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.

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




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




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


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


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


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


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


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


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


Three outputs show here

View output (workspace)

You can plot the output using the plot function

Lecture Overview




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


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


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


x x


x



x x x

Set Step time =0

Note: Assume all initial conditions = 0



Open “simulation parameters” window

Set “Stop time” = 30

12

RUNSimulation


Step Response for the mass-spring-damper system example

Output from Scope block Plot system response

Lecture Overview




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)



Select BLOCK set Location in Simulink Library

Step Sources

Transfer Function Continuous

Scope & To Workspace Sinks



x


xSet Step time =0




Open “simulation parameters” window

Set “Stop time” = 30

12

RUNSimulation


Same output as before (Slide 21)

Output from Scope block Plot system response

Lecture Overview




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


Create Subsystem using model in Example 1

STEP 1: Creating Blocks (Main window)

This is the Subsystem block isfrom the Subsystems library


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

Inport (named from “sum”

Outport(three outports)


STEP 3: Making connections (Main window)


STEP 4: Set Parameter (Main window)


Then view output response

Output from Scope block

Lecture Overview




Useful Information (1)

Ramp Function

Set Slope

Set Start time for Ramp function

Set initial value


Unit Step Function or Impulse

t(s)50

5

Input(t)

Start at 5.01 s

Start at 0 s


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)

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.

Documents

use simulink

differential equations

step response

blocksunit step inputexample

building models

elementary dynamic system

dynamic systems

damper system exampleoutput