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

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|Dear Friends,  

|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” '''|

|-

|-

| At the end of this tutorial, you will learn how to

| At the end of this tutorial, you will learn how to

|-

|-

|Define a continuous time system: second and higher order  

|Define a continuous time system: second and higher order  

|-

|-

|Plot response to '''step''' and sine inputs  

|Plot response to '''step''' and sine inputs  

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|-

|Do a '''Bode plot'''  

|Do a '''Bode plot'''  

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|-

|Study '''numer''' and ''' denom Scilab functions'''  

|Study '''numer''' and ''' denom Scilab functions'''  

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|-

|Plot ''' poles''' and '''zeros''' of a system  

|Plot ''' poles''' and '''zeros''' of a system  

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|-

| To record this tutorial, I am using  

| To record this tutorial, I am using  

|-

|-

|'''Ubuntu 12.04'''  as the operating system with

|'''Ubuntu 12.04'''  as the operating system with

|-

|-

|'''Scilab 5.3.3''' version  

|'''Scilab 5.3.3''' version  

|-

|-

| Before practising this tutorial, a learner should have basic knowledge of '''Scilab''' and '''control systems.'''   

| 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.'''  

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

|-

|-

|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.'''  

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|-

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

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

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|-

|Let us switch to the ''' Scilab console window. '''

|Let us switch to the ''' Scilab console window. '''

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|-

|Here type ''' s equal to poly open paranthesis zero comma open single quote s close single quote close paranthesis''' , press '''Enter.'''  

|Here type ''' s equal to poly open paranthesis zero comma open single quote s close single quote close paranthesis''' , press '''Enter.'''  

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|-

|The output is  ''' 's'. '''   

|The output is  ''' 's'. '''   

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|-

|There is another way to define ''' 's' ''' as '''continuous time complex variable. '''

|There is another way to define ''' 's' ''' as '''continuous time complex variable. '''

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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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|-

|Let us study the ''' syslin Scilab command.'''  

|Let us study the ''' syslin Scilab command.'''  

   

   

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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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|-

|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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|-

|Let us switch to the '''Scilab console''' window.  

|Let us switch to the '''Scilab console''' window.  

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|-

||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 '''

||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 '''

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|-

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

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

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|-

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

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

   

   

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|-

| 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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|-

| Press '''Enter.'''  

| Press '''Enter.'''  

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|-

|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 paranthesis open single quote step close single quote comma t comma sys capital G close the paranthesis semicolon'''  

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|-

|Press '''Enter. '''

|Press '''Enter. '''

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|-

|Then type ''' plot open paranthesis t comma y one close paranthesis semicolon'''  

|Then type ''' plot open paranthesis t comma y one close paranthesis semicolon'''  

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|-

|Press ''' Enter.'''

|Press ''' Enter.'''

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|-

|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.'''

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|-

|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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|-

|''' 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.'''  

|-

|-

|Let us switch to the '''Scilab console''' window.

|Let us switch to the '''Scilab console''' window.

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|-

|| Type ''' U two is equal to sine open paranthesis t close paranthesis semicolon'''  

|| Type ''' U two is equal to sine open paranthesis t close paranthesis semicolon'''  

|-

|-

| Press ''' Enter. '''

| 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 '''

|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'''

| 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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|-

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

|'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.  

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

|-

|-

|'Press '''Enter.'''  

|'Press '''Enter.'''  

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|-

| 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. '''

|-

|-

|'''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.  

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|-

|As expected, the output is also a ''' sine wave,''' and  

|As expected, the output is also a ''' sine wave,''' and  

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|-

|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.  

|-

|-

|This is a typical '''under-damped''' example.  

|This is a typical '''under-damped''' example.  

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|-

|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'''

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|-

|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.'''

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|-

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

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

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|-

|Open the ''' Scilab console''' and type  

|Open the ''' Scilab console''' and type  

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|-

|''' 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. '''

|-

|-

| Press '''Enter. '''

| Press '''Enter. '''

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|-

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

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

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|-

|Then type '''bode open paranthesis sys capital G comma fr close paranthesis '''

|Then type '''bode open paranthesis sys capital G comma fr close paranthesis '''

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|-

| and press ''Enter.'''  

| and press ''Enter.'''  

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|-

| The '''bode plot''' is shown  

| The '''bode plot''' is shown  

|-

|-

| 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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|-

|Switch to '''Scilab console. '''

|Switch to '''Scilab console. '''

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|-

|Type this on your ''' console.'''  

|Type this on your ''' console.'''  

