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
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?
Lumped parameter system
Distributed parameter system
Finite element modeling
Example
• Simple model
𝑚𝑥 𝑡 = −𝑘𝑥 𝑡 + 𝐵 𝑥(𝑡) + 𝐹 𝑡 + 𝑑(𝑡)
d(t)
Choose signal F(t) such that disturbance
d(t) is eliminated
Only signal x(t) can be measured
d
+
F
+
x
System
Compensator
Vibrations in electrical machines
• Structure of an AC induction motor
Rotor vibrations
y
• Radial vibrations
x
ω
• Torsional vibrations
ω
z
Actuator
• How can we apply force to the
stator?
• A common approach is to use a
magnetic bearing
rotor
• In our approach an additional
stator
winding mounted to the stator is
stator windings
used
Department of Automation
and Systems Technology
http://autsys.tkk.fi/en/
Laval-Jeffcott rotor model
• Simply a disk attached
to a shaft supported at
both ends
• Disk is rotating at
constant speed ω
y
x
z
ω
Example
• A more complex model
Plant:

Trc Trc   yem 
 xm  Am (t ) xm  
 
0   f ex 
 0


 ym  0  rc  xm

 rc
0 

y

 in  0   xm ,
rc 


Complex electromagnetic
equations inside
d
v
where
+
Act
yin

 yin 


x

A
x

S
(
t
)
Q
(
t
)
B


Actuator:  em em em  em
em
em  


v
 y  C (t ) x
em
em
 em
 2 Trc Pem (t ) rc   2 
Am (t )  

0
 I

and Pem (t ), Cem (t ), Qem (t ), Sem (t ) are
Laval-Jeffcott
rotor model
periodic
yem+
ym
Plant
Example continues
• But the task is again the same
Choose signal F(t) such
that disturbance d(t) is
eliminated
Process
d
Dist
v
Act
Only signal ym(t) can be
measured
ym
+
yin
yem+
Controller
Plant