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{| Border=1
 
{| Border=1
  
−
|| Time
+
|'''Time'''
  
−
|| Narration
+
|'''Narration'''
  
 
|-
 
|-
−
| 00.01
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| 00:01
−
|Dear Friends,  
+
|Dear Friends, Welcome to the spoken tutorial on ''' Advanced Control of Continuous Time systems'''.
  
 
|-
 
|-
−
| 00.02
+
| 00:09
−
| Welcome to the spoken tutorial on ''' “Advanced Control of Continuous Time systems” '''|
+
| At the end of this tutorial, you will learn how to:
  
 
|-
 
|-
−
| 00.09
+
|00:12
−
| At the end of this tutorial, you will learn how to
+
| Define a continuous time system: second and higher order
  
 
|-
 
|-
−
|00.12
+
|00:17
−
|Define a continuous time system: second and higher order
+
| Plot response to '''step''' and sine inputs
−
 
+
  
 
|-
 
|-
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|00.17
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| 00:20
−
|Plot response to '''step''' and sine inputs
+
| Do a '''Bode plot'''  
−
 
+
  
 
|-
 
|-
−
| 00.20
+
|00:22
−
|Do a '''Bode plot'''  
+
| Study '''numer''' and ''' denom Scilab functions'''  
  
 
|-
 
|-
−
|00.22
+
| 00:26
−
|Study '''numer''' and ''' denom Scilab functions'''  
+
| Plot ''' poles''' and '''zeros''' of a system.
−
 
+
  
 
|-
 
|-
−
| 00.26
+
| 00:30
−
|Plot ''' poles''' and '''zeros''' of a system
+
|To record this tutorial, I am using
  
 
|-
 
|-
−
| 00.30
+
|00:33
−
| To record this tutorial, I am using
+
|'''Ubuntu 12.04''' as the operating system with
  
 
|-
 
|-
−
|00.33
+
|00:36
−
|'''Ubuntu 12.04''' as the operating system with
+
|'''Scilab 5.3.3''' version.
  
 
|-
 
|-
−
|00.36
+
| 00:40
−
|'''Scilab 5.3.3''' version
+
| Before practicing this tutorial, a learner should have basic knowledge of '''Scilab''' and '''control systems.'''
  
 
|-
 
|-
−
| 00.40
+
| 00:48
−
| Before practising 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.'''  
 
| For '''Scilab,''' please refer to the '''Scilab tutorials''' available on the '''Spoken Tutorial website.'''  
  
 
|-
 
|-
−
|00.55
+
|00:55
 
|In this tutorial, I will describe how to define '''second-order linear system.'''  
 
|In this tutorial, I will describe how to define '''second-order linear system.'''  
  
 
|-
 
|-
−
|01.02
+
|01:02
 
| So, first we have to define '''complex domain variable 's'.'''  
 
| So, first we have to define '''complex domain variable 's'.'''  
  
 
|-
 
|-
−
 
+
|01:08
−
|01.08
+
|Let us switch to the ''' Scilab console window.'''
−
 
+
−
|Let us switch to the ''' Scilab console window. '''
+
  
 
|-
 
|-
−
 
+
|01:11
−
|01.11
+
|Here, type '''s equal to poly open parenthesis zero comma open single quote s close single quote close parenthesis''', press '''Enter.'''  
−
|Here type ''' s equal to poly open paranthesis zero comma open single quote s close single quote close paranthesis''' , press '''Enter.'''  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 01:25
−
| 01.25
+
|The output is''' 's'.'''   
−
 
+
−
|The output is ''' 's'. '''   
+
−
 
+
  
 
|-
 
|-
−
 
+
| 01:27
−
| 01.27
+
|There is another way to define''' 's' '''as '''continuous time complex variable.'''
−
|There is another way to define ''' 's' ''' as '''continuous time complex variable. '''
+
  
 
|-
 
|-
−
 
+
|01:32
−
|01.32
+
−
 
+
 
|On the '''console''' window, type:  
 
|On the '''console''' window, type:  
−
 
  
 
|-
 
|-
−
 
+
|01:35
−
|01.35
+
| '''s equal to percentage s''', press '''Enter.'''  
−
 
+
−
| ''' s equal to percentage s''', press '''Enter.'''  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
|01.41
+
|01:41
−
|Let us study the ''' syslin Scilab command.'''  
+
|Let us study the '''syslin Scilab command.'''  
 
