Lavitha Pereira: Created page with ''''Title of script''': Advanced Control Systems '''Author: Manas, Shamika''' '''Keywords: control, continuous time, response''' {| style="border-spacing:0;" ! Visua…'

2013-12-18T04:54:59Z

Created page with ''''Title of script''': Advanced Control Systems '''Author: Manas, Shamika''' '''Keywords: control, continuous time, response''' {| style="border-spacing:0;" ! <center>Visua…'

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'''Title of script''': Advanced Control Systems

'''Author: Manas, Shamika'''

'''Keywords: control, continuous time, response'''

{| style="border-spacing:0;"
! <center>Visual Cue</center>
! <center>Narration</center>

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 1'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Dear Friends,

Welcome to the spoken tutorial on “Advanced '''Control of Continuous Time systems'''”

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 2,3-Learning Objective Slide'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| At the end of this tutorial, you will learn how to:

1.Define a continuous time system: second and higher order

2.Plot response to step and sine inputs

3.Do a Bode plot

4.Study numer and denom Scilab functions

5. Plot poles and zeros of a system

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 4-System Requirement slide'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| To record this tutorial, I am using '''Ubuntu 12.04''' as the operating system with '''Scilab 5.3.3''' version

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 5- Prerequisite slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Before practising this tutorial, a learner should have basic knowledge of '''Scilab and control systems. '''

For scilab, please refer to the Scilab tutorials available on the '''Spoken Tutorial '''website.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 6'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| In this tutorial, I will describe how to define '''second-order linear system'''.

So, first we have to define '''complex domain variable s'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to the Scilab Console Window and type:

'''s <nowiki>=</nowiki> poly(0, ’s’)'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us switch to the '''Scilab Console''' Window.

Here type:

'''s equal to poly open paranthesis zero comma open single quote s close single quote close paranthesis'''

and press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Display the output polynomial
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The output is '''s'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| On the console window type:

s <nowiki>=</nowiki> %s

and press '''Enter'''.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| There is another way to define ''''s'''' as '''continuous time complex variable'''

On the '''Console '''window type:

'''s equal to percentage s'''

and press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 7'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us study the''' syslin Scilab command'''

Use the '''Scilab''' function ’'''syslin'''’ to define the continuous time system

'''G of s is equal to 2 over 9 plus 2 s plus s square'''

Use '''csim''' with '''step''' option to obtain the '''step response''' and then '''plot the step response. '''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to the Scilab Console Window and type:

sysG <nowiki>=</nowiki> syslin(’c’,2/(sˆ2+2*s+9))
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us switch to the '''Scilab Console''' Window.

Here type:

'''sys capital G equal to syslin open paranthesis open single quote c close single quote comma two divided by open paranthesis s square plus two asterik s plus nine close paranthesis close paranthesis '''

'''Here c is used as we are defining a continuous time system'''

'''Press Enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Display the output generated
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The output is linear second order system represented by

'''2 over 9 plus 2 s plus s square'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type:

t=0:0.1:10;

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type

'''t equal to zero colon zero point one colon ten semi colon'''

Press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Then type

y1 <nowiki>=</nowiki> csim(’step’, t, sysG);

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type

'''y one is equal to c sim open paranthesis open single quote step close single quote comma t comma sys capital G close the paranthesis semicolon'''

Press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Then type

plot(t, y1);

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type

'''plot open paranthesis t comma y one close paranthesis semicolon'''

Press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Display the output generated
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The output will display the '''step response''' of the given second order system.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 8'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us study the '''Second Order system response for sine input'''.

'''Sine inputs '''can easily be given as inputs to a second order system to a continuous time system.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to the Scilab Console Window and type this on your Scilab Console

u2=sin(t);

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us switch to the '''Scilab Console''' Window.

Type

'''U two is equal to sine open paranthesis t close paranthesis semi colon'''

Press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type y2 <nowiki>=</nowiki> csim(u2, t, sysG);

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| '''Then type'''

'''y two is equal to csim open paranthesis u two comma t comma sys capital G close the bracket semicolon'''

'''Press Enter.'''

