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Revision as of 11:39, 24 July 2014

Time Narration
00:01 Dear Friends,
00:02 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 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.

Contributors and Content Editors

Devraj, Gaurav, PoojaMoolya, Sandhya.np14