Subject: Re: standard packages for 1076.1
From: Ernst Christen (Ernst_Christen@avanticorp.com)
Date: Tue Oct 09 2001 - 08:34:43 PDT
The discussion started by Siep Onneweer about across and through
variables of magnetic systems is an interesting one. The proposed
package electrical_systems defines the magnetomotive force as the
across variable and flux as the through variable of nature magnetic.
As I understand it, Siep's main concern is that this approach does
not model energy storage correctly. He argues that an approach that
uses flux rate as the through variable addresses his concerns and
remarks that this has the additional benefit that the product of
across and through variable then equals power, as it does for the
electrical nature.
In his response, Peter Wilson states that "using the rate of flux
precludes the use of initial flux conditions." He continues to list
a number of applications where this would cause problems and
concludes that flux as the through variable is preferrable.
Siep acknowledges in his rebuttal the problem raised by Peter, but
suggests that introducing leakage paths would help to address the
problem, albeit inelegantly. In this respect he likens the issue to
that of a number of electrical capacitors connected in series.
I would like to bring two other perspectives into the discussion, one
that looks at the meaning of simulation results, the other, the ratio
of across and through variables. Before I do, let me make a few
comments.
Siep's suggestion that the product of across and through variable
should be power is a basic property of the Bond graph methodology,
which is an approach used mainly in system design that has some
parallels to across and through variables. With this as a guideline,
across and through variables and their units for the different
energy domains would be:
energy domain across variable through variable
----------------------------------------------------------------------
electrical voltage [V] current [A]
magnetic magnetomotive force [A] magnetic flux rate [V]
translational velocity [m/s] force [N]
rotational angular velocity[rad/s] torque [Nm]
fluidic pressure [Nm**-2] volume flow rate [m**3/s]
thermal temperature [K] entropy flow [W/K]
If we compare this with the proposed natures we notice that magnetic
and thermal are defined differently (magnetic with magnetic flux, and
thermal with heat flow as the through variable). Also, the radiant
energy domain is not represented in the above table. Its across and
through variables are luminous intensity [cd] and optical flux [lm],
whose product has the unit [cd**2*sr]. I don't know whether a set of
across and through variables for radiant systems exists whose product
has the unit of power. I doubt it because I believe any equivalence
of power and an optical phenomenon would depend on the wavelength.
We also notice that package mechanical_systems defines two additional
natures with alternative across variables: position [m], and angle
[rad], respectively. These are the integrals of the above across
variables over time, and the same relationship exists between magnetic
flux and flux rate. Both kinds of translational and rotational systems
have been used in the past for modeling, to my knowledge with no
problems except the nuisance of having to convert between the two if
both are used in the same design.
This brings me to the first topic I mentioned above, the meaning of
simulation results. Assume we define just one kind of natures for
translational, rotational, or magnetic energy domains. I believe there
is no major difference between the quality of simulation results for
a time domain simulation regardless of which of the two alternatives
in each case is chosen. However, there is some difference in the
physical meaning of a DC operating point, i.e. the quiescent point
defined by VHDL-AMS. Physically, the DC operating point is the state
of the system with no stimulus applied. For the three pairs of natures:
energy domain across through DC operating point means
------------------------------------------------------------------------
translational velocity force constant velocity =
uniform motion
translational position force constant position,
velocity=0
rotational ang. velocity torque constant ang.velocity =
uniform motion
rotational angle torque constant angle,
ang.velocity=0
magnetic mmf flux rate constant flux rate
magnetic mmf flux constant flux,
flux rate=0
While both versions of translational and rotational seem to have
intuitive and well-understood meanings, a constant flux rate is not so
clear. It induces a constant voltage and would mean a flux that grows
without bounds. This is disturbing to me because any physical device
will break down when the electrical field gets too strong. It would
mean the device breaks down (at least conceptually) if it is left in
its quiescent state for too long.
The second perspective is that of the ratio of across and through
variables, i.e. the resistance in the appropriate energy domain. We
have:
energy domain across through "resistor"
----------------------------------------------------------------------
electrical voltage current resistor
translational velocity force damper, dashpot
translational position force spring
rotational ang.velocity torque rot.damper, rot.dashpot
rotational angle torque rotary spring
fluidic pressure vol. flow rate orifice with laminar flow
thermal temperature heat flow rate thermal resistance
magnetic mmf flux rate ?
magnetic mmf flux ?
radiant luminous intens.optical flux ?
I don't know what phenomena could act as "resistors" in the two kinds
of magnetic or in the radiant energy domain. Are there equivalents of
capacitors and inductors? Both exist for electrical, velocity-based
translational, ang.velocity-based rotational, and fluidic energy domains.
Only the capacitor equivalent exists for thermal systems. For position-
based translational and angle-based rotational we have a capacitor
equivalent as well as equivalents to an element that in filter design
has been called FDNR (frequency-dependent negative resistance,
i=D*d2v/dt2). Filling in the missing pieces may be helpful to come to
a conclusion.
In summary, I believe that there is no real need to define across and
through variables such that their product equals power. The best example
that doesn't satisfy this criterion is the thermal energy domain with
temperature and heat flow rate as across and through variables: their
product has a unit of [W*K]. This definition has been used for many years,
and I am not aware of any problems with its use. This implies that
changing the definition of the magnetic nature to use flux rate as its
through variable is not mandatory, although it is possible. The meaning
of the results of a DC analysis seems to favor flux, but the analysis
of equivalent phenomena is outstanding. Finally, I believe that the
definition of the radiant nature requires further analysis since the
properties of its proposed across and through variables are quite
different from those of the across and through variables of other
natures.
Ernst Christen
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