Self-Sensing Active MagneticDampers for Vibration Control

Presenting by, JITHIN.K M-Tech, Machine Design Roll No: 9

Guided by,Dr. K.G.JollyH.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 the

electromagnetic actuators are used only to control the shaft vibrations.

The combination of mechanical suspension with an electromagnetic actuator is advantageous.• The system can be designed to be stable even in open loop.• Actuators are smaller compared to AMB configuration.

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

The self sensing system is based on the Luenberger observer.

Parameters can be obtained in two different ways• Nominal ones and identified ones.

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Modeling and Experimental Setup

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

Adoption of mechanical stiffness in parallel to electromagnets allows to compensate the -ve stiffness induced by electromagnets.The back-electromotive force produced 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 electromagnet j is expressed as:

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 Newton’s 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 electromagnet j = disturbance force applied to the mass The 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 no magnetic 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 to oscillate about it.

As far as the linearization is concerned, the larger is stiffness k relative to | |, the more negligible the nonlinear effects become.

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Identified ModelThe system used is a test rig used for static characterization of 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 are placed 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 expression ii. 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 value R at low frequency 1 Hz in our

case.iii. Identify based on the high frequency slope ofiv. 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 and identified 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 function obtained 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 whole procedure.

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The damping performances are evaluated by analyzing the time response of the closed-loop system when an impulse 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 the case 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. 197–203.

V.P.Singh, “Mechanical Vibrations”.

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Thank you…