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

|Dear Friends,  

| Welcome to the spoken tutorial on ''' Advanced Control of Continuous Time systems'''.

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

|* Define a continuous time system: second and higher order

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

|* Do a '''Bode plot'''  

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

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

|To record this tutorial, I am using

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

|'''Scilab 5.3.3''' version.

| Before practicing 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.'''

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

 

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

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

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

|The output is''' 's'.'''

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

|On the '''console''' window, type:  

| '''s equal to percentage s''', press '''Enter.'''  

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

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

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

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

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

| Press '''Enter'''.

||The output is linear second order system represented by

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

| Then, type '''t equal to zero colon zero point one colon ten semicolon'''  

| Press '''Enter.'''  

|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'''  

|Press '''Enter.'''

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

|Press '''Enter.'''

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

|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.'''  

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

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

| Press '''Enter.'''

|Then type: '''y two is equal to c sim open parenthesis 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.  

|Then type: '''plot open parenthesis t comma open square bracket u two semicolon y two close square bracket close parenthesis'''.

|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. '''

|'''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.  

|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'''!!  

|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.'''  

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

| and press '''Enter.'''  

| The '''bode plot''' is shown.  

| 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 '''Scilab console. '''

|Type this on your ''' console''':

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

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

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

|and press ''' Enter.'''

|Then type: '''t equal to zero colon zero point one colon ten semicolon '''

|Press '''Enter.'''  

|''' y is equal to c sim open parenthesis open single quote step close single quote comma t comma sys two close parenthesis semicolon'''.

|Press '''Enter'''.

|Then type '''plot open parenthesis t comma y close parenthesis'''.

|Press '''Enter.'''

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

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

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

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

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

|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 ''' Scilab console.'''

 

|For a general '''transfer function''', the numerator and denominator can be specified separately.

| Let me show you how.  

|Type on  '''console''':

|''' 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'''.

|Press '''Enter'''.  

|Another way of defining a system is to type:  

|'''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'''

|Press '''Enter.'''

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

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

|Press '''Enter.'''

|Both ways, we get the same output;

|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.'''

|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 console.

|Type this on your Scilab console:  

|'''sys three open parenthesis two close parenthesis'''.  

|Press Enter.

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

|Otherwise, you can type:  

|'''numer open parenthesis sys three close parenthesis'''.

|Press Enter.

|The numerator of '''system three''' is shown.  

|To get the denominator, type:  

|'''sys three open parenthesis three close parenthesis'''. Press Enter.  

|The denominator of the function is shown.  

|You can also type '''denom open parenthesis sys three close parenthesis'''.

|Press Enter.  

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

|Press Enter.  

|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.  

|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.  

| Watch the video available at the following link.

| It summarizes the Spoken Tutorial project.  

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

||The spoken tutorial project Team:

||Conducts workshops using spoken tutorials.  

||Gives certificates to those who pass an online test.

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

|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.  

|More information on this mission is available at spoken-tutorial.org/NMEICT-Intro.

|This is Ashwini Patil, signing off.

| Thank you for joining. Good Bye.