Difference between revisions of "Scilab/C4/Control-systems/English-timed"
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− | | Welcome to the spoken tutorial on ''' | + | | Welcome to the spoken tutorial on ''' Advanced Control of Continuous Time systems''' |
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| 00:09 | | 00:09 | ||
− | | At the end of this tutorial, you will learn how to | + | | At the end of this tutorial, you will learn how to: |
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|00:12 | |00:12 | ||
|Define a continuous time system: second and higher order | |Define a continuous time system: second and higher order | ||
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|00:17 | |00:17 | ||
|Plot response to '''step''' and sine inputs | |Plot response to '''step''' and sine inputs | ||
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|00:22 | |00:22 | ||
|Study '''numer''' and ''' denom Scilab functions''' | |Study '''numer''' and ''' denom Scilab functions''' | ||
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| 00:40 | | 00:40 | ||
− | | Before | + | | Before practicing this tutorial, a learner should have basic knowledge of '''Scilab''' and '''control systems.''' |
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|01:11 | |01:11 | ||
− | |Here type ''' s equal to poly open | + | |Here type ''' s equal to poly open parenthesis zero comma open single quote s close single quote close parenthesis''' , press '''Enter.''' |
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| 01:25 | | 01:25 | ||
− | |The output is ''' 's'. ''' | + | |The output is ''' 's'.''' |
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|On the '''console''' window, type: | |On the '''console''' window, type: | ||
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| ''' s equal to percentage s''', press '''Enter.''' | | ''' s equal to percentage s''', press '''Enter.''' | ||
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|Use the '''Scilab''' function ''' ’syslin’ ''' to define the continuous time system. | |Use the '''Scilab''' function ''' ’syslin’ ''' to define the continuous time system. | ||
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||''' G of s is equal to 2 over 9 plus 2 s plus s square''' | ||''' G of s is equal to 2 over 9 plus 2 s plus s square''' | ||
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|01:58 | |01:58 | ||
|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. | ||
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|02:09 | |02:09 | ||
− | ||Here type:''' sys capital G equal to syslin open | + | ||Here type:''' sys capital G equal to syslin open parenthesis open single quote c close single quote comma two divide by open parenthesis s square plus two asterisk s plus nine close parenthesis close parenthesis ''' |
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|02:32 | |02:32 | ||
− | | Here '''c''' is used | + | | Here '''c''' is used as we are defining a continuous time system. |
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|02:38 | |02:38 | ||
− | | Press '''Enter''' | + | | Press '''Enter'''. |
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||The output is linear second order system represented by | ||The output is linear second order system represented by | ||
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| 02:44 | | 02:44 | ||
|'''2 over 9 plus 2 s plus s square''' | |'''2 over 9 plus 2 s plus s square''' | ||
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|02:49 | |02:49 | ||
| Then type ''' t equal to zero colon zero point one colon ten semicolon''' | | Then type ''' t equal to zero colon zero point one colon ten semicolon''' | ||
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|02:57 | |02:57 | ||
| Press '''Enter.''' | | Press '''Enter.''' | ||
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| 02:59 | | 02:59 | ||
− | |Then type ''' y one is equal to c sim open | + | |Then type ''' y one is equal to c sim open parenthesis open single quote step close single quote comma t comma sys capital G close the parenthesis semicolon''' |
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| 03:15 | | 03:15 | ||
|Press '''Enter. ''' | |Press '''Enter. ''' | ||
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| 03:17 | | 03:17 | ||
− | |Then type ''' plot open | + | |Then type ''' plot open parenthesis t comma y one close parenthesis semicolon''' |
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|03:33 | |03:33 | ||
|Let us study the ''' Second Order system response for sine input.''' | |Let us study the ''' Second Order system response for sine input.''' | ||
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| 03:47 | | 03:47 | ||
|Let us switch to the '''Scilab console''' window. | |Let us switch to the '''Scilab console''' window. | ||
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|03:51 | |03:51 | ||
− | || Type ''' U two is equal to sine open | + | || Type ''' U two is equal to sine open parenthesis t close parenthesis semicolon''' |
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| 03:59 | | 03:59 | ||
| Press ''' Enter. ''' | | Press ''' Enter. ''' | ||
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| 04:01 | | 04:01 | ||
− | |Then type ''' y two is equal to c sim open | + | |Then type ''' y two is equal to c sim open parenthesis u two comma t comma sys capital G close the bracket semicolon ''' |
