1.MatlabReview

8/12/2019 1.MatlabReview

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MATLAB/Simulink

Basic MATLAB -

matrices

operators

script and function files

flow control

plotting

Basics of Simulink -

state-space models (1storder ordinary diff eqns)

setting integration properties

setting initial conditions

input types

getting data to the workspace


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Basic MATLAB

screen shot of the Matlab window

command window

optional windows

workspace

current directorytype commands here


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Matlabs help features

type help at the command prompt

and Matlab returns a list of help topics


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>> help lang

Matlabs language constructs


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>> help for

how to use Matlabs for statement


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you can also access on-line help by clicking the

question mark in the toolbar

separate window


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MATLAB Variables

all variables are stored in 32bit floating point format

no distinction between real and integer

>>a = 3;

>>a = 3.0;

same assignment for a

Matlab is case sensitive

>>A=3;

>>a=2;

Aa


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MATLAB Variables

can use numbers and underscore in variable names

>>case34=6.45;

names must start with a letter

>>case_34=6.45;

OK

>>34case=23.45; results in a syntax error

string (text) variables enclosed in single quotes.

The variable is stored as array of characters

>>title=This is the title;


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MATLAB Variables

to clear a variable from memory

>>a=4

>>clear a

if a variable is defined,typing the variable name returns its value

>>a=45.57;

a =

45.57 Matlab returns the value

>>a


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MATLAB Variables

Matlab will echo commands unless a semi-colon is used

>>a=23.2;

>>

>>a=23.2

a =

23.2>>

Matlab echoes the command


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MATLAB Variables

Vectors

column vectors row vectors1

a 2

3

a 1 2 3

>>a=[1;2;3];

>>a

a =

12

3

>>a=[1,2,3];

>>a

a =

1 2 3

use semi-colon

to separate rows

use comma

to separate columns


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MATLAB Variables

Matrices

2-dimensional matrices1 2 3

a4 5 6

>>a=[1,2,3;4,5,6];>>a

a =

1 2 3

4 5 6

again, separate columns with commas and rows with semi-colons


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MATLAB Variables

A vector is a special type of matrix

row vector is a 1 x n matrix, 1 row n columns

column vector is a n x 1 matrix, n rows 1 column

Indexing Matrix elements

>>a=[1,2,3];

>>a(2)ans =

2

could also reference by a(1,2)

note, a(2,1) would produce an error

because a only has one row


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MATLAB Variables

Indexing Matrix elements

>>a=[1,2,3;4,5,6];1 2 3

a4 5 6

more examples

>>a(2,3)

ans =

6

>>a(2,2)=9;

>>a

a =

1 2 3

4 9 6

addressingassigning


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MATLAB Variables

complex-valued numbers

Typically, the variable i or j is used to represent the

complex variable; e.g.

i 1

Then, a complex number is represented as

z = a + ib Re(z) = a

Im(z) = b


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MATLAB Variables


Unless i or j has been previously defined, Matlab assigns

i and j the complex variable value

In Matlab, a complex variable is represented in the

following format

(assuming all variables are cleared)

>>z=23+i*56;

>>zz =

23.00 + 56.00i

>>z=23+j*56;

>>zz =

23.00 + 56.00i

Matlab always uses the symboli to represent a complex number


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MATLAB Variables


What happens in this case?

>>i=3;

>> z=23+i*56;

>>z

z =

What happens in this case?

>>a=sqrt(-1);

>>z=23+a*56;

>>z

z =


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MATLAB Variables


Note, a real-valued number is a special case of a

complex-valued number

assigning any element of a matrix as complex-valuedmakes the entire matrix complex-valued

>>a=[1,2];

>>a

a =

1 2

>>a(1)=1+i*5;>>a

a =

1.00+5.00i 2.00+0.00i


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MATLAB Variables

Advanced data types

n-dimensional arrays

structures

cell arrays


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MATLAB Operations

Basic operationsaddition +

subtraction -

multiplication *

divisionright division /

left division \

>>a=3;b=4;>>c1=a/b;

>>c2=a\b;

?

c1=0.75

c2=1.3333.so, be careful!


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MATLAB Operations

Mixed Real and Complex valued Variables

if both variables are real-valued, a real-valued result is obtained

if one variable is complex-valued, Matlab recasts the real

variable as complex and then performs the operation. The

result is complex-valued

however, the type casting is done internally, the real-valued

variable remains real after the operation


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MATLAB Operations

Other (Scalar) Operations

Math representation Matlab interpretationxz y

xy e

y ln(x)

y log(x)

y sin(x)

y cos(x)

y tan(x)

1

1

1

y sin (x)

y cos (x)

y tan (x)

>>z=y^x;

>>y=exp(x);

>>y=log(x);

>>y=log10(x)

>>y=sin(x);

>>y=cos(x);

>>y=tan(x);

>>y=asin(x);

>>y=acos(x);

>>y=atan(x);


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MATLAB Operations

Examples

y x>>y=x^0.5;

>>y=x^(1/2);

>>y=sqrt(x);

All variables in the preceding operations can be

real or complex, negative or positive

for x < 0, y is complex. Matlab assumes you allow complex

valued numbers. If y is notto be complex, you must

provide error checking.