   
 
   
 
|-
 
|-
−
 
+
|01:44
−
|01.44
+
|Use the '''Scilab''' function''' ’syslin’ ''' to define the continuous time system.  
−
 
+
−
|Use the '''Scilab''' function ''' ’syslin’ ''' to define the continuous time system.  
+
−
 
+
  
 
|-
 
|-
−
 
+
|01:51
−
|01.51
+
||''' 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'''
+
−
 
+
−
 
+
  
 
|-
 
|-
−
|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'''.  
−
 
+
  
 
|-
 
|-
−
 
+
| 02:06
−
| 02.06
+
 
|Let us switch to the '''Scilab console''' window.  
 
|Let us switch to the '''Scilab console''' window.  
  
 
|-
 
|-
−
 
+
|02:09
−
|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'''
−
 
+
−
||Here type:''' sys capital G equal to syslin open paranthesis open single quote c close single quote comma two divide by open paranthesis s square plus two asterik s plus nine close paranthesis close paranthesis '''
+
  
 
|-
 
|-
−
 
+
|02:32
−
|02.32
+
| Here '''c''' is used, as we are defining a continuous time system.  
−
 
+
−
| Here '''c''' is used as we are defining a continuous time system.  
+
  
 
|-
 
|-
−
 
+
|02:38
−
|02.38
+
| Press '''Enter'''.
−
 
+
−
| Press '''Enter'''
+
  
 
|-
 
|-
−
 
+
| 02:40
−
| 02.40
+
−
 
+
 
||The output is linear second order system represented by  
 
||The output is linear second order system represented by  
−
 
  
 
|-
 
|-
−
| 02.44
+
| 02:44
−
|'''2 over 9 plus 2 s plus s square'''  
+
|'''2 over 9 plus 2 s plus s square'''.
−
+
−
 
+
  
 
|-
 
|-
−
|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'''  
−
 
+
−
 
+
  
 
|-
 
|-
−
|02.57
+
|02:57
 
| Press '''Enter.'''  
 
| Press '''Enter.'''  
−
 
  
 
|-
 
|-
−
| 02.59
+
| 02:59
−
|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'''  
+
|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
+
| 03:15
−
|Press '''Enter. '''
+
|Press '''Enter.'''
−
 
+
−
 
+
  
 
|-
 
|-
−
| 03.17
+
| 03:17
−
|Then type ''' plot open paranthesis t comma y one close paranthesis semicolon'''  
+
|Then type ''' plot open parenthesis t comma y one close parenthesis semicolon'''  
  
 
|-
 
|-
−
| 03.24
+
| 03:24
−
|Press ''' Enter.'''
+
|Press '''Enter.'''
  
 
|-
 
|-
−
|03.26
+
|03:26
−
|The output will display the ''' step response of the given second order system.'''
+
|The output will display the '''step response''' of the given second order system.
  
 
|-
 
|-
−
|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.'''  
−
 
+
  
 
|-
 
|-
−
 
+
| 03:39
−
| 03.39
+
|'''Sine inputs''' can easily be given as inputs to a  '''second order system to a continuous time system.'''  
−
 
+
−
|''' Sine inputs''' can easily be given as inputs to a  ''' second order system to a continuous time system.'''  
+
  
 
|-
 
|-
−
 
+
| 03:47
−
| 03.47
+
 
|Let us switch to the '''Scilab console''' window.
 
|Let us switch to the '''Scilab console''' window.
−
 
  
 
|-
 
|-
−
 
+
|03:51
−
|03.51
+
|| Type '''U two is equal to sine open parenthesis t close parenthesis semicolon'''.
−
 
