Chapter One:

SYSTEM MODELS

Prepared By:

Towfiqur Rahman

Jessore university of Science and Technology

BAngladesh

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The Concepts of a System

A system is an aggregation of objects where objects has regular interaction and interdependence to perform a certain task.

Example:

FABRICATIO

N DEPTPURCHASIN

G DEPT

ASSEMBL

Y DEPTSHIPPIN

G DEPT

PRODUCTION

CONTROL DEPT

COUSTOMER

ORDER

RAW

MATERIALSFINISHING GOOD

Fig: A factory System 2

BASIC COMPONENTS

Entity: An object “component” in the system

Attribute: A property of an entity

Activity: A process that cause changes in the system

System State: Description of system “entities, attributes, and

activities” at any point in time.

Example: If system is a class in a school, then students are entities,

books are their attributes and to study is their activity.

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System Environment

The changes that occurring outside the system and affecting the

system called system environment.

Two term are used in system environment.

i. Endogenous: activities occurring within the system.

ii. Exogenous: activities in the environment that affect system. If a system has no exogenous activities that called closed system and if has exogenous activities that called open system.

Example: In the factory system the factors controlling the arrival

of orders may be considered to be outside the influence of the factory. So it is the part of the environment.

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Stochastic & Deterministic Activities

When the outcome of an activity can be described completely in terms of its input, the activity is said to be deterministic . Where the effects of the activity vary randomly over various possible outcomes , the activity

is said to be stochastic.

Example : Among the 52 cards, if we pick exactly the card containing the number 3,then it is said to be deterministic . Otherwise, if we pick any card by not looking to the cards, then we can get any card and that is said to be stochastic.

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Continuous and Discrete Systems

Continuous System: In the system in which change are

predominantly smooth are called continuous system.

Example: In the factory machining proceeds are continuous

system.

Discrete System: In the system in which change are

predominantly discontinuous are called discrete system.

Example: In the factory the start and finish of a job are discrete

changes.

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System Modeling

System modeling: System modeling as the body of information

about a system gathered for the purpose of studying the system.

The task the model of a system may be divided into two subtasks.

i. Establishing the model structure: determines the system

boundary, identifies the entities, attributes and activates the system.

ii. Supplying the data: provide the values the attributes and

define the relationships involved in the activates.

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Types of Models

MODELS

PHYSICAL MATHEMATICAL

STATIC DYNAMIC STATIC DYNAMIC

NUMERICAL ANALYTICAL NUMERICAL

SYSTEM SIMULATION

Fig : Types of model8

Discussion of Model

Physical models: In a physical model the system attributes are represented by such measurements as a voltage .

Physical model are based on some analogy between such system as mechanical or electrical

Example: The rate at which the shaft of a direct current motor turns depends upon the voltage applied to the motor.

Mathematical models: In the mathematical models use symbolic notation and mathematical equation to represent a system. Attributes are represented by variables and the activates are represented by mathematical function.

Static models: show the value of attributes take when system in balance.

Dynamic models: follow the changes over the time that result from the system activates.

Analytical models: To finding the model that can solved and best fits the system being studied.

Example: linear differential equation.

Numerical methods: involve applying computational procedures to solve equations.

Example: the solution derived from complicated integral which need a power series.

System simulation: considered to be a numerical computation technique used with dynamic mathematical models.

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Static Physical Models

Static physical models: Static physical model is a scaled down

model of a system which does not change with time.

Example: An architect before constructing a building, makes a

scaled down model of the building, which reflects all it rooms, outer design and other important features. This is an example of static physical model.

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Dynamic Physical Models

Dynamic physical models :Dynamic physical models are ones

which change with time or which are function of time.

Example: In wind tunnel, small aircraft models are kept and air is

blown over them with different velocities. Here wind velocity changes with time and is an example of dynamic physical model.

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Static mathematical model:

A static model gives the relationships between the system attributes when the system is in equilibrium.

Example: Here we give a case of static mathematical model from industry. Generally there should be a balance between the supply and demand of any product in the market. Supply increases if the price is higher. But on the other hand demand decreases with the increase of price. Aim is to find the optimum price with which demand can match the supply. If we denote price by P, supply by S and demand by Q, and assuming the price equation to be linear we have

Q = a – bP

S = c + dP

S = Q

In the above equations, a, b, c, d are parameters computed based on previous market data. Let us take values of a = 600, b = 3000, c = –100 and d =2000. Value of c is taken negative, since supply cannot be possible if price of the item is zero. In this case no doubt equilibrium market price will be

P=a-c/ b+d =0.14,s=180

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Static mathematical model:The relationship between demand denoted by Q, and price, denoted by P, are represented here by the straight line marked “Demand” in fig:1.6 and supply, denoted by S, is plotted against price & the relationship is the straight line marked “supply”. Supply equals price where the two line cross.

Fig 1.5:Market model fig 1.6:Non-linear

market model.

More usually, the demand and supply are depicted by curveswith slopes downward and upward respectively (Fig. 1.6). It may not be possible to express the relationships by equations that can be solved easily. Some numerical or graphical methods are used to solve such relations.

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Dynamic mathematical model:

Dynamic mathematical model allow the change of system attributes to be derived as a function time.

Fig: graph shows displacement vs. time

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Principles Used in Modeling

a) Block-building: The system should be organized in a series of blocks

to simplify of the interactions within the system.

Example: Here each department has been treated as a separate block

with input output begin the work passed from department to department.

FABRICATIO

N DEPTPURCHASIN

G DEPT

ASSEMBL

Y DEPTSHIPPIN

G DEPT

PRODUCTION

CONTROL DEPT

Fig: A factory System

RAW MATERIALSFINISHING GOOD

COUSTOMER

ORDER

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b) Relevance: The model should only include those aspects of the system that

are relevant to the study objectives. while irrelevant information may do not any harm, it should be excluded because it increase the complexity and need doing more work to do solve.

Example: If the factory system aim to compare the effects of different operating

rules on efficiency, it should not to do consider the hiring employees.

c)Accuracy: The accuracy of the information for the model should be considered.

In the aircraft system the accuracy which the movement of the aircraft depends on the representation of the airframe. If the airframe regard as a rigid body then it necessary to recognize the flexibility of the airframe. An engineer responsible for estimating the fuel consumption satisfied with the simple representation. Another engineer responsible for considering the comfort the passenger, vibrations and will want the description of airframe.

d)Aggregation: Aggregation to be considered is the extent to which the number

of individual entities can be grouped together into larger entities.

Example: The production manager will want to consider the shops of the

departments as individual entities.

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References

System Simulation-Geoffrey Gordon

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THANK

YOU

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