arm 4 (i.e. the breadth of the
air gap 19, which is equal, except for a constant, to the position
x(t) of the swinging arm 4), and on the assumed value for flux
.phi.(t) . Except for negligible errors (i.e. those of a first
approximation) it can be determined that the value for reluctance
of iron R.sub.fe depends solely on the assumed value for flux
.phi.(t), while the value for reluctance of the air gap R.sub.0
depends solely on the position x(t), i.e.
R(x(t), .phi.(t))=R.sub.fe(.phi.(t))+R.sub.0(x(t))
N*i(t)=R(x(t), .phi.(t)) *.phi.(t)
N*i(t)=R.sub.fe(.phi.(t))*.phi.(t)+R.sub.0(x(t))* .phi.(t)
[0027] By solving the last equation given above with regard to
R.sub.0(x(t)), it is possible to obtain the value of the reluctance
of the air gap R.sub.0 knowing the value of the current i(t), which
value can easily be measured by an ammeter 20, knowing the value of
N (fixed and dependent on the structural properties of the coil
17), knowing the value of the flux .phi.(t), and knowing the
relationship between the reluctance of the iron (R.sub.fe and the
flux .phi. (known from the structural properties of the magnetic
circuit 18 and the magnetic properties of the material used, or
easily determined by experimental tests).
[0028] The relationship between reluctance at the air gap R.sub.0
and the position x can be obtained relatively simply by analysing
the properties of the magnetic circuit 18 (an example of a model of
the behaviour of the air gap 19 is represented by the equation
given below). Once the relationship between reluctance at the air
gap R.sub.0 and the position x is known, the position x can be
obtained from the reluctance at the air gap R.sub.0 by applying the
inverse relationship (applicable either by using the exact equation
or by applying approximate numerical calculation methods). The
above statements can be summarised in the following relationships
(where H.sub.fe(.phi.(t))=R.sub.fe(.phi.((t))*.phi.(t)): 1 R o ( x
( t ) ) = N i ( t ) - H fe ( ( t ) ) ( t ) R o ( x ( t ) ) = K 1 [
1 - - k 2 x ( t ) + k 3 x ( t ) ] + K 0 x ( t ) = R 0 - 1 ( R o ( x
( t ) ) ) = R 0 - 1 ( N i ( t ) - H fe ( ( t ) ) ( t ) )
[0029] The constants K.sub.0, K.sub.1, K.sub.2, K.sub.3 are
constants that can be obtained in experimental tests by using a
series of measurements on the magnetic circuit 18.
[0030] From the above, it is clear that if the flux .phi.(t) can be
measured it is possible to calculate relatively easily the position
x(t) of the swinging arm 4.
[0031] In a first embodiment, the flux .phi.(t) can be calculated
by measuring the current i(t) that circulates through the coil 17
by using the ammeter 20 of a known type, measuring the voltage v(t)
applied to the terminals of the coil 17 by using a voltmeter 21 of
known type, and knowing the value for resistance RES of the coil 17
(a value that is easy to measure) . This method of measuring the
flux .phi.(t) is based on the following relationships: 2 ( t ) t =
v ( t ) - RES i ( t ) ( T ) = 0 T ( v ( t ) - RES i ( t ) ) t + ( 0
)
[0032] The conventional moment 0 is chosen so as to find out
accurately the value of the flux .phi.(0) at said moment 0; in
particular, the moment 0 is normally chosen within a period of time
in which no current is flowing through the coil 17 and, therefore,
the flux .phi. is substantially zero (the effect of any residual
magnetisation is negligible), or the moment 0 is chosen according
to a given position of the swinging arm 4 (typically when the
swinging arm 4 is abutting against the pole pieces 10 of the
electromagnet 8), in correspondence with which the value of the
position x is known and therefore the value of the flux .phi. is
known.
[0033] The method stated above for calculating the flux .phi.(t) is
fairly accurate and fast (i.e. involving no delay); however, said
method has a few problems, owing to the fact that the voltage v(t)
applied to the terminals of the coil 17 is normally generated by a
switching amplifier incorporated into the driving block 14 and
therefore varies continuously between three values (+V.sub.supply,
0, -V.sub.supply) the continuous variation (with very abrupt rises
and falls) of the voltage v(t) makes it very difficult to measure
said voltage v(t) accurately and quickly and, consequently, to
estimate the flux .phi.(t). In order to increase accuracy, the
reading signal of the voltmeter 21 can be filtered in order to
attenuate the high frequencies, but such filtering inevitably
introduces a delay into the measuring process.
[0034] In another embodiment, the magnetic coil 16 is coupled to an
auxiliary turn (or coil) 22, to the terminals of which another
voltmeter 23 is connected; since the terminals of the turn 22 are
substantially open (the internal resistance of the voltmeter 23 is
so high as to be regarded as infinite without thereby introducing
appreciable errors), no current flows through the turn 22 and the
voltage v.sub.aux(t) at its terminals depends solely on the time
derivative of the flux .phi.(t), from which the flux can be deduced
by means of a operation of integration (as concerns the value
.phi.(0), see the considerations stated above): 3 ( t ) t = v aus (
t ) ( T ) = 0 T v aus ( t ) t + ( 0 )
[0035] From experimental tests it has been demonstrated that, in
contrast to the voltage v(t) at the terminals of the coil 17, the
voltage v.sub.aux(t) is substantially direct because of the effect
of magnetic inertia (particular the stray currents induced in the
iron) of the magnetic circuit 18 that damp the effects of the
abrupt variations in the voltage v(t) . In other words, the iron
part of the magnetic circuit 18 has a low-pass filter effect that
damps the abrupt variations in the voltage v(t) and makes the
voltage v.sub.aux(t) substantially direct without introducing
delays in measurement.
