Difference between revisions of "Scilab/C4/Discrete-systems/English-timed"

Latest revision as of 10:57, 10 March 2017

Time	Narration
00:01	Dear Friends, Welcome to the Spoken Tutorial on Discrete Time System.
00:07	In this tutorial, we will learn to:
00:09	Convert between state space and transfer function descriptions
00:14	Define a discrete time system and plot its step response
00:20	Discretize a continuous time system.
00:23	I am using Ubuntu 12.04 operating system and Scilab 5.3.3 for demonstration.
00:31	To practice this tutorial, you should have basic knowledge of Scilab.
00:36	If not, please refer to the Scilab tutorials, available on spoken-tutorial.org.
00:44	state space model:
00:46	x dot is equal to A x plus B u
00:49	y is equal to c x plus D u
00:52	is specified by sys three is equal to syslin into bracket into quotes c comma A comma B comma C comma D close bracket.
01:05	For pre-specified matrices A, B, C and D of suitable sizes.
01:11	Start Scilab on your computer.
01:15	Type: sys three is equal to syslin into bracket into quotes c comma four comma three comma six comma nine close bracket and press Enter.
01:32	Press Enter to continue the display.
01:35	This is an example for single state, single input single output.
01:40	The output will have matrices A, B, C and D and initial state x zero.
01:49	Type clc to clear the console.
01:52	Define, for example, matrices A, B, C, D on Scilab console as you see
02:00	A is equal to open square bracket two space three semicolon four space five close square bracket,
02:09	press Enter.
02:11	B is equal to open square bracket one semicolon two close square bracket,
02:17	press Enter.
02:19	C is equal to open square bracket minus three space minus six close the square bracket
02:27	and press Enter.
02:30	D is equal to two,
02:33	press Enter.
02:35	Let us substitute these matrices in the previous command:
02:39	sys four is equal to syslin into brackets into quotes c comma A comma B comma C comma D close bracket and press Enter
02:57	You will get the following output.
03:00	Press Enter to continue the display.
03:03	The output will have matrices A, B, C, D and initial state x zero, as you see.
03:11	Check whether poles of sys4 are same as eigenvalues of 'A'.
03:17	For this, you can use p l z r function and the spec function.
03:23	The s s two t f command can be used to obtain a transfer function of a state-space system sys S S.
03:33	Type on your Scilab Console "clc" to clear it.
03:37	And then type: sys capital 'T' capital 'F' is equal to s s two t f into bracket sys four close bracket and
03:50	press Enter.
03:52	You see this output.
03:54	It is in the form sys TF equal to ss two tf into bracket sys of SS.
04:01	Use ss two tf function for sys three defined earlier.
04:07	sys T F is a new variable for which 'denom' command is applicable.
04:12	It is not applicable to sys four, as it is in state space form.
04:18	Solve the following exercise.
04:20	Find a state space realization of the second order transfer function defined below.
04:26	Use t f two s s command.
04:30	For the new system in state space form, say sys S S, check if the eigenvalues of the matrix A and the poles of the transfer function G of s are the same.
04:43	Use the A, B, C, D matrices of the system sys S S to obtain the transfer function,
04:53	check if the answer is the original one.
04:56	We now define a discrete time system.
05:00	It is customary to use ’z’ for the variable in the numerator and denominator polynomials.
05:07	Recall that the variable ’z’ has a shortcut.
05:11	Instead of z is equal to poly into bracket zero comma inside quotes z use z is equal to percentage z.
05:21	Go to Scilab console.
05:23	Type "clc" to clear.
05:26	Type: z is equal to percentage z
05:29	and press Enter.
05:31	We now define a first order discrete time system.
05:35	On the Scilab Console, type:
05:39	D T System is equal to syslin into bracket into quotes small d comma z divided by inside bracket z minus zero point five close the bracket close outer bracket.
05:59	Press Enter.
06:02	We use the syslin function for this.
06:05	This time, we specify the domain to be discrete time instead of continuous time.
