ECEN/MAE 3723 – Systems I

MATLAB Lecture 2

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

What is Simulink? (1)

A software package for modeling, simulating, and analyzing dynamic systems.

Supports linear and nonlinear systems, modeled in continuous time, sample time, or a hybrid of the two.

Systems can also be multirate (i.e. different parts that are sampled or updated at different rates)

What is Simulink? (2)

For modeling, it provides a graphical user interface (GUI) for building models as block diagrams (using click-and-drag mouse operations)

Can build models in hierarchical fashion (using both top-down and bottom-up approaches)

You can simulate, analyze the output results, explore, revise your models and have FUN!

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Start a Simulink Session

Type simulinkon Matlab command window

Click on the SIMULINK icon on toolbar

Simulink Library Browser

SEARCH windowCREAT NEW MODEL icon

BLOCK set for model construction

LIBRARY

Create a New Model

CREAT NEW MODEL icon

Workspace where youconstruct your model

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Building a Model

Simulink Block Diagram – pictorial model of a dynamic system

Each block represents an elementary dynamic system that produces an output (either continuous or discrete output)

Lines represent connections of block inputs to block outputs

u(Input)

x(states)

y(Output)

Building a Model (2)

The following steps will guide you to construct a system/model:

STEP 1: Creating Blocks

STEP 2: Making connections

STEP 3: Set Parameters

STEP 4: Running Simulation

Building a Model (3)

Step 1: Creating Blocks

Click-Drag-Drop the Sine Wave block to Workspace Window

This is the Sine Wave block is

from the Sources library

Sources library

Save this model

Building a Model (4)

Step 1: Creating Blocks

These arefrom the

Sinks library

The Gain block isfrom the

Math library

The Mux block is from the Signals &Systems library

Building a Model (5)

Step 2: Making connectionsTo make connection: left-click while holding down control key (on keyboard) and drag from source port to a destination port

A connected Model

Building a Model (6)

Gain value = 5

Name the output parameter as “out1”

Double click the Gain block to set the parameter for the Gain block

Step 3: Set Parameters

Building a Model (7)

click “simulation parameters” to set up the desired parameters

You can change the “stop time” and then click the “OK button”

Click here to run the simulation

Step 4: Running Simulation

Building a Model (8)

View output via Scope block

Double click on Scope block to display output of the scopeNote: Scope block is similar to oscilloscope!

Output of the scope

Yellow: Input sine wavePurple: Output (sine wave with gain of 5

To fit graph to frame

Building a Model (9)

Three outputs show here

View output (workspace)

You can plot the output using the plot function

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Example 1:Differential Equations (1)

Example of a dynamic system: A mass-spring-damper system

1x Bx Kx f t

M

The Mathematical model of the system is describe by:

M

K B

x

f t

12 2

2x x x f t

Lets M=2kg; B = 2 Ns/m; K=2 N/m

Unit Step Input

Example 1:Differential Equations (2)

Use Simulink to simulate the step response of the system, i.e.

STEP 1: Creating Blocks

12 2

2x x x f t

f(t), N

1

0 Time, s

Select BLOCK set Location in Simulink Library

Step Sources

Sum Math Operation

Gain Math Operation

Integrator Continuous

Scope & To Workspace Sinks

Example 1:Differential Equations (2)

x x

STEP 2: Making connections

x

Example 1:Differential Equations (3)

STEP 3: Set Parameters

x x x

Set Step time =0

Note: Assume all initial conditions = 0

Example 1:Differential Equations (4)

STEP 4: Running Simulation

Open “simulation parameters” window

Set “Stop time” = 30

12

RUNSimulation

Example 1:Differential Equations (5)

Step Response for the mass-spring-damper system example

Output from Scope block Plot system response

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Example 2: Transfer Function (1)

Use the same mass-spring-damper system example and simulate the response using transfer function approach

12 2

2x x x f t

2

( ) 1

( ) 2 2 2

X s

F s s s

The transfer function of the equation (assume all initial conditions =0)

Example 2: Transfer Function (2)

STEP 1: Creating Blocks

Select BLOCK set Location in Simulink Library

Step Sources

Transfer Function Continuous

Scope & To Workspace Sinks

Example 2: Transfer Function (3)

STEP 2: Making connections

x

Example 2: Transfer Function (4)

xSet Step time =0

STEP 3: Set Parameters

Example 2: Transfer Function (5)

STEP 4: Running Simulation

Open “simulation parameters” window

Set “Stop time” = 30

12

RUNSimulation

Example 2: Transfer Function (6)

Same output as before (Slide 21)

Output from Scope block Plot system response

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Creating Subsystems (1)

Subsystem – similar to “Subroutine”Advantage of Subsystems:

Reduce the number of blocks display on the main window (i.e. simplify the model)

Group related blocks together (i.e. More organized)

Can create a hierarchical block diagram (i.e. you can create subsystems within a subsystem )

Easy to check for mistakes and to explore different parameters

Creating Subsystems (2)

Create Subsystem using model in Example 1

STEP 1: Creating Blocks (Main window)

This is the Subsystem block isfrom the Subsystems library

Creating Subsystems (3)

STEP 2: Double click Subsystem block and create a model in the Subsystem block

Inport (named from “sum”

Outport(three outports)

Creating Subsystems (4)

STEP 3: Making connections (Main window)

Creating Subsystems (5)

STEP 4: Set Parameter (Main window)

STEP 5: Running Simulation

Then view output response

Output from Scope block

Lecture Overview

What is Simulink?How to use Simulink

Getting Start with Simulink Building a model

Example 1 (Differential Equations )Example 2 (Transfer Function)Creating SubsystemsUseful Information

Useful Information (1)

Ramp Function

Set Slope

Set Start time for Ramp function

Set initial value

Useful Information (2)

Unit Step Function or Impulse

t(s)50

5

Input(t)

Start at 5.01 s

Start at 0 s

Useful Information (3)

To run programs, have to be in the current active directory or in a directory in the path (goto File Set path... )

To copy the SIMULINK Model from Simulink Workspace and add to report (Edit Copy model to clipboard)

Need help on SIMULINK (At Simulink Library Browser Click Help)