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|-

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

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

|-

|-

|and then press ''' Enter. '''

|and then press ''' Enter. '''

|-

|-

|Then type this on your ''' console.'''  

|Then type this on your ''' console.'''  

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|-

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

|''' 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.'''

|and press ''' Enter.'''

|-

|-

|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 '''

|-

|-

|Press ''' Enter.'''  

|Press ''' Enter.'''  

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|-

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

|-

|-

|Press '''Enter'''.

|Press '''Enter'''.

|-

|-

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

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

|-

|-

|Press ''' Enter.'''

|Press ''' Enter.'''

|-

|-

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

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

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|-

|To find the ''' roots of p'''  type this on your '''console - '''

|To find the ''' roots of p'''  type this on your '''console - '''

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|-

|''' Roots of p''' and press '''Enter.'''  

|''' Roots of p''' and press '''Enter.'''  

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|-

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

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

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|-

|The '''roots or poles''' of the system are shown.  

|The '''roots or poles''' of the system are shown.  

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|-

|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. '''

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|-

|'''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'''

|-

|-

|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'''

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|-

|'''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'''

|-

|-

|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.  

|-

|-

|Switch to ''' Scilab console. ;'''

|Switch to ''' Scilab console. ;'''

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|-

|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.

|-

|-

| Let me show you how.  

| Let me show you how.  

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|-

|Type on  '''console'''

|Type on  '''console'''

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|-

|''' 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'''

|''' 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'''  

|Press '''Enter'''  

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|-

|Another way of defining a system, is to type  

|Another way of defining a system, is to type  

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|-

|'''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'''

|'''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.'''

|Press '''Enter.'''

|-

|-

|Then type this on your '''console'''

|Then type this on your '''console'''

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|-

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

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

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|-

|Press '''Enter.'''

|Press '''Enter.'''

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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 '''

|-

|-

|The variable '''’sys’ is of type ’rational’. '''

|The variable '''’sys’ is of type ’rational’. '''

|-

|-

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

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

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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. '''

|-

|-

|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.  

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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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|-

|Switch to Scilab console.

|Switch to Scilab console.

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|-

|Type this on your Scilab console.  

|Type this on your Scilab console.  

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|-

|sys three open paranthesis two close paranthesis  

|sys three open paranthesis two close paranthesis  

|-

|-

|Press Enter.

|Press Enter.

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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  

|-

|-

|Otherwise, you can type  

|Otherwise, you can type  

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|-

|numer open paranthesis sys three close paranthesis.

|numer open paranthesis sys three close paranthesis.

|-

|-

|Press Enter

|Press Enter

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|-

|The numerator of system three is shown.  

|The numerator of system three is shown.  

|-

|-

|To get the denominator, type  

|To get the denominator, type  

|-

|-

|sys three open paranthesis three close paranthesis. Press Enter.  

|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.

|You can also type denom open paranthesis sys three close paranthesis.

|-

|-

|Press Enter.  

|Press Enter.  

|-

|-

|Then type p l z r open paranthesis sys three close paranthesis.

|Then type p l z r open paranthesis sys three close paranthesis.

|-

|-

|Press Enter.  

|Press Enter.  

|-

|-

|The output graph plots the poles and zeros.  

|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.  

|It is plotted on the complex plane.  

|-

|-

|In this tutorial, we have learnt how to:  

|In this tutorial, we have learnt how to:  

|-

|-

|Define a system by its transfer function.  

|Define a system by its transfer function.  

|-

|-

|Plot step and sinusoidal responses.  

|Plot step and sinusoidal responses.  

|-

|-

|Extract poles and zeros of a transfer function.  

|Extract poles and zeros of a transfer function.  

|-

|-

| Watch the video available at the following link

| Watch the video available at the following link

|-

|-

| It summarises the Spoken Tutorial project  

| It summarises the Spoken Tutorial project  

|-

|-

||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  

|-

|-

||The spoken tutorial project Team

||The spoken tutorial project Team

|-

|-

||Conducts workshops using spoken tutorials  

||Conducts workshops using spoken tutorials  

|-

|-

||Gives certificates to those who pass an online test  

||Gives certificates to those who pass an online test  

|-

|-

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

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

|-

|-

|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  

|-

|-

| 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.  

|-

|-

|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

|-

|-

|This is Ashwini Patil signing off.

|This is Ashwini Patil signing off.

|-

|-

| Thank you for joining Good Bye.

| Thank you for joining Good Bye.