Spring 2011

Electrical Systems I

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

TOYOTA Freer Movement Control System

4Wheel independent drive 4wheel independent steering 4wheel independent braking By ‘wheel-in-motor’

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

TOYOTA Freer Movement Control System

TOYOTA Freer Movement Control System

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

TOYOTA Freer Movement Control System for Auto-Parking

TOYOTA Freer Movement Control System for Auto-Parking

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Autonomous Robot Vehicle

Autonomous Robot Vehicle

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

견마형 로봇 차량의 주행 제어 알고리즘

T

T

V

2

F

F

1

F

2

F

u ¹

u

T

T

x

V

 ^M

^F

5

F

4

F

6

F

F

F

u

_u

T

T

_ x des

F

6

F

F

u

u

6WD6WS Vehicle

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Vz

6WD6WS Vehicle

Vz

Ψ

S4 Zu6

S6

Vx Vy

Ф

Θ

Zu2 S2

Zu1 S1

Z 2

S3 Zu4

Zu5 S5

w4 Zu3

w6

Fx2

Z u 2

Fx4 Fy4

Fx5 Fy5

w2

w1

w3

Fx6 Fy6 w5

Fx2



Fy2

Fx1 Fy1

Fx3 Fy3

Fy5

v

 

BLDC Wheel-in-Motor of 6WD6WS Vehicle

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Configuration of 6WD6WS Vehicle

Sectional View of BLDC Motor Sectional View of BLDC Motor

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Video of 6WD/6WS Vehicle equipped with Wheel- Video of 6WD/6WS Vehicle equipped with Wheel in Motor

Parallel & Circular Turning Remote Control Autonomous Driving

평행_제자리선회.wmv Remote_general_recent.avi Autonomous_path_tracking.avi

Hybrid and Electrical Vehicles Hybrid and Electrical Vehicles

Advantages

 Minimized both costs and technical issues

 Even weight distribution

 Even weight distribution

 Simplest packaging

 Improved vehicle chassis control

Targets

 To maintain or improve on Euro 4 emissions

 To maintain or improve on Euro 4 emissions

 To achieve a 30% overall reduction in CO ₂ tail pipe emissions of the baseline vehicle operating with the same fuel, over the NEDC cycle as per EC/98/69 and EC/70/220 for vehicles less than 3500kg.

EC/70/220 for vehicles less than 3500kg.

 Equivalent fuel economy  60mpg=25.4kpl (50% improvement in mpg on baseline vehicle)

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Hybrid and Electrical Vehicles Hybrid and Electrical Vehicles

Skoda Fabia (Compact SUV) ( p )

Hybrid 4WD Vehicle Configuration

Developed by MIRA (Skoda Fabia) 35 KW / 250 Nm Peak Torque

Hybrid 4WD Vehicle Configuration

1400 cc 100 HP ICE

3:1 reduction belt drive

 Peak torque = 750 Nm A total weight of around 150kg:

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

 Peak torque = 750 Nm

motors = 2x45kg, inverters=2x15kg, structure=30kg

4 WD In-wheel Electric Vehicle

Electric vehicle equipped with Front two in-wheel motors

Michelin Active Wheel with in-wheel motor, suspension and brake system

Electric vehicle equipped with four in-wheel motors

4 WD Electric Vehicle Combinations 4 WD Electric Vehicle Combinations

▪ Front/rear Two In-line Motors ▪ Front In-line Motor/Rear In-wheel motors

DrivMot vingtor 1

▪ Four In-wheel Motors ▪ Front Engine Drive/Rear Two In-wheel Motors

Brake 2 Brake 4 Motor 2

Main Controller

[MCU]

Trans- mission

Engine

Brake 1 Brake 3 Motor 1

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

6WD Skid Steering Vehicle 6WD Skid Steering Vehicle

Crusher APD

8WD/4WS Vehicle Equipped with 8 In-wheel Motor 8WD/4WS Vehicle Equipped with 8 In wheel Motor AHED

AHED_8x8_vehicle_vedio.wmv

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Basic Elements

 Active Elements: OP Amp etc.

(Has transistors/amplifiers that require active source of power to work)

P i El t I d t R i t C it t

 Passive Elements: Inductor, Resistor, Capacitor etc.

(Simply respond to an applied voltage or current.)

 Current : the rate of flow of charge

 Charge : (electric charge) the integral of current with respect to time [C]

dt i  dq

[sec]

[coulomb]

[ampere] 

 Charge : (electric charge) the integral of current with respect to time [C]

 Voltage : electromotive force needed to produce a flow of current in a wire [V]

Change in energy as the charge is passed through a component.

Basic Elements - Resistance

 Resistance : the change in voltage required to make a unit change in current.

