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 demonstation
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
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 the 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 sys lin into brackets into quotes c comma A comma B comma C comma D close the 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 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
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 the 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 to 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 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
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