Scilab/C4/Discrete-systems/English-timed

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