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| − | | Welcome to the spoken tutorial on ''' “Advanced Control of Continuous Time systems” ''' | + | | Welcome to the spoken tutorial on ''' “Advanced Control of Continuous Time systems” '''| |
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Revision as of 10:23, 9 June 2014
| Time | Narration |
| 00.01 | Dear Friends, |
| 00.02 | |
| 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 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. |
| 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 paranthesis zero comma open single quote s close single quote close paranthesis , 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 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 | 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 paranthesis open single quote step close single quote comma t comma sys capital G close the paranthesis semicolon |
| 03.15 | Press Enter.
|
| 03.17 | Then type plot open paranthesis t comma y one close paranthesis 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 paranthesis t close paranthesis semicolon |
| 03.59 | Press Enter.
|
| 04.01 | 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 | 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 paranthesis t comma open square bracket u two semicolon y two close square bracket close paranthesis
|
| 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 paranthesis sys capital G comma fr close paranthesis
|
| 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 asterik 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 paranthesis open single quote c close single quote comma nine divided by p close paranthesis |
| 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 paranthesis open single quote step close single quote comma t comma sys two close the paranthesis semicolon |
| 07.31 | Press Enter. |
| 07.33 | Then type plot open paranthesis t comma y close paranthesis |
| 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 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 | Press Enter
|
| 09.21 | Another way of defining a system, is to type |
| 09.24 | 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 | Press Enter.
|
| 09.42 | Then type this on your console |
| 09.44 | sys four is equal to syslin open paranthesis open single quote c close single quote comma g close paranthesis |
| 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 paranthesis two close paranthesis
|
| 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 paranthesis sys three close paranthesis. |
| 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 paranthesis three close paranthesis. Press Enter.
|
| 11.26 | The denominator of the function is shown. |
| 11.30 | You can also type denom open paranthesis sys three close paranthesis. |
| 11.36 | Press Enter.
|
| 11.38 | Then type p l z r open paranthesis sys three close paranthesis. |
| 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 summarises 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. |
