Scilab/C4/Discrete-systems/English-timed
From Script | Spoken-Tutorial
| 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
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| 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 demonstation
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| 00:31 | To practise 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 prespecified 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
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| 01:40 | The output will have matrices A, B, C and D and initial state x zero
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| 01:49 | Type clc to clear the console |
| 01:52 | Define for example matrices A, B, C, D on Scilab console as you see
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| 02:00 | A is equal to open square bracket two space three semicolon four space five close square bracket |
| 02:09 | Press enter
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| 02:11 | B is equal to open square bracket one semicolon two close the square bracket
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| 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
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| 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
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| 02:57 | You will get the following output.
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| 03:00 | Press enter to continue the display.
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| 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
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| 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
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| 04:20 | Find a state space realization of the second order transfer function defined below |
| 04:26 | Use t f two s s command
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| 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.
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| 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.
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| 05:00 | It is customary to use ’z’ for the variable in the numerator and denominator polynomials.
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| 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
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| 05:21 | Go to Scilab console.
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| 05:23 | Type clc to clear |
| 05:26 | Type z is equal to percentage z. |
| 05:29 | And press enter
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| 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
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| 06:05 | This time, we specify the domain to be discrete time, instead of continuous time.
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| 06:13 | For checking the step response, we have to define the input explicitly as ones,
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| 06:19 | for example, for 50 points. |
| 06:22 | Type on the Scilab Console
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| 06:25 | u is equal to ones into bracket one comma fifty close the bracket put a semicolon
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| 06:36 | And Press enter
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| 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
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| 07:11 | The output will be plotted. |
| 07:14 | Close the graphic window
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| 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
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| 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
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| 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 summarises 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
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| 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. |
