chapter 4
TRANSCRIPT
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 motor follows....
1.0 0 C
B Tmax
Torque
Tst
slip
sTmax
A
maxTs
Portion AB - unstable
Portion BC - stable
sTmax = R2 / X2
1.0 0
C
B Tmax
Torque
Tst
slip
sTmax
A
1.0 0
C
B Tmax
Torque
Tst
slip
sTmax i
A
R i
R i i
sTmax ii
R ii > R i
s
Tmax 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
vc Rotor Load
J, B
vr = V cos ct
vc = e sin ct
Two phase servo motor
Torque
speed
E1
E2 E3
E1 > E2 > E3
equation continues ....
Tm = f ( E, )
Using taylor series,
Tm = Tmo + --------
E E = E0
= 0
Tm
( E - E0 ) + --------
E = E0
= 0
Tm ( - 0
)
equation continues ....
Tm - Tmo = K1 ( E - E 0)
- K2 ( - 0)
Tm
= K1 E
- K2
= ( J s + B )
K1
------ = ------------
E K2 + Js + B
For position control,
the operating
point is Tm0= 0,
0 = 0 and
E0 = 0
Tm - Tmo = K1 ( E - E 0)
- K2 ( - 0)
Tm = K1E- K2
= ( J s + B )
Hence
(s) / E(s) =
K1 / (Js+B+K2)
To evaluate K1 & K2
Torque
speed
At = 0,
T = stall Torque
At T = 0,
= no load speed
Torque
speed
To evaluate K
1
K 1 =
stall Torque ( rated voltage )
rated control phase voltage
K2
Torque
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,
since the operating
point for position
control
is :
Tm
= 0 ,
= 0 and
E = 0
vr
vt Rotor
AC Tacho generator
vr = v cos ct
vt = Kt m sin ct
AC Tacho generator
vr = v cos
ct
vt = K
t m
sin ct
vt is the output
whose amplitude
is proportional
to the speed.
Hence Vt is an
amplitude
modulated
waveform
Rotor is thin
aluminium
cup.
Synchro pairs
- position error
detectors
Synchro
transmitter
Synchro control
transformer
vr
Synchro
Transmitter
a
b c
Synchro
Control
e
transformer
a
b c
vr e s1
s2
s3
vr = V
r sin
ct
vs1n = k Vr cos( + 120) sin ct
vs2n
= k V
r cos sin
ct
vs3n
= k V
r cos( + 240) sin
ct
vr e rotor
( Transmitter )
rotor
(Control Transformer)
Amplitude of e is
maximum
vr e rotor
(Control Transformer)
rotor
( transmitter )
Amplitude of e = 0
Amplitude of e is
proportional to
cosine of the angle
difference
Angle difference
= 90 + -
= 90 - ( - )
e = k’ Vr cos (90 - ( - )) sin ct
= k’ Vr sin (-) sin ct
= k’ Vr ( - ) sin ct
Stepper Motor
permanent magnet
variable reluctance
permanent magnet
N
S
Rotor
permanent magnet
A B
Stator
A B
N S
A ON B OFF
A B
N S S 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
N S
A B C D
1 0 1 0
Switching Table
N
S
N S
N S
A B C D
1 0 1 0
Switching Table
N
N S
S
0 1 1 0
1 0 1 0
A B C D
Switching Table
N
S N S
N
S
0 1 1 0
1 0 1 0
A B C D 90 CW
Switching Table
S
N S
N
A B C D
0 1 0 1
1 0 1 0
0 1 1 0
Switching Table
S
S N S
N
N
A B C D
0 1 0 1
1 0 1 0
0 1 1 0
90 CW
Switching Table
S
S N
N
A B C D
1 0 0 1
1 0 1 0
0 1 1 0
0 1 0 1
Switching Table
S
S S N
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
N S N
S
S
A B C D
1 0 1 0
90 CW
Switching Table
1 0 1 0 0 1 1 0 0 1 0 1
1 0 0 1 1 0 1 0
A B C D
CW
Switching Table
N
S
N S
N S
A B C D
1 0 1 0
Switching Table
N
S N S
N
S
0 1 1 0
1 0 1 0
A B C D 90 CW
Switching Table
S
S N S
N
N
A B C D
0 1 0 1
1 0 1 0
0 1 1 0
90 CW
Switching Table
S
S S N
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
N S N
S
S
A B C D
1 0 1 0
90 CW
Switching Table
1 0 1 0 0 1 1 0 0 1 0 1
1 0 0 1 1 0 1 0
A B C D
CW
For counterclockwise
rotation ????