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| 04:15 | | 04:15 | ||
− | | Press ''' Enter''' | + | | Press '''Enter'''. |
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||Here we are using ''' sysG, the continuous time second order system''' we had defined earlier. | ||Here we are using ''' sysG, the continuous time second order system''' we had defined earlier. | ||
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|04:25 | |04:25 | ||
− | |'Then type '''plot open | + | |'Then type '''plot open parenthesis t comma open square bracket u two semicolon y two close square bracket close parenthesis ''' |
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|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. | ||
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| 04:50 | | 04:50 | ||
− | | | + | |Press '''Enter.''' |
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| 05:06 | | 05:06 | ||
− | |As expected, the output is also a ''' sine wave | + | |As expected, the output is also a '''sine wave''' and |
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| 05:11 | | 05:11 | ||
− | |there is a '''phase lag''' between the input and output | + | |there is a '''phase lag''' between the input and output. |
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|'''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. | ||
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|This is a typical '''under-damped''' example. | |This is a typical '''under-damped''' example. | ||
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| 05:39 | | 05:39 | ||
− | | Do not use '''f r e q as a | + | | Do not use '''f r e q''' as a '''variable'''!! |
− | + | ||
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| 05:44 | | 05:44 | ||
− | |Open the ''' Scilab console''' and type | + | |Open the ''' Scilab console''' and type: |
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| 05:47 | | 05:47 | ||
− | |''' f r is equal to open square bracket zero point zero one colon zero point one colon ten close square bracket semicolon. ''' | + | |''' f r is equal to open square bracket zero point zero one colon zero point one colon ten close square bracket semicolon.''' |
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| 06:06 | | 06:06 | ||
− | |Then type '''bode open | + | |Then type '''bode open parenthesis sys capital G comma fr close parenthesis ''' |
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| and press ''Enter.''' | | and press ''Enter.''' | ||
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| 06:17 | | 06:17 | ||
− | | The '''bode plot''' is shown | + | | The '''bode plot''' is shown. |
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| Let us define another system. | | Let us define another system. | ||
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|We have an ''' over-damped system p equal to s square plus nine s plus nine ''' | |We have an ''' over-damped system p equal to s square plus nine s plus nine ''' | ||
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| Let us plot '''step response''' for this system. | | Let us plot '''step response''' for this system. | ||
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| 06:38 | | 06:38 | ||
− | |Type this on your ''' console | + | |Type this on your ''' console''': |
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| 06:40 | | 06:40 | ||
− | |''' p is equal to s square plus nine | + | |''' p is equal to s square plus nine asterisk s plus nine''' |
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| 06:49 | | 06:49 | ||
− | |Then type this on your ''' console | + | |Then type this on your ''' console''': |
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| 06:51 | | 06:51 | ||
− | |''' sys two is equal to syslin open | + | |''' sys two is equal to syslin open parenthesis open single quote c close single quote comma nine divided by p close parenthesis ''' |
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|Press ''' Enter.''' | |Press ''' Enter.''' | ||
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| 07:17 | | 07:17 | ||
− | |''' y is equal to c sim open | + | |''' y is equal to c sim open parenthesis open single quote step close single quote comma t comma sys two close the parenthesis semicolon''' |
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| 07:33 | | 07:33 | ||
− | |Then type ''' plot open | + | |Then type ''' plot open parenthesis t comma y close parenthesis''' |
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|''' Roots of p''' and press '''Enter.''' | |''' Roots of p''' and press '''Enter.''' | ||
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| 07:54 | | 07:54 | ||
− | |These '''roots''' are the poles of the system '''sys two''' | + | |These '''roots''' are the poles of the system '''sys two'''. |
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| 08:45 | | 08:45 | ||
− | |Switch to ''' Scilab console. | + | |Switch to ''' Scilab console.''' |
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| Let me show you how. | | Let me show you how. | ||
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| 08:57 | | 08:57 | ||
− | |Type on '''console''' | + | |Type on '''console''': |
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| 08:59 | | 08:59 | ||
