Introduction to Scicoslab

Transcription

1 Introduction to Scicoslab

2 Introduction Scicoslab is an open source alternative for modeling and simulation of dynamical system Latest version 4.4 can be downloaded from

3 getting help for a function o --> help roots searching a keyword o --> apropos keyword Getting Started

4 Scalar o --> x = 5 Complex o --> x = 3+4*%i Row Vector o --> x1 = [1 2 3] o --> x2 = [4, 5, 6] Column Vector o --> y = [1; 2; 3] 3x3 Matrix o A = [1 2 3;4 5 6;7 8 9] Variables

5 Complex Number operations Complex o --> x = 3+4*%i //3+4i real part of x o --> real(x) //3 Imaginary part of x o --> imag(x) //4 Magnitude of x o --> abs(x) //5 Complex conjugate of x o --> conj(x) //3-4i

6 Vectors and Matrix Generating Vector o --> x=[0:0.5:2] //[0,0.5,1,1.5,2] o --> x=linspace(0,2,5) //[0,0.5,1,1.5,2] Accessing vector elements. Vector and Matrix index start with 1. o --> A = [1 2 3;4 5 6;7 8 9] o --> x = A(1,3) //3 o --> y = A(2,:) //[4,5,6] o --> z = A(1:2,1:3) //[1,2,3;4,5,6] Polynomial matrix o --> p = poly([1 3],'s') // p=s 2-4s+3 o --> q = poly([3-4 1],'s','c') //q=s 2-4s+3

7 Exercise find the roots of s v=[2 1 1] p1=poly(v,'s','c') roots(p1) o i and i

8 + addition - subtraction * multiplication / right division \ left division ^,** exponentiation (power) conjugate transpose.* element wise multiplication./ element wise right division.\ element wise left division.^,.** element wise power Matrix operation

9 Matrix operation Example A=[1,2;3,4], B=[1,1;2,2], A*B? A.*B? A*B=[5,5;11,11] A.*B=[1,2;6,8] Find Inverse of matrix A -->inv(a) //[-2,1;1.5,-0.5] Build a 2x2 matrix C where the first row is the sum of the first row of matrix A and the second row of matrix B, and the second row is the sum of the second row of matrix A and first row of matrix B C=[A(1,:)+B(2,:);A(2,:)+B(1,:)] //[3,4;4,5]

10 < less than <= less than or equal to > greater than >= greater than or equal to == equal to ~= not equal to Relational operations

11 Flow control For iterator o --> for i=1:5 --> disp(i) --> end While iterator o --> i=1; --> while %t --> if i>5 then break; end --> disp(i); --> i=i+1; --> end Branching o if... then... else... end logical operator o & (and), (or), and ~(not)

12 x=[0:100]; y=x^2; plot(x,y) Plots

13 Scripts A scicoslab program is a set of instruction to be executed in a specific order Can be typed one by one at the prompt (interactive) or read from a file (script) The file is called a script and by convention use.sce as the file extension

14 Scripts Example Plotting o Generate a vector t with 50 element from 0 to 2π o Compute sin(t) o Plot sin(t) x=linspace(0,2*%pi,50) y=sin(x) plot(x,y) Check if a number is a prime. Hint: modulo(),%f,%t x=117; if x>2 then isprime=%t; for n=[2:sqrt(x)] if (modulo(x,n)==0) then isprime=%f; break; end end end

15 Functions It is possible to define new functions in scicoslab Use.sci as file extension Functions can have multiple inputs and outputs function [result1,result2]=add_sub(a,b) result1=a+b; result2=a-b; endfunction -->[a,b]=add_sub(1,2) // a=3, b=-1

16 Functions Example Root mean square o compute sum of v 2 o divide the sum with the number of element of v o compute the square root of the sum function result=rms(args) result=sqrt(sum(args.^2)/size(args,2)) endfunction

17 Input and Output Write variables to a binary file o --> a=eye(2,2);b=ones(a); o --> save('val,dat',a,b) //save variables a and b to file Load a binary file o o --> clear a;clear b //remove a and b from memory --> load('val.dat','a','b') //load variables a and b from file Write variables to an ascii file o o --> savematfile('val.txt','a','b','-ascii') --> fprintfmat('val.txt',a) Load an ascii file. o --> loadmatfile('-ascii','val.txt') //load val.txt and save it to variable val

18 Useful Features --> scipad(); -->browsevar();

19 Scicos Scicos provides a graphical editor for the construction and simulation of dynamical system The systems are constructed using block diagrams Block diagrams are reusable. Basic block diagrams are available in Scicos palettes

20 Scicos Example --> scicos; Palette > Pal Tree Simulate > Run

21 Modeling a Continuous Time System Example 1 : Bank account Deposit rate x(t) Interest G Amount of money y(t) Your money will grow following this equation

22 Example 1: Bank Account Scicos Model Simulation

23 Example 2: Transfer function Consider this transfer function Run simulation from scicoslab t=[0:0.01:5]; H=2/(s+2); y1=csim ('step',t,h); plot(t,y1)

24 Example 2: Transfer function Consider this transfer function Model this transfer function in scicos

25 Exercise Consider this transfer function Run simulation from scicoslab Model the transfer function in scicos