Difference between revisions of "Scilab/C4/Control-systems/English"

Revision as of 11:28, 28 December 2013

Title of script: Advanced Control Systems

Author: Manas, Shamika

Keywords: control, continuous time, response

Visual Cue

Narration

Slide 1

Dear friends, welcome to the spoken tutorial on “Advanced Control of Continuous Time systems”

Slide 2,3-Learning Objective Slide

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

Slide 4-System Requirement slide

To record this tutorial, I am using

Ubuntu 12.04 as the operating system
and Scilab 5.3.3 version

Slide 5- Prerequisite slide

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.

Slide 6

In this tutorial, I will describe how to define second-order linear system.

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

Switch to the Scilab Console Window and type:

s = poly(0, ’s’)

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.

Display the output polynomial

The output is 's'.

On the console window type:

s = %s

and press Enter.

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.

Slide 7

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.

Switch to the Scilab Console Window and type:

sysG = syslin(’c’,2/(sˆ2+2*s+9))

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.

Display the output generated

The output is linear second order system represented by

2 over 9 plus 2 s plus s square

Type:

t=0:0.1:10;

Press Enter.

Then type

t equal to zero colon zero point one colon ten semi colon

Press Enter.

Then type

y1 = csim(’step’, t, sysG);

Press Enter.

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.

Then type

plot(t, y1);

Press Enter.

Then type

plot open paranthesis t comma y one close paranthesis semicolon

Press Enter.

Display the output generated

The output will display the step response of the given second order system.

Slide 8

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.

Switch to the Scilab Console Window and type this on your Scilab Console

u2=sin(t);

Press Enter.

Let us switch to the Scilab Console window.

Type

U two is equal to sine open paranthesis t close paranthesis semi colon

Press Enter.

Type y2 = csim(u2, t, sysG);

Press Enter.

Then type

y two is equal to c sim 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.

Type plot(t, [u2; y2])

Press Enter.

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.

Slide 9, 10

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.

Slide 11

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 !!

Switch to the Scilab console and type

fr = [0.01:0.1:10]; // Hertz

Press Enter.

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.

Type bode(sysG, fr) and press Enter.

Then type

bode open paranthesis sys capital G comma fr close paranthesis

and press Enter.

The bode plot is shown

Slide 12

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.

Switch to the Scilab console and type

p=s^2 +9*s+9

Press Enter.

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.

Type sys2 = syslin('c', 9/p)

Press Enter.

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.

roots(p)

and press Enter.

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

Display the output

The roots or poles of the system are shown.

Slide 13, 14

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.

Switch to the Scilab Console Window and type this on your Scilab Console

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

Alternatively:

Type this on your Console

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

Then type this on your Scilab Console

--> sys4 = syslin(’c’,g) and press Enter

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

Slide 15,16

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.

Slide 17

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.

Switch to Scilab and type this on your Scilab Console

--> sys3(2) and press Enter

Type

numer(sys3)

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.

Display output

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.

Slide 18

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.

Show Slide 19

Title: About the Spoken Tutorial Project

Watch the video available at 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

* 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

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

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

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

* 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

On previous slide

This is Ashwini Patil signing off. Thank you for joining.

Contributors and Content Editors

Lavitha Pereira, Nancyvarkey

Difference between revisions of "Scilab/C4/Control-systems/English"

