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8/9/2019 Assignment Opt

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Q1. Define a system and its main types. What are important steps towards

creation of a model of a system? Develop a mathematical model of a simple

system of your choice and explain.

SYSTEM

A system is an organized, purposeful structure regarded as a whole and consisting of interrelatedand interdependent elements (components, entities, factors, members ,parts etc). These elementscontinually influence one another (directly or indirectly) to maintain their activity.

TYPES OF SYSTEMS

1. Physical or Abstract ystems!. "pen or #losed ystems.

$. tate %aintaining ystems.&. 'oal eeing ystems.. Purposeful ystems.*. +eactive ystems.

Physical systems are solid entities that may be static or dynamic in operation.

Example

The physical parts of the computer center are the offices , des and chairs that facilitate operation

of the computer. They can be seen and counted as they are static. n contrast, a programmed

computer is a dynamic demands or the priority of the information re-uested changes. Abstractsystems are conceptual or non physical entities.

STEPS INVOLVED IN CREATING MODEL OF A SYSTEM

1. efine system.!. /acground +esearch$. tate Pro0ect 'oal&. efine +elationships. evelop %odel

Mathematical model of a spring, mass ystem


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The elasticity, or stiffness k provides a restoring force as representedby a spring. The reaction force fk on each end of the spring is the sameand is equal to the product of stiffness k and the amount of deformationof the spring. End c has a position yc and end d has a position yd measured fromthe respective equilibrium positions.

The force equation, in accordancewith the Hooks law isfk = k ( yc yd!

"f the end d is stationary, then yd = # and the above equation reduces

to$k = k y

Q!. Differentiate "etween a state maintaining, a goal see#ing, a purposeful

and areactive system. $ive related examples from daily life to clarify each

class.

1. tate%maintaining system&

% state maintain system is one that can react in only one way to any one e&ternal orinternal event but it reacts differently to different e&ternal or internal events.

Example:

i. % heating system whose internal controller turns it on when the room temperature is below a

desired level, and turns it off when the temperature is above this level, is state maintaining."n

general most systems with 'stats e.g thermostats and humidistats are state maintaining.ii. % compass is also state maintain because in many different environments it points to the

magnetic north pole

2. $oal see#ing systems :


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)oal seeking systems is one that can respond differently to one or more different e&ternal

or internal events in one or more different e&ternal or internal states and that can respond differently to a

particular event in an unchanging environment until it produces a particular state.

Example&

i. *ystems with automatic pilots are goal seeking.

'. (urposeful ystem

A purposeful system is one which can produce the same outcome in different ways in the same

(internal or eternal) state and can produce different outcomes in the same and different states.

Thus a purposeful system is one which can change its goal under constant conditions.

Example&

i. 2uman /eings are the most familiar eamples of such systems.

4. )eactive systems

The reactive systems are those in which reaction ofan event or events in terms of aresponse are set.

Example&

A coin operated soft drin machineswitches on its advertising lights when someoneapproaches itwithin two meters distance. uchmachines are reactive systems.

Q'.What are ma*or parts of a model of a system? +ow one can identify them


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provide examples to descri"e each part.

Parts of a System:

1. Variables,

2. Parameters,

3. Functional Relationships,

4. Constraints,

. Criterion Functions.

1. Elements of a system&

The elements of a system are components that taentogether with interactions will produce a basic structureof the system.

Example&

A model of a missile may have apropulsion sub3system, a guidance sub3system, a controlsub3system and a structural sub3system and these subsystemscan be termed as main elements of thetotalsystem.

!. (arameters of a system&

(arameters of a system are -uantities that are assigned by the properties of system componentsor elements. 4or instance, in a system based on a mathematical e-uation

Examplef ( x ) = ax 2 + bx + c+

thea, b, and c are the parameters and ! is a "ariable.

'. -onstraints of a system&

t5s some factor that limits what the system canachieve. f it is not limited then the system might be able to achieve much more inrealizing its goal. The limiting factor may be internal or eternal

to the system. t may be a physicalcomponent, a condition, or an imposed policy of some ind.

Example&


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p=2x+3y

Constraints: x0

6.&Where physical models are used and how they are different from the actual

systems?