− | |''' sys three is equal to syslin open | + | |''' sys three is equal to syslin open parenthesis open single quote c close single quote comma s plus six comma s square plus six asterisk s plus nineteen close parenthesis''' |
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| 09:19 | | 09:19 | ||
− | |Press '''Enter''' | + | |Press '''Enter'''. |
− | + | ||
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| 09:21 | | 09:21 | ||
− | |Another way of defining a system, is to type | + | |Another way of defining a system, is to type: |
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| 09:24 | | 09:24 | ||
− | |'''g is equal to open | + | |'''g is equal to open parenthesis s plus six close parenthesis divided by open parenthesis s square plus six asterisk s plus nineteen close parenthesis''' |
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|Press '''Enter.''' | |Press '''Enter.''' | ||
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| 09:42 | | 09:42 | ||
− | |Then type this on your '''console''' | + | |Then type this on your '''console''': |
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| 09:44 | | 09:44 | ||
− | |'''sys four is equal to syslin open | + | |'''sys four is equal to syslin open parenthesis open single quote c close single quote comma g close parenthesis ''' |
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|Both ways, we get the same output; | |Both ways, we get the same output; | ||
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|'''six plus s over 19 plus six s plus s square ''' | |'''six plus s over 19 plus six s plus s square ''' | ||
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|'''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. | ||
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|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. ''' | ||
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|The syntax is p l z r of sys | |The syntax is p l z r of sys | ||
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|The plot shows x for poles and circles for zeros. | |The plot shows x for poles and circles for zeros. | ||
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| 10:48 | | 10:48 | ||
− | |Type this on your Scilab console | + | |Type this on your Scilab console: |
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| 10:50 | | 10:50 | ||
− | |sys three open | + | |sys three open parenthesis two close parenthesis |
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|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 | ||
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− | |Otherwise, you can type | + | |Otherwise, you can type: |
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| 11:05 | | 11:05 | ||
− | |numer open | + | |numer open parenthesis sys three close parenthesis. |
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| 11:11 | | 11:11 | ||
− | |Press Enter | + | |Press Enter. |
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− | |To get the denominator, type | + | |To get the denominator, type: |
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− | |sys three open | + | |sys three open parenthesis three close parenthesis. Press Enter. |
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| 11:30 | | 11:30 | ||
− | |You can also type denom open | + | |You can also type denom open parenthesis sys three close parenthesis. |
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|Press Enter. | |Press Enter. | ||
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| 11:38 | | 11:38 | ||
− | |Then type p l z r open | + | |Then type p l z r open parenthesis sys three close parenthesis. |
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− | |The output graph plots the poles and zeros. | + | |The output graph plots the '''poles''' and '''zeros'''. |
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− | |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. |
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|It is plotted on the complex plane. | |It is plotted on the complex plane. | ||
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− | |Define a system by its transfer function. | + | |* Define a system by its transfer function. |
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− | |Plot step and sinusoidal responses. | + | |* Plot step and sinusoidal responses. |
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| 12:11 | | 12:11 | ||
− | |Extract poles and zeros of a transfer function. | + | |* Extract poles and zeros of a transfer function. |
− | + | ||
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|12:15 | |12:15 | ||
− | | Watch the video available at the following link | + | | Watch the video available at the following link. |
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− | | It | + | | It summarizes the Spoken Tutorial project. |
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− | + | ||
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|12:22 | |12:22 | ||
− | ||If you do not have good bandwidth, you can download and watch it | + | ||If you do not have good bandwidth, you can download and watch it. |
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|12:27 | |12:27 | ||
− | ||The spoken tutorial project Team | + | ||The spoken tutorial project Team: |
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|12:29 | |12:29 | ||
