===============================================================================
1076.1 Ballot Resolution Commitee                     Comment Resolution Report
-------------------------------------------------------------------------------
CRR Number:             3
Topic Addressed:        Augmentation sets
Related CRs:            6, 7 (Hisashi Sasaki, Toshiba Corp., affirmative)
                        18, 142, 161, 162 (Steven Greenberg, Analogy, negative
                        changed to affirmative)
Relevant LRM Sections:  12.6.5
Resolution Status:      Partly in review by balloters
===============================================================================

Comment Reports Summary
~~~~~~~~~~~~~~~~~~~~~~~
----------------------------------------------------------------------
CR006
 
[page 66 line 1907] Could you give NOTE what is the main role the
characteristic expression of scalar subelement is, especially such
corresponding eqautions:
    chracteristic expression: Q'DOT
    coresponding equation: Q'DOT == 0.0

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
Supplementary explanation improve readability.
----------------------------------------------------------------------
CR007

[page 66 line 1919, 1921] Also could you give more supplementary explanation
on "the time derivative of ..." and "the integral over ...", because ,at a
glance, we cannot read the meaning. These are a provided by analog kernel a
priori, that is, they are numerical routine which is implementation dependant.

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
Supplementary explanation improve readability.
----------------------------------------------------------------------
CR018

lines 1939, 1940, and 1941 - I found it hard to understand what these
statements were getting at.  Part of the confusion was the phrase "its value".
I didn't know whether the pronoun "its" was refering to Q or to Q'Dot.  I also
struggled with the concept of setting Q equal to its value.  It seems to be a
tautology that Q is equal to its value.  There is something missing in this
description about when the value is taken and when the constraint is applied.

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
Maybe a note to explain that this augmentation set will be applied later in a
particular place in the discussion of the Analog kernel.
----------------------------------------------------------------------
CR142

The LRM is harder to understand because there are not enough examples. Even the 
original hard to understand LRM had more examples.
An example is the sentence "The difference between each scalar subelement of 
the prefix Q of each quantity of the form Q'DOT and the value of the scalar 
subelement is a charactersitic expression of the discontinuity augmentation 
set."

In a later report, I will explain how the addition of three leters to the above 
sentence could have saved hours of puzzlement over its meaning.  An additional 
phrase would have made it even more understandable.  An example might actually 
have communicated the intent.

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
If you have the following scalar quantity:

quantity v: velocity;

and in the model there is a statement:

v'dot == -G + v ** 2 * Air_res;

If a break statement is executed and the velocity has a value of 10 at the time 
of the break, then the following characteristic expression is added to the 
discontinuity augmentation set:

v - 10
----------------------------------------------------------------------
CR161

The sentence "The difference between each scalar subelement of the prefix Q of
each quantity of the form Q'DOT and the value of the scalar subelement is a
charactersitic expression of the discontinuity augmentation set." is very hard
to understand for two reasons.  First, it is not clear that it is talking
about the value of the scalar subelement of Q rather than the scalar
subelement of Q'DOT.  Second, it is hard to realize the significance of the
word "value" unless you already know what the sentence is trying to tell you.

The whole situation is not helped by the fact that there is no introductory
material for the section to describe what is the purpose of a discontinuity
augmentation set.  There is also no forward reference to the place where the
discontinuity augmentation set is used.

Also, I see no reason to keep it as a mystery that values of the quantities
will be found to make the characteristic expressions sufficiently close to 
zero.

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
The first stage of the fix would be to add three letters to the troublesome
sentence as follows:

"The difference between each scalar subelement of the prefix Q of each
quantity of the form Q'DOT and the value of the scalar subelement of Q is a
charactersitic expression of the discontinuity augmentation set."

To go a bit further to make the significance of "value" standout, you could
add a phrase to the sentence:

"The difference between each scalar subelement of the prefix Q of each
quantity of the form Q'DOT and the value of the scalar subelement of Q at the
time of the discontinuity is a charactersitic expression of the discontinuity
augmentation set."

A less obtuse way of putting it would be as follows:

For each quantity of the form Q'DOT, the difference between each scalar
subelement of the prefix Q and the value at the time of the discontinuity of
that scalar subelement of the prefix Q is a charactersitic expression of the
discontinuity augmentation set."

The rest of the sentences in the section could be similarly repaired.

Also an introductory sentence might read as follows:

"The discontinuity augmentation set provides additional constraints on the
analog solution at the time of a discontinuity. These additonal constraints
provide initial conditions for restarting the differential equation solution
at the discontinuity. See Section 12.6.5.1."

And finally as I mentioned in Report Number 1, you could add an example:

If you have the following scalar quantity:

quantity v: velocity;

and in the model there is a statement:

v'dot == -G + v ** 2 * Air_res;

If a break statement is executed and the velocity has a value of 10.0 at the
time of the break, then the following characteristic expression is added to
the discontinuity augmentation set:

v - 10.0
----------------------------------------------------------------------
CR162

I cannot figure out if complex_polar' is a typographical error or not.  I
don't have access to the IEEE math standard.

Assumming that complex_polar'( magnitude, phase ) means something like:

magnitude * e ** phase

and assumming that polar_to_complex( magnitude * e ** phase ) means something
like:

magnitude * ( cos( phase ) + i * sin ( phase ) )

The characteristic expression for each spectral source is

source - e ** ( magnitude * ( cos( phase ) + i * sin ( phase ) ) )

Proposed Resolution
~~~~~~~~~~~~~~~~~~~
It seems to me that the characteristic expression is more like

