Prescott, Arizona Campus
Department of Electrical and Computer Engineering
EE 402 Control Systems Laboratory
Fall Semester 2013
Lab Section 01
Thursday 1:25 – 4:05 pm
King Eng. Bldg. Rm 122
Lab Instructor:
Dr. Stephen Bruder
Lab 01
Control Systems Modeling & Analysis with MATLAB
Date Experiment Performed:
Thursday, September 05, 2013

Instructor’s Comments:
Comment #1

Comment #2
Date Report Submitted:
Monday, September 09, 2013
Group Members:
Student # 1 Name & Email
Student # 2 Name & Email
Grade:
EE 402 Control Systems Lab
TABLE OF CONTENTS
Fall 2013
PAGE
1.
Abstract .................................................................................................................................... 3
2.
Introduction ............................................................................................................................. 3
3.
Objectives ................................................................................................................................ 4
4.
Theory and Experimental Methods ......................................................................................... 5
5.
Equipment and Procedures ...................................................................................................... 6
5.i.
6.
System Analysis Using Simulink ..................................................................................... 7
Results and Discussion ............................................................................................................ 7
6.i.
Case I: C = 8,000 µF ........................................................................................................ 7
6.ii.
Case II: C = 800 µF .......................................................................................................... 8
6.iii.
Case III: C = 80 µF ....................................................................................................... 8
7.
Conclusion ............................................................................................................................... 9
8.
References ............................................................................................................................... 9
9.
Appendix ................................................................................Error! Bookmark not defined.
LIST OF TABLES
PAGE
Table 1 Title … ..............................................................................Error! Bookmark not defined.
LIST OF FIGURES
PAGE
Figure 1 An example of a Simulink based simulation [1]. ............................................................. 4
Figure 2 An electrical system example from class ......................................................................... 5
Figure 3 MATLAB code used to check answer.............................................................................. 6
Figure 4 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 8,000 µF) .................................. 7
Figure 5 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 8,000 µF) using Simulink ......... 8
Figure 6 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 800 µF) using Simulink ............ 8
Figure 7 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 80 µF) using Simulink .............. 9
LIST OF SYMBOLS
Names of Students in the Group
PAGE
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EE 402 Control Systems Lab
Fall 2013
1. ABSTRACT

A stand-alone summary of the report – the work done and results observed.

The abstract should address:
o What is the objective of the experiment?
o What type of experiment is performed to achieve the objective?
o What are the major results of the experiment?
o What conclusions can be made from these results?

Write this after you have finished all of the other sections!!

The abstract should be less than a page and closer to a ½ page in length.
2. INTRODUCTION
MATLAB®, which stands for matrix laboratory, is a 4th generation programming language
primarily focused on matrix/vector type numerical calculations; however, it also has support for
symbolic calculations (i.e., computer algebra) via the Symbolic Toolbox. MATLAB was
initially developed by Dr. Cleve Moler, a Computer Science professor at the University of New
Mexico, to allow his students easier access to linear algebra packages. Since then, it has been
widely adopted by engineering disciplines and is particularly popular amongst control engineers.
Simulink® is a companion product to MATLAB and is a powerful graphical programming
tool for modeling, analyzing, and designing control systems. Figure 1 gives an example of the
graphical design of a controller for experimental hardware developed by Educational Control
Products (ECP) [1].
Names of Students in the Group
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EE 402 Control Systems Lab
Fall 2013
Figure 1 An example of a Simulink based simulation [1].
Many excellent online tutorials exist for both MATLAB and Simulink.
In this lab we will explore some specific attributes of MATLAB/Simulink that will be of
particular interest to us in support of our later modeling, analysis, and design of control systems.
3. OBJECTIVES

Review some basics of the MATLAB programming language (pre-lab)

Introduce the Simulink graphical programming environment

Develop a preliminary competency with the symbolic toolbox

Model and analyze physical systems using both MATLAB and Simulink

Establish the relevance of the MATLAB/Simulink toolset for later control systems
designs.
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EE 402 Control Systems Lab
Fall 2013
4. THEORY AND EXPERIMENTAL METHODS
Consider the first electrical system example from class, reproduced in Figure 2 below.
L
i (t )
R
vin (t )
vout (t )
C
Figure 2 An electrical system example from class
The transfer function of the system with the denominator written as a monic polynomial is
R 1
1
s 
s
Vout ( s)
R
L LC   
RC
 G(S ) 
 
R
1
R
Vin ( s)
 L  s2  s  1
s2  s 
L LC
L LC
The roots of the denominator polynomial of the transfer function (also referred to as the poles
of the system) are
s1,2  
R 1

2L 2
 R  2 4 
  

 L  LC 
R 1 R 2C  4 L

2L 2
L2C
R
1


R 2C  4 L
2L 2L C

Note that, if 4L  R 2C , then the roots will become complex.
Given values for the passive components as R = 10  and L = 100 mH, what is the threshold
value for C below which the roots become complex?
C
Names of Students in the Group
F
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EE 402 Control Systems Lab
Fall 2013
5. EQUIPMENT AND PROCEDURES
Set the values for the passive components as R = 10 , L = 100 mH, and C = 8,000 µF. For
the case of a unit step input ( Vin ( s)  1/ s ), compute the partial fraction expansion for the output
voltage in the Laplace domain
Vout ( s ) 


and hence, solve for the output voltage in the time domain
vout (t ) 
,t  0
Check your result for vout (t ) using the Symbolic Toolbox (v_out_t = ilaplace(1/s * G)) and
plot vout (t ) vs time for t = 0,…, 0.2 seconds in Figure 4.
HINT:

In MATLAB, plot the symbolic variable “v_out_t” using:
o ezplot(v_out_t, [0 0.2])
o ylim([0 1.5])

In MuPAD, plot the symbolic variable “v_out_t” using:
o plot(v_out_t, {#X=0..0.2, #Y=0..1.5})
Past your code in Figure 3 below.
Figure 3 MATLAB code used to check answer
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EE 402 Control Systems Lab
Fall 2013
Figure 4 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 8,000 µF)
5.i. System Analysis Using Simulink
As shown in the pre-lab, Simulink can also be used to analyze control systems. Use Simulink
to build a simulation of your circuit.
6. RESULTS AND DISCUSSION
Using your Simulink simulation to compare the unit step response ( vin (t )  u(t ) ) of the
system with R = 10 , L = 100 mH, and three different values of C.
6.i. Case I: C = 8,000 µF
When C = 8,000 µF where are the poles (i.e., roots of the denominator of G(s)) of the system?
s1 
, s2 
Plot your system’s Simulink derived step response below:
Names of Students in the Group
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EE 402 Control Systems Lab
Fall 2013
Figure 5 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 8,000 µF) using Simulink
6.ii. Case II: C = 800 µF
When C = 800 µF where are the poles (i.e., roots of the denominator of G(s)) of the system?
s1 
, s2 
Plot your system’s Simulink derived step response below:
Figure 6 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 800 µF) using Simulink
6.iii.
Case III: C = 80 µF
When C = 80 µF where are the poles (i.e., roots of the denominator of G(s)) of the system?
s1 
Names of Students in the Group
, s2 
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EE 402 Control Systems Lab
Fall 2013
Plot your system’s Simulink derived step response below:
Figure 7 A plot of vout (t ) vs time for t = 0,…, 0.2 seconds (C = 80 µF) using Simulink
7. CONCLUSION
What can you say (qualitatively) about the effect of the location of the system’s poles on the
output response?
8. REFERENCES
[1] www.ecpsystems.com
Names of Students in the Group
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