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