Lavitha Pereira: Created page with ''''Title of script''': Discrete Time System '''Author: Manas, Aditya, Shamika''' '''Keywords: State space, Discrete time''' {| style="border-spacing:0;" ! Visual Cue<…'

2013-07-15T09:41:00Z

Created page with ''''Title of script''': Discrete Time System '''Author: Manas, Aditya, Shamika''' '''Keywords: State space, Discrete time''' {| style="border-spacing:0;" ! <center>Visual Cue<…'

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'''Title of script''': Discrete Time System

'''Author: Manas, Aditya, Shamika'''

'''Keywords: State space, Discrete time'''

{| style="border-spacing:0;"
! <center>Visual Cue</center>
! <center>Narration</center>

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 1
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| Dear Friends,

Welcome to the Spoken Tutorial on “'''Discrete Time System'''”

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 2-Learning Objectives
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| At the end of this tutorial, we will learn how to:

* Convert between '''state space and transfer function''' descriptions
* Define a '''discrete time system and plot its step response '''
* '''Discretize a continuous time system '''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 3- System Requirement slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * I am using '''Ubuntu 12.04''' operating system with '''Scilab 5.3.3''' for demonstation

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 4- Prerequisite slide
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * To practise this tutorial, you should have basic knowledge of '''Scilab.'''
* If not, please refer to the Scilab tutorials available on the '''Spoken Tutorial '''website.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 5- State Space Model

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The '''state space model'''
* '''x dot is equal to A x plus B u'''
* '''y is equal to c x plus D u'''
* is specified by '''sys three is equal to syslin into bracket into quotes c comma A comma B comma C comma D close bracket'''
* for prespecified '''matrices A, B, C and D''' of suitable sizes.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab and type this on your Scilab Console

'''sys3=syslin(’c’,4,3,6,9) Press''' '''Enter'''

'''Press Enter again'''

'''clc'''

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Start '''Scilab''' on your computer
* 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. Press enter to continue the display. '''
* This is an example for s'''ingle state, Single Input Single Output'''
* The output will have matrices '''A, B, C and D and initial state x zero'''
* Type''' clc '''to clear the '''console'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 6- State Space Model

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Define for example matrices '''A, B, C, D '''on '''Scilab console '''as you see

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab and''' type this on your Scilab Console'''

'''A <nowiki>=</nowiki> <nowiki>[2</nowiki> 3;4 5]'''

'''Press enter'''

'''B <nowiki>=</nowiki> <nowiki>[1;2]</nowiki>'''

'''Press enter'''

'''C <nowiki>=</nowiki> <nowiki>[-3</nowiki> -6]'''

'''Press enter'''

'''D <nowiki>=</nowiki> 2'''

'''Press Enter'''

'''sys4=syslin('c',A,B,C,D)'''

'''Press enter'''

'''Press enter again'''

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type this on your '''Scilab Console'''
* '''A is equal to open square bracket two space three semicolon four space five close square bracket '''
* '''Press enter'''
* '''B is equal to open square bracket one semicolon two close square bracket '''
* '''Press enter'''
* '''C is equal to open square bracket minus three space minus six close square bracket '''
* '''Press enter'''
* '''D is equal to two'''
* '''Press enter'''
* Let us substitute these matrices in the previous command
* '''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'''
* You will get the following output.
* Press enter to continue display.
* The output will have''' matrices A B C D and initial state x zero '''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 7- State Space Model
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Check whether '''poles''' of '''sys4''' are same as''' eigenvalues '''of '''A '''.
* For this you can use the function '''p l z r function''' and the '''spec function'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 8- State Space Model

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The '''s s two t f''' command can be used to obtain a '''transfer function of a state-space system''' '''sys S S'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Switch to Scilab and type on your Scilab Console

'''clc'''

'''sysTF <nowiki>=</nowiki> ss2tf(sys4)'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* '''clc to clear it'''
* '''Type sys capital T capital F is equal to s s two t f open bracket sys four close bracket '''
* '''Press enter'''
* You see this output

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 8- State Space Model
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * It is in the form''' sys TF equal to ss two tf into bracket sys of SS'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 9- State Space Model
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Use '''ss two tf '''function for '''sys three''' defined earlier
* '''sys T F '''is a new variable for which ''''denom' command '''is applicable and not applicable to''' sys four '''as it is in''' state space form'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 10, 11, 12- Exercise
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Solve the following exercise
* Find a '''state space realization''' of the '''second order transfer function''' defined below
* Use''' t f two s s''' command
* 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.
* Use the '''A, B, C, D matrices''' of the '''system''' '''sys S S '''to obtain the '''transfer function''' and check if the answer is the original one.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 13, 14- Discrete Time System

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We now define a '''discrete time system'''.
* It is customary to use ’'''z'''’ for the variable in the '''numerator and denominator polynomials.'''
* Recall that the variable ’'''z'''’ has a shortcut
* Instead of '''z is equal to poly into bracket zero comma inside quotes z ''': use''' z is equal to percentage z'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on your Scilab Console

