SE207: Modeling and Simulation

General instructions

Objectives

To be able to doSimulate systems of various types using

analog computersSimulate systems of various types using

digital computers( MATLAB +SIMULINK)Study and analyze responses of first and

second order systems

Grades

Lab Reports 8%Quizzes 7%

---------

Total 15%

Attendance

-1% for each unexcused absence You will not be able to submit the report if you

are absent in that lab All reports must be submitted within one week

(Before the start of the next lab) Food and drinks are not allowed in the lab

Format of the Report

Cover page: includes Name, ID#, title, date, Section

Introduction: Objectives Brief description of the experiment or the program Hardware needed (for the experiments)

Procedure of things to be done Solution of any problems mentioned in the lab

handout Program listing/ Simulation diagrams/plot of results Conclusions/comments/observations

SE 207: Modeling and Simulation

Lab # 1: Analog Computers

Analog signal

An analog signal are non quantized signals that are define on a time interval of interest.

Analog signal Discrete-time signal

Analog computers

Analog computers are electronic devices that performs calculations on analog signals.

Main elements of Analog ComputersResistors/potentiometersCapacitorsOperational Amplifiers (Op-Amp)

Analog Computers

Can be used to solve differential equations Heavily used in World War II for computing trajectories

of bombs Digital computers replace analog computers in

simulating systems analog computers are still used today in some

applications Advantages of analog computers over digital computers

Computation time Prototyping

New technologies Single chip analog computers Digital computers with analog co-processors

Operation Amplifier (Op-Amp)

The op-amp is an electronic component The op-amp output is K times the input K is a very large number (typically 1000000) Op-amps are used in different ways to make

different computing elements (summers, integrators,…)

K K

Amplifier

K

Feedback resistance

Rf

Input resistance

R1

ei if eR

Re

10

Equality is assumed when K is very large which will be the case here

Inverter

K

Feedback resistance

Rf

Input resistance

R1

ei if eR

Re

10

When Rf=R1 then eo= ─ ei

The circuit acts as inverter ( signing the sign)

Summer

K

Feedback resistance

Rf

Input resistance

R1

e1

3

32

21

10 e

R

Re

R

Re

R

Re fff

e3

e2

R2

R3

Integrator

K

Feedback Capacitor

Cf

Input resistance

R1

e1

t

f

t

f

edzzeRC

dzzeRC

e0 02

20 1

10 )0()(

1)(

1e2

R2

When the feedback element is a capacitor then the circuit acts as an integrator.

The initial condition is specified by the initial charge in capacitor