Scilab Notes and ETC, Slides of Mathematics

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Introduction to Scilab

application to feedback control

Yassine Ariba

Brno University of Technology - April 2014

Sommaire

1 Introduction

2 Basics

3 Matrices

4 Plotting

5 Programming

6 For MATLAB users

7 Xcos

8 Application to feedback control

9 Classical control design

Introduction What is Scilab?

What is Scilab?

Scilab is the contraction of Scientific Laboratory. Scilab is :

a numerical computing software,

an interpreted programming environment,

used for any scientific and engineering applications,

multi-platform : Windows, MacOS et Linux,

Created by researchers from

Inria in the 90’s, the software

is now developed by Scilab

Entreprises

www.scilab.org

Introduction What is Scilab?

Scilab includes hundreds of functions for various applications

Mathematics and simulation

2D and 3D visualization

Optimization

Statistics

Control system design and analysis

Signal processing

Application development

More informations : www.scilab.org

Introduction Getting started

Getting started

Firstly, Scilab can be used in an interactive way by typing instructions on

the console.

type scilab code on the prompt -->

type enter, to execute it.

Scilab return its answer on the console or in a new window for graphics.

Introduction Getting started

A first simple example :

--> A = 2;

--> t = [0:0.01:10]; --> y = A * sin (3* t ); --> plot (t , y );

Line 1 : assign the value 2 to the variable A.

Line 2 : define a vector t that goes from 0 to 10 with a step of 0.01.

Line 3 : compute a vector y from some mathematical operations.

Line 4 : plot y with respect to t on a 2D graphic.

Note that “ ; ” prevents from printing the result of an instruction.

Introduction Getting started

A second simple example :

Let consider a system of linear equations

2 x 1 + x 2 = − 5

4 x 1 − 3 x 2 + 2x 3 = 0

x 1 + 2x 2 − x 3 = 1

Let solve it with Scilab

--> A = [2 1 0 ; 4 -3 2 ; 1 2 -1];

--> b = [ -5;0;1]; --> x = inv ( A )* b x =

Introduction Getting started

Scilab provides a graphical environment with several windows.

the console

command history

file browser

variable browser

and others : editor, graphics, help, ...

Basics Elementary operations

Elementary operations

Simple numerical calculations :

ans =

--> 4^2/ ans =

--> 2(1+2 %i ) ans =

2. • 4. i

--> %i ^ ans =

--> cos (3)^2 + sin (3)^ ans =

--> exp (5) ans =

--> abs (1+ %i ) ans =

Basics Elementary operations

elementary operations

+ addition

• subtraction

* multiplication

/ right division

\ left division

ˆ exponents

elementary functions

sin cos tan cotg

asin acos atan sec

sinh cosh tanh csc

abs real imag conj

exp log log10 log

sign modulo sqrt lcm

round floor ceil gcd

--> conj (3+2* %i ) ans =

3. • 2. i

--> log10 (10^4) ans =

Basics Variables

Variables

A variable can be directly defined via the assignment operator : “ = ”

--> a = 2.5; --> b = 3; --> c = a * b c =

--> c + d ! - - error 4 Undefined variable : d

Variable names may be defined with letters a → z, A → Z, numbers 0

→ 9 and few additional characters %, , !, #, ?, $.

Scilab is case sensitive.

Do not confused the assignment operator “ = ” with the mathematical

equal.

Variable declaration is implicit, whatever the type.

Basics Variables

Pre-defined variables

%i imaginary number i =

%e Euler’s number e

%pi constant π

%inf infinity ∞

%t ou %T boolean true

%f ou %F boolean false

--> cos (2* %pi ) ans =

--> %i ^ ans =

Matrices Defining and handling vectors

Defining and handling vectors

A vector is defined by a list of numbers between brackets :

--> u = [0 1 2 3] u =

Automatic creation

--> v = [0:0.2:1] v =

1. 0.2 0.4 0.6 0.8 1.

Syntax : start:step:end

Mathematical functions are applied element-wise

--> cos ( v ) ans =

1. 0.980 0.921 0.825 0.696 0.

Matrices Defining and handling vectors

column vectors can also be defined with semi colon separator “ ; ”

--> u = [1;2;3] u =

Some useful functions :

length return the length of the vector

max return the maximal component

min return the minimal component

mean return the mean value

sum return the sum of all components

prod return the product of all components

--> length ( v ) ans =

--> mean ( v ) ans =