Self-Sensing Active Magnetic

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Self-Sensing Active MagneticDampers for Vibration Control

Presenting by,JITHIN.K

M-Tech, Machine Design

Roll No: 9

Guided by,Dr. K.G.Jolly

H.O.D

Mechanical Dept.


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INTRODUCTION

Viscoelastic and fluid film dampers.

Passive, semi-active and active dampers.

Electromechanical dampers

Absence of all fatigue and tribology issues.

Smaller sensitivity to the operating conditions.

Wide possibility of tuning even during operation.

Predictability of the behavior.Active magnetic bearings

Shaft is completely supported by electromagnets

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Active magnetic dampers

Rotor is supported by mechanical means and theelectromagnetic actuators are used only to control the

shaft vibrations.

The combination of mechanical suspension with anelectromagnetic actuator is advantageous.

The system can be designed to be stable even in openloop.

Actuators are smaller compared to AMB configuration.

Our aim is to investigate self sensing approach in thecase of AMD configuration.

The self sensing system is based on the Luenbergerobserver.

Parameters can be obtained in two different ways

Nominal ones and identified ones. 3


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Modeling and Experimental Setup

A single degree of freedom mass spring oscillatoractuated by two opposite electromagnets.

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Adoption of mechanical

stiffness in parallel to

electromagnets allows to

compensate the -ve stiffness

induced by electromagnets.

The back-electromotive forceproduced can be exploited to

estimate mechanical variables

from the measurement of

electrical ones.

Fig. 1 Model

Nominal model


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This leads to the so-called selfsensing configuration that

consists in using the electromagnet either as an actuator

and a sensor.

Voltage and current are used to estimate the airgap.

Each electromagnet can be considered as a two-port

element (electrical and mechanical).

The energy stored in the electromagnetj is expressed as:

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where the force can be obtained as

(1)

(2)


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The total flux and the coil current are

related by a nonlinear function

(3)

where is the radial airgap of electromagnet j(4)

where is the nominal airgap

Owing to Newtons law in mechanical domain, the

Faraday and Kirchoff law in the electrical domain, the

dynamic equations of the system are

(5)


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where, R = coil resistance

= voltage applied to electromagnetj

= disturbance force applied to the massThe system dynamics is linearized around a working

point corresponding to a bias voltage imposed to both

electromagnets

(6)

where is the initial force generated by the

electromagnet due to the current .


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The resulting linearized state space model is

where A,B and C are dynamic, action and output

matrices respectively, defined as

(7)

(8)

with the associated input and output state vectors

and .


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The terms in the matrices derive from the linearization of

the nonlinear functions defined in eqs. (2) and (3)

(9)

where are the inductance, the current-force

factor, the back-electromotive force factor, and the

negative stiffness of one electromagnet respectively.

Assuming that ferromagnetic material of the actuator

does not saturate, has infinite magnetization and there is nomagnetic leakage in the air gap,

(10)


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Where , characteristic factor of electromagnets.

S = cross-sectional area of the magnetic circuit.

The presence of a mechanical stiffness large enough to

overcome the negative stiffness of the electromagnets makes

the linearization point stable and compels the system tooscillate about it.

As far as the linearization is concerned, the larger is

stiffness krelative to | |, the more negligible the nonlineareffects become.


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Identified Model

The system used is a test rig

used for static characterizationof radial magnetic bearings.

Fig. 2 Photo of the test rig

This rig consists in a

horizontal arm hinged at one

extremity with a pivot and

actuated with a single axis

magnetic bearing.

Six springs in parallel areplaced to provide a stabilizing

stiffness to the system.Fig. 3 Test rig scheme


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It consist of two electromagnets, power amplifier, Bently

Proximitor eddy current sensor and current sensor.

Damping may be introduced into the structure by simply

feeding back the position sensor signal by means of a

proportional-derivative controller.

Two sets of parameters have been used to build the models.

i. Based on expressionii. Have been identified experimentally under two

assumptions.

k, c, and m are determined from physical dimensions,

direct measurements, and impact response in open-

circuit electromagnets conditions.

The electromechanical parameters and are

equal.


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The proposed identification procedure isi. Obtain the transfer function admittance in Fig. 4.

ii. Measure the resistance valueR at low frequency 1 Hz in our

case.iii. Identify based on the high frequency slope of

iv. Identify such that the zero-pole pair due to the

mechanical resonance corresponds to the experimental ones.


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The good correlation between the experimental andidentified plots validates the proposed procedure.


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Controller unit

To introduce active magnetic damping into the system.

The control is based on the Luenberger observer approach.

It consists in estimating in real-time the unmeasured states

- displacement and velocity from the processing of the

measurable states i.e. the current.


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Experimental results

The open-loop voltage to displacement transfer functionobtained from the model and experimental tests are

compared.

The same transfer functions in closed-loop operation with

the controller designed are compared in the case of

identified parameters.

In this case, the correspondence is quite good, which

corroborates the control approach, and validates the wholeprocedure.


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The damping performances are evaluated by analyzing

the time response of the closed-loop system when animpulse excitation is applied to the system.

The controller based on the identified electromechanical

parameters give better results than the nominal model.

Good damping can be conveniently achieved for active

magnetic dampers obtained with the simplified model.

This controller does not destabilize the system, as it is thecase for full suspension self-sensing configurations.


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CONCLUSION

The study of an observer-based self-sensing active

magnetic damper has been presented both in simulation and

experimentally.

The closed-loop system has good damping performances

than open-loop system.

The modeling approach and the identification procedure

have been validated experimentally comparing the open-

loop and the closed-loop frequency response to the model.The self-sensing configuration provides good robustness

performances even for relatively large parameter deviations.


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References

A.Tonoli, N. Amati, M. Silvagni, 2008, Transformer Eddy

Current Dampers for the Vibration Control, ASME J. Dyn.

Syst., Meas., Control, 130, p.031010.

E. H. Maslen, D. T. Montie and T. Iwasaki, 2006,

Robustness Limitations in Self-Sensing Magnetic Bearings,ASME J. Dyn. Syst., Meas., Control, 128, pp. 197203.

V.P.Singh, Mechanical Vibrations.


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Thank you

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Self-Sensing Active Magnetic