# Modeling and Analysis of Dynamic Systems

#### Tom Mattson

Staff Emeritus
Gold Member
This lonely little Forum hasn't seen much traffic, and I suspect it's because most of you don't know exactly what the field of Systems Engineering actually entails. Given the importance of "the systems approach" to modern engineering, I think a tutorial thread is in order.

The discussion will be based on the book, Modeling and Analysis of Dynamic Systems, 2ed, by Close and Frederick, Houghton Mifflin, 1993.

The topics in this introduction are going to be as follows:
1. Introduction
2. Translational Mechanical Systems
3. Standard Forms for System Models
4. Rotational Mechanical Systems
5. Electrical Systems
6. Analytical Solution of Linear Models
7. The Laplace Transform
8. Transfer Function Analysis
9. Developing a Linear Model (from a nonlinear system)
10. Electromechanical Systems
11. Thermal Systems
12. Hydraulic Systems

And if I can figure out how to post diagrams online:
13. Block Diagrams
14. Feedback System Modeling and Design Tools
15. Computer Analysis

Related General Engineering News on Phys.org

#### Tom Mattson

Staff Emeritus
Gold Member
Introduction

Section 1.1 Rationale

The first thing to establish is why one would want to learn how to model dynamic systems, and why one would put such a diverse array of such systems all together in the same discussion.

The first answer comes almost instantly upon asking the question: System models are valuable heuristic devices to estimating the response of engineering systems before they are built. This enables engineers to predict whether or not a system is up to the task for which it is designed before any precious material resources are committed to the project.

Second, there is a need to educate engineers in the analysis of systems that components of different types, such as mechanical, electrical, thermal, and hydraulic (the four types that will be discussed in this thread). It is essential that a mechanical engineer, for instance, knows how his system will interface with electrical components, such as controllers. It may even be desirable that he learn how to design controllers himself. Neither does an electrical engineer work in a vacuum. Any electrical system generates heat, and the engineer designing the system must know how to include the thermal aspect of his system into the system model.

Third, the equations that describe the different types of systems are strikingly similar, and learning how to analyze one type automatically gives the student the ability to analyze the others. For instance, consider the equation:

c1(d2u/dt2)+c2(du/dt)+c3u=0

The above equation models a damped mechanical oscillatorif:

u=x, the displacement of the oscillator from equilibrium
c1=m, the mass of the oscillator
c2=b, the damping coefficient
c3=k, the spring constant.

The same models an LRC circuit if:

u=q, the charge on the capacitor
c1=L, the inductance
c2=R, the resistance
c3=1/C, the reciprocal of the capacitance.

As we shall come to see, the above equation has analogs in rotational mechanical systems, thermal systems, and hydraulic systems as well.

Given both the necessity of analyzing systems outside of one's explicit discipline, and of the mathematical similarity of such diverse system models, it only makes sense to include discussion of the various types all in one place.

edit: fixed superscript bracket

#### vzhzjt

Recommend - Feedback Controls Systems Book

Mr. Mattson,

Can you recommend a good control systems book at the associate degree level.

I have books by Ogatta, Dorf, Schaum's, Phillips & Nagel, etc.

I am looking for book which describes controls at a basic level ... similar to the way cutnell & Johnson's Physics book 5th edition describes Physics.

I do have a Master's Degree in Systems Engineering, but am trying to obtain a more fundamental understanding of the subject.

Note: I have the 1st edition of Close and Frederick (1978), great book.

Thanks for any input.

#### Andre

Tom,

I toy a bit with Earth science and climate. It occurs to me that those all react as physical systems, quite obviously, however I think there is too little modelling and analysis done.

