Control Systems EE 4314 Lecture 7 February 4, 2014 Spring 2014 Woo Ho Lee [email protected].
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Transcript of Control Systems EE 4314 Lecture 7 February 4, 2014 Spring 2014 Woo Ho Lee [email protected].
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Announcement• Lab#2: Identification of DC motor transfer function– Location: NH250– Feb. 4, Tuesday
• 101A (3:30-5:20PM)• 102A (5:30-7:20PM)
– Feb. 5, Wednesday • 103A (2:00-3:50PM)• 104 (4:00-5:50PM)
• Class website: www.uta.edu/ee/ngs/ee4314_control– Homework #1: Due by Feb. 6.– Lab #1 report is due by Feb. 13.– Lab #2 handout is posted.
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Woo Ho Lee Control Systems EE 4314, Spring 2014
TAs Update
• TAs:– Sajeeb Rayhan: Home work grading and office hours
• [email protected]• Office hours: Tue/Thu 10AM-12PM, Mon 4PM-6PM at NH250
– Corina Bogdan: Lab preparation & homework and report grading• Email: [email protected]• Office: NH250
– Joe Sanford: Lab lecture• Email: [email protected]• Office: NH250
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Labs 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)
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Labs #2 Schedule Lab #2: NH250– 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)
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Session (12)101A & 101B101A 101B
Saad Akhtar X
Sanjeeb Banjara X
Asrat Beshah
Blake Farmer
Hawariya Gebremedhien
Nadim Giotis X
Daniel Goodman X
Leighlan Jensen X
Kevin Oseguera X
Prabesh Poudel X
Eric Reiser X
Caroline Storm x
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Session (11) 102A & 102B
102A 102B
Laury Arcos
Matthew Barboza X
Monica Beltran X
Victoria Brandenburg X
Israel Fierro X
John Fierro X
Haile Fintie
Samuel Luce
Blen Mamo X
Nisha Shrestha
Christopher Williams x
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Session (12) 103A & 103B103A 103B
Joshua Berry X
Pasquier Biyo X
Aaron Dyreson X
Pursottam Giri X
Prem Kattel X
Gregory Martin x
Bardia Mojra X
Vihang Parmar X
Abison Ranjit X
Thyag Ravi X
Sharad Timilsina X
Hannah Vuppula X
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Electromechanical Systems
• Physics– Law of motors: • Convert electric energy (i) to mechanical work (F)
– Law of generator: • Mechanical motion electric voltage
Where : strength of magnetic field: length of a coil: velocity of the conductor: Force acting on the conductor: voltage across the conductor
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Magnetic Force on Current Carrying Wire
• Force I: currentB: strength of magnetic field: length of a wire that carries current I through a magnetic field
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Torque in Magnetic Field
• Force • Torque • Torque constant
a=radius of wire loop
B
F
F
I
I
𝑙
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Torque in Permanent Magnet DC Motor
• Torque • Torque constant
n = number of loops
n=5
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Woo Ho Lee Control Systems EE 4314, Spring 2014
DC Motor
• Find dynamic equations• Find transfer function 𝑚
𝑣𝑎=
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Woo Ho Lee Control Systems EE 4314, Spring 2014
DC Motor
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Woo Ho Lee Control Systems EE 4314, Spring 2014
DC Motor Block Diagram
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Loudspeaker
• Force acting on moving mass
l=2ann: number of turnsa: radius of core 𝐹
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Magnetic Levitation Model
• Applying KVL
• Applying Newton’s law
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Heat Flow
• Heat flow
q: heat energy flow (J/sec)R: thermal resistanceT: temperature
• Relation between temperature of the substance and heat flow
C: thermal capacity
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Heat Flow
• Find the differential equations that determine the temperature in the room (four sides are thermally insulated)
𝑇 1
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Heat Flow
• Find the differential equations that determine the temperature in the room (four sides are thermally insulated)
𝑇 1
)=
=
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Water Tank Example
• Physics governing fluid flowContinuity equation: wherem: fluid mass within the system ( win: mass flow rate into the system
wout: mass flow rate out of the system
Differential equation that governs the height of water) (1)A: area of the tank: density of waterh: height of water
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Water Tank Example
• Fluid flow through an orifice (2)where: hydrostatic pressure : ambient pressure
• Substituting (2) into (1) gives ) (3)• Linearization involves selecting the operating point (4)
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Water Tank Example
• Substituting (2) into (1) gives = = = ] (5)
• Substituting (5) into (3) gives ]) (6)• Since =
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Hydraulic Actuator with Valve
• Find nonlinear differential equations relating the movement of the control surface to the input displacement x of the valve.
Input
Output
Fluid inFluid out
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Hydraulic Actuator• Flow goes inside of piston
• Flow come out of piston
• Continuity relation
A: piston area• Force equation
m: mass of piston and attached rod• Moment equation
I: moment of inertia of the control surface and attachment• Kinematic relationship between and y
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Key Equations for Dynamic Models• Mechanical system
– Newton’s 2nd law (translation): F=ma – Newton’s 2nd law (rotation): M=I – Hook’s law: F=kx
• Electrical system– KCL (Kirchhoff’s current law): 𝐼in= 𝐼out
– KVL (Kirchhoff’s voltage law ): V closed loop=0– Ohm’s law
• Electromechanical system– Law of motors:
Convert electric energy (i) to mechanical work (F)
– Law of generator: Mechanical motion electric voltage
– Torque developed in a rotor: – Back emf:
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Chapter 3: Block Diagrams
• Block Diagram Model: – Helps understand flow of information (signals) through a complex system– Helps visualize I/O dependencies– Elements of block diagram:
• Lines: Signals• Blocks: Systems• Summing junctions• Pick-off points
Transfer Function Summer/Difference Pick-off point+
H(s)U(s) Y(s) +
U2
U1 U1+U2 U U
U
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Three Examples of Elementary Block Diagrams
(a) Cascaded system G1(s)G2(s) (b) Parallel system G1(s)+ G2(s)
(b) Negative feedback system𝐺1(𝑠)
1+𝐺1 (𝑠 )𝐺2 (𝑠)
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Block Diagram: Simplification Rules
=
=
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Block Diagram: Reduction Rules
=
=
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Block Diagram Simplification
• Example: Simplify the block diagram
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Woo Ho Lee Control Systems EE 4314, Spring 2014
Example