Scilab/C4/Control-systems/Gujarati

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 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.
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 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.
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.
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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.

Contributors and Content Editors

Jyotisolanki