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

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.

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Gaurav, PoojaMoolya, Sandhya.np14