Scilab/C4/Control-systems/English-timed
From Script | Spoken-Tutorial
| 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. |
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| 12:29 | Conducts workshops using spoken tutorials. |
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| 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. |
