introduction to scilab 5.3 and xcos - university of cassino

Introduction to Scilab 5.3 and Xcos

Gianluca Antonelli

Universita degli Studi di [email protected]

http://webuser.unicas.it/lai/roboticahttp://www.docente.unicas.it/gianluca antonelli

Gianluca Antonelli Scilab 5.3

http://webuser.unicas.it/lai/robotica

http://www.docente.unicas.it/gianluca_antonelli

License

Copyright (c) 2011 GIANLUCA ANTONELLI.Permission is granted to copy, distribute and/or modify this documentunder the terms of the GNU Free Documentation License, Version 1.2 orany later version published by the Free Software Foundation; with noInvariant Sections, no Front-Cover Texts, and no Back-Cover Texts.A copy of the license is available at www.gnu.org


Introduction

The open source platform for numerical computation

Available at http://www.scilab.org


The others

Matlab

Octave

Freemat

Scicoslab

. . .


Running Scilab

From Linux or Windows just selecting the application from theGraphical Menu

From Linux also from the shell typing ./scilab from the correct path


Scilab command line

Scilab command line is denoted with the symbol

-->

It accepts variables declaration, expressions, script and function calls

Scilab scripts and functions are ASCII files

To re-use a previous command type the up arrow ↑


Help

help opens a new window where browse for commands and searchkeywords

help name fun opens the help window directly at the pagecorresponding to the function name fun

An on-line help is available http://www.scilab.org/product/man/

A comparison between Matlab/Scilab function inhttp://www.scilab.org/product/dic-mat-sci/M2SCI doc.htm


Variables

A variable can be defined simply with the syntax

-->name = instruction;

The ; symbol prevents to print on screen the results

Standard rules common to languages as C or Pascal apply for Scilabvariables

Names are case sensitive: a 6=A

To see the variable value just type its name on the prompt or use thetool browsevar()


Workspace

Variables and functions stay in the workspace

commands of general use are

who

who_user

clear

load

save

diary

browsevar()


Variable types

A specific set of operators is available for the corresponding type

Common types are

constant , polynomial , function , handle ,

string , boolean , list , rational ,

state -space , sparse , boolean sparse

The type of a variable can be obtained

typeof(variable_name)


Write protected variables

Certain variables are predefined and write-protected%i i =

√−1 immaginary unit

%pi π = 3.1415927 . . . pi grek%e e = 2.718281 . . . number of Nepero%eps ε = 2.2 · 10−16 precision (machine dependent)%inf infinity%nan NotANumber%s s polynomial variable%z z polynomial variable%t true boolean variable%f false boolean variable


Matrices

To insert a matrix the syntaxes are

-->A = [1, 2, 3; 4, 5, 6; 7, 8, 9];

-->A = [1, 2, 3

-->4 5 6

-->7,8,9]

A =

1. 2. 3.

4. 5. 6.

7. 8. 9.


Scalars and vectors

Scalars and vectors are matrices!

-->a=[1 3 5];

-->size(a)

ans =

1. 3.

-->b=3;size(b)

ans =

1. 1.


Incremental vectors

-->x=1:4

x =

1. 2. 3. 4.

-->x=1:2:10

x =

1. 3. 5. 7. 9.

Also available linspace(x0,xf,npti) and logspace(...)


Accessing matrix elements

A(i,j) access the element in row i and column j

A(2,4:6) select the columns from 4 to 6 of the second row

B=A(1:3,4:6) assign to B the selected submatrix

A(:,5) select the column 5

A([1 3],5) select a 1x2 vector of two elements: A(1,5) and A(3,5)


Matrix operations

A wide number of operations are available, in addition to the basicoperations such as sum, product, transpose, matrix esponential,inverse, rank, kernel, etc.

