1. Vibration Control Presentation in Control engineering research seminar 21.2.2011

2. Why vibration control Vibrations occur almost everywhere few examples: Linear motionRotation

3. 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

4. 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

5. 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

6. System modeling How accurate the system modeling should be? Finite element modeling Distributed parameter system Lumped parameter system

7. Example Simple model d(t) x F d System + + Choose signal F(t) such that disturbance d(t) is eliminated Only signal x(t) can be measured Compensator

8. Vibrations in electrical machines Structure of an AC induction motor

9. Rotor vibrations Radial vibrations Torsional vibrations x y z ω ω

10. 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

11. 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

12. Example A more complex model ymym v d y em Plant Act + + y in Laval-Jeffcott rotor model Plant: where Actuator: Complex electro- magnetic equations inside

13. Example continues But the task is again the same Plant Act v d y em y in + + Controller Dist ymym Process Choose signal F(t) such that disturbance d(t) is eliminated Only signal y m (t) can be measured