Difference between revisions of "Scilab/C4/Discrete-systems/English-timed"
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| 00:02 | | 00:02 | ||
| − | | Welcome to the Spoken Tutorial on | + | | 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 | + | |I am using '''Ubuntu 12.04''' operating system and ''' Scilab 5.3.3''' for demonstration. |
| − | + | ||
|- | |- | ||
| 00:31 | | 00:31 | ||
| − | |To | + | |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 | + | | If not, please refer to the Scilab tutorials available on''' spoken-tutorial.org'''. |
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|01:05 | |01:05 | ||
| − | |for | + | |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. |
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|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.''' |
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|01:32 | |01:32 | ||
| − | |''' | + | |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'''. |
| − | + | ||
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| 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'''. |
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|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 | ||
| − | |||
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|02:09 | |02:09 | ||
| − | |'''Press enter''' | + | |'''Press enter'''. |
| − | + | ||
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|''' B is equal to open square bracket one semicolon two close the square bracket''' | |''' B is equal to open square bracket one semicolon two close the square bracket''' | ||
| − | |||
| − | |||
|- | |- | ||
|02:17 | |02:17 | ||
| − | |'''Press enter ''' | + | |'''Press enter '''. |
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|02:27 | |02:27 | ||
| − | |And '''Press enter''' | + | |And '''Press enter'''. |
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|02:33 | |02:33 | ||
| − | | '''Press Enter''' | + | | '''Press Enter'''. |
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|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 sys lin into brackets into quotes c comma A comma B comma C comma D close the 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'''. |
|- | |- | ||
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|- | |- | ||
|03:33 | |03:33 | ||
| − | |Type on your '''Scilab Console''' '''clc to clear it''' | + | |Type on your '''Scilab Console''' '''clc to clear it'''. |
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| 03:50 | | 03:50 | ||
| − | |''' | + | |Press '''Enter'''. |
| − | + | ||
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|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'''. |
|- | |- | ||
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| 04:01 | | 04:01 | ||
| − | |Use '''ss two tf''' function for '''sys three''' defined earlier | + | |Use '''ss two tf''' function for '''sys three''' defined earlier. |
| − | + | ||
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| 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'''. |
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|04:18 | |04:18 | ||
| − | ||Solve the following exercise | + | ||Solve the following exercise. |
| − | + | ||
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|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. |
|- | |- | ||
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| 04:26 | | 04:26 | ||
| − | |Use ''' t f two s s''' command | + | |Use ''' t f two s s''' command. |
| − | + | ||
| − | + | ||
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|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. | ||
| − | |||
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| 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''', |
|- | |- | ||
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|We now define a ''' discrete time system.''' | |We now define a ''' discrete time system.''' | ||
| − | |||
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|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.''' | ||
| − | |||
|- | |- | ||
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| 05:07 | | 05:07 | ||
| − | |Recall that the variable ''' ’z’''' has a shortcut | + | |Recall that the variable ''' ’z’''' has a shortcut. |
|- | |- | ||
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|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''' | ||
| − | |||
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|Go to '''Scilab console.''' | |Go to '''Scilab console.''' | ||
| − | |||
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|05:23 | |05:23 | ||
| − | |Type '''clc to clear''' | + | |Type '''clc to clear'''. |
|- | |- | ||
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| 05:29 | | 05:29 | ||
| − | | And '''press enter''' | + | | And '''press enter'''. |
| − | + | ||
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| 05:31 | | 05:31 | ||
| − | |We now define a first order discrete time system | + | |We now define a first order discrete time system. |
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| 05:35 | | 05:35 | ||
| − | |On the ''' Scilab Console''' type | + | |On the ''' Scilab Console''' type: |
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|- | |- | ||
| 05:59 | | 05:59 | ||
| − | |''' Press enter''' | + | |''' Press enter'''. |
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| 06:02 | | 06:02 | ||
| − | |We use the ''' ’syslin’ '''function for this | + | |We use the ''' ’syslin’ '''function for this. |
| − | + | ||
| − | + | ||
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| 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.''' | ||
| − | |||
| − | |||
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| 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,''' | ||
| − | |||
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| 06:22 | | 06:22 | ||
| − | | Type on the ''' Scilab Console''' | + | | Type on the ''' Scilab Console''': |
| − | + | ||
|- | |- | ||
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|''' 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''' | ||
| − | |||
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| 06:36 | | 06:36 | ||
| − | |And '''Press enter''' | + | |And '''Press enter'''. |
| − | + | ||
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| 06:48 | | 06:48 | ||
| − | |'''clc to clear the console''' | + | |'''clc to clear the console'''. |
|- | |- | ||
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| 07:02 | | 07:02 | ||
| − | |And ''' Press enter''' | + | |And ''' Press enter'''. |
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| 07:05 | | 07:05 | ||
| − | |Now type ''' plot of y and press Enter ''' | + | |Now type ''' plot of y and press Enter '''. |
| − | + | ||
| − | + | ||
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| 07:14 | | 07:14 | ||
| − | |Close the graphic window | + | |Close the graphic window. |
| − | + | ||
|- | |- | ||
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|'''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 ''' | ||
| − | |||
| − | |||
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| 08:04 | | 08:04 | ||
| − | |On the ''' | + | |On the '''Console''' type''' clc to clear''' and then type: |
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| 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'''. |
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| 08:25 | | 08:25 | ||
| − | |''' | + | |Press '''Enter''' to continue display. |
|- | |- | ||
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| 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'''. |
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| 08:44 | | 08:44 | ||
| − | |We can convert this to a '''transfer function representation in discrete time''' using ''' s s to t f''' function | + | |We can convert this to a '''transfer function representation in discrete time''' using ''' s s to t f''' function. |
| − | + | ||
| − | + | ||
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| 08:58 | | 08:58 | ||
| − | |''' | + | | 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'''. |
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| In this tutorial we have learnt to: | | In this tutorial we have learnt to: | ||
| − | |||
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|'''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. |
|- | |- | ||
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| 09:39 | | 09:39 | ||
| − | | It | + | | It summarizes the Spoken Tutorial project. |
| − | + | ||
| − | + | ||
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|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. |
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|09:47 | |09:47 | ||
| − | ||The spoken tutorial project Team | + | ||The spoken tutorial project Team: |
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||Conducts workshops using spoken tutorials | ||Conducts workshops using spoken tutorials | ||
| − | |||
|- | |- | ||
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|09:52 | |09:52 | ||
| − | ||Gives certificates to those who pass an online test | + | ||Gives certificates to those who pass an online test. |
| − | + | ||
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||For more information, please write to contact@spoken-tutorial.org | ||For more information, please write to contact@spoken-tutorial.org | ||
| − | |||
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|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. |
| − | + | ||
| − | + | ||
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| 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. |
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| 10:27 | | 10:27 | ||
| − | |This is Anuradha Amruthkar from IIT Bombay signing off. | + | |This is Anuradha Amruthkar from IIT Bombay, signing off. |
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| Line 639: | Line 586: | ||
|10:31 | |10:31 | ||
| − | | Thank you for joining Good Bye. | + | | Thank you for joining. Good Bye. |
Revision as of 16:20, 3 March 2015
| Time | Narration |
| 00:01 | Dear Friends, |
| 00:02 | 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 the 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 sys lin into brackets into quotes c comma A comma B comma C comma D close the 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 the 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 the 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 to 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. |
