Book Recommendation for Introduction to Systems Dynamics

Dear Group,
I am a non-engineer looking to understand the frequency response to first, second order systems. My background is not in math or
engineering, but I have read up on some books for signal processing (eg fft).
Would anyone be able to recommend a good beginner book (like undergraduate level or less) that I could read to gain a good understanding of this topic? A book called, "Signals and Systems" by Oppenheim had been recommended to me before, but I found that book rather difficult.
Thanks!
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On 04/21/2011 09:13 AM, beginner wrote:

What part of frequency response analysis are you trying to understand? Perhaps if you could give a synopsis of your story.
Oppenheim is the classic signal processing book in the field; anything that you read about signal processing or system dynamics is going to touch on that material. Oppenheim _isn't_ a good self-help book, IIRC (although it's a great book to be taught out of, and it makes a great reference).
If you're primarily concerned with controlling systems that you've modeled, then you want to look for titles that have the phrase "Dynamic Systems" and the word "Control" in them.
The primary thing to remember about frequency domain analysis is that in many ways it's a really screwy way of looking at the world. Its utility doesn't come from how easy it is to learn -- its utility comes from how much you can do with it once you've gotten your head wrapped around it. It provides a huge bag of tools that can be used to analyze linear systems. Since many real-world systems can, to some extent, be described with linear models, this means that frequency domain analysis can allow you to do huge amounts of work with relative ease. So everyone who does this seriously gets their heads wrapped around it (to the point where several people may well respond by saying "what do you mean, 'screwy'?"), even though it can be difficult at first.
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Tim Wescott
Wescott Design Services
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Thank you for responding to my post. I will try to describe what it is I would like to understand. I came across this analysis by looking at some papers that looked at frequency response (single input/output) of real life data, not from a simulation or model in which amplitude and phase were used to describe the "system". I came to find out this is what is refered to as bode plots. Since then I have been trying to "play" with some data to see what it would look like. I have read some easier to understand signal processing books (i think it was a book by lyon) that was not very difficulty to read considering I do not have a math background.
Since then, I have come across some engineers who do this stuff, and they all recommended Oppenheim's text, but as I mentioned it was a bit difficut for me to understand (because I don't have a background in differential equations, and has been a long time since complex numbers). I do understand the basics of looking at the say a second order system that has 2 integraters and gains fedback, but I would like to learn more about that part of it. Something simple that starts from the beginning...like "What is a first, second order system?", "How can you look at a bode plot and interpret it?"...something basic, that may allow me to move to the next level. From the engineers I heard they "model" these systems, and I would also like to understand what exactly is meant by "modeling" the system as well.
I know this is like skipping steps as I don't have the math background, but was hoping there would be something like the signal processing book I read which as I mentioned was not so difficulty due to the authors explaination and simplification. I realize a strong background in differential equations will probably help, but I was hoping there would be something that may help explain things in simple terms, or started from the beginning so that I could handle the reading.
Thanks again for the response!
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wrote:

Thank you for responding to my post. I will try to describe what it is I would like to understand. I came across this analysis by looking at some papers that looked at frequency response (single input/output) of real life data, not from a simulation or model in which amplitude and phase were used to describe the "system". I came to find out this is what is refered to as bode plots. Since then I have been trying to "play" with some data to see what it would look like. I have read some easier to understand signal processing books (i think it was a book by lyon) that was not very difficulty to read considering I do not have a math background.
Since then, I have come across some engineers who do this stuff, and they all recommended Oppenheim's text, but as I mentioned it was a bit difficut for me to understand (because I don't have a background in differential equations, and has been a long time since complex numbers). I do understand the basics of looking at the say a second order system that has 2 integraters and gains fedback, but I would like to learn more about that part of it. Something simple that starts from the beginning...like "What is a first, second order system?", "How can you look at a bode plot and interpret it?"...something basic, that may allow me to move to the next level. From the engineers I heard they "model" these systems, and I would also like to understand what exactly is meant by "modeling" the system as well.
I know this is like skipping steps as I don't have the math background, but was hoping there would be something like the signal processing book I read which as I mentioned was not so difficulty due to the authors explaination and simplification. I realize a strong background in differential equations will probably help, but I was hoping there would be something that may help explain things in simple terms, or started from the beginning so that I could handle the reading.
Thanks again for the response!
Remember that all this frequency-based stuff is essentially for *linear* systems, so the DEs involved are also linear. The laplace notation used is a shorthand way of representing those equations, if you're focussing on things like Bode and Nyquist, then you work almost exclusively with the laplace form, *but* remember that these days, where sampling is almost unversal, the sampled, or 'z' domain is at least as common.
You really need to make the effort to understand the basic maths behind both laplace and z transforms if you want to work with dynamic system analysis, without both you'll encounter stoppers all the time. If your final objective is process control, eg. refineries, then you'll find that the frequency domain stuff is almost never applied in practice, the process models are mostly too fragile to support anything more than its most basic application. But a thorough study of time, frequency and sampled domains will give you a basis that you need, whatever area you're working in.
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On 04/21/2011 12:06 PM, beginner wrote:

You may also try the ARRL Handbook. It's written from a radio perspective, but it tries to aim at a person with a non-math background. Unfortunately, frequency response stuff is highfalutin math disguised as simple algebra -- try to use it without understanding the underlying differential equations part, and you'll be constantly bumping into places you can't go, and you won't know why.

Essentially, an n-th order system is one with n integrators (or delay stages, if it's sampled time). So a 2nd-order system has two integrators, 3rd has three, etc.

Try this. It's a bit ragged -- it badly needs an upgrade -- but it may get the point across.
http://www.wescottdesign.com/articles/zTransform/z-transforms.html

They mean "mathematical model", which is a set of differential equations that describe the system behavior over time, and in response to stimulus. This is a combination of mathematics (getting the equations to represent what you think you need to represent), and art (choosing what behaviors you think need to be represented, while leaving out the infinite number of other factors that would take forever to include, and forever to analyze if they were there).

You could try my book. It's written for someone who's been out of school a long time, and has forgotten much. Unfortunately it's aimed primarily at the practitioner who's working on a sampled-time system, so I really don't go into continuous-time systems much at all. Moreover, the comments I get back from it indicate that it's best for someone who got the training long ago but then forgot -- even though I tried to make it a gentle slope, folks who haven't had training in differential equations find it a bit of an uphill battle. So make sure you find a site that'll let you browse through it before you commit to any money.
It may be a good idea to just see if you can take a differential equations class. If you don't have a community college local, I'll bet there's some on-line thing you could do.
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Tim Wescott
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perfect...thank you for taking the time. All great suggestions. Much appreciated!
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