Announcement on Jan. 21
• Textbook: Not available at UTA bookstore. Ordered 1/16.
• Office hour: Tue/Thu 3:30 pm – 5:00 pm NH250 Lab
• TAs:
– Sajeeb Rayhan: Home work grading and office hours
• mdsajeeb.rayhan@mavs.uta.edu
• Office hours: Tue/Thu 10AM-12PM at NH250
– Corina Bogdan: Lab preparation & report grading
• ioanacorina.bogdan@mavs.uta.edu
– Nahum Torres & Joe Sanford: Lab instruction
• nahum.torres-arenas@mavs.uta.edu
• Lab#1: MATLAB & Simulink sessions
– Location: ELAB 256
– Session1: January 21, Tuesday 6:30PM-8:30PM
– Session2: January 23, Thursday 6:30PM-8:30PM
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Labs #2-6 Schedule
• Four Sessions (Total: 42 students)
 Session 101: Tue: 3:30PM-5:20PM (12 students)
 101A (6)
 101B (6)
 Session 102: Tue: 5:30PM-7:20PM (11 students)
 102A (6)
 102B (5)
 Session 103: Wed: 2:00PM-3:50PM (12 students)
 103A (6)
 103B (6)
 Session 104: Wed: 4:00PM-5:50PM (7 students)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Labs #2-6 Schedule
 Lab #2:
–
–
–
–
101A and 102A: Feb. 4 (Tue)
103A and 104: Feb. 5 (Wed)
101B and 102B: Feb. 11 (Tue)
103B: Feb. 12 (Wed)
Tuesday
Wednesday
101 (3:30-5:20)
103 (2-3:50)
102 (5:30-7:20)
104 (4-5:50)
 Lab #3:
–
–
–
–
101A and 102A: Feb. 18 (Tue)
103A and 104: Feb. 19 (Wed)
101B and 102B: Feb. 25 (Tue)
103B: Feb. 26 (Wed)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Labs #2-6 Schedule
 Lab #4:
–
–
–
–
101A and 102A: Mar. 18 (Tue)
103A and 104: Mar. 19 (Wed)
101B and 102B: Mar. 25 (Tue)
103B: Mar. 26 (Wed)
Tuesday
Wednesday
101 (3:30-5:20)
103 (2-3:50)
102 (5:30-7:20)
104 (4-5:50)
 Lab #5:
–
–
–
–
101A and 102A: Apr. 1 (Tue)
103A and 104: Apr. 2 (Wed)
101B and 102B: Apr. 8 (Tue)
103B: Apr. 9 (Wed)
 Lab #6:
–
–
–
–
101A and 102A: Apr. 15 (Tue)
103A and 104: Apr. 16 (Wed)
101B and 102B: Apr. 22 (Tue)
103B: Apr. 23 (Wed)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Session (12)101A & 101B
101A
101B
Saad Akhtar
Sanjeeb Banjara
Asrat Beshah
Blake Farmer
Hawariya Gebremedhien
Nadim Giotis
Daniel Goodman
Leighlan Jensen
Kevin Oseguera
Prabesh Poudel
Eric Reiser
Caroline Storm
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Session (11) 102A & 102B
102A
102B
Laury Arcos
Matthew Barboza
Monica Beltran
Victoria Brandenburg
Israel Fierro
John Fierro
Haile Fintie
Samuel Luce
Blen Mamo
Nisha Shrestha
Christopher Williams
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Session (12) 103A & 103B
103A
103B
Joshua Berry
Pasquier Biyo
Aaron Dyreson
Pursottam Giri
Prem Kattel
Gregory Martin
Bardia Mojra
Vihang Parmar
Abison Ranjit
Thyag Ravi
Sharad Timilsina
Hannah Vuppula
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Session 104 (7)
104
Kishor Budhathoki
Andrew Garner
Mezhar Hajizadeh
Emrys Maier
Ipesh Pandey
Joshua Prickett
Bishwas Silwal
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Lecture 3: Dynamic Models
• Dynamics of Mechanical Systems
– Newton’s 2nd law
• F=ma (translation)
• M=I (rotation)
– Mass-Spring-Dashpot Model
• Mass (m)
• Spring (Spring force 𝐹𝑠 = 𝑘𝑥)
• Dashpot (Damping force 𝐹𝑑 = 𝑏𝑥)
Spring: store energy, dashpot: dissipate energy
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Newton’s 2nd Law:
Translational Motion
• Newton’s 2nd law governs the relation between
acceleration and force
• Acceleration is proportional to force, and inversely
proportional to mass
F=ma
where,
• F = the vector sum of all forces applied to each
body in a system, newton (N)
• a = the vector acceleration of each body w.r.t. an
inertial reference frame (m/sec2)
• m = mass of the body (kg)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Newton’s 2nd Law:
Rotational Motion
• Newton’s 2nd law governs the relation between angular
acceleration and moment (torque)
• Angular acceleration is proportional to moment, and
inversely proportional to moment of inertia
M=I
where,
• M = the sum of all external moments about the
center of mass of a body in a system, (N-m)
•  = the angular acceleration of the body w.r.t. an
inertial reference frame (rad/sec2)
• I = body’s moment of inertia about its center of
mass (kg-m2)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Moment of Inertia I
– It is a measure of an object’s resistance to changes to its
rotation. Equivalent to mass of an object.
