is a discrete time system always a distributed system?

I guess you would first need a good definition of "distributed system". Ask your prof what he means. As an example, a microcontroller running from a clock can be considered a discrete time system. Is a single chip a distributed system? That depends on what scale you look at it. You could argue that as soon as you can divide a system in independent functional blocks it can be considered a distributed system. Time has nothing to do with that.

--DF

Typically a lumped system is one in which "things" respond or behave as a whole in an infintesimal amouint of time, relative to the scale of course as Deefoo said. In a distributed system, however, the time rate of change must be taken into account.

Asking your prof for clarificiation or an example would be a very good idea. But here is an example of what I think he means.

In a discrete time system, things change only at certain intervals. Think of two flip flops with a common clock. The input to the first FF goes low to high. It isn't until the following clock cycle that the input to the second FF goes low to high. Hence the time behavior of the circuit can't be neglected. Next think of two resistors in series with a 5v source and a switch (that is initally open). When the switch closes, the voltage will appear, for all practical purposes instaneously at all points in the circuit. Since the time can be neglected, it can be called a lumped system.

First, any real system is always a distributed system. Its also time varying and nonlinear, so you can throw away all that Laplace transform stuff they've been teaching you.

Fortunately almost all systems can be described as lumped-parameter, linear time invariant systems, so if the trash guy hasn't shown up yet you can go pull those books out of the trash. Whenever you say a system is lumped, or linear, or time-invariant, you are really saying "I'm going to _treat_ this system as lumped (or whatever) because it's a good enough approximation for the problem at hand".

I disagree with your professor.

A time-invariant system that shows pure delay must have some distributed parameters. A time-varying system, however, can show pure delay without having any distributed parameters. Consider the following two systems:

System A has a 200km length of coax cable with a velocity factor of

0.66. Therefore it incorporates a pure delay of 1ms. If you put a signal into that coax it shows up 1ms later, no matter when you put it in. That property -- of showing _everything_ that happened exactly 1ms in the past, requires a distributed parameter to describe the behavior of the coax.

System B has a sample-and-hold circuit consisting of a buffer, a switch and a capacitor. Every 2ms the switch closes for an instant of time, and the capacitor charges to match the input voltage of the buffer, then it holds that voltage until the next switch closure. This system has an average of 1ms of delay, just like system A did with it's coax. However, the behavior of the system is different: at any point in time the output voltage of the system is equal to what the input voltage was at the _instant_ that the switch was last closed. This only requires one parameter -- the voltage on the capacitor -- to describe.

Discrete-time control systems are like system B. Because of the sampling process they are time-varying, and unless the plant has some significant distributed parameter the system as a whole can be described exactly as a time-varying lumped-parameter system. If you want to go into detail you _do_ have to take the processing lag from the sampling moment to the moment that control is available into account, but this can be easily modeled with lumped parameters.

You can get into all sorts of arguments about how the underlying state of the processor is huge, and must be described as distributed -- and that's correct. It's also moot, because when you model a system you're only interested in finding the simplest model that's still complex enough to adequately solve the problem at hand.

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Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Albert E gave us this: ?Everything should be made as simple as possible, but not simpler.?

The unstated assumption is that the model retains sufficient fidelity to explore the issues in question.

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JosephKK
Gegen dummheit kampfen Die Gotter Selbst, vergebens.  
--Shiller

Many engineering classes leave this unstated. As a result many engineers make the assumption without realizing it. I've helped enough people fix problems arising from assuming sufficient models that I always ask the question -- look at the end of my second paragraph above.

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Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

[... simple ...]

Also, it is sometimes good to ask what we mean by "simple".

I've seen people waste hours over the fact that they had not correctly defined "simple" for the problem at hand.

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kensmith@rahul.net   forging knowledge

We are in agreement then. Thank you for the further clarification. I also have had experiences similar to Ken's

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JosephKK
Gegen dummheit kampfen Die Gotter Selbst, vergebens.  
--Shiller