Scilab/C4/Discrete-systems/English-timed
From Script | Spoken-Tutorial
| 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. |