Let me give an example. Please take not of this link,http://jlevine.lbl.gov/BenStackintro.html [Broken]

This is the system to analyse:

Benthic foraminifera, because they live in the deep ocean, are less sucseptible to local climate fluctuations than are their cousins in near-surface water. First of all, the ocean bottom is insulated from seasonal changes, wind, and weather by the enormous amount of water overlying it. Second, because of the sheer volume of the deep ocean, and because of the way the oceans mix, any slight variations which penetrate to the deep part of the ocean will necessarily be very small by the time the small fluctuations spread out along the ocean bottom. The accumulation of small, but measureable, fluctuations in isotopic composition of benthic foraminifera gives us an estimate of how climate all over the world has changed through time.
Now let's http://jlevine.lbl.gov/BenStackCompare.html [Broken]

Both the SPECMAP stack of Imbrie et al. (1984) and the Low Latitude stack of Bassinot et al. (1994) are records of d18O from planktonic foraminifera, and thus record somewhat different aspects of climate than does d18O of benthic foraminifera. Planktonic foraminifera live near the surface of the ocean, and are subjected to climate changes including changes in wind and current direction, seasons, storm and monsoon cycles, salinity variations, in addition to local and global temperature fluctuations and global ice volume changes. Benthic foraminifera are insulated by the thick layer of ocean above them from most of these changes, but they do respond to changes in global mean temperature and global ice volume. Therefore, one might expect to see some similarity and some disagreement between the Benthic Stack and the planktonic stacks. This is, in fact, what we observe.

In the plot below, we show the Benthic Stack (black) along with the two planktonic stacks: SPECMAP is in blue and the Low Latitude Stack is in red. The Benthic Stack is similar in shape to the planktonic stacks, but it differs in detail. Notably absent in the Benthic Stack is the ~20 kyr variation thought to be driven by the precession of the Earth's orbit and spin axis. In fact, not more that 4% of the total variance of the Benthic Stack is at periods between 16 and 25 kyr. Some of the larger amplitude of SPECMAP and the Low Latitude stacks at precession frequencies may be due to the fact that these planktonic stacks were tuned to both obliquity and precession forcing, in the case of SPECMAP, and to a complete climate model that included eccentricity, in the case of the Low Latitude stack. It is also likely that the planktonic stacks are reflecting some aspect of climate which does not penetrate to the deep ocean, and which does respond to precession forcing. Interestingly, the Benthic Stack shows that global mean temperature and global ice volume are not driven by precession. In other words, precession may affect local surface water phenomena, but global ice volume and temperature are only marginally affected by precession.
We could consider the ocean being a lineair higher order open loop system, I guess with a very low eigen freqency. Now since the SPECMAP and Low lattitude stack represent the variations of the ocean surface, we could assume that they are the input forcing function of that ocean system, whilst the Benthic stack acts as the response or output part of that systems.

With that in mind I think we see something that can't be, can it?

Last edited by a moderator:

#### Tom Mattson

Staff Emeritus
Gold Member
vzhzjt said:
Mr. Mattson,

Can you recommend a good control systems book at the associate degree level.
Hi,

I think that Close and Frederick is the most suitable (I was lucky enough to take the course from Close himself). It is meant to be a first course in systems analysis, with differential equations as a co-requisite.

#### H-bar None

I'm an former EET student I like the systems approach to problems and simulation. I'm in majoring in physics now and I can see the need to grasp this subject. I was at the lab and I saw several positions offered in robotics astronomy and computational physics which depends heavily on simulation of dynamical systems.

I have been working with STELLA by High Performance Systems. The book,Dynamic Modeling by Bruce Hannon and Matathias Ruth is a great. The book comes a run-time version of Stella.

Another book is Modeling Engineering Systems; I forget the author. The book uses EXCEL to simulate systems up to 4th order.

#### Tom Mattson

Staff Emeritus
Gold Member
H-bar None said:
Hi, glad you think so. Now that there is some interest, I'll have to get back to presenting notes.

#### rabbalb

hello Tom

can u provide me some questions for chs 7 8 10?
ive done the book but i want more practice
thank you

#### vrc

hey,

good topic!
and to continue I'd like to get some parts of the book, because I have an examanition comming and want to prepare myself as max as I can

I have a mechanical background,so analysis os one big aspect of it,you're review made it look like this must be a grat book for analysis !

so where could I geat parts/ebook ?

thank you vm

grtz

#### Integral

Staff Emeritus
Gold Member
Please note that the last post, before yours, in this thread is over 7yrs old. Tom is no longer active. Don't hold your breath waiting for a reply.

#### vrc

ow never watch the date, sorry :surprised

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving