[email protected] ENGR-25_MATLAB_OverView-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical

[email protected] • ENGR-25_MATLAB_OverView-2.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp1 MATLABChp1 MATLABOverView: OverView:

Part-2Part-2



Learning GoalsLearning Goals

Turn On MATLAB and use as a calculator

Create Basic Cartesian Plots Write and Save simple “Script”

Program-files Execute Conditional Statements

• IF, THEN, ELSE, >, <, >=, etc.

Execute Loop Statements• FOR & WHILE



Systems of Linear EquationsSystems of Linear Equations Consider an

Electrical Circuit for Which we need to Find the OutPut Electrical Potential

Ix

1 k

1 k 1 k

1 k12 V

2kIx

+

Vo

V1V2

Ix

1 k

1 k 1 k

1 k12 V

2kIx

+

Vo

V1V2

Using the ENGR43 Method of Nodal Analysis we find

01000100

00111

V 120010

02000101

21

21

21

21

xo

xo

xo

xo

IVVV

IVVV

IVVV

IVVV

MTH6 Provides Methods to solve this System of Eqns



Systems of Linear Equations Systems of Linear Equations contcont

We Will Use MATLAB’s “Left” Division Solver

Write the System of Eqns (below) in Matrix/Array Form In MATLAB need to

InPut the • 4x4 COEFFICIENT

Matrix, A

• 4x1 CONSTRAINT Vector, b

0

0

12

0

1000100

0111

0010

2000101

2

1

x

o

I

V

V

V

01000100

00111

V 120010

02000101

21

21

21

21

xo

xo

xo

xo

IVVV

IVVV

IVVV

IVVV

A b

x



Systems of Linear Equations Systems of Linear Equations contcont

Use MATLAB to Solve 4Eqns in 4Unkowns>> A = [1,0,-1,-2000; 0,1,0,0; 1,-1,1,0; 0,0,1,-1000];

>> b = [0;12;0;0];

>> Soln = A\b

Soln =

9.0000

12.0000

3.0000

0.0030

Row Separator

Left Division

Thus the Solution by MATLAB

Amps 003.0

Volts 3

Volts 12

Volts 9

2

1

x

o

I

V

V

V



Left Division SyntaxLeft Division Syntax

“Normal”; i.e., RIGHT Division:

P/Q• Read as “P divided by Q”

LEFT (a.k.a. “Back”), RIGHT Division:

S\R• Read as “R divided by S”

READ

READ



Left Div & Matrix InverseLeft Div & Matrix Inverse Use MATLAB to Solve 4Eqns in 4Unkowns>> A = [1,0,-1,-2000; 0,1,0,0; 1,-1,1,0; 0,0,1,-1000];

>> b = [0;12;0;0];

>> Soln = A\b

The Matrix “Inverse”(More on This Later)

By MTH6• x is the Solution Vector

bx

Abx 11 AAA

bxx 11 AAA

bx

\A



Performing MATLAB OpsPerforming MATLAB Ops You can perform

operations in MATLAB in two ways:

1. In the interactive mode, in which all commands are entered directly in the Command window

2. By running a MATLAB program stored in script “m” file.– A Script file contains

MATLAB commands, so running it is equivalent to typing all the commands - one at a time - at the Command window prompt.

– Run the file by typing its name at the Command window prompt



% Comments% Comments COMMENTS are NONexecutable Statements

that help Document or Explain Script Files The comment symbol (%) may be put

anywhere in the line. MATLAB ignores everything to the right of the % symbol.

>>% This is a comment.

>>x = 2+3 % So is this.

x =

5

Note that the portion of the line before the % sign is executed to compute x.



MATLAB Editor/DebuggerMATLAB Editor/Debugger



Script File UsageScript File Usage The name of a script file must begin with a

letter, and may include digits and the underscore character, up to 63 characters.

Do not give a script file the same name as a variable

Do not give a script file the same name as a MATLAB command or function. • You can check to see if a

command, function or file name already exists by using the exist command



DeBugging Script FilesDeBugging Script Files Program errors usually fall into

one of the following categories.1. Syntax errors such as omitting a parenthesis or

comma, or spelling a command name incorrectly. MATLAB usually detects the more obvious errors and displays a message describing the error and its location.