06:13	For checking the step response, we have to define the input explicitly as ones.
06:19	for example: for 50 points,
06:22	type on the Scilab Console:
06:25	u is equal to ones into bracket one comma fifty close the bracket put a semicolon
06:36	and press Enter.
06:38	Instead of csim, we have to use the flts function to simulate this system.
06:45	Type on the Scilab Console:
06:48	"clc" to clear the console.
06:51	y is equal to f l t s into bracket u comma D T System close bracket put a semi colon
07:02	and press Enter.
07:05	Now, type: plot of y and press Enter.
07:11	The output will be plotted.
07:14	Close the graphic window.
07:17	It is helpful to discretize a given continuous time system.
07:21	This is done using the dscr function.
07:25	Let us define a continuous system s is equal to percent s and
07:32	sys G is equal to syslin into bracket into quotes c comma two divided by into bracket s square plus two multiplied by s plus nine close bracket close outer bracket and press Enter.
07:56	Let us discretize the system sys G with a sampling period of zero point one.
08:04	On the Console, type "clc" to clear and then type:
08:08	sys five is equal to d s c r into bracket sys G comma zero point one close the bracket and then press Enter.
08:25	Press Enter to continue display.
08:28	As you see, system is discretized as A, B, C, D matrices and inital state x zero.
08:38	Notice that we obtain the discretized system in the state space representation.
08:44	We can convert this to a transfer function representation in discrete time using s s two t f function.
08:54	For this, go to the Scilab Console Window.
08:58	Type "clc" and clear it.
09:01	Now, type: sys six is equal to s s two t f into bracket sys five comma zero point one close the brackets and press Enter.
09:18	The output gives the transfer function.
09:22	In this tutorial, we have learnt to:
09:24	Convert between state space and transfer function descriptions
09:28	Define a discrete time system and plot its step response
09:33	Discretize a continuous time system.
09:36	Watch the video available at the following link.
09:39	It summarizes the Spoken Tutorial project.
09:43	If you do not have good bandwidth, you can download and watch it.
09:47	The spoken tutorial project team:
09:49	Conducts workshops using spoken tutorials.
09:52	Gives certificates to those who pass an online test.
09:56	For more information, please write to: contact@spoken-tutorial.org
10:04	Spoken Tutorial project is a part of the Talk to a Teacher project.
10:08	It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
10:15	More information on this mission is available at: spoken-tutorial.org/NMEICT-Intro.
10:27	This is Anuradha Amruthkar from IIT Bombay, signing off.
10:31	Thank you for joining. Good Bye.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14

Difference between revisions of "Scilab/C4/Discrete-systems/English-timed"

Latest revision as of 10:57, 10 March 2017

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@@ Line 7: / Line 7: @@
 |-
 | 00:01
-|Dear Friends,
+|Dear Friends,  Welcome to the Spoken Tutorial on '''Discrete Time System'''.
-|-
-| 00:02
-| Welcome to the Spoken Tutorial on '''Discrete Time System'''.
 |-
@@ Line 19: / Line 15: @@
 |-
 |00:09
-|* Convert between '''state space''' and '''transfer function''' descriptions
+| Convert between '''state space''' and '''transfer function''' descriptions
 |-
 |00:14
-|* Define a '''discrete time system''' and plot its '''step response'''
+| Define a '''discrete time system''' and plot its '''step response'''
 |-
 | 00:20
-|* Discretize a continuous time system.
