Experiment 8

SIMULINK

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Simulink

Introduction to simulink

SIMULINK is an interactive environment for modeling, analyzing, and simulating a

wide variety of dynamic systems. SIMULINK provides a graphical user interface for

constructing block diagram models using “drag-and-drop” operations. A system is

configured in terms of block diagram representation from a library of standard

components. SIMULINK is very easy to learn. A system in block diagram

representation is built easily and the simulation results are displayed quickly.

Simulation algorithms and parameters can be changed in the middle of a simulation

with intuitive results, thus providing the user with a ready access learning tool for

simulating many of the operational problems found in the real world. SIMULINK is

particularly useful for studying the effects of nonlinearities on the behavior of the

system, and as such, it is also an ideal research tool. The key features of SIMULINK

are

Interactive simulations with live display.

A comprehensive block library for creating linear, nonlinear, discrete or hybrid

multi-input/output systems.

Seven integration methods for fixed-step, variable-step, and stiff systems.

Unlimited hierarchical model structure.

Scalar and vector connections.

Mask facility for creating custom blocks and block libraries. SIMULINK provides

an open architecture that allows you to extend the simulation environment:

You can easily perform “what if” analyses by changing model parameters – either

interactively or in batch mode – while your simulations are running.

Creating custom blocks and block libraries with your own icons and user

interfaces from MATLAB, Fortran, or C code.

You can generate C code from SIMULINK models for embedded applications and

for rapid prototyping of control systems.

You can create hierarchical models by grouping blocks into subsystems. There are

no limits on the number of blocks or connections.

SIMULINK provides immediate access to the mathematical, graphical, and

programming capabilities of MATLAB, you can analyze data, automate

procedures, and optimize parameters directly from SIMULINK.

The advanced design and analysis capabilities of the toolboxes can be executed

from within a simulation using the mask facility in SIMULINK.

The SIMULINK block library can be extended with special-purpose blocksets. The

DSP Blockset can be used for DSP algorithm development, while the Fixed-Point

Blockset extends SIMULINK for modeling and simulating digital control systems

and digital filters.

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Getting Start :

You start Simulink by clicking on the SIMULINK button on the MATLAB desktop

tool bar.

As an alternative method: type simulink in the command window

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There are several groups of Simulink blocks in the Simulink icon such as Commonly

Used Blocks, Continuous, Discontinuities, Math Operations, Sinks and Sources, etc.

Selecting Commonly Used Blocks will provide a list of blocks shown in Fig. 2.

Fig 2 : a list of blocks in Commonly Used Block group

Selecting Continuous will provide a list of blocks shown in Fig. 3. The ones that we

often use are Transfer Fcn, State-space and Integrator.

Selecting the Sources icon yields the library shown in Fig. 4. The most commonly

used sources are Clock (which is used to generate a time vector), Step (which

generates a step input), and Constant (that generate a constant function).

The Sinks icon as shown in Fig. 5 provides a set of Sinks blocks that are used to

display

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simulated results. The most often used blocks may be To Workspace (to which a

variable passed is written to a vector in the MATLAB Workspace), Scope (to

represent data graphically).

Fig 3: A list of blocks in Continuous group

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Fig 3: A list of blocks in source group

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Fig 3: A list of blocks in Sinks group

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Block Libraries

Block icon Name Use

Continuous

State-Space Implement a linear state-space system

Transfer Fcn Implement a linear transfer function

Math Operations

Derivative Merge scalar, vector or matrix signals

Divide Multiply or divide inputs

Function

Apply a specified expression to the

input

Gain Multiplies the input by a constant

value (gain)

Integrator Integrate the input signal

Math Function Perform a mathematical function

Product Multiply inputs

Sum Add or subtract inputs

Transport

Delay

Delay the input by a given amount of

time

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Signal Routing

Demux Split vector signals into scalars or

smaller vectors

Mux Extract and output the elements of a

bus or vector signal

Sinks

Scope Display signals generated during a

simulation

To Workspace Write data to the workspace

XY Graph Display an X-Y plot of signals using

a

MATLAB figure window

Sources

Clock Generate a time vector

Constant Generate a constant

Ramp Output a ramp signal

Sine Wave Generate a sine wave signal

Step General a step signal

Table 1 Summary of Commonly Used Simulink Blocks

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Example 1. Simulation of an Equation.

In this example we will use Simulink to model an equation. Let's consider

where the displacement x is a function of time t, frequency w, phase angle phi, and

amplitue A. In this example the values for these parameters are set as follows:

frequency=5 rad/sec;phase=pi/2;A=5.

1. From Simulink's library drag the following blocks to the Model Window

Blocks to be dragged to

the model window

Where located in Simulink library

browser

Ramp Sources

Constant Sources

Gain Math Operation

Sum Math Operation

Product Math Operation

Trigonometry Function Math Operation

Scope Sinks

Mux Signal Routing

2. The next step is to connect these blocks as shown.

x(t)=2cos(5t+pi/2)

cos

Trigonometric

Function

Scope

Ramp

Product

5

Gain

pi/2

Constant1

5

Constant

00

Double click on the blocks and enter the appropriate values as prompted by the pop-

up dialog windows. Note that the cosine function can be selected from the pull-down

menu in the pop-up window. In the arrangement shown above, the input signal (a

ramp function) is to be displayed along with the output (displacement) via the use of

the mux tool . To view the plots, double click on the scope.

3. Make sure all blocks are connected correctly then run the simulation (CTRL+T).

You may need to select the Autoscale button on the scope display window to obtain a

better display of the plots.

