Scilab/C4/Discrete-systems/English-timed

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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.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14