2. Errors due to an incorrect mathematical procedure are called runtime errors. Their occurrence often depends on the particular input data. – A common example is division by zero



Locating Program ErrorsLocating Program Errors

To locate program errors, try:1. Use a simple version of the problem

which can be checked by hand toTest your program

2. Display any intermediate calculations by removing semicolons at the end of statements.

3. Use the debugging features of the Editor/Debugger.



Programming StyleProgramming Style

1. Comments sectiona. The name of the program and any key words

in the first line.

b. The date created, and the creators' names in the second line.

c. The definitions of the variable names for every input and output variable. • Include definitions of variables used in the calculations

and units of measurement for all input and all output variables!

d. The (file)name of every user-defined function called by the program.



Programming Style Programming Style contcont

1. Input section • Include input data and/or the input functions and

comments for documentation.

2. Calculation section

3. Output section • This section might contain functions for displaying

the output on the screen or creating a plot



InPut/OutPut CommandsInPut/OutPut Commands

Command Description

disp(A)Displays the contents, but not the name, of the array A.

disp(’text’)Displays the text string enclosed within quotes.

x = input(’text’)Displays the text in quotes, waits for user input from the keyboard, and stores the value in x.

x = input(’text’,’s’)

Displays the text in quotes, waits for user input from the keyboard, and stores the input as a TEXT STRING in x.



Script File ExampleScript File Example

Problem: The speed v of a falling object dropped with no initial velocity is given as a function of time t by v = gt.• Where g is the Acceleration of Gravity; a

CONSTANT = 32.2 ft/s2

Use MATLAB to Plot v as a function of t for 0 ≤ t ≤ tf

• Where tf is the final time entered by the user.



FallSpeed Plot for tFallSpeed Plot for tff = 7 sec = 7 sec



Exploit the TextBookExploit the TextBook Throughout each chapter margin notes identify

where key terms are introduced. Each chapter contains tables summarizing the

MATLAB commands introduced in that chapter. At the end of each chapter is a summary guide to

the commands covered in that chapter. Appendix A contains tables of MATLAB

commands, grouped by category, with the appropriate page references.

There are three indexes. 1. lists MATLAB commands and symbols, 2. lists SimuLink blocks 3. lists topics.



MATLAB Help → Hidden TabMATLAB Help → Hidden Tab



Command Window Help-FcnsCommand Window Help-Fcns help funcname: Displays in the Command

window a description of the specified function funcname.

lookfor topic: Displays in the Command window a brief description for all functions whose description includes the specified key word topic.

doc funcname: Opens the Help Browser to the reference page for the specified function funcname, providing a description, additional remarks, and examples.



Relational OperatorsRelational Operators

Symbol Meaning

< Less than

<= Less than or equal to

> Greater than

>= Greater than or equal to

== Equal to

~= Not equal to

0 if FALSE 1 if TRUE

>> x = [6,3,9]; y = [14,2,9];

>> z = (x < y)

z =

1 0 0

>>z = (x > y)

z =

0 1 0

>>z = (x ~= y)

z =

1 1 0

>>z = ( x == y)

z =

0 0 1

>>z = (x > 8)

z =

0 0 1



The The FindFind Function Function

find(x) computes an array containing the INDICES of the NONzero elements of the numeric array x. For example

The resulting array y = [1, 3] indicates that the first and third elements of array x are nonzero.

