Control Systems EE 4314 Lecture 7 February 4, 2014 Spring 2014 Woo Ho Lee whlee@uta.edu

Control SystemsEE 4314

Lecture 7February 4, 2014

Spring 2014Woo Ho Lee

whlee@uta.edu

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

• mdsajeeb.rayhan@mavs.uta.edu• Office hours: Tue/Thu 10AM-12PM, Mon 4PM-6PM at NH250

– Corina Bogdan: Lab preparation & homework and report grading• Email: ioanacorina.bogdan@mavs.uta.edu• Office: NH250

– Joe Sanford: Lab lecture• Email: joe.sanford@MAVS.UTA.EDU• Office: NH250

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

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

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

Woo Ho Lee Control Systems EE 4314, Spring 2014

Torque in Permanent Magnet DC Motor

• Torque • Torque constant

n = number of loops

n=5

Woo Ho Lee Control Systems EE 4314, Spring 2014

DC Motor

• Find dynamic equations• Find transfer function 𝑚

𝑣𝑎=

Woo Ho Lee Control Systems EE 4314, Spring 2014

DC Motor

Woo Ho Lee Control Systems EE 4314, Spring 2014

DC Motor Block Diagram

Woo Ho Lee Control Systems EE 4314, Spring 2014

Loudspeaker

• Force acting on moving mass

l=2ann: number of turnsa: radius of core 𝐹

Woo Ho Lee Control Systems EE 4314, Spring 2014

Magnetic Levitation Model

• Applying KVL

• Applying Newton’s law

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

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

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

)=

=

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

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)

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 =

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

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

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:

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

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)

Woo Ho Lee Control Systems EE 4314, Spring 2014

Block Diagram: Simplification Rules

=

=

Woo Ho Lee Control Systems EE 4314, Spring 2014

Block Diagram: Reduction Rules

=

=

Woo Ho Lee Control Systems EE 4314, Spring 2014

Block Diagram Simplification

• Example: Simplify the block diagram

Woo Ho Lee Control Systems EE 4314, Spring 2014

Example