Switching Table
1 0 1 0 0 1 1 0 0 1 0 1
1 0 0 1 1 0 1 0
A B C D
CW
Switching Table
1 0 1 0 0 1 1 0 0 1 0 1
1 0 0 1 1 0 1 0
A B C D
CW
C
CW
Variable Reluctance
A1
A2
1 2
3
4
A ON
1 opp A1
3 opp A2
Variable Reluctance
A1
A2
1 2
3
4
A OFF B ON
2 opp B1
4 opp B2
30 CCW
Variable Reluctance
A1
A2
1 2
3
4
B OFF C ON
3 opp C1
1 opp C2
30 CCW
Variable Reluctance
A1
A2
1 2
3
4
C OFF A ON
4 opp A2
2 opp A1
and so on …. 30 CCW
S = no. of stator slots
R = no. of rotor slots
= 360 (1/R - 1/S)
= 30
for CW operation
switching sequence
is ACB.
Multistack
arrangement
Variable Reluctance
Stepper
Rotor
Stator A
B
C
air gap
= 360 / ( n T )
degrees
n = no. of stacks
T = no. of teeth
= 360/ (3 4)
= 30
Hydraulic components
Hydraulic power supply
reservoir
pump with prime mover
• oil lines
• valves
Hydraulic actuators
Hydraulic components
pumps :
positive
displacement
type
piston
vane
gear
Atmos.
pressure
Piston Pump
Inlet Outlet
Pump out flow rate
Qp =
vol. of cylinder
no. of cylinders
speed
Pump can
act as
hydraulic
motor also
Hydraulic Linear Actuator
(Double acting Cylinder)
Pump
Sump
Sump Pump Sump
Spool valve
Sump Pump Sump
x Q K v 1/A
v 1/s
y
Sump Pump Sump x
y
z
a
b
a
b
x
y+
y+ = b
a + b x
z
y-
y- = a
a + b z
x y+ z
-
b a + b
kv /As
a a + b
Sump Pump Sump x
y
z
a
b
B M
z
Suppose
Q = K v x - K r P
Where P is the
pressure of hydraulic
supply
b a + b
K v
+
-
Kr P
1 A s + Q
a
a + b
x z -
To find the
relation between
P and
connected load,
P A = force =
( M s2 + B s ) z
P ( s ) =
= G (s) z (s)
(say)
b a + b
K v
+ -
1 A s + Q
a
a + b
x
z
G(s) P
K r
-
Pneumatic Components
Flapper Nozzle
Device.
b
a Output
(pressure)
Air
supply
Orifice
Pb Ps
x
e
A Flapper valve
Flapper valve
characteristic.
Pb
e
Linear part
(slope K = Pb / e) Pb
Pa
Output
(displacement)
Input
pressure
Pneumatic bellows.
a
b
x
pb
Ps
x b/(a+b) Kf
a a+b
Ab
Kb
+
-
Pb
Pb (s) / x (s)
ba
KbAba
Kf
ba
b
/1
a
b
x
Pb R
C
Pc
RCssPb
sPc
PcCsR
PcPb
1
1
)(
)(
Kf
a a+b
+ -
b a+b
x Pb
1
1+RCs
A Flapper valve
with relay
x Input
(displacement)
Fla
pp
er
To
atmosphere Output
(pressure) P
Air
supply
Pb
ball
Ps
Pneumatic
actuator
Input
(pressure) Spring
Backing
plate Output
(displacement)