– It should be specified with respect to a chosen axis of
rotation.
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Moment of Inertia I
– Moment of inertia becomes smaller when mass is
concentrated on the axis of rotation
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Moment of Inertia I
Rotation in the
middle of bar
Distributed mass
Lumped mass
L
L
L
m
m
m
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Moment of Inertia I
Rotation in the
middle of bar
Distributed mass
Lumped mass
L
L
L
m
m
m
𝐼 = 𝑚𝐿2
Woo Ho Lee, Control Systems EE 4314, Spring 2014
1 2
𝐼 = 𝑚𝐿
3
1
𝐼=
𝑚𝐿2
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15
Spring Model
Two springs in parallel
Woo Ho Lee, Control Systems EE 4314, Spring 2014
Two springs in series
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Spring Model
Two springs in parallel
Two springs in series
When k=k1=k2, keq=2k
When k=k1=k2, keq=0.5k
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Spring and Dashpot Model
m
?
m
?
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Mass Spring Dashpot System
• Derive equation of motion
f
• Transfer function 𝐺 𝑆
– Input: force f
– Output: displacement y
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Mass Spring Dashpot System
• Applying Newton’s 2nd law,
f
𝑚𝑦 = −𝑏𝑦 − 𝑘𝑦 + 𝑓
• Taking the Laplace transform
𝑚𝑠 2 + 𝑏𝑠 + 𝑘 𝑌 𝑠 = 𝐹(𝑠)
• Transfer function 𝐺 𝑆 =
Woo Ho Lee, Control Systems EE 4314, Spring 2014
𝑌(𝑠)
𝐹(𝑠)
=
1
𝑚𝑠 2 +𝑏𝑠+𝑘
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MATLAB Simulation
Mass Spring Dashpot System
• Transfer function 𝐺 𝑆 =
𝑌(𝑠)
𝐹(𝑠)
=
1
𝑚𝑠 2 +𝑏𝑠+𝑘
• m=1, k=1
• Case study
– b=1 (underdamped <1)
– b=2 (critically damped =1)
– b=3 (over damped >1)
num = 1
den = [1 b 1]
sys = tf(num, den)
step(sys)
Woo Ho Lee, Control Systems EE 4314, Spring 2014
f
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Mass Spring Dashpot System
• Automobile suspension system
Problem: Find the transfer function
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Mass Spring Dashpot System
• Automobile suspension system
• The equation of motion for the system
• Taking the Laplace transform
• Transfer function
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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Cruise Control Model
• Example 2.1
– Write the equations of motion
– Find the transfer function
• Input: force u
• Output: velocity
Cruise control model
Woo Ho Lee, Control Systems EE 4314, Spring 2014
Free-body diagram
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Cruise Control Model
• Example 2.1
– Applying Newton’s 2nd law
𝑚𝑥 = −𝑏𝑥 + 𝑢
𝑏
𝑢
𝑥+ 𝑥=
𝑚
𝑚
– Since v = 𝑥, 𝑣 = 𝑥
𝑏
𝑢
𝑣+ 𝑣=
𝑚
𝑚
- Transfer function
Woo Ho Lee, Control Systems EE 4314, Spring 2014
Free-body diagram
25
Week 2, Lecture 3: Reading and
Practice
Reading for week 2:
- Franklin Textbook Chapter 2, Dynamic Models:
- 2.1: Dynamics of Mechanical Systems
- 2.2: Models of Electric Circuits
- Modern Control Engineering by K. Ogata
- Chapter 3 Mathematical Modeling of Mechanical Systems and
Electrical Systems
Woo Ho Lee, Control Systems EE 4314, Spring 2014
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