[0036] As stated above it is clear that by using the reading of the
voltage v.sub.aux(t) of the auxiliary turn 22, calculation of the
value of the flux .phi.(t) is more accurate and/or faster than
using the reading of the voltage v(t) at the heads of the coil
17.
[0037] As well as for estimating the position x(t) of the swinging
arm 4, measurement of the flux .phi.(t) can be used by the control
unit 11 for verifying the value of the force f(t) of attraction
exerted by the electromagnet 8 on the swinging arm 4, where: 4 f (
t ) = - 1 2 R ( x ( t ) , ( t ) ) x 2 ( t ) f ( t ) = - 1 2 R 0 ( x
( t ) ) x 2 ( t )
[0038] On the basis of the value of the position x(t) of the
swinging arm 4, it is possible to calculate the value of the speed
v(t) of the swinging arm 4 by using a simple time-derivative
operation on the position x(t); however, the value for speed v(t)
obtained with such a derivation operation has much interference,
since, as is known, the derivation operation markedly amplifies
high-frequency interference. To reduce the incidence of such
interference it is necessary to carry out the filtering operations
with low-pass type filters which, however, introduce inevitable
delays in estimating the value of the speed v(t).
[0039] According to another embodiment, both the position x(t) and
the speed v(t) can be calculated by using a process of calculation
of the iterative type; this process is based on the equation
(described above):
i(t)=R.sub.0(x(t))*.phi.+H.sub.fe(.phi.(t))
[0040] deriving said equation with respect to time and applying the
laws of partial derivation gives the equation: 5 i ( t ) t = R 0 (
x ( t ) ) x x ( t ) t ( t ) + R 0 ( x ( t ) ) ( t ) t + H fe ( ( t
) ) ( t ) t x ( t ) t = i ( t ) t - R 0 ( x ( t ) ) ( t ) t - H fe
( ( t ) ) ( t ) t R 0 ( x ( t ) ) x ( t )
[0041] reading from left to right it can be seen that: the time
derivative of the current i(t) can be calculated easily by deriving
the measurement signal of the ammeter 20 (this signal is generally
very clean (i.e. free from noise) and free from abrupt variations
and, therefore, can be time-derived with no particular
problems);
[0042] the partial derivative of the reluctance R.sub.0 of the air
gap 19 with respect to the position x can be calculated as a simple
derivation of the equation R.sub.0=R.sub.0(x) described above;
[0043] the time derivative of the position x(t) is the speed
v(t);
[0044] the flux .phi.(t) can be calculated by using one of the two
methods described above;
[0045] the reluctance R.sub.0 of the air gap 19 can easily be
calculated from the equation R.sub.0=R.sub.0(x) described above if
the value of the position x is known;
[0046] the partial derivative of the quantity of ampere-turns Hfe
of the iron with respect to the flux .phi. can be obtained easily
if the structural properties of the magnetic circuit 18 are known;
and
[0047] the time derivative of the flux .phi.(t) can be calculated
with one of the two methods described above.
[0048] Assuming that we are starting from a conventional moment t=0
in which both the value of the flux .phi. and the value of the
position x are known (as described above, this moment 0 is normally
chosen at the moment in which the swinging arm 4 is in a given
position, typically abutting against the pole pieces 10 of the
electromagnet 8).
[0049] Starting from the moment t=0, the value of the reluctance
R.sub.0 of the air gap 19 is calculated at the moment t=0 using the
value of the position x(0) at the moment 0; inserting this value
into the last equation described above (and previously also
calculating the other values in this equation by the method
indicated earlier), it is possible to calculate very easily the
value of the speed v(0) at the moment t=0.
[0050] If a substantially negligible error is committed, it may be
assumed that the speed v remains substantially constant for a
period of time dt (of a very small amplitude and depending on the
desired accuracy); on the basis of this hypothesis, after the time
dt, the position x(0+dt) at the moment 0+dt will be:
x(0+dt)=x(0+v(0)*dt
[0051] in this way the value of the position x(0+dt) at the moment
0+dt is calculated, and the operations described above are repeated
until the value of the speed v(0+dt) at the moment 0+dt is
determined, and so on.
[0052] The method described above has the merit of supplying
accurately and quickly either the value of the position x, or the
value of the speed v.
[0053] In the description given above two methods have been
provided for estimating the time derivative of the flux .phi.(t)
(hence the value of the flux .phi.(t) can be calculated), and two
methods for calculating the position x(t) and the speed v(t).
According to one embodiment a choice is made to use only one method
for calculating the time derivative of the flux .phi.(t) and one
method for calculating the position x(t) and the speed v(t).
According to another embodiment the choice is made to use both
methods for calculating the time derivative of the flux .phi.(t)
and/or both the methods for calculating the position x(t) and the
speed v(t), and to use an average (weighted if necessary with
respect to the estimated accuracy) of the results of the two
methods used, or to use one result in order to verify the other (if
there is a notable inconsistency between the two results it is
likely that an error in estimating will be verified).
[0054] Finally, it is useful to observe that the methods described
above for estimating the position x(t) and the speed v(t) can be
used only when there is a current passing through the coil 17 of an
electromagnet 8. For this reason, as described above, the
estimation block 15 works with both the electromagnets 8, so as to
use the estimation performed with one electromagnet 8 when the
other is switched off. When both the electromagnets are on, the
estimation block 15 performs an average of the two values x(t)
calculated with both electromagnets 8, weighted if necessary on the
basis of the accuracy attributed to each value x(t) (generally the
estimation of the position x made with respect to an electromagnet
8 is more accurate when the swinging arm 4 is relatively close to
the pole piece 10 of said electromagnet 8.
* * * * *