Control Systems EE 4314 Lecture 7 February 4, 2014 Spring 2014 Woo Ho Lee [email protected]

Control SystemsEE 4314

Lecture 7February 4, 2014

Spring 2014Woo Ho Lee

[email protected]

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.

2


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

mailto:[email protected]

mailto:[email protected]


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)

4


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)

5


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

6


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

7


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

8


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


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


Torque in Magnetic Field

• Force • Torque • Torque constant

a=radius of wire loop

B

F

F

I

I

𝑙


Torque in Permanent Magnet DC Motor

• Torque • Torque constant

n = number of loops

n=5


DC Motor

• Find dynamic equations• Find transfer function 𝑚

𝑣𝑎=


DC Motor


DC Motor Block Diagram


Loudspeaker

• Force acting on moving mass

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


Magnetic Levitation Model

• Applying KVL

• Applying Newton’s law


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


Heat Flow

• Find the differential equations that determine the temperature in the room (four sides are thermally insulated)

𝑇 1


Heat Flow

• Find the differential equations that determine the temperature in the room (four sides are thermally insulated)

𝑇 1

)=

=


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


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)


Water Tank Example

• Substituting (2) into (1) gives = = = ] (5)

• Substituting (5) into (3) gives ]) (6)• Since =


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


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


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:


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


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)


Block Diagram: Simplification Rules

=

=


Block Diagram: Reduction Rules

=

=


Block Diagram Simplification

• Example: Simplify the block diagram


Example

Documents

Control Systems EE 4314 Lecture 7 February 4, 2014 Spring 2014 Woo Ho Lee [email protected]