Control & Computing group Department of Electrical ...belur/scilab/virtual_labs_basic.pdf ·...

Scilab: basic/matrix operations

Dr. Madhu N. Belur

Control & Computing groupDepartment of Electrical Engineering

Indian Institute of Technology BombayEmail: belur@ee.iitb.ac.in

Outline Vectors/matrices Plotting if-then-else-end and for-end Polynomials Other useful commands

Outline

1 Vectors/matrices

2 Plotting

3 if-then-else-end and for-end loops

4 Polynomials

5 Other useful commands

Madhu Belur, CC group, EE, IITB Scilab/Linear Algebra

Today’s focus

Scilab is free.

Matrix/loops syntax is same as for Matlab.

Scilab provides all basic and many advanced tools.

Signal processing, Control systems, block-diagram-simulation(xcos), Electrical, networks, op-amps, device simulation, ++

Toolboxes: image/video processing, wavelets, neural networks,filter design, hardware-interfacing for real time control, ++

French National Space Agency (CNES) (like India ISRO) usesonly Scilab (search google Martin CNES Scilab )

Teaching Matlab is like MBBS colleges teaching to-be-doctorshow to use only very expensive medicines

Today: basic matrix operations and loops syntax, plotting

Also: signal processing: DSP,

Today’s focus

Scilab is free.

Today’s focus

Scilab is free.

Today’s focus

Scilab is free.

Today’s focus

Scilab is free.

Today’s focus

Scilab is free.

Today’s focus

Scilab is free.

Defining a matrix

A=[1 3 4 6] and A=[1 3 4 6];

B=[1 3 4 6;5 6 7 8] // next row by ;

length(A), ones(A), zeros(B), zeros(3,5)

size(A), size(A,’c’), size(A,’r’)

B(1,3)

B(1,3) = -45

quote ( ’ ) for transpose of A

Defining a matrix

A=[1 3 4 6] and A=[1 3 4 6];

B=[1 3 4 6;5 6 7 8] // next row by ;

B(1,3)

B(1,3) = -45

Defining a matrix

A=[1 3 4 6] and A=[1 3 4 6];

B=[1 3 4 6;5 6 7 8] // next row by ;

B(1,3)

B(1,3) = -45

Defining a matrix

A=[1 3 4 6] and A=[1 3 4 6];

B=[1 3 4 6;5 6 7 8] // next row by ;

B(1,3)

B(1,3) = -45

Random numbers/matrices

rand(9) generates a 1× 1 random number (uniformly distributedbetween 0 and 1, etc: see help).If A is an n × p matrix, thenB = rand(A) // defines a random matrix B of the size of A.(A is not overwritten. The matrix B is defined.)

Multiplication and addition

(Vectors are also matrices: with number of rows/columns = 1).Suppose A and B are matrices of 3 rows and 4 columns.A+B // same sizes of A and B requiredA*B // Not defined. size(A,’c’) 6= size(B,’r’)A*B’ // dimensions allow multiplicationA+4 // understood as elementwise additionA*4 and 4*A // understood as elementwise multiplicationA•*B // understood as elementwise multiplication of matrices

for and if-then-end

v = -3:10 // vector from -3 to 20 (default increment 1)

v=1:2.3:10 // vector of ‘suitable length’

for i=1:10, // (or for i=v,)disp(i)

i==4 // check this for undefined i, for i=5 and i=4

if (true or false) thendo something

(else, elseif-else, etc possible)

for and if-then-end

commands into a file

Write all commands, etc in a file (using Notepad or Scilab-editor).sce extension recommendedexec filename or exec(’filename’,2) // does not echo your filefilename could be a ‘function’ : very important

commands into a file

Write all commands, etc in a file (using Notepad or Scilab-editor).sce extension recommendedexec filename or exec(’filename’,2) // does not echo your filefilename could be a ‘function’ : very important

function

Recommended .sci extensionfile1.sci (can have multiple functions with different function names)These names should not already exist!// —- file1.sci begins blah-blahfunction total = addition(a,b)total = a+bendfunction// — file1.sci endsScilab prompt:–¿ exec(’file1.sci’,2)–¿ q = addition(4,5)

eigenvalues (spectrum), trace

det(A), spec(A), trace(A)

sum prod

disp(i) (display i) or disp(’Text to be

displayed’)

rank, svd

sum prod

displayed’)

rank, svd

sum prod

displayed’)

rank, svd

plot and plot2d

x = 0:0.3:3

y = x•ˆ2 // elementwise squaring

plot(x) and plot(x,y) // independent, dependent-variable(s)