+| Discretize a continuous time system.
 |-
@@ Line 66: / Line 62: @@
 |-
 |01:15
 |Type: '''sys three is equal to syslin into bracket into quotes c comma four comma three comma six comma nine close bracket''' and press '''Enter.'''
 |-
 |01:32
 |Press '''Enter''' to continue the display.
 |-
 |01:35
 |This is an example for '''single state, single input single output'''.
 |-
 | 01:40
 |The output will have matrices  A, B, C and D and '''initial state x zero'''.
 |-
 | 01:49
 |Type '''clc ''' to clear the '''console'''.
 |-
 |01:52
 |Define, for example, matrices  A, B, C, D on '''Scilab console''' as you see
@@ Line 104: / Line 90: @@
 |-
 |02:09
 |press '''Enter'''.
 |-
 |02:11
 |''' B is equal to open square bracket one semicolon two close square bracket''',
@@ Line 120: / Line 102: @@
 |-
 | 02:19
 |''' C is equal to open square bracket minus three space minus six close the square bracket'''
 |-
 |02:27
 |and press '''Enter'''.
 |-
 |02:30
 | '''D is equal to two''',
 |-
 |02:33
 | press '''Enter'''.
 |-
 | 02:35
 |Let us substitute these matrices in the previous command:
@@ Line 181: / Line 154: @@
 |-
 | 03:37
 |And then type: '''sys''' capital 'T' capital 'F' is equal to s s two t f into bracket sys four close bracket ''' and
 |-
 | 03:50
 |press '''Enter'''.
 |-
 |03:52
 |You see this output.
 |-
 | 03:54
 | It is in the form '''sys TF equal to ss two tf into bracket sys of SS'''.
 |-
 | 04:01
 |Use '''ss two tf''' function for '''sys three''' defined earlier.
 |-
 | 04:07
+| '''sys T F''' is a new variable for which''' 'denom' command''' is applicable.
-| '''sys T F''' is a new variable for which''' 'denom' command''' is applicable.
 |-
 | 04:12
 | It is not applicable to '''sys four''', as it is in '''state space form'''.
 |-
 |04:18
 ||Solve the following exercise.
 |-
 |04:20
 |Find a '''state space realization''' of the '''second order transfer function''' defined below.
 |-
 | 04:26
 |Use '''t f two s s''' command.
 |-
 | 04:30
 |For the new system in '''state space form''', say '''sys S S''', check if the eigenvalues of the matrix A and the '''poles''' of the '''transfer function G of s''' are the same.
 |-
 | 04:43
 |Use the A, B, C, D matrices of the '''system sys S S ''' to obtain the ''' transfer function''',
 |-
 | 04:53
+|check if the answer is the original one.
-|check if the answer is the original one.
 |-
 | 04:56
 |We now define a '''discrete time system.'''
 |-
 | 05:00
 |It is customary to use ’z’ for the variable in the numerator and denominator polynomials.
 |-
 | 05:07
 |Recall that the variable ’z’ has a shortcut.
 |-
 | 05:11
 |Instead of '''z is equal to poly into bracket zero comma inside quotes z''' use '''z is equal to percentage z'''.
 |-
 | 05:21
 |Go to '''Scilab console.'''
 |-
 |05:23
 |Type "clc" to clear.
 |-
 | 05:26
 |Type: '''z is equal to percentage z'''
 |-
 | 05:29
 | and press '''Enter'''.
 |-
 | 05:31
 |We now define a '''first order discrete time system'''.
 |-
 | 05:35
 |On the '''Scilab Console''', type:
@@ Line 321: / Line 252: @@
 |-
 | 06:02
 |We use the '''syslin''' function for this.
 |-
 | 06:05
 | This time, we specify the '''domain''' to be '''discrete time''' instead of '''continuous time.'''
 |-
 | 06:13
 | For checking the '''step response,''' we have to define the '''input''' explicitly as '''ones'''.
 |-
 | 06:19
 |for example: for '''50 points''',
 |-
 | 06:22
 | type on the '''Scilab Console''':
 |-
 | 06:25
 |'''u is equal to ones into bracket one comma fifty close the bracket put a semicolon'''
 |-
 | 06:36
 |and press '''Enter'''.
 |-
 | 06:38
 |Instead of '''csim,'''  we have to use the '''flts''' function to '''simulate''' this system.
 |-
 | 06:45
 |Type on the '''Scilab Console''':
 |-
 | 06:48
 |"clc" to clear the '''console'''.
