S i m u l i n k Prof. Muhammad Saeed Mathematical Modeling and Simulation UsingMATLAB 1

S i m u l i n kS i m u l i n k

Prof. Muhammad Saeed

Mathematical Modeling and Simulation

UsingMATLABMATLAB

1

2

Introduction How to start?

Block Library Model Blocks Virtual Non-virtual User-defined Ports Time States Continuous Discrete Hybrid Parameters Normal Tunable Sample Time Subsystems

3

4

Creating Models Block Selection

Sources Sinks System Blocks

Block Editing Color Size Alignment Labeling Parameters and states

Connecting BlocksGroup Blocks

5

y

To WorkspaceSine Wave3

Sine Wave2

Sine Wave1

Sine Wave

Scope2

Scope1

Scope

Product

4

Gain2

5

Gain1

4

Gain

30

Display1

200

Display

20

Constant3

10

Constant2

20

Constant1

10

Constant

Add

Model Blocks:

Source Sink Multiplication and Division Addition and Subtraction

6

y3

To Workspace3

y2

To Workspace2

y1

To Workspace1

Sum ofElements

Product3

MatrixMultiply

Product2

Product1

Dot Product

18

Display2

30

Display1

1 1 21 2 21 3 5

Constant7

1 2 34 5 61 1 2

Constant6

[2 2 2 2 2]

Constant5

[1 2 3 4 5]

Constant4

[2 2 2 2 2]

Constant3

[1 2 3 4 5]

Constant2

1 1 21 2 21 3 5

Constant1

Model Blocks:

Sum Dot Product Vector Multiplication Matrix Multiplication

Element by Element By Matrix Rule

7

sin

TrigonometricFunction

y4

To Workspace4

y3

To Workspace3

y2

To Workspace2

y1

To Workspace1

y

To Workspace

floor

Rounding Function

Product of Elements

P(u)O(P) = 7

Polynomial

max

MinMax

eu

Math Function

5

Display1

10

Display

[3x3]

Constant6

-C-

Constant5

[1 2 3 4 5]

Constant4

2 -1 3 3 4 6-3 -1 8

Constant3

2 -1 3 3 4 6-3 -1 8

Constant2

2 -1 3 3 4 6-3 -1 8

Constant1

-10

Constant

|u|

Abs

Model Blocks:Built-in Functions

abs max, min Logarithmic, exponential Trigonometric Polynomial Product Rounding off

8

Model Blocks:User-defined Functions

Embedded Matlab FunctionFunction of Matlab FunctionsMatlab Function

XY Graph

Scope1

Scope

sin(u)*cos(u)

Fcn

MATLABFunction

Exp

u ydampOsc

EmbeddedMATLAB Function

Clock2

Clock1

Clock

9

Differential Equation Models

1.

Sine WaveScope

1s

Integrator

10

Gain

y

To Workspace

Sine Wave

1s

Integrator

10

Gain

Clock

10

Differential Equation Models

2.

Sine WaveScope

1s

Integrator

10

Gain

11

Differential Equation Models

12

Differential Equation Models

13

Differential Equation Models

Step

x' = Ax+Bu y = Cx+Du

State-Space Scope

14

3.

Differential Equation Models

15

Differential Equation Models

Step

x' = Ax+Bu y = Cx+Du

State-Space Scope

16

If else For While switch

17

5

c

10

b

-1

a

else { }In1 Out1

If ActionSubsystem3

elseif { }In1 Out1

If ActionSubsystem2

elseif { }In1

In2Out1

If ActionSubsystem1

if { }In1

In2Out1

If ActionSubsystem

u1

u2

u3

if(u1 ~=0 & u2<10)

elseif(u2<0)

elseif(u3<u2)

else

If

8

Display3

0

Display2

0

Display1

0

Display

8

Constant3

1

Constant2

3

Constant1

10

Constant

IF Block

18

END