You may find the sinusoidal plots to be a bit "jaggy". You may want to improve the

resolution of the displayed plot by redefining the Max Step Side value ("auto" is set a

default value) in Simulation Parameters window (with keystrokes CTRL+E in the

model window). Just for fun, you may want to experiement with different choice of

solver. ODE45 is a default choice. You are encouraged to learn more about the solver

methods by checking out the help files in Matlab command window. For instance,

help ODE45 for parameters in non-stiff differential equations.

How Simulink Works

Simulink is a software package that enables you to model, simulate, and analyze

systems whose outputs change over time. Such systems are often referred to as

dynamic systems. The Simulink software can be used to explore the behavior of a

wide range of real-world dynamic systems, including electrical circuits, shock

absorbers, braking systems, and many other electrical, mechanical, and

thermodynamic systems. This section explains how Simulink works.

Simulating a dynamic system is a two-step process. First, a user creates a block

diagram, using the Simulink model editor, that graphically depicts time-dependent

mathematical relationships among the system's inputs, states, and outputs. The user

then commands the Simulink software to simulate the system represented by the

model from a specified start time to a specified stop time.

What Is a Solver?

A solver is a component of the Simulink software. The Simulink product provides an

extensive library of solvers, each of which determines the time of the next simulation

step and applies a numerical method to solve the set of ordinary differential equations

that represent the model. In the process of solving this initial value problem, the

solver also satisfies the accuracy requirements that you specify. To help you choose

the solver best suited for your application, Choosing a Solver Type provides

background on the different types of solvers while Choosing a Fixed-Step Solver and

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Choosing a Variable-Step Solver provide guidance on choosing a specific fixed-step

or variable-step solver, respectively.

Discrete Continuous Variable-Order

Fixed-Step Explicit Not Applicable Explicit Fixed-Step

Continuous Solvers

Not Applicable

Implicit Not Applicable Implicit Fixed-Step

Continuous Solvers

Not

Applicable

Variable-

Step

Explicit Choosing a

Variable-Step

Solver

Explicit Continuous

Variable-Step Solvers

Variable-Order

Solvers

Implicit Implicit Continuous

Variable-Step Solvers

Variable-Order

Solvers

Choosing a Solver Type

The Simulink library of solvers is divided into two major types in the Solver Pane:

fixed-step and variable-step. You can further divide the solvers within each of these

categories as: discrete or continuous, explicit or implicit, one-step or multistep, and

single-order or variable-order.

5.1) Simulation Parameters and Solver

You set the simulation parameters and select the solver by choosing Parameters from

the Simulation menu. SIMULINK displays the Simulation Parameters dialog box,

which uses three “pages” to manage simulation parameters. Solver, Workspace I/O,

and Diagnostics.

SOLVER PAGE

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The Solver page appears when you first choose Parameters from the Simulation

menu or when you select the Solver tab. The Solver page allows you to:

Set the start and stop times – You can change the start time and stop time for

the simulation by entering new values in the Start time and Stop time fields.

The default start time is 0.0 seconds and the default stop time is 10.0 seconds.

Choose the solver and specify solver parameters – The default solver provide

accurate and efficient results for most problems. Some solvers may be more

efficient that others at solving a particular problem; you can choose between

variable-step and fixed-step solvers. Variable-step solvers can modify their

step sizes during the simulation. These are ode45, ode23, ode113, ode15s,

ode23s, and discrete. The default is ode45. For variable-step solvers, you can

set the maximum and suggested initial step size parameters. By default, these

parameters are automatically determined, indicated by the value auto. For

fixed-step solvers, you can choose ode5, ode4, ode3, ode2, ode1, and

discrete.

Output Options – The Output options area of the dialog box enables you to

control how much output the simulation generates. You can choose from three

popup options. These are: Refine output, Produce additional output, and

Produce specified output only.

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NOW, make this example:

Using Simulink plot this function

Sine Wave4

Sine Wave3

Sine Wave2

Sine Wave1

Sine Wave

Scope

.5

Constant

Add

2 1 1 1 1( ) .5 cos cos3 cos5 cos7 cos9 ....

3 5 7 9x t t t t t t

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Exercise

Question 1 :

Model the equation that converts Celsius temperature to Fahrenheit. Obtain a display

of Fahrenheit-Celsius temperature graph over a range of 0 to C100 .

325

9 CF TT

First, consider the blocks needed to build the model. These are:

A ramp block to input the temperature signal, from the source library.

A constant block, to define the constant of 32, also from the source library.

A gain block, to multiply the input signal by 9=5, from the Linear library.

A sum block, to add the two quantities, also from the Linear library.

A scope block to display the output, from the sink library.

To create a SIMULINK block diagram presentation select new… from the File menu.

This provides an untitled blank window for designing and simulating a dynamic

system. Copy the above blocks from the block libraries into the new window by

depressing the mouse button and dragging. Assign the parameter values to the Gain

and Constant blocks by opening (double clicking on) each block and entering the

appropriate value. Then click on the close button to apply the value and close the

dialog box. The next step is to connect these icons together by drawing lines

connecting the icons using the left mouse button (hold the button down and drag the

mouse to draw a line).

You should now have the SIMULINK block diagram as shown below:

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The Ramp block inputs Celsius temperature. Open this block, set the Slope to 1, Start

time to 0, and the Initial output to 0. The Gain block multiplies that temperature by

the constant 9/5. The sum block adds the value 32 to the result and outputs the

Fahrenheit temperature. Pull down the Simulation dialog box and select Parameters.

Set the Start time to zero and the Stop Time to 100. Double click on the Scope, click

on the Auto Scale, the result is displayed as shown below

Question2:

Implement the below function by Simulink

32 2 X

Make sure that the range of the function appears in scope between (-3,10).