Vibration Control
description
Transcript of Vibration Control
Vibration Control
Presentation in Control engineering research seminar
21.2.2011
Why vibration control
• Vibrations occur almost everywhere
few examples:
Linear motion Rotation
Why vibrations control
• Vibrations are damped to get
– Less noise to surroundings-> comfort for users
– Decrease conduction of vibration into the structures-> comfort for users/operators
– Less wear of parts and need for maintenance-> less costs
Passive and active vibration control
Vibrations can be controlled
PassivelyACTIVELY
Materials and structures are chosen/designed such that the vibrations are minimized
+ cheap to design and maintain
- works well only on small frequency band
An actuator is added to the system to exert opposite force to damp vibrations
+ more effective on all frequencies and for all kinds of disturbances- expensive to design and maintain
Active vibration control
• Vibration control consists of (as almost every control problem)
System modeling
Measurement and estimation
Control
- How the system is modeled?- How accurate model should be chosen?
- What can be measured directly?- What needs to be estimated?- Depends on the model structure
- What can be controlled?- Depends on the model structure
and the measurements
System modeling• How accurate the system modeling should be?
Finite element modeling
Distributed parameter system
Lumped parameter system
Passive
ACTIVE
Example
• Simple model
d(t)
xF
d
System+
+
Choose signal F(t) such that disturbance d(t) is eliminated
Only signal x(t) can be measured
Compensator
𝑚 �̈� (𝑡 )=−𝑘𝑥 (𝑡 )+𝐵�̇� (𝑡)+𝐹 (𝑡 )+𝑑(𝑡)
Vibrations in electrical machines
• Structure of an AC induction motor
Rotor vibrations
• Radial vibrations
• Torsional vibrations
x
y
z
ω
ω
Actuator
• How can we apply force to the stator?
• A common approach is to use a magnetic bearing
• In our approach an additional winding mounted to the stator is used
Department of Automation and Systems Technology
http://autsys.tkk.fi/en/
rotor
stator
stator windings
ω
Laval-Jeffcott rotor model
• Simply a disk attached to a shaft supported at both ends
• Disk is rotating at constant speed ω
xy
z
Example
• A more complex model
ymvd
yemPlantAct
+
+
yin
Laval-Jeffcott rotor model
( )0 0
0
0,
0
T Temrc rc
m m mex
m rc m
rcin m
rc
yx A t x
f
y x
y x
( ) ( )
( )
inem em em em em em
em em em
yx A x S t Q t B
vy C t x
Plant:
22 ( )( )
0( ), ( ), ( ), ( )
Trc em rc
m
em em em em
P tA t
Iand P t C t Q t S t are periodic
where
Actuator:
Complex electro-magnetic equations inside
Example continues
• But the task is again the same
PlantAct
v
d
yemyin+
+
Controller
Dist
ym
ProcessChoose signal F(t) such that disturbance d(t) iseliminated
Only signal ym(t) can be measured