source - ( magnitude * ( cos( phase ) + i * sin ( phase ) ) )

so perhaps there is only an extraneous use of the exp function in the original
definition.

===============================================================================

Analysis and Action Taken
~~~~~~~~~~~~~~~~~~~~~~~~~
Each section defining augmentation sets now has an introduction that describes 
briefly the purpose of the augmentation set. This introductory text addresses 
the concern raised in CR006. Note that the introductions refer to three sets, a 
structural set, an explicit set, and an augmentation set. Splitting the 
previous basic set into the new structural set and explicit set was necessary 
to address other comments.

To address the issue raised in CR007, we have added a sentence to the time 
domain augmentation set clarifying the meaning of the time  derivative and the 
integral over time.

The text of the definitions in the discontinuity augmentation set has been 
improved according to the balloter's suggestion to address the issue raised in 
CR161. CR142 and CR161 also suggest to add an example. Since there were several 
comments suggesting to add examples to complement the  definitions, we will 
address the issue of examples separately to attain consistency.

The definition of some characteristic expression in the frequency domain 
augmentation set and the noise augmentation set were improved and corrected in 
order to address the issue raised in CR162.

Additionally, we improved the text in some other definitions and made some 
corrections and clarifications.

We moved the definitions from the elaboration section 12.4.6 to the new section 
12.6.5 in the execution section. This is motivated by the fact that 
augmentation sets may have to be determined during execution at each analog 
solution point. The previous section 12.6.5 (the analog solver) has been 
renumbered to the new section 12.6.6.

===============================================================================

Revised Definitions
~~~~~~~~~~~~~~~~~~~
new section 12.6.5
12.6.5 Augmentation Sets

    An !augmentation set! is a set of characteristic expressions, 
    each corresponding to the scalar subelement of a source 
    quantity or the scalar subelement of an implicit quantity of 
    the form Q'DOT, Q'INTEG, and Q'DELAYED(T). The corresponding
    scalar subelement is said to be the !tag! of the characteristic 
    expression. The tolerance group of the characteristic 
    expression is the tolerance group of the tag.

    There are five different augmentation sets. The !current
    augmentation set!, together with the structural set and an 
    explicit set, is used by the analog solver to determine the 
    values of the quantities.
    