Analogous to  Damping Element [ ] [ ( )]

[ ] Change in voltage V

R Ohm

Change in current A

   

 Resistor

R R

R

V R i R V

   i

 R 

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Basic Elements - Capacitance p

 Capacitance: the change in the quantity of electric charge required

 Capacitance: the change in the quantity of electric charge required to make a unit change in voltage.

Analogous to  Spring Element (Stores Potential Energy)

[ ]

[ ( )]

[ ] Coulomb

C Farad F

 V 

 Capacitor: two conductor separated by non-conducting medium.

/ ,

/ de

,

1

i  dq dt , e  q C   i C , de  i dt

( ) 1 (0)

c c

t

c c

q q

dt C

e t i dt e

   

Basic Elements - Inductance

 Inductance: An electromotive force induced in a circuit if the circuit lies in a time

 Inductance: An electromotive force induced in a circuit, if the circuit lies in a time -varying magnetic field.

A l  I i El (S Ki i E )

[ ] [ ( )]

[ / sec]

L V Henry H

 A 

Analogous to  Inertia Element (Stores Kinetic Energy)

[ ]

 Inductor:

di

e L

 dt V s ( )  LsI s ( )

0

( ) 1 (0)

t

L L L

i t e dt i

  L   ^{I s ( )  Ls 1 V s ( )}

( ) i t

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

( )

Series & Parallel Resistance

S i R i t P ll l R i t



R₁

i1



R₁ R₂

 Series Resistance  Parallel Resistance



R₂ i2

e1 e₂

e

R



e

2 1

1 1 1

R R R  2

1 R

R 

1 1

,

e  iR e  iR

1 1

,

0

)

(

2

1

e i R R

e

e    

2 1 2

1 e 0 e e

e    



1 2

1 2

1 2 1 2

1 1

( )

e e e

i i i e

R R R R R

      

Series/Parallel Capacitance?

Kirchhoff’s laws

+

1. The algebraic sum of the potential difference around a closed path equals zero.

+ _

+ 

+

E 

1 2

E 0

 

   

E 

_ _

2. The algebraic sum of the currents entering (or leaving) a nod is equal to zero.

i node i

i node

i

0

3 0

2

1  i  i  i

Current in = Current out

i

1 2 3

i i i

  

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Mathematical Modeling of Electrical Systems g y

The switch S is closed at t=0

di 0 di

E L Ri or L Ri E

dt dt

    

At the instant that switch S is closed, the current i (0)  0

 ^{( ) (0)}  ^{( )} E ^E

L sI s i RI s

   s

(0) 0 ( ) ( ) E

i   Ls  R I s 

Laplace Transformation :

( ) ( ) ( )

s

1 1

( ) E E

I s  

    

Examples of Circuit Analysis p y

ex) R-L-C Circuit

( ) 0

1

L R C

V V V e t di

    

1 

, , ( )

1

L R c C

c

V L di V iR V i dt V t

dt C

dV i

dt C

   





( )

V

( )

( ) dt C

L di Ri e t V t dt   

e(t)

V

i

( L R 1 ) ( ) I E ( )

( ) ( ) ( )

( ) 1

( ) ( 1 )

Ls R I s E s Cs

I s

E s Ls R

  



  Laplace Transform,

( ) 1 ( )

V s  I s ( Ls R )

  Cs

2

( ) ( )

1

( ) ( ) 1 ( )

1 ( 1)

o

o

V s I s

Cs

V s Cs E s E s

LC RC



  Step Response?

1 (

1)

( )

o

Ls R LCs RCs

Cs

 

 

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Complex Impedance i

p p

 Z(s) 

e

) (

) ) (

( Z

s s E

I  E ( s )  Z ( s ) I ( s ) )

(s

Z

Complex Impedance p p

The complex impedance Z(s) of a two-terminal circuit is : the ratio of E(s) to I(s)

i

The complex impedance Z(s) of a two terminal circuit is : the ratio of E(s) to I(s)

( ) E s ( ) ( ) ( ) ( )

Z E Z I

1

( )

Z s Z s

( )

e

e

( ) ( ) , ( ) ( ) ( )

Z s ( ) E s Z s I s

 I s 

( ) ( ) ( ) ( ) ( ) ( )

E Z I E Z I

e

1 2

( ) ( ) ( ), ( ) ( ) ( )

( ) ( ) ( )

E s Z s I s E s Z s I s

E s E s E s

 

 

 

1 2

1 2

( ) ( ) ( ) ( ) ( ) ( ) ( ) Z s I s Z s I s

Z s Z s I s

 

 

Direct derivation of transfer function, without writing differential equations first.