+
−
|| Type ''' U two is equal to sine open paranthesis t close paranthesis semicolon'''  
+
  
 
|-
 
|-
−
 
+
| 03:59
−
| 03.59
+
| Press '''Enter.'''
−
| Press ''' Enter. '''
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 04:01
−
| 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'''.
−
 
+
−
|Then type ''' y two is equal to c sim open paranthesis u two comma t comma sys capital G close the bracket semicolon '''
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 04:15
−
| 04.15
+
| Press '''Enter'''.
−
 
+
−
| Press ''' Enter'''
+
  
 
|-
 
|-
−
 
+
|04:17
−
|04.17
+
||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.  
+
−
 
+
  
 
|-
 
|-
−
 
+
|04:25
−
|04.25
+
|Then type: '''plot open parenthesis t comma open square bracket u two semicolon y two close square bracket close parenthesis'''.
−
 
+
−
|'Then type '''plot open paranthesis t comma open square bracket u two semicolon y two close square bracket close paranthesis '''
+
−
 
+
  
 
|-
 
|-
−
 
+
| 04:39
−
| 04.39
+
−
 
+
 
|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.  
−
 
−
 
−
 
  
 
|-
 
|-
−
 
+
| 04:50
−
| 04.50
+
|Press '''Enter.'''  
−
 
+
−
|'Press '''Enter.'''  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 04:52
−
| 04.52
+
| This plot shows the '''response of the system''' to a '''step input''' and '''sine input. '''It is called the '''response plot. '''
−
 
+
−
| This plot shows the '''response of the system''' to a '''step input''' and '''sine input.''' It is called the '''response plot. '''
+
  
 
|-
 
|-
−
 
+
| 05:01
−
| 05.01
+
−
 
+
 
|'''Response Plot''' plots both the input and the output on the same graph.  
 
|'''Response Plot''' plots both the input and the output on the same graph.  
  
 
|-
 
|-
−
 
+
| 05:06
−
| 05.06
+
|As expected, the output is also a '''sine wave''' and  
−
 
+
−
|As expected, the output is also a ''' sine wave,''' and  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 05:11
−
| 05.11
+
|there is a '''phase lag''' between the input and output.
−
 
+
−
|there is a '''phase lag''' between the input and output
+
  
 
|-
 
|-
−
 
+
| 05:15
−
| 05.15
+
|'''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.  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 05:23
−
| 05.23
+
−
 
+
 
|This is a typical '''under-damped''' example.  
 
|This is a typical '''under-damped''' example.  
−
 
  
 
|-
 
|-
−
 
+
|05:26
−
|05.26
+
|Let us plot ''' bode plot of 2 over 9 plus 2 s plus s square'''.
−
 
+
−
|Let us plot ''' bode plot of 2 over 9 plus 2 s plus s square'''
+
  
 
|-
 
|-
−
 
+
| 05:32
−
| 05.32
+
|Please note, command ''''f r e q'''' is a '''Scilab''' command for '''frequency response.'''
−
 
+
−
|Please note command ''''f r e q'''' is a '''Scilab''' command for '''frequency response.'''
+
  
 
|-
 
|-
−
 
+
| 05:39
−
| 05.39
+
| Do not use '''f r e q''' as a '''variable'''!!
−
 
+
−
| Do not use '''f r e q as a variable !!'''  
+
−
 
+
  
 
|-
 
|-
 +
| 05:44
 +
|Open the ''' Scilab console''' and type:
  
−
| 05.44
 
−
 
−
|Open the ''' Scilab console''' and type
 
 
|-
 
|-
−
 
+
| 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. '''
+
−
 
+
  
 
|-
 
|-
−
| 06.00
+
| 06:00
−
| Press '''Enter. '''
+
| Press '''Enter.'''
  
 
|-
 
|-
−
| 06.03
+
| 06:03
 
|The '''frequency''' is in '''Hertz.'''  
 
|The '''frequency''' is in '''Hertz.'''  
  
 
|-
 
|-
−
 
+
| 06:06
−
| 06.06
+
|Then type '''bode open parenthesis sys capital G comma fr close parenthesis'''.
−
 
