Chapter 4

Control System

Components

DC Control Components

• potentiometer

• tachogenerator

• dc servo motor

• dc amplifier

amplification of

slowly varying

signals is

difficult -

hence....

ac / carrier

control

Systems

ac control system components

• synchro pair

• ac tachogenerator

• ac amplifier

• ac servo motor

ac servo motor

• special induction motor

• 2 - phase electric

supply

Torque speed

curve of an

induction motorfollows....

vr

vcRotor Load

J, B

vr = V cos ωωωωct

vc = e sin ωωωωct

Two phase servo motor

1.0 0C

BTmax

Torque

Tst

slip

sTmax

A

maxTs

Portion AB - unstable

Portion BC - stable

sTmax = R2 / X2

1.0 0

C

BTmax

Torque

Tst

slip

sTmax

A

1.0 0

C

BTmax

Torque

Tst

slip

sTmax i

A

R i

R i i

sTmax ii

R ii > R i

sTmax ii > sTmax i

1.0 slip

C

B

Make X2 = R2

sTmax = 1

0

Portion BC

extended for

the full speed

range.

Salient features of ac servo motor

•Rotor with high resistance

•Low inertia

•Two phase operation

vr

vcRotor Load

J, B

vr = V cos ωωωωct

vc = e sin ωωωωct

Two phase servo motor

Torque

speed

E1

E2E3

E1 > E2 > E3

Eo

Tm

= f ( E, ωωωω )

Using Taylor series,

Tm

= Tmo

+ --------

∂∂∂∂ E E = E0

ωωωω=

ωωωω0

∂∂∂∂ Tm (E- E0) ∂∂∂∂ Tm

-------∂∂∂∂ ωωωω

+

(ωωωω - ωωωω0)

E = E0

ωωωω = ωωωω0

Tm

- Tmo

= K1

( E - E 0)

- K2(ωωωω - ωωωω0)

∆∆∆∆ Tm = K1 ∆∆∆∆ E

- K2 ∆∆∆∆ ωωωω

= ( J s + B ) ∆∆∆∆ ωωωω

∆∆∆∆ ωωωω K1

------ = ------------

∆∆∆∆ E K2 + Js + B

For position control,

the operating

point is Tm0

= 0,

ωωωω0 = 0 and

E0 = 0

To evaluate K1 & K2

Torque rated voltage

speed

At ωωωω = 0,

T = stall Torque

At T = 0,

ωωωω = no load speed

Torque rated voltage

speed

To evaluate K1

K 1 =

stall Torque ( rated voltage )

rated control phase voltage

K2

Torque rated voltage

speed

To evaluate

K 2 =

stall Torque ( rated voltage )

no load speed ( rated voltage )

Since the slope of torque speed curve reduces

as rated voltage reduces .......

We take

K 2 =

1 stall torque ( rated voltage)

2 no load speed ( rated voltage)

for position control,

vr

vtRotor

AC Tacho generator

vr = v cos ωωωωct

vt = Kt ωωωωm

sin ωωωωct

vr = v cos ωωωωct

vt = Kt ωωωωm sin ωωωωct

vt is the output whose amplitude

is proportional to the speed.

Vt is an amplitude Modulated

waveform

Synchro pairs

- position error detectors

Synchro transmitter

Synchro control transformer

vr

Synchro

Transmitter

a

bc

Synchro

Control

e

transformer

a

bc

vres1

s2

s3

θθθθ αααα

vr

= Vr

sin ωωωωct

vs1n

= k Vrcos(θθθθ + 120°°°°) sin ωωωωc

t

vs2n

= k Vr

cos θθθθ sin ωωωωct

vs3n

= k Vr

cos(θθθθ + 240°°°°) sin ωωωωct

vr erotor

( Transmitter )

rotor

(Control Transformer)

Amplitude of e is maximum

vr erotor

(Control Transformer)

rotor

( transmitter )

Amplitude of e = 0

i.e. Amplitude of e is proportional

to cosine of the angle difference

Angle difference

= 90 + αααα - θθθθ

= 90 - ( θθθθ - αααα )

θθθθ αααα

e = k’ Vr cos (90 - (θθθθ - αααα)) sin ωωωωct

= k’ Vr sin (θθθθ-αααα) sin ωωωωct

= k’ Vr ( θθθθ - αααα ) sin ωωωωct

Stepper Motor

• permanent magnet

• variable reluctance

• hybrid Motor

Stepper motors provide a means for precise positioning and speed

control without the use of feedback sensors. The basic operation of a

stepper motor allows the shaft to move a precise number of degrees

each time a pulse of electricity is sent to the motor. Since the shaft of

the motor moves only the number of degrees that it was designed for

when each pulse is delivered, you can control the pulses that are sent

and control the positioning and speed. The rotor of the motor

produces torque from the interaction between the magnetic field in the

stator and rotor..

permanent magnet

N

S

Rotor

permanent magnet

A B

Stator

A B

N S

A ON B OFF

A B

N SS N

A ON B OFF

N

S

C

D

C ON D OFF

N

S

N

S

C

D

C ON D OFF

Switching Table

N

S

NS

NS

A B C D

1 0 1 0

Switching Table

N

NS

S

0 1 1 0

1 0 1 0

A B C D

Switching Table

N

SNS

N

S

0 1 1 0

1 0 1 0

A B C D 90 °°°° CW

Switching Table

S

NS

N

A B C D

0 1 0 1

1 0 1 0

0 1 1 0

Switching Table

S

SNS

N

N

A B C D

0 1 0 1

1 0 1 0

0 1 1 0

90 °°°° CW

Switching Table

S

SN

N

A B C D

1 0 0 1

1 0 1 0

0 1 1 0

0 1 0 1

Switching Table

S

SSN

N

N

A B C D

1 0 0 1

1 0 1 0

0 1 1 0

0 1 0 1

90 °°°° CW

Switching Table

N

NSN

S

S

A B C D 90 °°°° CW

1 0 1 0

0 1 1 0

0 1 0 1

1 0 0 1

1 0 1 0

Switching Table

1 0 1 00 1 1 00 1 0 1

1 0 0 11 0 1 0

A B C D

CW

CC

W

Variable Reluctance

A1

B1

C1

A2B

2

C2 1

2

3

4

A ON

1 opp A1

3 opp A2

A1

B1

C1

A2B

2

C2 1

2

3

4

A OFF B ON : 2 opp B1 and 4 opp B2

30°°°° CCW

A1

B1

C1

A2B

2

C2 1

2

3

4

B OFF C ON : 3 opp C1 and 4 opp C2

30°°°° CCW

A1

B1

C1

A2B

2

C2 1

2

3

4

C OFF A ON : 4 opp A2 and 2 opp A1

30°°°° CCW

for CW

operation

switching

sequence ?

S = no. of stator slots

R = no. of rotor slots

θθθθ = 360°°°° (1/R - 1/S)

Multistack arrangement

Multistack stepper motors can produce smaller step sizes because

the motor is divided along its axial length into magnetically isolated

sections, or stacks. Each of these sections is excited by a separate

winding, or phase. In this type of motor, each stack corresponds to a

phase, and the stator and rotor have the same tooth pitch.

Rotor

StatorA

B

C

air gap

θθθθ = 360 / ( n ×××× T ) degrees; n = no. of stacks T = no. of teeth