Continuous Systems concepts for McSimAPN.
MJMcCann-Consulting

Imitates Analogue computer: Interactive operation, diagrammatic network, control and model are interoperable, hot-wirable.
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Continuous Systems Modelling
In the early 1960s digital computers began to be able to match the computational speed of some analogue computers for solving sets of differential equations. I started out with analogue computers before that; hence my interest in replicating their features. They were naturally parallel computing devices just as the components of the real world systems which they modelled.
Early digital mimics of analogue computers were DAS (digital analogue simulator) and descendants MIDAS, CIDAS that ran on IBM 360 machines. Then came a move to using statement structured languages to define the equations sets to be solved. (for example: IBM's CSMP360, SL/1, and the still existant ACSL) This was much faster in operation as the code was compiled instead of being interpretted.
But the natural visual link between model and prototype was lost as was the ability to play with a running model.
Now computers are quite fast enough to give the illusion of parallel computing and the ability to interact with a model. For technical computing the SIMULINK part of the MATLAB software is a very powerful tool with the graphical, network idea well used.
Another alternative is the SciLab/Scicos software which is open source, and free.
McSimAPN is nothing like as powerful as MATLAB based SIMULINK, but it does combine the ability to merge discrete event simulation with analogue simulation, and retains the interactive behaviour of the old fashioned analogue machines.

Limitations in Non-Linear Ordinary Differential Equations.
N-L ODEs provide the formal basis for the definition of models of dynamical systems. It is axiomatic that there is always an independent variable (here taken to be time) and all activities take place in parallel with respect to that variable.
Generally linear systems of equations with constant coefficients can be solved analytically (maybe with a matrix route to getting eigenvalues).
Real systems aren't linear. Even writing equations is often a bit of a stretch, when all that can be done is to describe what happens under some conditions. A definition of a logic process may have to be included or a recognition of a sudden change in parameters when an event (e.g. a collision) occurs.
Such things can be replicated in hardware models (analogue computers) and programmed into numerical models even if writing differential equations is not meaningful. Where the numerical integration proceeds at the same speed as the real world (real-time simulation) the possibility of including links to real hardware (hardware in the loop) components allows part model, part reality to be investigated.

McSimAPN Repertoire
McSimAPN provides a repertoire of components that have proved useful to me in many years of modelling complex dynamical systems in electrical, mechanical, chemical, biological, financial, demographic and economic fields and the physical sciences in general.
The intent is that they can be assembled (as is done with SIMULINK) into models of almost anything dynamic, without necessarily defining a set of ODEs explicitly.

Analogue Computer as Design Guide
In the (electronic) analogue computer there was little or no distinction between the model variables, represented as voltages or currents and the control signals that provided for running the model, selecting links and performing initialization or terminal calculations.
Algebraic loops were not generally a problem. An algebraic equation is equivalent to a loop and a hard-wired loop just settles to its own equilibrium (if that means an amplifier saturates it's manageable) without invoking Newton Raphson methods or the like.
Analogue computers can be frozen (HOLD) and good quality integrators will stay at (very nearly) constant voltage. In that state changes can be made to parameters and even to connections (implying changing the equations).
Indeed, if the computation is slow, especially if it is representing a more or less steady state, or a rapidly cycling repetitive process the changes can be made to a running model without interuption. Twiddling the knobs to explore and adjust behaviour was a normal part of running an analogue computer.
The underlying idea behind McSimAPN is to imitate those characteristics and take advantage of the digital computer's ability to freeze a computation perfectly, to need no scaling and to be able to deliver any amount of non-linear and logical components at will. To that, McSimAPN adds the ability to bring discrete event simulation into the same models.

MJMcCann-Consulting

Help Index:
Index/Search

Background
Simulation Concepts
Continuous Systems
Discrete Systems
McSimAPN Structure
McSimAPN Operation

Using McSimAPN
Start McSimAPN
Save Model,data
Create Blocks
Run-Hold-Reset
Link Excel+VBA

PetriNet Block Types
A activity/action
B belt conveyor
C container/constant
D diverter(random)

Analogue Block Types
E exponents
F flux/flow
G function Generator
H hysteresis
I integrator
J inductor
K logic element
L logarithms
M memory
N note/label
O oscilloscope/graph
p not assigned
Q quantizer/rounding
R relay on/off
S sin/asin/atan
T timer/clock
U user link Excel
V visual voltmeter
W sWitch selector/MUX
X multiply
y not assigned
Z random (fuZZ)
& signed summation
% division/difference
@ access/move values

Invitation. McCann can help if you have a design or operational problem that needs some technical support that is outside your team's experience, some quantitative assessment of what is really the cause of the difficulties, some design alternatives or just a fresh look by an intelligent interrogator.
If you have a problem with the behaviour of a market sector, plant, process or item of equipment and would like to get a quantitative handle on it to improve yield or optimise performance, then contact us. We are always ready to give a little time to discuss a new puzzle, in confidence, of course. We'll only worry about fees when we have some defined work. We can be flexible about how we work with you.
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MJMcCann-Consulting,
POB 902,
Chadds Ford PA
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T: 1 302 654-2953
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E: mjmccann@iee.org
Request. Please let us know how you found this software and your interests by sending an email to mjmccann@iee.org Thank you Date: 2012.02.26
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