+
−
|Then type '''bode open paranthesis sys capital G comma fr close paranthesis '''
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 06:15
−
| 06.15
+
| and press '''Enter.'''  
−
 
+
−
| and press ''Enter.'''  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 06:17
−
| 06.17
+
| The '''bode plot''' is shown.
−
 
+
−
| The '''bode plot''' is shown  
+
  
 
|-
 
|-
−
 
+
| 06:20
−
| 06.20
+
−
 
+
 
| Let us define another system.  
 
| Let us define another system.  
−
 
  
 
|-
 
|-
−
 
+
| 06:23
−
| 06.23
+
|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 '''
+
−
 
+
  
 
|-
 
|-
−
 
+
| 06:32
−
| 06.32
+
−
 
+
 
| Let us plot '''step response''' for this system.  
 
| Let us plot '''step response''' for this system.  
−
 
  
 
|-
 
|-
−
 
+
| 06:36
−
| 06.36
+
−
 
+
 
|Switch to '''Scilab console. '''
 
|Switch to '''Scilab console. '''
  
 
|-
 
|-
−
 
+
| 06:38
−
| 06.38
+
|Type this on your ''' console''':
−
 
+
−
|Type this on your ''' console.'''  
+
  
 
|-
 
|-
−
 
+
| 06:40
−
| 06.40
+
|''' p is equal to s square plus nine asterisk s plus nine'''
−
 
+
−
|''' p is equal to s square plus nine asterik s plus nine'''
+
  
 
|-
 
|-
−
 
+
| 06:47
−
| 06.47
+
|and then press ''' Enter.'''
−
 
+
−
|and then press ''' Enter. '''
+
  
 
|-
 
|-
−
 
+
| 06:49
−
| 06.49
+
|Then type this on your '''console''':
−
 
+
−
|Then type this on your ''' console.'''  
+
  
 
|-
 
|-
−
 
+
| 06:51
−
| 06.51
+
|'''sys two is equal to syslin open parenthesis open single quote c close single quote comma nine divided by p close parenthesis'''
−
 
+
−
|''' sys two is equal to syslin open paranthesis open single quote c close single quote comma nine divided by p close paranthesis '''
+
  
 
|-
 
|-
−
 
+
| 07:04
−
| 07.04
+
−
 
+
 
|and press ''' Enter.'''
 
|and press ''' Enter.'''
  
 
|-
 
|-
−
 
+
| 07:07
−
| 07.07
+
|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 '''
+
  
 
|-
 
|-
−
 
+
| 07:14
−
| 07.14
+
|Press '''Enter.'''  
−
 
+
−
|Press ''' Enter.'''  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 07:17
−
| 07.17
+
|''' y is equal to c sim open parenthesis open single quote step close single quote comma t comma sys two close parenthesis semicolon'''.
−
 
+
−
|''' y is equal to c sim open paranthesis open single quote step close single quote comma t comma sys two close the paranthesis semicolon'''
+
  
 
|-
 
|-
−
 
+
| 07:31
−
| 07.31
+
−
 
+
 
|Press '''Enter'''.
 
|Press '''Enter'''.
  
 
|-
 
|-
−
 
+
| 07:33
−
| 07.33
+
|Then type '''plot open parenthesis t comma y close parenthesis'''.
−
 
+
−
|Then type ''' plot open paranthesis t comma y close paranthesis'''
+
  
 
|-
 
|-
−
 
+
| 07:39
−
| 07.39
+
|Press '''Enter.'''
−
 
+
−
|Press ''' Enter.'''
+
  
 
|-
 
|-
−
 
+
| 07:41
−
| 07.41
+
|The '''response plot for over damped system is shown.'''  
−
 
+
−
|The ''' response plot for over damped system is shown.'''  
+
  
 
|-
 
|-
−
 
+
| 07:46
−
| 07.46
+
|To find the '''roots of p''' type this on your '''console - '''
−
 
+
−
|To find the ''' roots of p''' type this on your '''console - '''
+
  
 
|-
 
|-
−
 
+
| 07:49
−
| 07.49
+
|'''roots of p''' and press '''Enter.'''  
−
 
+
−
|''' Roots of p''' and press '''Enter.'''  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 07:54
−
| 07.54
+
|These '''roots''' are the poles of the system '''sys two'''.
−
 