A library of operations are available under the Linear Algebra sectionof the help

Some operations are also defined to be performed on the singleelements of the matrix


Polynomial operations

Defining a variable as polynomial allows to access several specificoperations

-->my_pol = 3*%s^2 + 2*%s

my_pol =

2

2s + 3s

-->roots(my_pol)

ans =

0

- 0.6666667


Polynomial operations

Define a polynomial from the coefficient: poly

Define a polynomial from its expression (previous example)

Define a polynomial by operations on elementary polynomials

Extract the coefficients of a polynomial: coeff

Evaluate the polynomial in one single point: horner

Symbolic substitution of the polynomial variable with another


Rational operations

Rational functions are the division between two polynomials

Several commands defined to their use similar to the polynomial type


Script

It is a collection of commands saved in a single ASCII file whoseextension is conventionally .sce

It is executed typing

-->exec(’file_name.sce’);


Functions

A function is a piece of code returning an output given several inputswhose syntax is

function [y1 ,...,ym] = fun(x1 ,...,xn)

commands

endfunction

Several functions can be saved in a single ASCII file whose extensionis conventionally .sci


Functions

User-defined functions are not available until not explicitely called bygetf(’name file.sci’)

Loading, saving or clearing the variables causes Scilab to do the sameto the functions!

Functions see all the workspace

Inputs are passed by reference if the function does not change theirvalue otherwise by copy


Programming

Common programming constructions

for, end

while, end

if, then, else, end

select, case, else, end

Logical operators: & | ˜

& and| or˜ not


Load/Save data

Data in the workspace can be saved in a binary file:save(’name file’)

Data previously saved can be loaded in the workspace:load(’name file’)

C and Fortran-like commands are available to save formatted data inASCII files

Data saved with older version of Matlab can also be loaded


Graphics

Graphics commands are executed on windows different from the mainone (the Scilex window)

To create a new graphic window

xset(’window ’,num)

scf(num)

General windows-related commands are

clf(num), xclear(num),

xselect(), xdel(num)


Plot2d

The command plot2d draws bidimentional curves

It uses the current graphic window superimposing the curves

It creates a new graphic window if none is open

Several drawing possibilities depending on the syntax

plot2d ([x],y,<opt_args >)


Plot2d

plot2d(x,y) where x and y are vectors of the same size draws a curvewith x data in the horizontal and y data in vertical axes

plot2d(y) where y is a vector assumes x=1:n

plot2d(x,y) where x is a vector and y is a matrix assumes the samehorizontal data for the columns of y

plot2d(x,y) where x and y are matrices draws each column of yversus the corresponding column of x


Plot2d

Let us draw a sinusoidal signal with ω = 5 and phase φ = π/4 for twoperiods

-->w=5;f=%pi/4;tf=(4*%pi -%pi/4)/w;

-->t=linspace(0,tf ,100);plot2d(t,sin(w*t+f))

Refer to the syntax to change colors, add symbols, add labels, title,etc.


Understanding a graphic window

The graphic window is an object containing several childs: figure,axis, curves

In the previous example the relationship is given by

Figure (1)

- Axes(1)

- Compund(1)

- Polyline(1)


Modyfing the graphic properties

A GUI opens with the command xset() that allows to change thegraphic context

From the graphic window it is possible to browse the properties of theobjects under the menu [edit]

From a script/function it is possible to have an handle to an objectand modyfing its parameters

h=gcf()

h=gca()

h=gce()


More axes on the same figure

The subplot(ijk) command divides the figure in a matrix of i rowsand j columns and select the k element

subplot(211); plot2d(ya)

subplot(212); plot2d(yb)


Exporting your figure

Several commands exist to export your figure such as

xs2eps , xs2fig , xs2gif ,

xs2ppm , xs2ps

and, only for Windows,

xs2bmp , xs2emf


Dynamic Systems

A powerful tool to the numerical study of

Input-Output dynamic systemsInput-State-Output dynamic systemsFeedback analysisFeedback control design


Transfer function

-->s=%s;

-->num=1+s;den=(s+2)*(s+3);

-->P=syslin(’c’,num ,den)

P =

1 + s

---------

2

6 + 5s + s

-->typeof(P)

ans =

rational


Transfer function

-->z=%z;

-->Pd=syslin(’d’,1,z-0.5)

Pd =

1

-------

- 0.5 + z

-->typeof(Pd)

ans =

rational


State space representation

-->A = [-5 -1

--> 6 0];

-->B = [-1; 1];

-->C = [-1 0];

-->D =0;

-->Sss = syslin(’c’,A,B,C,D)



Sss =

Sss(1) (state -space system :)

!lss A B C D X0 dt !

Sss(2) = A matrix =

- 5. - 1.

6. 0.

Sss(3) = B matrix =

- 1.

1.



Sss(4) = C matrix =

- 1. 0.

