Lab Exercise 4 Dynamic System Analysis

1
Lab Exercise 4 Dynamic System Analysis

• AME 20213
• Matthew Bennington
• mbenning_at_nd.edu

2
Outline

• Introduction and Objective
• First Order System
• Second Order System
• Background and Equipment
• Part I
• Part II
• Part III
• Grading
• Schedule
• Testing Matrix

3
Intro and Objective

• Dynamic Response Characterization
• To Understand a Systems Response to a Given
  Input
• Objective To Characterize A First (Part I),
  Second Order System (Part II) and Unknown Order
  System (Part III).

4
First-Order System
General Equation
Time Constant
For Part I
5
First-Order System
Solution
6
First Order System (Cont.)

• Response to Step-Input Forcing

System Response
M(t)1 e-t/t
M(t)0.632 _at_ t/t1
7
Second Order System
Damping Ratio
Natural Frequency
For Part II
8
Second Order System
9
Equipment

• Thermocouple
• Digital Oscilloscope (DO)
• Frequency Generator (Model will Vary)
• RLC Circuit
• Unknown Circuit

10
Part I Experimental Setup
TRJA
Digital Oscilloscope
Thermocouple
Ice Bath
11
Part I Data
To
12
Part I Data
13
PART II Experimental Setup
Digital Oscilloscope
2
Function Generator
RLC
1
14
Part II Electric Circuit (RLC)
Variable Resistor R 1 O to 910 O
L 5 mH (R 9.0 O)
Eo
Ei
C0.68 µF
15
Data Part II
?t
Eo
Ei
16
Data Part II
.
17
Data Part II Cont.
F(?)
M(?)
?/?n
?/?n
18
Part III Experimental Setup
Digital Oscilloscope
2
Function Generator
??
1
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Part III Data
20
Grading-LAB REPORT

• Deliverables
• 1) Plot the thermocouple data and determine the
  time constant directly. Transform the variables
  and perform a linear least-squares regression
  analysis. From that determine the time constant.
  Compare the time constants obtained from the two
  methods. Which method is more accurate and why?
• 2) From your knowledge of the thermocouple, which
  (A or B) would have a larger time constant and
  why?
• 3) Complete RLC response data table
• 4) Using these results and a program or M-fle,
  construct two plots on of M(?) and other of F(?)
  versus the normalized frequency ratio. These
  plots must contain the data along with the
  theoretical curves.
• 5) Does the data support the conclusion the RLC
  circuit behaves as a second-order system in both
  cases? Finally, compare the values of the
  damping ratio found with the value of R/Rc. Do
  this by comparing the data with the corresponding
  values determined using various values of R/Rc
  in the given equations. How well do the
  experimental and theoretical values of ? compare?
• 6) Identify the range over which the unknown
  circuit varies in Magnitude ratio the most. With
  the data from this range identify what type of
  system the unknown circuit represents.

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Schedule, etc.

• 2 students per group, duplicate group s are not
  allowed
• Variation Achieved by choosing different
  thermocouples, assigning different Variable
  Resistance Values and Frequency Multipliers and
  different unknown circuit settings
• Use Technical Report Format
• Chapter 3 of the text for guidelines
• Lab will be run in Fitzpatrick B 14
• Be there for the day you sign up, no excuses.

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Test Matrix
6
7
5
4
8
3
9
Resistor Dial Setting
2
10
11
1
Frequency Multiplier (K)
Max
Min