+
−
|These '''roots''' are the poles of the system '''sys two'''
+
  
 
|-
 
|-
−
 
+
| 07:59
−
| 07.59
+
−
 
+
 
|The '''roots or poles''' of the system are shown.  
 
|The '''roots or poles''' of the system are shown.  
  
 
|-
 
|-
−
 
+
| 08:02
−
| 08.02
+
|Please plot '''Step response''' for this system along similar lines, as for '''over damped system.'''
−
 
+
−
|Please plot '''Step response''' for this system along similar lines, as for '''over damped system. '''
+
  
 
|-
 
|-
−
 
+
| 08:11
−
| 08.11
+
−
 
+
 
|'''G of s is equal to 2 over 9 plus 6 s plus s square''' which is a '''critically damped system'''
 
|'''G of s is equal to 2 over 9 plus 6 s plus s square''' which is a '''critically damped system'''
  
 
|-
 
|-
−
 
+
| 08:20
−
| 08.20
+
−
 
+
 
|Then '''G of s is equal to two over 9 plus s square''' which is an '''undamped system'''
 
|Then '''G of s is equal to two over 9 plus s square''' which is an '''undamped system'''
  
 
|-
 
|-
−
 
+
| 08:28
−
| 08.28
+
−
 
+
 
|'''G of s is equal to 2 over 9 minus 6 s plus s square''' which is an '''unstable system'''
 
|'''G of s is equal to 2 over 9 minus 6 s plus s square''' which is an '''unstable system'''
  
 
|-
 
|-
−
 
+
| 08:36
−
| 08.36
+
−
 
+
 
|Check '''response to sinusoidal inputs''' for all the cases and '''plot bode plot''' too.  
 
|Check '''response to sinusoidal inputs''' for all the cases and '''plot bode plot''' too.  
  
 
|-
 
|-
−
 
+
| 08:45
−
| 08.45
+
|Switch to ''' Scilab console.'''
−
 
+
−
|Switch to ''' Scilab console. ;'''
+
  
 
|-
 
|-
−
 
+
| 08:48
−
| 08.48
+
−
 
+
 
|For a general '''transfer function''', the numerator and denominator can be specified separately.
 
|For a general '''transfer function''', the numerator and denominator can be specified separately.
  
 
|-
 
|-
−
 
+
| 08:55
−
| 08.55
+
−
 
+
 
| Let me show you how.  
 
| Let me show you how.  
−
 
  
 
|-
 
|-
−
 
+
| 08:57
−
| 08.57
+
|Type on  '''console''':
−
 
+
−
|Type on  '''console'''
+
  
 
|-
 
|-
−
 
+
| 08:59
−
| 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'''.
−
 
+
−
|''' 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'''
+
  
 
|-
 
|-
−
 
+
| 09:19
−
| 09.19
+
|Press '''Enter'''.
−
 
+
−
|Press '''Enter'''  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 09:21
−
| 09.21
+
|Another way of defining a system is to type:
−
 
+
−
|Another way of defining a system, is to type  
+
  
 
|-
 
|-
−
 
+
| 09:24
−
| 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'''
−
 
+
−
|'''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'''
+
−
 
+
  
 
|-
 
|-
−
 
+
| 09:40
−
| 09.40
+
−
 
+
 
|Press '''Enter.'''
 
|Press '''Enter.'''
−
 
  
 
|-
 
|-
−
 
+
| 09:42
−
| 09.42
+
|Then type this on your '''console''':
−
 
+
−
|Then type this on your '''console'''
+
  
 
|-
 
|-
−
 
+
| 09:44
−
| 09.44
+
|'''sys four is equal to syslin open parenthesis open single quote c close single quote comma g close parenthesis'''.
−
 
+
−
|'''sys four is equal to syslin open paranthesis open single quote c close single quote comma g close paranthesis '''
+
  
 
|-
 
|-
−
 
+
| 09:55
−
| 09.55
+
−
 
+
 
|Press '''Enter.'''
 