− | ||Conducts workshops using spoken tutorials | + | ||Conducts workshops using spoken tutorials. |
− | + | ||
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|12:32 | |12:32 | ||
− | ||Gives certificates to those who pass an online test | + | ||Gives certificates to those who pass an online test. |
− | + | ||
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|12:36 | |12:36 | ||
− | ||For more details, please write to contact@spoken-tutorial.org | + | ||For more details, please write to contact@spoken-tutorial.org. |
− | + | ||
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|12:43 | |12:43 | ||
− | |Spoken Tutorial Project is a part of the Talk to a Teacher project | + | |Spoken Tutorial Project is a part of the Talk to a Teacher project. |
− | + | ||
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| 12:55 | | 12:55 | ||
− | |More information on this mission is available at spoken-tutorial.org/NMEICT-Intro | + | |More information on this mission is available at spoken-tutorial.org/NMEICT-Intro. |
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− | |This is Ashwini Patil signing off. | + | |This is Ashwini Patil, signing off. |
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|13:08 | |13:08 | ||
− | | Thank you for joining Good Bye. | + | | Thank you for joining. Good Bye. |
Revision as of 14:21, 3 March 2015
Time | Narration |
00:01 | Dear Friends, |
00:02 | Welcome to the spoken tutorial on Advanced Control of Continuous Time systems |
00:09 | At the end of this tutorial, you will learn how to: |
00:12 | Define a continuous time system: second and higher order |
00:17 | Plot response to step and sine inputs |
00:20 | Do a Bode plot |
00:22 | Study numer and denom Scilab functions |
00:26 | Plot poles and zeros of a system |
00:30 | To record this tutorial, I am using |
00:33 | Ubuntu 12.04 as the operating system with |
00:36 | Scilab 5.3.3 version |
00:40 | Before practicing this tutorial, a learner should have basic knowledge of Scilab and control systems. |
00:48 | For Scilab, please refer to the Scilab tutorials available on the Spoken Tutorial website. |
00:55 | In this tutorial, I will describe how to define second-order linear system. |
01:02 | So, first we have to define complex domain variable 's'. |
01:08 | Let us switch to the Scilab console window. |
01:11 | Here type s equal to poly open parenthesis zero comma open single quote s close single quote close parenthesis , press Enter. |
01:25 | The output is 's'. |
01:27 | There is another way to define 's' as continuous time complex variable. |
01:32 | On the console window, type: |
01:35 | s equal to percentage s, press Enter. |
01:41 | Let us study the syslin Scilab command. |
01:44 | Use the Scilab function ’syslin’ to define the continuous time system. |
01:51 | G of s is equal to 2 over 9 plus 2 s plus s square |
01:58 | Use csim with step option, to obtain the step response and then plot the step response. |
02:06 | Let us switch to the Scilab console window. |
02:09 | Here type: sys capital G equal to syslin open parenthesis open single quote c close single quote comma two divide by open parenthesis s square plus two asterisk s plus nine close parenthesis close parenthesis |
02:32 | Here c is used as we are defining a continuous time system. |
02:38 | Press Enter. |
02:40 | The output is linear second order system represented by |
02:44 | 2 over 9 plus 2 s plus s square |
02:49 | Then type t equal to zero colon zero point one colon ten semicolon |
02:57 | Press Enter. |
02:59 | Then type y one is equal to c sim open parenthesis open single quote step close single quote comma t comma sys capital G close the parenthesis semicolon |
03:15 | Press Enter. |
03:17 | Then type plot open parenthesis t comma y one close parenthesis semicolon |
03:24 | Press Enter. |
03:26 | The output will display the step response of the given second order system. |
03:33 | Let us study the Second Order system response for sine input. |
03:39 | Sine inputs can easily be given as inputs to a second order system to a continuous time system. |
03:47 | Let us switch to the Scilab console window. |
03:51 | Type U two is equal to sine open parenthesis t close parenthesis semicolon |
03:59 | Press Enter. |
04:01 | Then type y two is equal to c sim open parenthesis u two comma t comma sys capital G close the bracket semicolon |
04:15 | Press Enter. |
04:17 | Here we are using sysG, the continuous time second order system we had defined earlier. |
04:25 | 'Then type plot open parenthesis t comma open square bracket u two semicolon y two close square bracket close parenthesis |
04:39 | Make sure that you place a semicolon between u2 and y2 because u2 and y2 are row vectors of the same size. |
04:50 | Press Enter. |
04:52 | This plot shows the response of the system to a step input and sine input. It is called the response plot. |
05:01 | Response Plot plots both the input and the output on the same graph. |
05:06 | As expected, the output is also a sine wave and |
05:11 | there is a phase lag between the input and output. |
05:15 | Amplitude is different for the input and the output, as it is being passed through a transfer function. |
05:23 | This is a typical under-damped example. |
05:26 | Let us plot bode plot of 2 over 9 plus 2 s plus s square |
05:32 | Please note command 'f r e q' is a Scilab command for frequency response. |
