CHEE319_tutorial1

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CHEE 319

Introduction to the MATLAB SIMULINK Program

Using Simulink to perform open-loop simulations

MATLAB, which stands for MATrix LABoratory, is a technical computing environment for high-

performance numeric computation and visualization. SIMULINK is a part of MATLAB that canbe used to simulate dynamic systems. To facilitate model definition, SIMULINK adds a new

class of windows called block diagram windows. In these windows, models are created and edited

primarily by mouse- driven commands. Part of mastering SIMULINK is to become familiar with

manipulating model components within these windows. The purpose of this tutorial is to introduce

you to SIMULINK and give you experience simulating dynamic systems.

Launching SIMULINK

In this tutorial, you will use SIMULINK to generate an open-loop set-point and load response fora linear process. In the second part of the tutorial, you will generate the closed-loop set-point and

load responses.

Open MATLAB. Start Simulink by typing simulinkin the Matlab command prompt >>.

Once the simulink library window block opens, you will create a new Model.

To create a model, click on File in the simulink block, followed by new and then Model. A

blank page opens. You are now ready to build a Simulink model. Save the empty model

by choosing Save from the File menu in the untitled window. Name the model, examplesim.

From this point on, the model will be referred to as examplesim.

This tutorial is part 1 of two tutorials. In the first part, you will build a model of the open-loop

system for a nonlinear process and determine the response of the system to sinusoidal, step and

ramp inputs. We make use of the Differential Equation Editor (DEE) to perform the simulations.

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Problem Statement

In class, we developed a dynamic model of the gravity tank. A schematic diagram of the process

is shown below.

The dynamics of the process are given by:

dh

dt =

Fo

A

Apv

A (1)

dv

dt =

hg

L

Kfv2

ApL (2)

where A and Ap are the cross-sectional areas of the tank and the outlet pipe, g (=9.8 m/sec2) is

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the gravitation constant, L is the length of the outlet pipe, h is the height of liquid in the tank,

v is the average velocity of the fluid in the outlet pipe, Kf is the pipe friction constant, is the

density of the fluid and Fo is the inlet flowrate of fluid to the tank. It is assumed that the tank

and the outlet pipe are cylindrical.

The tank has a radius Rof 2 m. The inner radius of the pipe, r, is 0.125 m. The outlet pipe is 10

m in length. The density of the fluid is 1000 kg/m3. The friction constant is 4.0.

We will now simulate the dynamic behavior of the nonlinear process using the SIMULINK differ-

ential equation editor (DEE). You can input the differential equation as they are formulated using

the DEE.

To invoke the DEE editor, typeDEEat the MATLAB command prompt. This will open the

DEE window.

Click and drag the DEE icon to your untitled SIMULINK worksheet.

Double Click on the DEE to invoke the entry window. You must enter the number of in-

puts, the differential equations, the initial conditions and the output functions that you are

interested in.

For this case, there is 1 input, the inlet flow. To enter the system of equations, you must use

the DDE syntax. The variables that you are solving for are given as entries in the array x.

Leth=x(1) andv=x(2). The input variable, Fo, is given as the first entry in the array u, i.e.,

u(1). All other variables of the system must be set to their numerical values.

To solve the system, you must supply the initial conditions. Let h(0)=3 and v(0)=4.

Finally, enter the output functions that you are interested in, i.e., x(1) and x(2). Once you

close the DEE editor window you will see that the DEE block has one input Fo and two

outputs h and v.

Copy a Step Input block from the Sources menu, place the block to the left of DEE editor

window and connect it to the input. The Step Input block generates a step function. The

step time (time at which the step occurs), initial value, and final value of the function can be

specified.

Copy two (2) To Workspace blocks to the right of the DEE block and connect the outputs

of the DEE block to the two (s) new To Workspace blocks. Double-click on the new blocks

and set the Variable name to h and v, respectively. The model developed to this point is a

model of the open-loop system. To facilitate the analysis, you can choose to change the Save

format of the output variables by selecting the ARRAY in the save format item of the menu.

Now we are ready to simulate the open-loop response of the system. To select the integration

technique and parameters to be used during simulations, pull down the Simulation menu and

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choose Parameters. A dialog box is opened showing all the simulation parameters that can

be modified. Set the Stop Time to 500 and the Max Step Size to 1. Because the system

is easy to integrate numerically , SIMULINK can and will take integration step sizes equal

to the default value. If this occurs, the appearance of the response will not be smooth. By

setting Max Step Size to 1, the outputs u and v will be output to the workspace each timeinterval and the simulated response will be smoother. Start the simulation by selecting Start

from Simulation menu. The resulting h, v and t variables in the workspace will be for the

open-loop unit set-point response.

Once a simulation has been completed, the resulting data can be manipulated and analyzed

using MATLAB. Select the MATLAB command window and type

>> plot(t,h)

to view the response. Theplot command opens a MATLAB Figure window and generates a

plot inside the window. To add x and y axis labels and a title type xlabel(Time) ylabel(h)

title(Step Response (Open-Loop)). Repeat this for the variable v.

Perform the following steps. i) Assuming an inlet flow of 0.45 m3/sec, find the steady-state values

for the height of liquid in the tank and the outlet pipe fluid velocity. Report the steady-state

value and show the resulting plots of h and v. ii) Starting for this steady-state, perform a 0.25

m3/sec step increase and a 0.25 m3/sec step decrease in inlet flowrate. Report the two new sets of

steady-state values. Generate a first plot showing both step responses for the level and a second

showing the step responses for the velocity. Briefly comment on the extent of nonlinearity of this

process.

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