Difference between revisions of "Scilab/C4/Discrete-systems/English-timed"
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Sandhya.np14 (Talk | contribs) |
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| 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. |
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| 03:11 | | 03:11 | ||
| − | |Check whether '''poles''' of ''' sys4''' are same as '''eigenvalues''' of '' | + | |Check whether '''poles''' of ''' sys4''' are same as '''eigenvalues''' of 'A'. |
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| 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''' | + | |Type on your '''Scilab Console''' "clc" to clear it. |
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| 03:37 | | 03:37 | ||
| − | |And then type: '''sys''' capital | + | |And then type: '''sys''' capital 'T' capital 'F' is equal to s s two t f into bracket sys four close bracket ''' and |
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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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| 04:43 | | 04:43 | ||
| − | |Use the | + | |Use the A, B, C, D matrices of the '''system sys S S ''' to obtain the ''' transfer function''', |
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| 05:00 | | 05:00 | ||
| − | |It is customary to use ’z’ for the variable in the | + | |It is customary to use ’z’ for the variable in the numerator and denominator polynomials. |
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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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|05:23 | |05:23 | ||
| − | |Type | + | |Type "clc" to clear. |
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| 05:26 | | 05:26 | ||
| − | |Type '''z is equal to percentage z | + | |Type: '''z is equal to percentage z''' |
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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 | + | |On the '''Scilab Console''', type: |
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| 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.''' |
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| 06:45 | | 06:45 | ||
| − | |Type on the '''Scilab Console''' | + | |Type on the '''Scilab Console''': |
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| 06:48 | | 06:48 | ||
| − | | | + | |"clc" to clear the '''console'''. |
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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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| 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. |
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| 08:04 | | 08:04 | ||
| − | |On the '''Console''', type | + | |On the '''Console''', type "clc" to clear and then type: |
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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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| 08:38 | | 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.''' |
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| 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 two t f''' function. |
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| 08:54 | | 08:54 | ||
| − | |For this go to the '''Scilab Console Window''' | + | |For this, go to the '''Scilab Console Window'''. |
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| 08:58 | | 08:58 | ||
| − | | Type | + | | Type "clc" and clear it. |
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| 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'''. |
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| 09:22 | | 09:22 | ||
| − | | In this tutorial we have learnt to: | + | | In this tutorial, we have learnt to: |
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| 09:24 | | 09:24 | ||
| − | |* Convert between '''state space and transfer function | + | |* Convert between '''state space''' and '''transfer function''' descriptions |
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| 09:28 | | 09:28 | ||
| − | |* Define a ''' discrete time system and plot its step response''' | + | |* Define a ''' discrete time system''' and plot its '''step response''' |
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| − | |* '''Discretize a continuous time system. | + | |* '''Discretize''' a continuous time system. |
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|09:47 | |09:47 | ||
| − | ||The spoken tutorial project | + | ||The spoken tutorial project team: |
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|09:49 | |09:49 | ||
| − | ||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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|09:56 | |09:56 | ||
| − | ||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 | + | |'''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. | ||
|- | |- | ||
Revision as of 15:38, 9 February 2016
| 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 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. |
