is a discrete time system always a distributed system?

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I am a new bee in control, I am studying how to distinguish between a
lumped system and a distributed system. Today in my class, I hear my
prof told that a discrete time system is always a distributed system. I
got confused is that true if so, would anyone can explain it for me?

Thanks

 

[Deefoo]

I am a new bee in control, I am studying how to distinguish between a
lumped system and a distributed system. Today in my class, I hear my
prof told that a discrete time system is always a distributed system. I
got confused is that true if so, would anyone can explain it for me?

Thanks

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

 

[Noway2]

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.

 

[Tim Wescott]

I am a new bee in control, I am studying how to distinguish between a
lumped system and a distributed system. Today in my class, I hear my
prof told that a discrete time system is always a distributed system. I
got confused is that true if so, would anyone can explain it for me?

Thanks

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.

 

[Joseph2k]

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.

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.

 

[Tim Wescott]

Tim Wescott wrote:



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.

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.

 

[Ken Smith]

Joseph2k wrote: [... simple ...]

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

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.

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.

 

[Joseph2k]

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.

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