    The determination of an augmentation set consists of the
    creation of the corresponding characteristic expressions 
    and the determination of their tag and their tolerance group,
    and it makes the augmentation set the current augmentation set.

new section 12.6.5.1
at line 2411 (809)
    The quiescent state augmentation set is the collection of
    characteristic expressions that, when combined with the structural
    set and an explicit set, allow the analog solver to determine the 
    quiescent or "DC" values of the quantities of the model.

new section 12.6.5.2
at line 2424 (822)
    The time domain augmentation set is the collection of
    characteristic expressions that, when combined with the structural
    set and an explicit set, allow the analog solver to determine the 
    values of the quantities of the model over time.

at line 2429 (827)
    The difference between each scalar subelement of each quantity of
    the form Q'DOT and the derivative with respect to time of the 
    corresponding scalar subelement of its prefix Q is a characteristic 
    expression of the time domain augmentation set.

at line 2444 (842)
    The derivative with respect to time and the integral over time
    have their conventional mathematical meaning.

new section 12.6.5.3
at line 2446 (844)
    The discontinuity augmentation set is the collection of 
    characteristic expressions that, when combined with the structural 
    set and an explicit set, define initial conditions following a
    discontinuity that express the conservation of charge and flux 
    in electrical systems (or their equivalents in other natures).

at line 2451 (849)
    The difference between each scalar subelement of the prefix Q of
    each quantity of the form Q'DOT and the numeric value of that 
    scalar subelement of Q when the discontinuity augmentation set is 
    determined is a characteristic expression of the discontinuity 
    augmentation set.

at line 2454 (852)
    The difference between each scalar subelement of each quantity of 
    the form Q'INTEG and the numeric value of that scalar subelement 
    when the discontinuity augmentation set is determined is a 
    characteristic expression of the discontinuity augmentation set.

at line 2457 (855)
    The difference between each scalar subelement of each quantity of 
    the form Q'DELAYED(T) and the numeric value of that scalar 
    subelement when the discontinuity augmentation set is determined 
    is a characteristic expression of the discontinuity augmentation 
    set.

new section 12.6.5.4
at line 2461 (859)
    The frequency domain augmentation set is the collection of
    characteristic expressions that, when combined with the structural
    set and the small-signal form of an explicit set, allow the 
    values of the quantities of the model at a specified frequency
    to be calculated.

at line 2464 (862)
    The difference between each scalar subelement of each spectral
    source quantity and the value of the expression (magnitude * 
    (ieee.math_real.cos( phase ) + ieee.math_complex.cbase_j * 
    ieee.math_real.sin( phase ))), where magnitude and phase denote
    the corresponding scalar subelements of the magnitude simple
    expression and phase simple expression from the declaration of
    the spectral source quantity, is a characteristic expression of
    the frequency domain augmentation set.

at line 2479 (877)
    The difference between each scalar subelement of each quantity
    of the form Q'DELAYED(T) and the corresponding scalar subelement
    of its prefix Q multiplied by the value of the expression
    (ieee.math_real.cos( ieee.math_real.math_two_pi * T * FREQUENCY) 
    - ieee.math_complex.math_cbase_j * 
    ieee.math_real.sin( ieee.math_real.math_two_pi * T * FREQUENCY))
    is a characteristic expression of the frequency domain 
    augmentation set.

at line 2484 (882)
    Note--These definitions use functions and constants defined in 
    packages math_real and math_complex of IEEE Standard P1076.2.
    These packages are considered to be in a library with the
    logical name ieee.

new section 12.6.5.5
at line 2487 (885)
    The noise augmentation set is the collection of characteristic 
    expressions that, when combined with the structural set and the
    small-signal form of an explicit set, allow the noise values
    of the quantities of the model at a specified frequency to be
    calculated (see 12.8).

at line 2497 (895)
    The difference between each scalar subelement of each quantity
    of the form Q'DELAYED(T) and the corresponding scalar subelement
    of its prefix Q multiplied by the value of the expression
    (ieee.math_real.cos( ieee.math_real.math_two_pi * T * FREQUENCY) 
    - ieee.math_complex.math_cbase_j * 
    ieee.math_real.sin( ieee.math_real.math_two_pi * T * FREQUENCY))
    is a characteristic expression of the noise augmentation set.

at line 2501 (899)
    Note--These definitions use functions and constants defined in 
    packages math_real and math_complex of IEEE Standard P1076.2.
    These packages are considered to be in a library with the
    logical name ieee.

===============================================================================