|Press '''Enter.'''
  
 
|-
 
|-
−
 
+
| 09:58
−
| 09.58
+
−
 
+
 
|Both ways, we get the same output;  
 
|Both ways, we get the same output;  
−
 
  
 
|-
 
|-
−
 
+
| 10:01
−
| 10.01
+
|'''six plus s over 19 plus six s plus s square'''.
−
 
+
−
|'''six plus s over 19 plus six s plus s square '''
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:07
−
| 10.07
+
|The variable '''’sys’ is of type ’rational’.'''
−
 
+
−
|The variable '''’sys’ is of type ’rational’. '''
+
  
 
|-
 
|-
−
 
+
| 10:10
−
| 10.10
+
−
 
+
 
|Its numerator and denominator can be extracted by various ways.  
 
|Its numerator and denominator can be extracted by various ways.  
  
 
|-
 
|-
−
 
+
| 10:16
−
| 10.16
+
|'''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.  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:22
−
| 10.22
+
|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. '''
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:30
−
| 10.30
+
|The '''poles''' and '''zeros''' of the system can be plotted using '''p l z r''' function.  
−
 
+
−
|The poles and zeros of the system can be plotted using p l z r function.  
+
  
 
|-
 
|-
−
 
+
| 10:37
−
| 10.37
+
|The syntax is '''p l z r of sys'''.
−
 
+
−
|The syntax is p l z r of sys  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:41
−
| 10.41
+
|The '''plot''' shows 'x for poles' and 'circles for zeros'.  
−
 
+
−
|The plot shows x for poles and circles for zeros.  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:46
−
| 10.46
+
−
 
+
 
|Switch to Scilab console.
 
|Switch to Scilab console.
  
 
|-
 
|-
−
 
+
| 10:48
−
| 10.48
+
|Type this on your Scilab console:
−
 
+
−
|Type this on your Scilab console.
+
  
 
|-
 
|-
−
 
+
| 10:50
−
| 10.50
+
|'''sys three open parenthesis two close parenthesis'''.
−
 
+
−
|sys three open paranthesis two close paranthesis
+
−
 
+
  
 
|-
 
|-
−
 
+
| 10:55
−
| 10.55
+
|Press Enter.This gives the numerator of the rational function '''sys three''' that is '6 + s'.  
−
 
+
−
|Press Enter.
+
  
 
|-
 
|-
−
 
+
| 11:03
−
| 10.56
+
|Otherwise, you can type:
−
 
+
−
|This gives the numerator of the rational function 'sys three' that is 6 + s
+
−
 
+
  
 
|-
 
|-
−
 
+
| 11:05
−
| 11.03
+
|'''numer open parenthesis sys three close parenthesis'''.
−
 
+
−
|Otherwise, you can type
+
−
 
+
  
 
|-
 
|-
−
 
+
| 11:11
−
| 11.05
+
|Press Enter.
−
 
+
−
|numer open paranthesis sys three close paranthesis.
+
  
 
|-
 
|-
−
 
+
| 11:13
−
| 11.11
+
|The numerator of '''system three''' is shown.
−
 
+
−
|Press Enter
+
  
 
|-
 
|-
−
 
+
| 11:17
−
| 11.13
+
|To get the denominator, type:
−
 
+
−
|The numerator of system three is shown.
+
  
 
|-
 
|-
−
 
+
| 11:19
−
| 11.17
+
|'''sys three open parenthesis three close parenthesis'''. Press Enter.
−
 
+
−
|To get the denominator, type
+
  
 
|-
 
|-
−
 
+
| 11:26
−
| 11.19
+
−
 
+
−
|sys three open paranthesis three close paranthesis. Press Enter.
+
−
 
+
−
 
+
−
|-
+
−
 
+
−
| 11.26
+
−
 
+
 
|The denominator of the function is shown.  
 
|The denominator of the function is shown.  
  
 
|-
 
|-
−
 
+
| 11:30
−
| 11.30
+
|You can also type '''denom open parenthesis sys three close parenthesis'''.
−
 
