Simulation Concepts.
MJMcCann-Consulting

Analogy, imitation, limited scope, complexity,
McSim APN: discrete event and continuous
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McSimAPN does it all!
McSimAPN is made to work rather like an (electronic) ANALOGUE COMPUTER for both discrete event and continuous systems.
Blocks are connected together to mimic the real world prototype. With a major added facility: it will simulate discrete event processes using the concepts of PETRI NETS to provide a simulation tool that has the discrete event modelling and the continuous systems modelling in one seamless combination. Well, that's the idea anyway. There are limits, of course and big complex problems may need more powerful tools, but seeing how simple the model can be and still provide insight is a valuable intellectual process.

Simulation vs Equation Solving
McSimAPN is made to work rather like an (electronic) ANALOGUE COMPUTER for a reason. It is a tool to imitate the real world. As (the simulated) time evolves, the progress can be watched. The user can intervene, either when the model pauses or simply by clicking on a block to switch it on or off or to change its behaviour. It thus becomes an interactive tool, not just a means of solving a set of equations and waiting to see if it can complete the calculation (compare with MathcadTM, MatlabTM, SimulinkTM).

Argument by Analogy.
All simulations and mathematical models of real world systems are arguments by analogy. They are only valid if the analogy holds.
Analogue computers mimic the behaviour of their real world prototypes. Generally they are seen as being set up to integrate (solve) the differential equations that someone has decided are a representation of reality.
There does not have to be a differential equation formulation, because a model can be assembled by using the components to mimic the real world things which they represent and joing them up in the model to match the way they link together in the real world. The McSimAPN scheme makes little reference to differential equations (but see the paragraph below).

Limitations and Boundaries
A computable model is an analogy in formal language to describe some aspects of the behaviour of a subset of the real world.
It is defined by what is left out.
The definition of the boundary, be it explicit or implicit, assumes that what is outside can affect the inside (via the exogenous variables) but what is inside (described by endogenous variables) can deliver changes to the outside BUT those changes do not feedback into the interior.

Non-Linearity and Boundedness
No real physical system has unlimited range of values. Steel breaks, plastics melt, objects collide, temperature has an absolute lower bound.
There are no singularities in the real world. Therefore all "realistic" models are constrained.
Sometimes McSimAPN deliberately does this to avoid computational problems.
A special case is that some operations are cyclic (rotating machinery, bearings and headings in navigation, osillators, day clocks). McSimAPN can cope with this.

Precision and Resolution.
While sometimes precise calculations can be made for design purposes, it is rare that simulations of real complex systems can have all their parameters well enough known to do better than indicate likely behaviour.
The irregularities and variability of things like friction, material properties and unknown (often called "random") influences make precision unattainable.

Simulation for Understanding
With precision unreachable, what purpose simulation?
If you don't understand something, it's out of control. If you can't quantify the underlying causal relationships that explain its behaviour, then you don't understand it.

I use simulation and (mathematical, computer) modelling as a means of finding out if I (or my client) understands the system we are dealing with.
Having a computable model means that it is well posed in the sense that just enough information is available to explain behaviour.
Behaviour that doesn't appear in model, but is seen in reality indicates the model is missing something.
Conversely, strange behaviour in a model is a warning that the real prototype may exhibit it or that the model is wrong.
Resolving these mismatches leads to the understanding.

Differential Equations.
Part of McSimAPN requires integration. Over centuries, a lot of work has gone into getting near perfect numerical solutions to differential equations.
In McSimAPN, I have used the simpest possible, Euler integration method, because here the objective is a working model, not ultimate precision.
. Computational errors due to the crude integration can be reduced by finer resolution and, anyway, so long as the model doesn't become computationally unstable, all numerical integration schemes are conservative (in the sense of conservation of energy, momentum,mass) and the errors can be reduced below the level due to uncertainty in the model parameters.
Critically for this tool, using a discrete time stepping method allows a merger of discrete events with continous processes which needs special procedures in other methods such as Runge-Kutta.
McSimAPN does allow time-step size to change without breaking the model.

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
19317 USA.
T: 1 302 654-2953
F: 1 302 429 9458
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
File: simcon.htm