[Martin Taylor 970310 10:50]

[Hans Blom, 970310c]

(Martin Taylor 970306 14:10)

>Hans says that one cannot talk about the varying values between the

>observed sample points. But the real system has values at all

>moments in time, whether they are observed or not.Given the formalism of difference equations, where data are defined

only at the points T, T=Dt, T+2dt, T+3dt, etc, it is indeed

impossible to talk about intermediate times. As to the "real" system,

it can usually be expressed in this formalism. Shannon says so ;-).

I find this an obtuse answer, given the context of the original. The

question was whether "one-jump" correction would be found, without

oscillation, in a correct MCT control system in which dt was defined

by the observation sample interval of the REAL control system being

simulated.

The only way to test this is to use a simulation sampling interval much

shorter than the sampling intrval of the real system being simulated. If

you don't do that, you have no idea whether your simulation results apply

to the real system or whether they are contaminated by huge amounts of

aliasing.

There's a basic principle here: NEVER believe any simulation results that

happen in a single simulation sampling interval. They may be right (in

Tracy Harms' word, "true") but they may not. Unlike the real world, in

which we cannot determine "truth", in the simulation world we can. We can

observe and modify the simulation world to match the assumed real world

as closely as we like, and observe whether our results change as we change

the match precision.

If we find that our simulation results change appreciably when we change

the degree of match of the simulation with the (assumed) real world, we have

reason to worry about the "truth" of those results when they are applied

to the "real" real world. Of course, no matter how well the simulation

matches the assumed real world, we know nothing of its "truth" when applied

to the real real world. All we know is whether what we get from the

assumed real world fails us when we use it in the real real world. As,

I think, both Tracy and Bill Powers assert in their different ways in their

recent dialogue.

As for "Shannon says so"...Shannon says nothing about systems in which the

observation bandwidth is less than the signal bandwidth, except that the

signal CANNOT be reconstituted exactly except by a pure fluke. And it's

not Shannon who says that the signal can be reconstituted exactly if the

signal bandwidth is confined to the observation bandwidth (i.e. samples

at least every 1/2W seconds). It's a fact of Fourier analysis.

If you don't KNOW that the signal bandwidth has no components outside the

band set by the sampling rate, you cannot make assertions about the behaviour

of the simulated world except at the sampling moments (at best). And if you

don't test your model by sampling more often than the period in which it

claims to have generated some significant event, you don't know at all

whether that event occurs even in the assumed real world, let alone the

real real world.

Check the behaviour of the MCT model that observes every Dt seconds, using

a simulation that samples every dt seconds, where Dt > 10*dt.

Martin