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MATLAB Operations

Matrices

Only matrices of the same dimension can be added and subtracted

For multiplication, the inner dimensions must be the same

1 2 3

4 5 6

A 2 3 4

5 6 7

B

4 5

6 7

8 9

C

No error Error

>>D=A+B;

>>D=A-B;

>>D=A*C;

>>D=C*A;

>>D=A+C;

>>D=A*B;

>>D=B*A;Matrix multiplication

not commutative


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MATLAB Operations

Left(\) and Right(/) Matrix division

Math representation Matlab interpretation

1C A B

1C BA

>>C=A\B;

>>C=B/A;

Remember, Amust be square and full rank

(linearly independent rows/columns)


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MATLAB Operations

Matrix Transpose

Math representation Matlab interpretation

TC A >>C=A;

For complex-valued matrices, complex conjugate transpose

1 2 3

4 5 6

A

1 4

2 5

3 6

B

>>B=A;

1 j2 3 j4 a

1 j2

3 j4

b

>>b=a;


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MATLAB m-files

Two types of m-files

script files

collection of commands that Matlab executes

when the script is run

function files

collection of commands which together

represent a function, a procedure or a method

Both types are separate files with a .m extension


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MATLAB m-files

To create an m-file, open the Matlab text editor

Click on the page icon

The Matlab text editor window will open


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MATLAB m-files

Script Files

On the command line

>>x=3.0;

>>y=x^2;

>>y

y =9.0

>>

In the script file named test.m

On the command line

>>test

y =

9.0

>>


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MATLAB m-files

Script Files

script files share the workspace memory

>>x=5.0;

>>test>>y

y =

25.0

>>

test.m script


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MATLAB m-files

Script Files

script files can call other script files

>>outter

y =

36.0

>>

inner.m script

outter.m script


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MATLAB m-files

Function Files

Matlab identifies function files from script files byusing the function and return keywords

the name of the function file must be

the same name as the function


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The function file x2.m

MATLAB m-files

Function Files

>>r=3;

>>d=x2(r);>>d

d =

9.0

>>

>>h=x2(4.2);

>>hh =

17.64

>>


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MATLAB m-files

Function Files

Multiple Inputs and Outputs

outputs in square brackets, [ ] inputs in parentheses ( )


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variables created in the function are not retainedin the workspace, except for the output variables

the function does not have access to workspacevariables, except for the inputs

MATLAB m-files

Function Files

variables passed to the function are copies of theworkspace variables. Changing their value inside the

function has no effect on their value in the workspace.


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MATLAB Flow Control

The while and if statements

if expression

statements

end

if expression

statements1

else

statements2end

Matlab evaluates expressionas logical true or false

false equivalent to zero

true equivalent to any non-zero number

statements, any valid Matlab command

while expression

statements

end


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MATLAB Flow Control

evaluating expression

any valid equationa=4;

b=5;

c=5;

if a+bif b-c TrueFalse

watch out for round-off

and word length error

if sin(0)

if sin(pi)

sin(pi) = 1.22e-16

False

True

conditional operators== equal to

< less than

> greater than

= greater than or equal to

~= not equal to

logical operators

& and

| or

while(3


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MATLAB Flow Control

The for statement

for index=start : [increment:] endstatements

end

index,start, increment, and enddo not need to be integer valued

incrementis optional, if incrementis not specified

incrementdefaults to 1

indexcan be incremented positive (increment> 0) ornegative (increment< 0)

loop stops when index> end (or index< end)


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MATLAB Flow Control

example

script file to cycle through x values

function file to generate the y values


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MATLAB Plotting

Basic 2D plotting functions

plot(x1,y1[,x2,y2,x3,y3.....])

xlabel(x axis name)

ylabel(y axis name)

title(graph name)

Additional functions

grid ongrid off

axis([xmin,xmax,ymin,ymax])


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MATLAB Plottingexample y = sin(t)

the plot function alone


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script file to generate

a graph of y = sin(t)

MATLAB Pl tti


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function file to generate

a graph of y = sin(t)

>>graphsin

>>


MATLAB Pl tti


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legend remembers

the order the graphs

were plotted

MATLAB PlottingAdding a Legend for multiple graphs

Si li k B i


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Simulink Basics

click the Simulink button

the Simulink window

Simulink Basics


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click the new button

the simulink model window

Simulink Basics

create a new model oropen an existing one

Si li k E l


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Simulink Example

Best thing to do is to go through an example

Response to a step command

2ndorder, constant coefficient, linear differential equation

1 0 0y c y c y b f (t)

Si li k E l


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Simulink Example

Get an equivalent block diagram for the system

use integrators to get dy/dt and y

use mouse to drag blocks into

the model window and to

connect blocks with arrows


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add gain and summer blocks

Simulink Example

Simulink Example


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Simulink Example

add the step input block

Simulink Example


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Simulink Example

add the output block

Simulink Example


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Simulink Example

Now, double click the blocks to open and set the blocks parameters

set initial condition

set gain value

set variable name

set output format to array

Simulink Example


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Simulink Example

To set the simulation parameters.

select Simulation -> Simulation Parameters

set Start and Stop time (in seconds)

set numerical integration type

Simulink Example


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Simulink Example

Time to run the simulation

click the run button to begin the simulation

when the simulation is complete, Ready appears at the bottom

Simulink Example


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Simulink Example

Simulink will automatically save a variable named tout to

the workspace.

This variable contains the time values used in the simulation,important for variable time integration types

Simulink also will create the output variable(s) you specified

Simulink Example


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Simulink Example

>>plot(tout,yoft)

graph of the step response

Simulink Example


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Simulink Example

Another approach to solving the 2ndorder single DOF

problem, is to cast it as a 1storder 2 DOF problem

1

2

x y

x y

1 2

2 o 1 2 o 1

x x

x b f c x c x

In Matrix (or State Space) form. u

y

x Ax B

Cx

o 1

0 1

c c

Ao

0

b

B

1 0C

1

2

x

x

x

u f

Simulink Example


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Simulink Example

1stOrder State-Space Models

Simulink Example


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Simulink ExampleMulti Input Multi Output Systems

use Mux and Demux blocks to combine and extract vector signals

specify number of signals

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1.MatlabReview