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Control Systems CSE 301

Session 2013

Lab Manual 8

Date:6-4-2016

In this lab, you will use Matlab to solve the following problems:

Block Diagram Reduction

hree metho!s are available:

1" #olution via #eries, $arallel an! %ee!ba&' &omman!s"

2" #olution via (lgebrai& )perations*" #olution via (ppen! an! +onne&t &omman!s"

Solution !ia Series" #arallel and $eedback commands

he &lose! loop transfer fun&tion is obtaine! by using following &omman!s

su&&essively, where the arguments are the I obe&ts: series./1,/2 for a &as&a!e

&onne&tion of /1.s an! /2.s, parallel./1,/2 for a parallel &onne&tion of /1.s

an! /2.s an! feedback./,,sign for a &lose! loop &onne&tion with /.s as a

forwar! path, .s as the fee!ba&' path an! sign is -1 for negative fee!ba&'"

 Exercise:

Determine the &lose! loop transfer fun&tion of the following system using the above

metho!

Solution !ia %lgebraic &'erations

(nother metho! is to use the algebrai& operations su&&essively on I transfer 

fun&tions as follows: /1/2 for &as&a!e, /13/2 for parallel,G

1±G∗ H    for 

fee!ba&'" hen using !ivision we follow with the fun&tion minreal .sys to &an&el

&ommon terms in the numerator an! !enominator"

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 Exercise:

5epeat the previous eer&ise using the algebrai& operations

Solution !ia %''end and Connect Commands

his metho! !efines the topology of the system, may be use! effe&tively for 

&ompli&ate! systems" In this metho! following step are ta'en:

1" he subsystems are !efine! by I transfers fun&tions"

2" he subsystems are appen!e! using the &omman! G7append ./1, /2, /*,

/4,8, /n, or gathere! into multiple inputs multiple output system" ere / is

the single system an! /i are the I transfer fun&tions of the subsystems"

*" he eternal inputs an! outputs are spe&ifie!" %or this pro&ess first the all the

subsystem are assigne! a number, e"g, /* is *, base! upon the fa&t that it is the

thir! subsystem in the appen! argument" 9ow the eternal inputs an! outputs

are spe&ifie!, e"g, inputs71 ; 6< an! outputs7* 4< is use! to !efine that

eternal inputs be the inputs of the subsystems 1, ;, an! 6 an! the eternal

outputs to be the outputs of the subsystems * an! 4"

%inally at this point, we tell the program how all of the subsystems whose

input &omes from another subsystem=s output" en&e, we !efine a matri Q

that has a row for ea&h subsystem, where the first &olumn &ontains the

subsystem=s number> the subse?uent &olumns &ontain the number of 

subsystems from whi&h the input &omes, e"g", a typi&al row might be as

follows * 6 -@;" (n I &lose! loop transfer fun&tion is &reate! by the &omman! 7tf.

6" he &ommon terms are &an&elle! by using &omman! 7minreal.

Lab %ssessment

%in! the &lose! loop transfer fun&tion for the mo!el for human eye movement