Here we are using''' sysG, the continuous time second order system '''we had defined earlier.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type plot(t, <nowiki>[u2;</nowiki> y2])

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type

'''plot open paranthesis t comma open square bracket u two semicolon y two close square bracket close paranthesis'''

Make sure that you place a '''Semicolon between u2 and y2 because u2 and y2 are row vectors of the same size'''

Press '''Enter'''.

This plot shows the '''response of the system''' to a '''step input and sine input.''' It is called the '''response plot'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 9, 10'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| '''Response Plot''' plots both the input and the output on the same graph.

As expected,

* the output is also a '''sine wave''', and
* there is a '''phase lag between the input and output'''
* '''amplitude''' is different for the input and the output as it is being passed through a transfer function.
* This is a typical '''under-damped''' example

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 11'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us plot '''bode plot''' of 2 over 9 plus 2 s plus s square

Please note command ''''f r e q' '''is a '''Scilab''' command for '''frequency response.'''

Do not use '''f r e q''' as a '''variable''' !!

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to the Scilab console and type

fr <nowiki>=</nowiki> <nowiki>[0.01:0.1:10];</nowiki> // Hertz

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Open the '''Scilab''' '''Console''' and type

'''f r is equal to open square bracket zero point zero one colon zero point one colon ten close square bracket semicolon. '''

Press '''Enter.'''

The '''frequency '''is in''' Hertz. '''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type bode(sysG, fr) and press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type

'''bode open paranthesis sys capital G comma fr close paranthesis'''

and press '''Enter.'''

The '''bode plot''' is shown

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 12'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Let us define another system

We have an '''over-damped system p equal to s square plus nine s plus nine'''

Let us plot '''step response''' for this system

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to the Scilab console and type

p=s^2 +9*s+9

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Switch to Scilab console

Type this on your '''Scilab Console'''

'''p is equal to s square plus nine asterik s plus nine'''

and then press '''Enter'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type sys2 <nowiki>=</nowiki> syslin('c', 9/p)

Press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Then type this on your '''Scilab Console'''

'''sys two is equal to syslin open paranthesis open single quote c close single quote comma nine divided by p close paranthesis'''

and press '''Enter.'''

Then type

'''t equal to zero colon zero point one colon ten semi colon'''

'''Press Enter.'''

'''y is equal to c sim open paranthesis open single quote step close single quote comma t comma sys two close the paranthesis semicolon'''

'''Press enter'''

Then type''' plot open paranthesis t comma y close paranthesis. '''

'''Press enter'''

The '''response plot for over damped system''' is shown.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| roots(p)

and press Enter.
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| To find the '''roots of p '''type this on your on '''Scilab''' '''console'''.

'''Roots of p'''

and press '''Enter'''.

These '''roots are the poles''' of the system '''sys two'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Display the output'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The '''roots or poles''' of the system are shown

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 13, 14'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Please plot '''Step response''' for this system

along similar lines as for '''over damped system'''.

'''G of s is equal to 2 over 9 plus 6 s plus s square''' which is a '''critically damped system'''

Then '''G of s is equal to two over 9 plus s square''' which is an '''undamped system'''

'''G of s is equal to 2 over 9 minus 6 s plus s square''' which is an '''unstable system'''

Check '''response''' to '''sinusoidal inputs''' for all the cases and '''plot bode plot '''too.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Switch to the Scilab Console Window and type''' this on your '''Scilab Console'''

--> '''sys3 <nowiki>=</nowiki> syslin(’c’,s+6,sˆ2+6*s+19)''' and press '''Enter'''

Alternatively:

Type this on your '''Console'''

--> '''g <nowiki>=</nowiki> (s+6)/(sˆ2+6*s+19)''' and press '''Enter'''

Then type this on your '''Scilab Console'''

--> '''sys4 <nowiki>=</nowiki> syslin(’c’,g)''' and press '''Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Switch to Scilab console.