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Complex Impedance

R

i e  Ri , E s ( )  R I s ( )

Resistance :

p p

R

e

1 de

( ) Z s  R

i

+ -

- C

1

1 1

( ) ( ) ( ) ( )

de i dt C

sE s I s E s I s



  

Capacitance :

e`

( ) ( ) ( ) ( )

( ) 1

C Cs

Z s Cs

 

i L

+ -

- di , ( ) ( )

e  L E s  L s I s

Inductance :

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Examples of Complex Impedance

i + R L C

+

ex1)

Series Impedances

+ - + - + -

e

e

e

, ,

1

R L

de

e iR e L di i

dt dt C

  

) ( )

( )

( )

( E E E

E

C L

R e e

e

e    E ( s )  E _R ( s )  E _L ( s )  E _C ( s )

( ) ( ) 1 ( ) RI s LsI s I s

   cS

( )

) 1 (

s Cs I Ls

R 



 



  



Z(s)

E(s)

Examples of Complex Impedance

Parallel Impedances

+

ex2) i

( ) ( ) ( )

L R C

i    i i i E s  Z s I s

Parallel Impedances

i

i i

+

L R C

e

( ) ( ) ( ) ( ) ( ) ( ) ( )

L R C

I s I s I s I s E s E s E s

  

 

-

( ) ( ) ( ) ( ) ( ) ( )

1 1 1

( ) ( ) ( ) ( )

L R C

Z s Z s Z s

Z Z Z E s

  

 

    

 ( ) ( ) ( )  1 ( )

( )

L R C

Z s Z s Z s

Z s E s

 



1 1

( ) 1 1 1 1 1

( ) ( ) ( ) Z s

Z Z Z L R Cs

  

   

Z(s)

( ) ( ) ( )

R L C

Z s Z s Z s Ls R

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Examples of Complex Impedance

Deriving transfer functions of Electrical circuits by the use of complex impedances.

1 2 2

( ) ( ) ( ) ( ) ( ) , ( ) ( ) ( )

i o

E s  Z s I s  Z s I s E s  Z s I s

E

E

Z

(s)

Z

(s)

I(s) I(s)

( )

( ) E s Z s

1 2

( ) ( )

( ) ( ) ( )

o i

E s Z s

E s  Z s Z s



L R

+ ( )

( )

( ) ( ) ( ) E s

Z s

E s  Z s Z s

 ex)

C e

e

1 2

( ) ( ) ( ) E s

Z s  Z s

1 2

( ) , ( ) 1

Z s  L s  R Z s 

Transfer Functions of Cascaded Elements

Consider two RC circuits

C

C

i

i

1

e i e _{o 1} e _{i 2} e _{o 2}

( ) 1

E

1

1 1 1

( ) 1

( ) 1 ( )

o i

E s

E s  R C s  G s



2 2 2

( ) 1

( ) 1 ( )

o i

E s

E s  R C s  G s



2

( ) ( ) ? E

s 

1

( ) E s

2

e o 1

e i

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Loading Effect

Transfer Functions of Cascaded Elements Loading Effect

1 



1 



1

1

1 1 2 2

1 1 1 1

( ) ( ) ( ) ( ), ( ) ( ) ( ) ( ) 0, ( ) ( )

i o

E s I s I s R I s I s I s R I s I s E s I s

C s C s C s C s

       

( ) 1 1

. : E s

T F  

Transfer Functions of Cascade Elements

( )

G s G ( )

1

( )

X s X s

( ) X s

( )

Input Impedance, Output Impedance

1

( )

G s G s

( )

( ) ( ) ( )

X s

X s

X s

1 2

1 1 2

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

X s X s X s

G s G s G s

X s X s X s

   

If the "input Impedance" of the second element is infinite, the output of the first

element is not affected by connecting it to the second element. y g

Then, G s ( )  G s G s

( )

( )

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

Transfer Functions of Cascade Elements

Isolating Amplifier g p

i

( ) V s

This amplifier circuit has to

1. Not affect the behavior of the source circuit.

( ) ( ) ( ) ( )

( ) ( )

i

i s s

V s Z s V s V s

Z Z

 



1. Not affect the behavior of the source circuit.

2. Not be affected by the loading circuit.

This isolating amplifier circuit has to have

( ) ( )

i s

Z s  Z s

State-Space Mathematical Modeling of Electrical Systems p g y

By Kirchhoff's voltage law

,

1 ,

c i o c

dv

L di Ri v e i e v

dt    dt  C 

y g

Assume, initial condition is 0,

( ) ( )

( )

( ),

( ) 1 ( ) LsI s RI s V s E s V s I s

    Cs

2

( ) 1

. :

( ) 1

o i

T F E s

E s  LCs RCs

 

Seoul National Univ.

School of Mechanical

and Aerospace Engineering

Spring 2011

State-Space Mathematical Modeling of Electrical Systems

1 1

e  R e  e  e

 

Differential equation :

State Space Mathematical Modeling of Electrical Systems

o o o i

e e e e

L LC LC

  

1 2

x  e x   e

State variable :

Differential equation :

1 _o

,

x e x e

State variable :

,

i o

u  e y  e  x

Input and output : p p

State-space equation :

0 1 0

   

      

State space equation :