+ow industry is employing physical models for simulationpurposes?

Ma#e a detailed study for one system.

(hysical models and ctual models&

A model is a simplified representation of a system at some particular point in time or space

intended to promote understanding of the real system.

Physical models allow visualization, from eamining the model, of information about the thing

the model represents. A model can be a physical ob0ect such as an architectural model of a

building. 7ses of an architectural model include visualization of internal relationships within the

structure or eternal relationships of the structure to the environment.

odel of building

A physical model of something that can move, lie a vehicle or machine, may be completely

static, or have parts that can be moved manually, or be powered. A physical model may show

inner parts that are normally not visible.


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ctual system is some ind of a woring system may be on a small scale or on a large scale.

Example&

80ector Air removal Actual system

+ow industry employing physical models for simulation

ndustry uses simulation and modelling to observe the output

Example&

#onsider a consulting company which has 1!9 employees. These 1!9 employees are composedof *9 rooies and *9 professionals. The company wishes to maintain the total number ofemployees at 1!9 so it hires a new rooie for each professional who -uits. +ooies don5t -uit:Professionals -uit at a rate of 19 per month and it taes * months to develop a professional froma rooie. Additionally, the company bills out rooies at ;19


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f we run this model we find it eists in essentially a steady state,

=ow, in the 19th month the company notices its revenue has dropped from ;1.m The company finds that itstill has 1!9 employees, yet there are now $9 professionals and ?9 rooies

As it turns out, there was an organizational policy change made in month $ which seemed toannoy professionals more than in the past, and the -uit rate 0umped from 19 to 1 professionals amonth. The system, with it5s built in hiring rule, essentially an auto pilot no thought action, hiredone rooie for each professional that -uit. @hat this one time transition in -uit rate actually didwas set off a * month transition within the organization leading to a new e-uilibrium state with

$9 professionals and ?9 rooies. The following graph represents this transition.


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Thus, one of the real benefits of modeling and simulation is its ability to accomplish a time and

space compression between the interrelationships within a system. This brings into view theresults of interactions that would normally escape us because they are not closely related in timeand space. Modeling and simulation can provide a way of understanding dynamiccomplexity.

Example !&

/0D2)/3 4E+/-3 M5DE3

Complete Vehicle Model


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The main driveline subsystems are

8ngine

Transmission

Transmission controller

Behicle and tires

Coupling the Engine to the Transmission

Torque Converter Stage

Cie clutch, a tor-ue converter couples two independent driveline aes in such a way as to

transfer angular motion and tor-ue from an input to an output shaft. 2owever, unlie a clutch, a


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tor-ue converter never locs and the output shaft never eactly reaches the speed of the input.

(The tor-ue converter transfers motion by hydrodynamic viscosity, not by surface friction.) Thus

a tor-ue converter does not step through discrete stages and avoids the motion discontinuities

inherent in friction clutches.

Engine Speed and Power

The 8ngine +P% scope shows the engine speed in revolutions per minute (rpm), as well as theengine output power delivered to the Tor-ue #onverter, in watts (@). @hen the transmission

shifts to second gear at 19 seconds, the engine reaches its maimum speed and power.


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Vehicle Speed

The Vehicle Velocity scope displays the vehicle's linear velocity in miles per hour (mph).

Drive atio

The peed ratio scope measures the effective gear ratio of the speed transmission by computing

the ratio of the output shaft to the input shaft angular velocities, respectively. (This ratio is the

reciprocal of the drive ratio.) As the transmission shifts through each gear from 1 to &, its speed

ratio goes up, and the drive ratio goes down.


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Q6. Explain discrete and continuous models. +ow a stochastic model differ

froma deterministic model, explain these differences using some systems?


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1. Discrete model The state variables change only at a countable number of points in time.

These points in time are the ones at which the event occurs


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4or eample, suppose you wish to predict whether the net customer will buy either a red car, a

gray car, or a green car. The possible values of y are JredJ, JgrayJ, or JgreenJ, and the

distribution p(y) might have the form

y p(y)

red .$

gray .&9

green .!

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The model does not tell you precisely what the net customer will do, but does allow aggregate

what3if predictions of the following type.

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