 |-
 | 06:51
 |''' y is equal to f l t s into bracket u comma D T System close bracket put a semi colon'''
 |-
 | 07:02
 |and press '''Enter'''.
 |-
 | 07:05
 |Now, type: '''plot of y''' and  press '''Enter'''.
 |-
 | 07:11
 |The output will be plotted.
 |-
 | 07:14
 |Close the '''graphic window'''.
 |-
 | 07:17
 |It is helpful to '''discretize''' a given '''continuous time system.'''
 |-
 | 07:21
 |This is done using the '''dscr''' function.
 |-
 | 07:25
 |Let us define a continuous system '''s is equal to percent s''' and
 |-
 | 07:32
 |'''sys G is equal to syslin into bracket into quotes c comma two divided by into bracket s square plus two multiplied by s plus nine close bracket close outer bracket''' and press '''Enter'''.
 |-
 | 07:56
 |Let us '''discretize''' the system '''sys G''' with a '''sampling period''' of zero point one.
 |-
 | 08:04
 |On the '''Console''', type "clc" to clear and then type:
 |-
 | 08:08
 |'''sys five is equal to d s c r into bracket sys G comma zero point one close the bracket''' and then press '''Enter'''.
 |-
 | 08:25
 |Press '''Enter''' to continue display.
 |-
 | 08:28
+|As you see, system is discretized as A, B, C, D matrices and '''inital state x zero'''.
-|As you see, system is discretized as A, B, C, D matrices and '''inital state x zero'''.
 |-
 | 08:38
+|Notice that we obtain the '''discretized system''' in the '''state space representation.'''
-|Notice that we obtain the '''discretized system''' in the '''state space representation.'''
 |-
 | 08:44
 |We can convert this to a '''transfer function representation''' in '''discrete time''' using ''' s s two t f''' function.
 |-
 | 08:54
 |For this, go to the '''Scilab Console Window'''.
 |-
 | 08:58
+| Type "clc" and clear it.
-| Type "clc" and clear it.
 |-
 | 09:01
 |Now, type: '''sys six is equal to s s two t f into bracket sys five comma zero point one close the brackets''' and press '''Enter'''.
 |-
 | 09:18
+|The output gives the '''transfer function'''.
-|The output gives the '''transfer function'''.
 |-
 | 09:22
 | In this tutorial, we have learnt to:
 |-
 | 09:24
+| Convert between '''state space''' and '''transfer function''' descriptions
-|* Convert between '''state space''' and '''transfer function''' descriptions
 |-
 | 09:28
+| Define a ''' discrete time system''' and plot its '''step response'''
-|* Define a ''' discrete time system''' and plot its '''step response'''
 |-
 | 09:33
+| '''Discretize''' a continuous time system.
-|* '''Discretize''' a continuous time system.
 |-
@@ Line 524: / Line 390: @@
 |-
 | 09:39
 | It summarizes the Spoken Tutorial project.
 |-
 |09:43
 ||If you do not have good bandwidth, you can download and watch it.
 |-
 |09:47
 ||The spoken tutorial project team:
 |-
 |09:49
+||Conducts workshops using spoken tutorials.
-||* Conducts workshops using spoken tutorials.
 |-
 |09:52
+|| Gives certificates to those who pass an online test.
-||* Gives certificates to those who pass an online test.
 |-
 |09:56
+||For more information, please write to: contact@spoken-tutorial.org
-||For more information, please write to:
-contact@spoken-tutorial.org
 |-
 |10:04
 |'''Spoken Tutorial''' project is a part of the '''Talk to a Teacher''' project.
 |-
 | 10:08
+| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
-| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
 |-
 | 10:15
+|More information on this mission is available at: spoken-tutorial.org/NMEICT-Intro.
-|More information on this mission is available at:
-spoken-tutorial.org/NMEICT-Intro.
 |-
 | 10:27
 |This is Anuradha Amruthkar from IIT Bombay, signing off.
 |-
 |10:31
 | Thank you for joining. Good Bye.