Introduction to Modeling-Mathematical Modeling and Simulation-Lecture Slides, Slides of Mathematical Modeling and Simulation

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Introduction to Modeling

Mathematical Modeling

& Simulation

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The Marks distribution:

**1. Quizzes 5%

2. Tests 40%
3. Home works 15%
4. Final Exam. 40%**

Recommended Text:

1. B. S. Bennett, “Simulation Fundamentals, ” **Prentice Hall.

2. Notes by Dr. Nasir M Mirza.
3. User Guide for MATLAB-SIMULINK.**

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What is Model-based Reasoning?

• It is Methodology for analyzing, understanding, and predicting behavior of a system, process, or phenomena using a model. - For what kind of Systems: - engineering process (continuous) – chemical plants, aircraft, traffic system, - information process (computer-based or digital) - computer network, telephone system, - economic process – country’s economy, world economy, software industry etc. - Social systems – suburban culture, welfare system

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Steps for Developing a Model

• Identify problem area;
• Conduct background research;
• State project goal;
• Define relationships;
• Develop a model;
• Then develop a computational algorithm;
• Perform tests;
• Visualize results;
• Interpret results and compare with experiments;
• Communicate results and associated issues.

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What is a System!

What exactly is a system? ??

• System has Entities that are separable from the rest of the universe (we call this the environment ) by a physical or conceptual boundaries, for example:
• It satisfies the concept of reticulation, i.e., a system can be looked upon as being made up of interacting parts. For example,  A human body made up of various organs and the nervous system;  A coffee maker has container for water, a boiler (evaporator), a passages, a filter among other parts.  A bicycle has also many sub-systems. Docsity.com

Examples of Systems

A human body is a complex system and is made up of various organs and the nervous system.

It has very large number of sub- systems as shown here.

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Examples of Systems

A bicycle is also

complex system and is made up of various parts:

tyres, seats, handles, chain system, paddles,

brake system, wheels and support structure

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Examples of Systems

A nuclear power plant is also a complex system that has reactor vessel, pumps, pressurizing system, steam generators, turbines, cooling towers, and containment building among many other sub- systems

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Representation of a System

A system is a set of elements that are united by some interactions or inter-dependences to perform at least one specified function. A system is generally described in two types:

• Static representation ;
• dynamic representation.

In first type, we identify all possible sub-systems to be included in the model without bringing about any change to the system. Here we eliminate the effect of time.

Then, in second type changes in the state of the system are allowed. Docsity.com

If we look at the system from viewpoints of its purpose,

then it can be classified it in the following four main types:

Classification: Purpose is the Viewpoint

• State Maintaining Systems,
• Goal Seeking Systems,
• Purposeful Systems,
• Reactive Systems.

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The Goal Seeking Systems

• The goal seeking systems are

devised to find possible new states or goals.

• For example, an antiaircraft missile

with automatic pilot is a goal seeking system.

• As the goal’s position coordinates

keep on changing with time, the system keeps on updating its goal states.

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The Purposeful Systems

• The purposeful

systems have their pre-

defined purpose and they can device methods to seek their goals under changing conditions.

• Here it is important to note that conditions are the changing and they are part of the system.

Trains are most familiar example of such systems.

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Figure shows a simple tree structure displaying a hierarchy of model structure. The heavier branch lines connecting model attributes indicate the degree of importance attached to them.

Hierarchy of Models

MODEL

Discrete Event

Physical Abstract

Continuous Variable

Equation oriented Block oriented

Stochastic Deterministic

Static Dynamic

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• Many industries require the construction & testing of replica models for specific purposes.
• For many years, engineers have been making full- scale mockups and scaled models to test the actual system.
• The chemical, mechanical, civil, environmental, space, and airline engineers have been employing full-scale mockups for training and research purposes.
• It used to be the case that aircraft were subjected to wind tunnel testing during the course of design.
• In other words, the economics of flight necessitated wind tunnel testing of replica models as part of the airframe design process.

Hierarchy: Physical or Replica Models

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