Revision as of 11:28, 28 December 2013

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@@ Line 7: / Line 7: @@
-{| style="border-spacing:0;"
+{|border=1
 ! <center>Visual Cue</center>
 ! <center>Narration</center>
@@ Line 13: / Line 13: @@
 |-
 | 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,
+| 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'''”
-Welcome to the spoken tutorial on “Advanced '''Control of Continuous Time systems'''”
 |-
@@ Line 23: / Line 21: @@
 .Define a continuous time system: second and higher order
-.Plot response to step and sine inputs
+.Plot response to '''step''' and '''sine''' inputs
-.Do a Bode plot
-.Study numer and denom Scilab functions
-. Plot poles and zeros of a system
+.Do a '''Bode plot'''
+.Study '''numer''' and '''denom Scilab functions
+'''
+. 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:1pt solid #000000;padding:0.097cm;"| To record this tutorial, I am using
+*'''Ubuntu 12.04''' as the operating system
+*and '''Scilab 5.3.3''' version
 |-
@@ Line 43: / Line 41: @@
-For scilab, please refer to the Scilab tutorials available on the '''Spoken Tutorial '''website.
+For '''Scilab''', please refer to the '''Scilab''' tutorials available on the '''Spoken Tutorial '''website.
 |-
@@ Line 50: / Line 48: @@
-So, first we have to define '''complex domain variable s'''.
+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’)'''
+'''s = 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.
@@ Line 68: / Line 66: @@
 |-
 | 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: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
+s = %s
 and press '''Enter'''.
@@ Line 97: / Line 92: @@
-Use '''csim''' with '''step''' option to obtain the '''step response''' and then '''plot the step response. '''
+Use '''csim''' with '''step''' option, to obtain the '''step response''' and then '''plot the step response. '''
 |-
@@ Line 111: / Line 106: @@
-'''Here c is used as we are defining a continuous time system'''
+Here '''c''' is used as we are defining a continuous time system.
-'''Press Enter'''
+Press '''Enter'''.
 |-
@@ Line 137: / Line 132: @@
 | 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);
+y1 = csim(’step’, t, sysG);
 Press Enter.
@@ Line 178: / Line 173: @@
 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.
+| 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.
@@ Line 195: / Line 190: @@
 | 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'''
+'''y two is equal to c sim open paranthesis u two comma t comma sys capital G close the bracket semicolon'''
-'''Press Enter.'''
+Press '''Enter.'''
@@ Line 212: / Line 207: @@
-Make sure that you place a '''Semicolon between u2 and y2 because u2 and y2 are row vectors of the same size'''
+Make sure that you place a '''semicolon''' between '''u2''' and '''y2''' because '''u2''' and '''y2''' are row vectors of the same size.
@@ Line 227: / Line 222: @@
 * the output is also a '''sine wave''', and
-* there is a '''phase lag between the input and output'''
+* 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.
+* '''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
+* 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
+| 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'''
@@ Line 241: / Line 235: @@
 Do not use '''f r e q''' as a '''variable''' !!
@@ Line 251: / Line 244: @@
 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
+| 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
@@ Line 274: / Line 267: @@
 |-
 | 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
+| 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
+Let us plot '''step response''' for this system.
 |-
@@ Line 288: / Line 281: @@
 | 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'''
+Type this on your '''Scilab console'''
@@ Line 312: / Line 305: @@
 '''t equal to zero colon zero point one colon ten semi colon'''
-'''Press Enter.'''
+Press '''Enter.'''
@@ Line 318: / Line 311: @@
-'''Press enter'''
+Press '''Enter.'''
@@ Line 324: / Line 317: @@
-'''Press enter'''
+Press '''Enter.'''
-The '''response plot for over damped system''' is shown.
+The '''response plot''' for over damped system is shown.
 |-
@@ Line 339: / Line 334: @@
-These '''roots are the poles''' of the system '''sys two'''
+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: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
+| 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'''.
-along similar lines as for '''over damped system'''.
@@ Line 376: / Line 368: @@
---> '''g <nowiki>=</nowiki> (s+6)/(sˆ2+6*s+19)''' and press '''Enter'''
+--> '''g = (s+6)/(sˆ2+6*s+19)''' and press '''Enter'''
 Then type this on your '''Scilab Console'''
@@ Line 382: / Line 374: @@
 --> '''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.
+| 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.
+For a general '''transfer function''', the numerator and denominator can be specified separately. Let me show you how.
@@ Line 402: / Line 394: @@
-'''Press enter'''
+Press '''Enter.'''
@@ Line 411: / Line 403: @@
-Press '''enter'''
+Press '''Enter.'''
@@ Line 426: / Line 419: @@
-Its '''numerator and denominator''' can be extracted by various ways.
+Its numerator and denominator can be extracted by various ways.
-'''Sys of two , numer of sys '''or '''numer of g '''gives the '''numerator'''
+'''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'''.
+The denominator can be calculated using '''sys(3)''' or '''denom of sys functions'''.
@@ Line 462: / Line 455: @@
-Press enter
+Press '''Enter.'''
-This gives the '''numerator''' of the rational function ’'''sys three'''’ that is '''6 + s'''
+This gives the numerator of the rational function ’'''sys three'''’ that is '''6 + s'''
-Otherwise you can type
+Otherwise, you can type
 '''numer open paranthesis sys three close paranthesis'''
-The '''numerator''' of '''sys three''' is shown
+The numerator of '''sys three''' is shown.
-To get the '''denominator '''type
+To get the denominator, type
 '''sys three open paranthesis three close paranthesis. Press enter'''
-The '''denominator '''of the function is shown.
+The denominator of the function is shown.
-You can also type '''denom open paranthesis sys three close paranthesis. Press enter'''
+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'''
+Then type '''p l z r open paranthesis sys three close paranthesis.'''
+Press '''Enter.'''
 |-
@@ Line 490: / Line 488: @@
 | 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 shows '''cross''' and '''circle'''' for '''poles''' and '''zeros''' of the system respectively.
 It is plotted on the '''complex plane'''.
@@ Line 518: / Line 516: @@
 | 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/>
+* If you do not have good bandwidth, you can download and watch it