'''clc'''

'''z=%z'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Go to '''Scilab console'''.
* Type '''clc to clear '''
* Type '''z is equal to percentage z. '''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 15- Discrete Time System
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We now define a first order discrete time system

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on your Scilab Console

'''DTSystem <nowiki>=</nowiki> syslin(’d’, z/(z – 0.5))'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* '''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 . '''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 15- Discrete Time System
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * We use the same ’'''syslin'''’ function as before.
* This time, we specify the '''domain to be discrete time, '''instead of''' continuous time.'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 16- Discrete Time System

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * For checking the '''step response''', we have to define the '''input '''explicitly as '''ones''', for example, for '''50 points'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type this on your Scilab Console

'''u <nowiki>=</nowiki> ones(1, 50);'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* u''' is equal to ones open bracket one comma fifty close bracket semicolon'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 16- Discrete Time System

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Instead of '''csim''', the function we have to use the ’'''flts'''’ function to '''simulate this system'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type this on your Scilab Console

'''clc'''

'''y <nowiki>=</nowiki> flts(u, DTSystem);'''

Press '''Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type this on your '''Scilab Console'''
* '''clc to clear console'''
* '''y is equal to f l t s open bracket u comma D T System close bracket semi colon'''
* '''Press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on your Scilab Console

'''plot(y)'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* '''plot of y and then press Enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Display output
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The output will be plotted.
* Close the graphic window

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 17- Discrete Time System

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * It is helpful to '''discretize''' a given '''continuous time system'''.
* This is done using the '''dscr''' '''function'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on Scilab Console

'''s=%s'''

'''sysG=syslin('c', 2/(s^2+2*s+9))'''

'''Press enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us define a continuous system '''s is equal to percent s'''
* '''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'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 18- Discrete Time System
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Let us '''discretize the system''' '''sys''' '''G''' with a '''sampling period of zero point one'''.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on your scilab console

'''clc'''

'''sys5=dscr(sysG, 0.1)'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* '''clc to clear '''
* s'''ys five is equal to d s c r into bracket capital sys G comma zero point one close bracket and then press''' '''Enter'''
* '''Press enter to continue display'''
* As you see''' system is discretized as A B C D matrices and inital state x zero'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 19- Discrete Time System

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Notice that we obtain the '''discretized system in state space representation'''.
* We can convert this to a '''transfer function representation in discrete time''' using the '''s s to t f''' function

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Type on your Scilab Console

'''clc'''

'''sys6 <nowiki>=</nowiki> ss2tf(sys5, 0.1)'''

'''Press Enter'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Type on your '''Scilab Console'''
* '''clc and clear it'''
* '''sys six is equal to s s two t f into bracket sys five comma''' '''zero point one close the brackets and press enter'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Display output
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * The output gives the transfer function.

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| Slide 20- Summary
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| In this tutorial we have learnt to:

* Convert between '''state space and transfer function descriptions'''
* Define a '''discrete time system and plot its step response'''
* '''Discretize a continuous time system.'''

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 21'''

'''Title: About the Spoken Tutorial Project'''

* Watch the video available at [http://spoken-tutorial.org/What_is_a_Spoken_Tutorial http://spoken-tutorial.org/What_is_a_Spoken_Tutorial]

* It summarises the Spoken Tutorial project

* If you do not have good bandwidth, you can download and watch it

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Watch the video available at the following link
* It summarises the Spoken Tutorial project
* If you do not have good bandwidth, you can download and watch it <br/>

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 22'''

'''Title: Spoken Tutorial Workshops'''

The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact@spoken-tutorial.org

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| The Spoken Tutorial Project Team

* Conducts workshops using spoken tutorials

* Gives certificates for those who pass an online test

* For more details, please write to contact at spoken hyphen tutorial dot org

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''Show Slide 23'''

'''Title: Acknowledgement'''

* Spoken Tutorial Project is a part of the Talk to a Teacher project

* It is supported by the National Mission on Education through ICT, MHRD, Government of India

* More information on this Mission is available at

* [http://spoken-tutorial.org/NMEICT-Intro http://spoken-tutorial.org/NMEICT-Intro]

| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| * Spoken Tutorial Project is a part of the Talk to a Teacher project
* It is supported by the National Mission on Education through ICT, MHRD, Government of India
* More information on this Mission is available at
* spoken hyphen tutorial dot org slash NMEICT hyphen Intro

|-
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:none;padding:0.097cm;"| '''On previous slide'''
| style="border-top:none;border-bottom:1pt solid #000000;border-left:1pt solid #000000;border-right:1pt solid #000000;padding:0.097cm;"| This is Anuradha Amrutkar from IITB signing off. Thanks for joining. Thank you.

|}

Scilab/C4/Discrete-systems/English - Revision history

Lavitha Pereira: Created page with ''''Title of script''': Discrete Time System '''Author: Manas, Aditya, Shamika''' '''Keywords: State space, Discrete time''' {| style="border-spacing:0;" ! Visual Cue<…'