EP314Process Dynamics and Control

Laboratory Session : #1

Software Interface

Command window: Type your instructions here and press ENTER to execute them.

Workspace: shows a list of variables created by MATLAB.

Software Interface

Example: Declare a variable, a with value of 1

Software Interface

Workspace: shows alist of variablescreated by MATLAB.As you can see, thevalue of a is shown.

Software Interface

Another way to create a variable Is to press this button.

MATLAB will prompt you to enter the variable name.

Software Interface

By double clicking on b, the variable editor window appears. You can type in new values into b by filling in the cells.

Software Interface

By double clicking on b, the variable editor window appears. You can type in new values into b by filling in the cells.

To clear text in Command Windows: clcTo clear all variables at workspace: clear allTo close all figure: close all

Declaring & Manipulating variables

MATLAB can be used to initialize and manipulate many types of variables.

Single value i.e.: a =1; Matrix i.e.: A = [1;2] ; %(2x1) matrix String i.e.: name = John;

Try It Yourself !!! Create a matrix (3x1) named var1 with the values of

1, 3, 5 in it. Create a matrix (1x7) named var2 with the values of

1, 3, 5, 6, 8, 10, 11 in it.

Declaring & Manipulating variables

Matrix can be created by enclosing a set of number in squarebracket, [ ].Create a matrix (1x10) named varA by entering in MATLABCommand Windows as followed:varA = [1 2 3 4 5 6 7 8 9 10] OR varA = [1 2 3 4 5 6 7 8 9 10] ;varA = [1,2,3,4,5,6,7,8,9,10] OR varA = [1,2,3,4,5,6,7,8,9,10] ;

Note: semicolon at the end is to suppress the result at commandwindows. Keep in mind, variable name are case sensitive.

The easiest way to create a matrix (10x1) from varA is to take the transpose of varAvarB = varA; OR varB = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10];

Try It Yourself !!! Create a matrix (3x3)

=

Accessing Matrix Values

To access a specific value inside a matrix, use this command:

matrixName(rowNumber, colNumber)

Example: Given a matrix, M as>> M = [1,2,3,4,5;3,4,5,6,7]M =

1 2 3 4 53 4 5 6 7

Determine value for 2nd row and 4th column>> ans = M(2,4)ans =

6

Whole Columns and Rows

To access a specific value inside a matrix, use this command:

matrixName(rowNumber, colNumber)

Use : to indicate all columns or rows. Example: Given a matrix, M as

>> M = [1,2,3,4,5;3,4,5,6,7]M =

1 2 3 4 53 4 5 6 7

Determine values for 2nd row>> ans = M(2,:)ans =

3 4 5 6 7

Matrix Zeroes, Ones, & Random

To create the matrix as below, use this command:

Zeroes zeros(rowNumber, colNumber) Ones ones(rowNumber, colNumber) Random rand(rowNumber, colNumber)

Example:

=0 00 00 0

>> Z=zeros(3,2)

=1 1 11 1 1

>> K = ones(2, 3)

=0.8147 0.9134 0.27850.9058 0.6324 0.54690.1270 0.0975 0.9575

>> R = rand(3, 3)

Operator

+ Addition

- Subtraction

* Multiplication

/ Division

^ Power

Operator

+ Addition

- Subtraction

.* Multiplication

./ Division

.^ Power

Mathematical Mathematical Array

Now, we do simple mathematical operation with matrix, M and N

Given: >>M=[2,4;5,1]; N=[1,4;3,2];Compute as follows:>> Ans1 = 2*M>> Ans2 = M + N>> Ans3 = Ans1*Ans2>> Ans4 = sqrt(M)

Now, we do simple mathematical operation with matrix, M and N

Given: >>M=[2,4;5,1]; N=[1,4;3,2];Compute as follows:

>> Ans1 = 2*MAns1 =

4 810 2

>> Ans3 = Ans1*Ans2Ans3 =

76 5646 86

>> Ans2 = M + NAns2 =

3 88 3

>> Ans4 = sqrt(M)Ans4 =

1.4142 2.00002.2361 1.0000

+ Addition

- Subtraction

* Multiplication

/ Division

^ Power

Operator

+ Addition

- Subtraction

.* Multiplication

./ Division

.^ Power

Mathematical Mathematical Array

Now, Mathematical Array operation with matrix, M and N

Given: >>M=[2,4;5,1]; N=[1,4;3,2];>> ans1 = M.^3>> ans2 = M^3>> ans3 = ans1.*ans2>> ans4 = ans1*ans2

Multiplies each element M(I,j)*N(I,j)

Cross matrix multiplication

Now, Mathematical Array operation with matrix, M and N

Given: >>M=[2,4;5,1]; N=[1,4;3,2];

>> ans1 = M.^3ans1 =

8 64125 1

>> ans3 = ans1.*ans2ans3 =

864 691216875 81

>> ans2 = M^3ans2 =

108 108135 81

>> ans4 = ans1*ans2ans4 =

9504 604813635 13581

Plotting graphs

plot(x,y) Plot the vector x versus the vector y

semilogx(x,y) Plot the vector x versus the vector yThe x-axis is log10, y-axis is linear

semilogy(x,y) Plot the vector x versus the vector yThe x-axis is linear, y-axis is log10

loglog(x,y) Plot the vector x versus the vector yBoth are log10 axes.

title(Text) Put Text at the top of the plot

xlabel(TextX) Label the x-axis TextX

ylabel(TextY) Label the y-axis TextY

subplot(row,col,no) Subdivides the plot in the Figure

grid Draws grid line

legend(M,N,K) Add legend for M, N, & K profiles

Available Plot Formats

Function for Customized Plots

Typical Plot

Plotting graphsStep 1: Prepare dataset

>> t = 1:0.5:10;>> y1 = 2*t.^2 + 2*t + 9;>> y2 = 3*t.^2 + 0.6*t + 0.1;

Step 2: Now create plot y1 vs t, and y2 vs t together

>> plot(t,y1,b)>> plot(t,y2,g)

Step 3: Add title and axis label

>> title(Quadratic plots)>> xlabel(The x-axis label, t)>> ylabel(The y-axis label, y)

Step 4: Add legend and grid

>> legend(y1,y2)>> grid

x = [xi dx xf]

Final value

increment

Starting value