For a general '''transfer function, the numerator and denominator '''can be specified separately. Let me show you how.

Type this on your '''Scilab Console'''

'''sys three is equal to syslin open paranthesis open single quote c close single quote comma s plus six comma s square plus six asterik s plus nineteen close paranthesis'''

Press '''Enter'''

Another way of defining a system is to type

'''g is equal to open paranthesis s plus six close paranthesis divided by open paranthesis s square plus six asterik s plus nineteen close paranthesis'''

'''Press enter'''

Then type this on your '''Scilab Console'''

'''sys four is equal to syslin open paranthesis open single quote c close single quote comma g close paranthesis'''

Press '''enter'''

Both ways, we get the same output

'''six plus s over 19 plus six s plus s square'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 15,16'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The variable ’'''sys'''’ is of type ’'''rational'''’.

Its '''numerator and denominator''' can be extracted by various ways.

'''Sys of two , numer of sys '''or '''numer of g '''gives the '''numerator'''

The '''denominator '''can be calculated using '''sys(3) or denom of sys functions'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 17
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The '''poles and zeros''' of the system can be plotted using '''p l z r''' function.

The syntax is '''p l z r of sys'''

The plot shows '''x for poles''' and '''circles for zeros.'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Switch to Scilab and '''type this on your '''Scilab Console'''

--> '''sys3(2)''' and press '''Enter'''

'''Type'''

'''numer(sys3)'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Switch to '''Scilab '''console.

Type this on your '''Scilab Console'''

'''sys three open paranthesis two close paranthesis'''

Press enter

This gives the '''numerator''' of the rational function ’'''sys three'''’ that is '''6 + s'''

Otherwise you can type

'''numer open paranthesis sys three close paranthesis'''

The '''numerator''' of '''sys three''' is shown

To get the '''denominator '''type

'''sys three open paranthesis three close paranthesis. Press enter'''

The '''denominator '''of the function is shown.

You can also type '''denom open paranthesis sys three close paranthesis. Press enter'''

Then type '''p l z r open paranthesis sys three close paranthesis. Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Display output'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The '''output graph''' plots the '''poles and zeros'''.

It shows '''cross and circle for poles and zeros''' of the system respectively

It is plotted on the '''complex plane'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Slide 18'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| In this tutorial we have learnt how to:

* Define a system by its '''transfer''' function.
* Plot '''step and sinusoidal responses'''.
* Extract '''poles and zeros''' of a '''transfer''' function.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 19'''

'''Title: About the Spoken Tutorial Project'''

* Watch the video available at [http://spoken-tutorial.org/What_is_a_Spoken_Tutorial http://spoken-tutorial.org/What_is_a_Spoken_Tutorial]

* It summarises the Spoken Tutorial project

* If you do not have good bandwidth, you can download and watch it

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Watch the video available at the following link
* It summarises the Spoken Tutorial project
* If you do not have good bandwidth, you can download and watch it <br/>

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 20'''

'''Title: Spoken Tutorial Workshops'''

The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact@spoken-tutorial.org

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact at spoken hyphen tutorial dot org

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide '''

'''Title: Acknowledgement''' 21

* Spoken Tutorial Project is a part of the Talk to a Teacher project

* It is supported by the National Mission on Education through ICT, MHRD, Government of India

* More information on this Mission is available at

* [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-Intro]

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Spoken Tutorial Project is a part of the Talk to a Teacher project
* It is supported by the National Mission on Education through ICT, MHRD, Government of India
* More information on this Mission is available at
* spoken hyphen tutorial dot org slash NMEICT hyphen Intro

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''On previous slide'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| This is Ashwini Patil signing off. Thank you for joining.

|}

Scilab/C4/Control-systems/English - Revision history

Nancyvarkey at 09:20, 3 February 2014

Nancyvarkey at 05:58, 28 December 2013

Lavitha Pereira: Created page with ''''Title of script''': Advanced Control Systems '''Author: Manas, Shamika''' '''Keywords: control, continuous time, response''' {| style="border-spacing:0;" ! Visua…'