System Modelling Course

7/30/2019 System Modelling Course

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System Modeling Coursework

P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,

Manipal Institute of Technology, Manipal

Karnataka 576 104 INDIA

Ph: 0820 2925154, 2925152Fax: 0820 2571071

Email: [email protected]

, [email protected]

Blog:www.godsfavouritechild.wordpress.com

Class 1: Introduction to Mathematical Modeling
mailto:[email protected]:[email protected]://www.godsfavouritechild.wordpress.com/http://www.godsfavouritechild.wordpress.com/mailto:[email protected]:[email protected]


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July December 2008 prv/System Modeling Coursework/MIT-Manipal 2

WARNING!

I claim no originality in all these notes. These are thecompilation from various sources for the purpose ofdelivering lectures. I humbly acknowledge the

wonderful help provided by the original sources inthis compilation.

For best results, it is always suggested you read thesource material.


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Contents

What is mathematical modeling?

Steps in Mathematical Modeling

Mathematical Modeling cycle

Types of Mathematical Modeling Summary Review Questions References


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What is mathematical modeling?

Mathematical modeling usually begins with a

situation in the real world, sometimes in therelatively controlled conditions of a laboratory and

sometimes in the much less completely understood

environment of meadows and forests, offices and

factories, and everyday life.


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What is the prerequisite?

A close study of the system, the accumulation and

organization of information, is really the first step inmodel building.


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Step No.2

The next step (after the recognition of the problem

and its initial study) is an attempt to make theproblem as precise as possible.

One important aspect of this step is to identify andselect those concepts to be considered as basic inthe study and to define them carefully.


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Step No.3

The third step (after study and formation of a real

model) is usually much less well defined andfrequently involves a high degree of creativity.

One looks at the real model and attempts to identifythe operative processes at work. The goal is theexpression of the entire situation in symbolic terms.


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Step No. 4

After the problem has been transformed into

symbolic terms, the resulting mathematical system isstudied using appropriate mathematical ideas andtechniques.

The motivation for the mathematical study is not toproduce new mathematics, i.e., new abstract ideas ornew theorems, although this may happen, butinstead to produce new information about thesituation being studied


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Step No. 5

The final step in the model-building process is the

comparison of the results predicted on the basis of themathematical work with the real world.

The most desirable situation is that the phenomena actually

observed are accounted for in the conclusions of themathematical study and that other predictions are

subsequently verified by experiment.

What if the model and the phenomena do not match?


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Mathematical Modeling Cycle


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Types of Mathematical Models

Linear vs

Non linear

Deterministic vs Stochastic

Static vs

dynamic

Lumped parameters vsdistributed parameters


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Summary

A mathematical model of a system is defined as a set ofequations that represents the dynamics of the systemaccurately.

The dynamics of any systems, whether they are mechanical,electrical, thermal, economic, biological, and so on, may bedescribed in terms of differential equations.

Such differential equations may be obtained by using

physical laws governing a particular system, for example,Newtons laws for mechanical systems and Kirchhoffs lawsfor electrical systems.


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Review Questions

1.

What are the disadvantages of mathematical

modeling?2. How are the modeling types classified?3. List the steps involved in mathematical involved4. What are the alternatives for mathematical

modeling?5. Why simulation is required in modeling


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References

Daniel Maki & Maynard Thompson; Indiana

Universityamongst others


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And, before we break

None knows the weight of another's burden

Thanks for listening

System Modelling Course

Documents

Transcript of System Modelling Course