05:39 | Do not use f r e q as a variable!! |
05:44 | Open the Scilab console and type: |
05:47 | f r is equal to open square bracket zero point zero one colon zero point one colon ten close square bracket semicolon. |
06:00 | Press Enter. |
06:03 | The frequency is in Hertz. |
06:06 | Then type bode open parenthesis sys capital G comma fr close parenthesis |
06:15 | and press Enter.' |
06:17 | The bode plot is shown. |
06:20 | Let us define another system. |
06:23 | We have an over-damped system p equal to s square plus nine s plus nine |
06:32 | Let us plot step response for this system. |
06:36 | Switch to Scilab console. |
06:38 | Type this on your console: |
06:40 | p is equal to s square plus nine asterisk s plus nine |
06:47 | and then press Enter. |
06:49 | Then type this on your console: |
06:51 | sys two is equal to syslin open parenthesis open single quote c close single quote comma nine divided by p close parenthesis |
07:04 | and press Enter. |
07:07 | Then type t equal to zero colon zero point one colon ten semicolon |
07:14 | Press Enter. |
07:17 | y is equal to c sim open parenthesis open single quote step close single quote comma t comma sys two close the parenthesis semicolon |
07:31 | Press Enter. |
07:33 | Then type plot open parenthesis t comma y close parenthesis |
07:39 | Press Enter. |
07:41 | The response plot for over damped system is shown. |
07:46 | To find the roots of p type this on your console - |
07:49 | Roots of p and press Enter. |
07:54 | These roots are the poles of the system sys two. |
07:59 | The roots or poles of the system are shown. |
08:02 | Please plot Step response for this system along similar lines, as for over damped system. |
08:11 | G of s is equal to 2 over 9 plus 6 s plus s square which is a critically damped system |
08:20 | Then G of s is equal to two over 9 plus s square which is an undamped system |
08:28 | G of s is equal to 2 over 9 minus 6 s plus s square which is an unstable system |
08:36 | Check response to sinusoidal inputs for all the cases and plot bode plot too. |
08:45 | Switch to Scilab console. |
08:48 | For a general transfer function, the numerator and denominator can be specified separately. |
08:55 | Let me show you how. |
08:57 | Type on console: |
08:59 | sys three is equal to syslin open parenthesis open single quote c close single quote comma s plus six comma s square plus six asterisk s plus nineteen close parenthesis |
09:19 | Press Enter. |
09:21 | Another way of defining a system, is to type: |
09:24 | g is equal to open parenthesis s plus six close parenthesis divided by open parenthesis s square plus six asterisk s plus nineteen close parenthesis |
09:40 | Press Enter. |
09:42 | Then type this on your console: |
09:44 | sys four is equal to syslin open parenthesis open single quote c close single quote comma g close parenthesis |
09:55 | Press Enter. |
09:58 | Both ways, we get the same output; |
10:01 | six plus s over 19 plus six s plus s square |
10:07 | The variable ’sys’ is of type ’rational’. |
10:10 | Its numerator and denominator can be extracted by various ways. |
10:16 | Sys of two , numer of sys or numer of g gives the numerator. |
10:22 | The denominator can be calculated using sys(3) or denom of sys functions. |
10:30 | The poles and zeros of the system can be plotted using p l z r function. |
10:37 | The syntax is p l z r of sys |
10:41 | The plot shows x for poles and circles for zeros. |
10:46 | Switch to Scilab console. |
10:48 | Type this on your Scilab console: |
10:50 | sys three open parenthesis two close parenthesis |
10:55 | Press Enter. |
10:56 | This gives the numerator of the rational function 'sys three' that is 6 + s |
11:03 | Otherwise, you can type: |
11:05 | numer open parenthesis sys three close parenthesis. |
11:11 | Press Enter. |
11:13 | The numerator of system three is shown. |
11:17 | To get the denominator, type: |
11:19 | sys three open parenthesis three close parenthesis. Press Enter. |
11:26 | The denominator of the function is shown. |
11:30 | You can also type denom open parenthesis sys three close parenthesis. |
11:36 | Press Enter. |
11:38 | Then type p l z r open parenthesis sys three close parenthesis. |
11:44 | Press Enter. |
11:47 | The output graph plots the poles and zeros. |
11:50 | It shows 'cross and circle' for 'poles and zeros' of the system respectively. |
11:58 | It is plotted on the complex plane. |
12:01 | In this tutorial, we have learnt how to: |
12:03 | * Define a system by its transfer function. |
12:08 | * Plot step and sinusoidal responses. |
12:11 | * Extract poles and zeros of a transfer function. |
12:15 | Watch the video available at the following link. |
12:19 | It summarizes the Spoken Tutorial project. |
12:22 | If you do not have good bandwidth, you can download and watch it. |
12:27 | The spoken tutorial project Team: |
12:29 | Conducts workshops using spoken tutorials. |
12:32 | Gives certificates to those who pass an online test. |
12:36 | For more details, please write to contact@spoken-tutorial.org. |
12:43 | Spoken Tutorial Project is a part of the Talk to a Teacher project. |
12:47 | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India. |
12:55 | More information on this mission is available at spoken-tutorial.org/NMEICT-Intro. |
13:06 | This is Ashwini Patil, signing off. |
13:08 | Thank you for joining. Good Bye. |