Difference between revisions of "Scilab/C4/Discrete-systems/English-timed"

|Dear Friends,  

 

| Welcome to the Spoken Tutorial on '''Discrete Time System'''.

| In this Tutorial we will learn to:

|Convert between '''state space and transfer function''' descriptions   

|Define a '''discrete time system and plot its step response '''

| ''' Discretize a continuous time system'''.  

|I am using '''Ubuntu 12.04''' operating system and ''' Scilab 5.3.3''' for demonstration.  

|To practice this tutorial, you should have basic knowledge of ''' Scilab.'''

| If not, please refer to the Scilab tutorials available on''' spoken-tutorial.org'''.  

| ''' state space model'''

| 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 pre-specified ''' matrices A, B, C and D''' of suitable sizes.  

| 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.'''  

|This is an example for '''single state, Single Input Single Output'''.

 

|The output will have matrices  ''' A, B, C and D and initial state x zero'''.

 

|Define for example matrices ''' A, B, C, D''' on '''Scilab console''' as you see  

|''' 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 the square bracket'''  

|'''Press enter '''.

 

|And '''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'''

| Press enter to continue the display.   

|The output will have ''' matrices A B C D and initial state x zero ''' as you see.

|Check whether '''poles''' of ''' sys4''' are same as '''eigenvalues''' of '''A .'''

|For this you can use '''p l z r function''' and the '''spec function'''.  

|The ''' s s two t f''' command can be used to obtain a '''transfer function of a state-space system sys S S. '''

|Type on your '''Scilab Console''' '''clc to clear it'''.

 

|And then ''' type sys capital T capital F is equal to s s two t f into bracket sys four close the  bracket ''' and  

|Press '''Enter'''.

| It is in the form ''' sys TF equal to ss two tf into bracket sys of SS'''.

 

| It is not applicable to '''sys four''' as it is in '''state space form'''.  

 

|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''',   

 

|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'''

 

|Type '''clc to clear'''.  

 

|Type ''' z is equal to percentage z.'''  

 

| And '''press enter'''.

 

|We now define a first order discrete time system.  

 

|On the ''' Scilab Console''' type:

| ''' 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'''.

 

|We use the ''' ’syslin’ '''function for this.

 

| This time, we specify the ''' domain to be discrete time,''' instead of '''continuous time.'''

 

| For checking the ''' step response,''' we have to define the '''input''' explicitly as '''ones,'''  

 

|for example, for '''50 points.'''  

 

| Type on the ''' Scilab Console''':

 

|''' u is equal to ones into bracket one comma fifty close the bracket put a semicolon'''

 

|And '''Press enter'''.

 

|Instead of '''csim,'''  we have to use the '''’flts’''' function to '''simulate this system.'''  

 

|Type on the '''Scilab Console '''

 

|'''clc to clear the console'''.

 

|''' y is equal to f l t s into bracket u comma D T System close the bracket put a semi colon'''

 

|And ''' Press enter'''.

 

|Now type ''' plot of y and  press Enter '''.

 

|Close the graphic window.  

 

|This is done using the '''dscr function.'''  

 

|Let us define a continuous system ''' s is equal to percent s''' and

 

|'''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 '''

 

|Let us '''discretize the system sys G''' with a '''sampling period of zero point one.'''

 

|On the '''Console''' type''' clc to clear''' and then type:

 

|We can convert this to a '''transfer function representation in discrete time''' using ''' s s to t f''' function.  

 

|For this go to the ''' Scilab Console Window'''

 

|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'''.

 

| 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.'''

 

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