+
−
|You can also type denom open paranthesis sys three close paranthesis.
+
  
 
|-
 
|-
−
 
+
| 11:36
−
| 11.36
+
−
 
+
 
|Press Enter.  
 
|Press Enter.  
−
 
  
 
|-
 
|-
−
 
+
| 11:38
−
| 11.38
+
|Then type '''p l z r open parenthesis sys three close parenthesis'''.
−
 
+
−
|Then type p l z r open paranthesis sys three close paranthesis.
+
  
 
|-
 
|-
−
 
+
| 11:44
−
| 11.44
+
−
 
+
 
|Press Enter.  
 
|Press Enter.  
  
 
|-
 
|-
−
 
+
| 11:47
−
| 11.47
+
|The output graph plots the '''poles''' and '''zeros'''.  
−
 
+
−
|The output graph plots the poles and zeros.  
+
  
 
|-
 
|-
−
 
+
| 11:50
−
| 11.50
+
|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.  
+
−
 
+
  
 
|-
 
|-
−
 
+
| 11:58
−
| 11.58
+
−
 
+
 
|It is plotted on the complex plane.  
 
|It is plotted on the complex plane.  
−
 
  
 
|-
 
|-
−
 
+
| 12:01
−
| 12.01
+
−
 
+
 
|In this tutorial, we have learnt how to:  
 
|In this tutorial, we have learnt how to:  
  
 
|-
 
|-
−
 
+
| 12:03
−
| 12.03
+
−
 
+
 
|Define a system by its transfer function.  
 
|Define a system by its transfer function.  
  
 
|-
 
|-
−
 
+
| 12:08
−
| 12.08
+
| Plot step and sinusoidal responses.  
−
 
+
−
|Plot step and sinusoidal responses.  
+
  
 
|-
 
|-
−
 
+
| 12:11
−
| 12.11
+
| Extract poles and zeros of a transfer function.  
−
 
+
−
|Extract poles and zeros of a transfer function.  
+
−
 
+
  
 
|-
 
|-
−
|12.15
+
|12:15
−
| Watch the video available at the following link
+
| Watch the video available at the following link.
  
 
|-
 
|-
−
 
+
| 12:19
−
| 12.19
+
| It summarizes the Spoken Tutorial project.
−
 
+
−
| It summarises the Spoken Tutorial project  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
|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  
+
  
 
|-
 
|-
−
 
+
|12:27
−
|12.27
+
||The spoken tutorial project Team:
−
 
+
−
||The spoken tutorial project Team
+
  
 
|-
 
|-
−
 
+
|12:29
−
|12.29
+
||Conducts workshops using spoken tutorials.
−
 
+
−
||Conducts workshops using spoken tutorials  
+
−
 
+
  
 
|-
 
|-
−
 
+
|12:32
−
|12.32
+
||Gives certificates to those who pass an online test.
−
 
+
−
||Gives certificates to those who pass an online test  
+
−
 
+
  
 
|-
 
|-
−
 
+
|12:36
−
|12.36
+
||For more details, please write to contact@spoken-tutorial.org.
−
 
+
−
||For more details, please write to contact@spoken-tutorial.org  
+
−
 
+
  
 
|-
 
|-
−
 
+
|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  
+
−
 
+
−
 
+
  
 
|-
 
|-
−
 
+
| 12:47
−
| 12.47
+
−
 
+
 
| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.  
 
|-
 
|-
−
 
+
| 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
+
  
 
|-
 
|-
−
 
+
| 13:06
−
| 13.06
+
|This is Ashwini Patil, signing off.
−
 
+
−
|This is Ashwini Patil signing off.
+
  
 
|-
 
|-
−
 
+
|13:08
−
|13.08
+
| Thank you for joining. Good Bye.
−
 
+
−
| Thank you for joining Good Bye.
+

Latest revision as of 11:04, 10 March 2017

Time Narration
00:01 Dear Friends, 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 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.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.

Contributors and Content Editors

Devraj, Gaurav, PoojaMoolya, Sandhya.np14

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