>>x = [-2, 0, 4];

>>y = find(x)

y =

1 3

>> M = [4 -9 23; 0 78 -11; 32 0 0 ]

M = 4 -9 23

0 78 -11

32 0 0

>> NonZeroM = find(M)

NonZeroM =

1

3

4

5

7

8



AnotherAnotherfindfind ExampleExample

>> M = [4 -9 23; 0 78 -11; 32 0 0 ]

M = 4 -9 23

0 78 -11

32 0 0

>> NonZeroM = find(M)

NonZeroM =

1

3

4

5

7

8



The The FindFind Distinction Distinction

Note the difference between the result obtained by x(x<y) and the result obtained by find(x<y).>>x = [6,3,9,11];y = [14,2,9,13];

>>values = x(x<y)

values =

6 11

>>how_many = length(values)

how_many =

2

>>indices = find(x<y)

indices =

1 4



The The ifif Statement Statement The general form of the if statement

The elseif statement can be REPEATED if Needed

The else and elseif statements may be OMITTED if not required

if expression

commands

elseif expression

commands

else

commands

end



ifif Example Example Use MATLAB to

Evaluate the Piecewise Function

010

901010

910415

x

xx

xx

y

The Script File



ifif Example OutPut Example OutPut

010

901010

910415

x

xx

xx

y

>> x = -11;

>> if_Test_0506

y =

10

>> x = 7.3;

>> if_Test_0506

y =

83

>> x = 13;

>> if_Test_0506

y =

118.1665



LoopsLoops

There are two types of EXPLICIT Loops in MATLAB

1. The for loop, used when the number of passes is known ahead of time

2. The while loop, used when the looping process must terminate when a specified condition is satisfied

– In this case the the number of passes is not known in advance.

i.e., WHILEs use Dynamic Termination



forfor Loop Example Loop Examplem = 1; % Array-Building index

x(1) = 10; % 1st element of x = 10

for k = 2:3:11

m = m+1;

x(m+1) = x(m) + k^2;

end k takes on the values 2, 5, 8, 11. The variable

m indicates the index of the array x. When the loop is finished the array x will have the values x(1)=10 , x(2)=14, x(3)=39, x(4)=103, x(5)=224.



whilewhile Loop Example Loop Examplex = 5;k = 0;

while x < 25

k = k + 1;

y(k) = 3*x;

x = 2*x-1;

end

The loop variable x is initially assigned the value 5, and it keeps this value until the statement x = 2*x - 1 is encountered the first time. Its value then changes to 9. Before each pass through the loop, x is checked to see if its value is less than 25. If so, the pass is made. If not, the loop is skipped.



CAVEATCAVEAT

Beware MATLAB Script file (“.m file) naming conventions• The name of a script file MUST begin with

a letter, and May include digits and the underscore character, up to 63 chars.

• May NOT include the DASH (-)

ca·ve·at ( P ) Pronunciation Key (kv-t, kv-, käv-ät), n.

A WARNING or CAUTION: “A final caveat: Most experts feel that clients get unsatisfactory results when they don't specify clearly what they want” (Savvy).



Demos: Demos: forfor & & whilewhile

Prob 1-39 → Evaluate with for

10

1

35k

k

ksum • Also list the value of the individual Terms

Prob 1-40 → Use while to find the number of terms, qmax, such that

max

1

999973.1qk

k

kTotal



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

AppendiAppendixx



Problem 1-39Problem 1-39>> run Prob1dash39term = 5term = 40term = 135term = 320term = 625term = 1080term = 1715term = 2560term = 3645term = 5000sum = 15125



Problem 1-40Problem 1-40

>> run Prob1dash40min no. terms = 15

Sum-Total for max-terms = 8.8165e+003



FallS

peed

Co

de

FallS

peed

Co

de

% Bruce Mayer, PE% ENGR25 * 26Jan10% Program fall_speed_1001.m% Plots speed of a falling object in USA units%% Input Var:% tf = final time (in seconds)%% Output Var:% t = array of times at which speed is computed (in sec)% s = array of speeds (feet/sec converted to mph)%% Parameter Value:g = 32.2; % Acceleration in USA customary units%% Input section:tf = input('Enter final time in seconds = ');%% Calculation section:dt = tf/500; % time step for 501 values% Create an array of 501 time values.t = [0:dt:tf];% Compute speed values in mph.s = (g*t)*(60/88); % 88fps = 60mph%% Output section:disp('fall speed at t-final'); disp(s(length(s))); disp('mph')plot(t,s), xlabel('t (sec)'),ylabel('s (mph)'), title('Falling Speed vs Time'), grid

Documents

[email protected] ENGR-25_MATLAB_OverView-2.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Licensed Electrical