plot(x’,y’) // Now 2nd argument can have many columns

x = 0:0.3:3’; y2 = x•ˆ2; y3 = x•ˆ3;

plot(x, [y2 y3]),

plot2d(x, [y2 y3], [2, -4]) // help plot and plot2d

plot and plot2d

x = 0:0.3:3

y = x•ˆ2 // elementwise squaring

plot(x) and plot(x,y) // independent, dependent-variable(s)

plot(x’,y’) // Now 2nd argument can have many columns

x = 0:0.3:3’; y2 = x•ˆ2; y3 = x•ˆ3;

plot(x, [y2 y3]),

plot2d(x, [y2 y3], [2, -4]) // help plot and plot2d

Defining polynomials

Polynomials play a very central role in control theory: the transferfunction is a ratio of two polynomials.Key commands:

• s=poly(0,’s’) • s=poly(0,’s’,’roots’)

• p=s^2+3*s+2 • p=poly([2 3 1],’s’,’coeff’)

• roots(p) • horner(p,5)

• a = [1 2 3] • horner(p,a) • horner(p,a’)

• w=poly(0,’w’) • horner(p,%i*w)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

cfp=coeff(p) constant term first

diffpcoff=cfp(2:length(cfp)).*[1:length(cfp)-1]

diffp=poly(diffpcoff,’s’,’coeff’)

degree(p) can be used instead of length(cfp)-1

Of course, derivat(p)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

Differentiation

p=poly([1 3 4 -3],’s’,’coeff’)

csv: comma separated values filewrite csv : writes data into a csv file.read csv : reads data from a csv file.horner find inv and pinvdft (+ and − 1: options compulsory!)Useful inbuilt variables:%i, %s, %z, %e, %epsa=5×10−3 : a = 5D-3also a = 5d-3 & 5e-3 & 5E-3Commands/variables are case sensitive!

The command ‘find’

find([%T %F %T %F %T %F %F])gives ‘indices’ of TRUE’s.x=[4 5 6 7]x < 5.5true indices of x=find(x < 5.5)y=[5 6 7 8 9 0 -1]y(true indices of x)

Conclusions

Matrices and polynomials provide rich source of problems

Due to good (and cheap/free) computational tools availablecurrently, the future lies in computational techniques

Scilab provides powerful tools

We saw: for horner poly coeff roots find

Control & Computing group Department of Electrical ...belur/scilab/virtual_labs_basic.pdf ·...

Documents

Scilab Manual for Control System Design by Prof Dilip

User manual Scilab Cloud API Cloud API - User manual v5_0.pdf1 Scilab Cloud API – User Manual – v5 – 2018-06-29 User manual Scilab Cloud API ... - Simplify and control your application

Scilab Control

Least square fit of a line/polynomial to input/output databelur/scilab/workshop-engg/r...Least square t of a line/polynomial to input/output data Dr. Madhu N. Belur Control & Computing

Belur, Halebib - Own-Free-Website.comimg.webme.com/userfiles/krejsa/Belur- Halebib.pdf · Belur, Halebib Belur is a Town Municipal Council in Hassan district in the state of Karnataka

Scilab in System and Control by Dr. Balasaheb M. Patre, SGGS

Control System Toolbox in Scilab

Rachel Kalpana K. & Madhu N. Belur. Department of Electrical ...belur/talks/pdfs/minimumECC.pdf · Rachel Kalpana K. & Madhu N. Belur. Department of Electrical Engineering Indian

Spencer’s New store launch Belur Launchcorporate.spencersretail.com/mr/2015/dec/Coverage Report - Belur... · Spencer’s New store launch Belur Launch ... Bartaman Kolkata Howray

Swami Abhedananda Convention Centre at Belur Math · Swami Abhedananda Convention Centre at Belur Math Appeal Ramakrishna Math and Ramakrishna Mission PO Belur Math, Dist Howrah,

Belur Math 1 - Ramakrishna Mission

Scilab Textbook Companion for Control Systems Engineering

Utilizing Scilab and Xcos for real-time control and measurement

Halebidu and Belur Guide

SCILAB REFERENCE MANUAL Scilab Group

Belur Math Pilgrimage Final.p65

Belur Math 1

Scilab Textbook Companion for Automatic Control Systems by ...mailinglists.scilab.org/attachment/4035244/0... · Scilab Textbook Companion for Automatic Control Systems by B. C. Kuo

Scilab 01 Gioi Thieu Scilab

Control Systems with Scilab · Control Systems with Scilab Aditya Sengupta Indian Institute of Technology Bombay apsengupta@iitb.ac.in December 1, 2010, Mumbai. A simple ﬁrst order