Sss(5) = D matrix =

0.

Sss(6) = X0 (initial state) =

0.

0.

Sss(7) = Time domain =

c

-->typeof(Sss)

ans =

state -space


Conversion ss to/from tf

Conversions are always possible

tf2ss

ss2tf

Conversions are subtles, refer to dynamic systems textbooks

Affected by round-off errors

See minss, minreal


Extract information from tf

The tf is a rational and all the corresponding functions can be applied:

-->out = roots(P.den)

out =

- 2.

- 3.


Extract information from ss

Extract, e.g., the dynamic matrix

Sss.A

Extract all matrices

[A,B,C,D]=abcd(Sss);


Smart view of ss systems

-->ssprint(Sss)

. |-5 -1 | |-1 |

x = | 6 0 |x + | 1 |u

y = |-1 0 |x


Pole-zero map - continuous time

plzr(P);sgrid


Pole-zero map - discrete time

plzr(P);zgrid


Root locus

The basic command is evans(Stf)


Root locus

Default points useless! use evans(Stf,kmax)


Root locus design

The basic operation needed to design with the root locus tool is tocalculate the value of k that corresponds to a certain point in thelocus:

-->k=-1/real(horner(Stf ,[1,%i]*locate (1)))

locate returns the coordinates of a point in the graphic selected withthe mousehorner computes a rational or polynomial in a given point


Nichols

black(); chart()


Nichols

The curve is parametrized according to a constant range(!)

Continuous time: [10−3, 103] HzDiscrete time: [10−3, 0.5]

Better to use the whole syntax assigning frequency range:

black(sl , [fmin ,fmax] [,step] [,comments])


Bode

bode(); gainplot()

Same considerations done for the Nichols diagram

Better to use:

bode(sl, [fmin ,fmax] [,step] [,comments])


Nyquist

nyquist(); m circle()

Same considerations done for the Nichols and Bode diagrams

Better to use:

nyquist(sl, [fmin ,fmax] [,step] [,comments])


Horner & Phasemag

horner() evaluates a polynomial/rational in a point

Evaluate F (jω) (in dB and deg) with ω = 5

-->F=syslin(’c’,1,%s+2);

-->out=horner(F,5*%i)

out =

0.0689655 - 0.1724138i

-->[phi ,db]=phasemag(out)

db =

- 14.62398

phi =

- 68.198591


A final bird’s-eye view

Stability margins (g margin, p margin)

Continuous-discrete time conversion (cls2dls)

Simple numerical simulation of dynamics systems

Numerical resolution of differential equations (ode)

Observability, controllability, Kalman filter

Controller design commands


Xcos

Graphical dynamic system simulator

Library of blocks

Continuous/discrete time systemsAdd custom blocks in C/Fortran/ScilabGenerate C codeReal-time HIL testsHard real-time executable


How it looks like


Run Xcos

Within the Scilab environment

From the command prompt --> xcos

Menu -> Applications -> Xcos


Continuous time on a PC?

Xcos emulates continuous-time dynamic systems via numericalalgorithms (see discretization on textbooks)

Conceptually similar to the differential vs difference equations

In alternative Xcos executes blocks when an activation input is given

Activation signals are used also for discrete-time systems


What is a block?

A graphical function with (eventual)

InputStateOutputScalar/vectorial quantitiesContinuous/discrete timeActivation inputsActivation outputs


What is a superblock?

Is a block containing other blocks

Same concept as functions inside other functionsImprove readability of the diagram


Palettes

A library of blocks


A basic diagram

Drag-and-drop a source. . . a transfer function and a scope


A basic diagram

the whole diagram


A basic diagram

Select all the parameters


A basic diagram

Run!


Blocks’ parameters

Avoid the use of constants in the blocks’ parameters

Use variables instead:

put all the variables in a file (var.sce)open Diagram -> Context and write exec(’var.sce’)

use the variables in the blocks

In alternative global variables


Importing data

From proper blocks

Reading from binary or formatted files

From the workspace


Exporting data

To graphic windows (scope. . . )

To binary or formatted files

To the workspace

Specific graphic output for matrices


Beyond the simple diagram

The Debug block

Creation of custom blocks

Use of C functions

Generation of code C from a Xcos diagram

Batch simulation of diagrams


introduction to scilab 5.3 and xcos - university of cassino

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