THought I was done Huh?

<[Bill Leach 950601.14:35 U.S. Eastern Time Zone]


      [Bet y'all thought that last missive was all of it huh?]

From "Electronic Engineer's Handbook" McGraw-Hill

[This book contains the best and most complete control system theory
treatment of the books that I have. ie: There is more on Kalman
filters than any of us would ever want to see!]

  By and large, models constitute the realm of discourse within which
  system engineering is carried on. More pragmatically, a model is a
  prerequisite to the use of analytical methods in engineering design.

  By _modeling_ we mean any deliberate intelligible cognitive activity
  aimed at abstracting, and reproducing in some convenient realm of
  discourse, features of an object or system (the prototype) of interest
  to the modeler. The activity is deemed cognitive ...

  Of late, models are becoming generally recognized as indispensable tools
  for effective understanding of the behaviour of complex systems. Yet
  mathematical modeling is still, at best, an art. There is no
  comprehensive, consistent body of theory which constitutes a theory of
  modeling. ...

  Engineering systems modeling is a blending of physical and mathematical
  theory. It is a sterile activity if either is left out. In the
  sciences, models are sought which illuminate natural phenomena. The
  objective is to strip away all that is not essential so that our
  observations of reality can be characterized and understood in terms of
  some ultimate simplicity. ... In this context a model is a _THEORY_
  constituting a set of propositions of laws from which facts exhibited
  in nature can be deduced.

  This last notion illustrates what has come to be called the _scientific
  method_. The scientific method of establishing an understanding of any
  physical phenomenon is generally identified as consisting of three
  phases (1) _initial observation_, (2) _formulation of a theory_, and (3)
  prediction of new observations and experimentation. Moreover, the
  completion of the last stage frequently suggests refinements ... The
  emphasis on observation has its roots in the empiricist philosophy
  which has been at the heart of modern science.


  One useful classification of models distinguishes three types:
  (1) _native models_ (the past trends of a single variable are used to
  predict future behaviour of that variable); (2) _simple correlative
  models (past observations are used to correlate several interrelated
  variables in order to forecast future trends); and (3) _causal models_
  (the response of certain variables due to changes in others is


  A fundamental distinction can be drawn between the first two model
  types and causal models. Naive and simple correlative models are
  _descriptive_, whereas causal models are _explanatory_. ...


  Compared with ontological issue of parsimony, an even thornier issue
  the epistemological problem of model _validation_. Without a clear
  understanding of the relationship between a model and its prototype, it
  is not clear how necessary and sufficient conditions for validation can
  be established (or even how "validation" can be defined unambiguously).
  The problem of how a model, e.g., a mathematical system, relates to its
  prototype, e.g. a physical or a social system, is rarely addressed. In
  consequence, discussions of validation are diverse and inconclusive. ...


  In Par. 5-1 we asserted that systems engineering deals with the
  understanding of system as such, for which an understanding of the
  components is necessary but not sufficient. From this point of view,
  perhaps the epitome of systems engineering is the sense of an exemplar
  of archetype, is _control theory_, and the essence of control theory is
  found in the concept of _feedback_.


[And Bill P. will truly _love_ this next one]

  The basic idea of feedback is intuitive and simple. From the
  perspective of a human operator attempting any control action, whether
  that of positioning a lamp on a table, steering an automobile, or any of
  the innumerable actions we take continually and instinctively, our
  action is almost invariably tempered by our continuing observation of
  any discrepancy between intent and status thus far. [The next one
  however is in serious error unless the author meant "results" when he
  said "output"] This is negative feedback: The control action is a
  function of the difference between the desired output and the actual

From "Electronic Engineer's Reference Book" Butterworths

[From a descriptive standpoint there is almost nothing worth quoting from
this book however, the diagram for "closed loop control" is worth

          junction ____________ __________ _________
             /-\ | | | | | |
0i -------->|X|-->|Controller|->|Actuator|->|Process|------>0o
             \-/ | | | | | | |
Reference ^ ------------ ---------- --------- |
signal | |
                                                  Signal from Signal from