SelfSensing Active Magnetic Dampers for Vibration Control Guided

Self-Sensing Active Magnetic Dampers for Vibration Control Guided by, Dr. K. G. Jolly H. O. D Mechanical Dept. Presenting by, JITHIN. K M-Tech, Machine Design Roll No: 9

INTRODUCTION Ø Viscoelastic and fluid film dampers. Ø Passive, semi-active and active dampers. Ø 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. Ø Active magnetic bearings – Shaft is completely supported by electromagnets 2

Ø Active magnetic dampers – Rotor is supported by mechanical means and the electromagnetic actuators are used only to control the shaft vibrations. Ø 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. Ø Our aim is to investigate self sensing approach in the case of AMD configuration. Ø The self sensing system is based on the Luenberger observer. Ø Parameters can be obtained in two different ways • Nominal ones and identified ones. 3

Modeling and Experimental Setup Nominal model Ø A single degree of freedom mass spring oscillator actuated by two opposite electromagnets. ØAdoption of mechanical stiffness in parallel to electromagnets allows to compensate the -ve stiffness induced by electromagnets. ØThe back-electromotive force produced can be exploited to estimate mechanical variables from the measurement of electrical ones. Fig. 1 Model 4

ØThis leads to the so-called selfsensing configuration that consists in using the electromagnet either as an actuator and a sensor. ØVoltage and current are used to estimate the airgap. ØEach electromagnet can be considered as a two-port element (electrical and mechanical). ØThe energy stored in the electromagnet j is expressed as: (1) where the force can be obtained as (2) 5

ØThe total flux and the coil current are related by a nonlinear function (3) where is the radial airgap of electromagnet j where is the nominal airgap (4) ØOwing to Newton’s law in mechanical domain, the Faraday and Kirchoff law in the electrical domain, the dynamic equations of the system are (5) 6

where, R = coil resistance = voltage applied to electromagnet j = disturbance force applied to the mass ØThe 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. 7

ØThe resulting linearized state space model is (7) where A, B and C are dynamic, action and output matrices respectively, defined as (8) with the associated input and output state vectors and. 8

ØThe 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. ØAssuming that ferromagnetic material of the actuator does not saturate, has infinite magnetization and there is no magnetic leakage in the air gap, (10) 9

Where , characteristic factor of electromagnets. S = cross-sectional area of the magnetic circuit. ØThe 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. ØAs far as the linearization is concerned, the larger is stiffness k relative to | |, the more negligible the nonlinear effects become. 10

Identified Model ØThe system used is a test rig used for static characterization of radial magnetic bearings. ØThis rig consists in a horizontal arm hinged at one extremity with a pivot and actuated with a single axis magnetic bearing. Fig. 2 Photo of the test rig ØSix springs in parallel are placed to provide a stabilizing stiffness to the system. Fig. 3 Test rig scheme 11

ØIt consist of two electromagnets, power amplifier, Bently Proximitor eddy current sensor and current sensor. ØDamping may be introduced into the structure by simply feeding back the position sensor signal by means of a proportional-derivative controller. ØTwo 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 opencircuit electromagnets conditions. The electromechanical parameters and are equal. 12

Ø The proposed identification procedure is i. 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 of iv. Identify such that the zero-pole pair due to the mechanical resonance corresponds to the experimental ones. 13

ØThe good correlation between the experimental and identified plots validates the proposed procedure. 14

Controller unit ØTo introduce active magnetic damping into the system. ØThe control is based on the Luenberger observer approach. ØIt consists in estimating in real-time the unmeasured states - displacement and velocity from the processing of the measurable states i. e. the current. 15

Experimental results ØThe open-loop voltage to displacement transfer function obtained from the model and experimental tests are compared. ØThe same transfer functions in closed-loop operation with the controller designed are compared in the case of identified parameters. ØIn this case, the correspondence is quite good, which corroborates the control approach, and validates the whole procedure. 16

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ØThe damping performances are evaluated by analyzing the time response of the closed-loop system when an impulse excitation is applied to the system. ØThe controller based on the identified electromechanical parameters give better results than the nominal model. ØGood damping can be conveniently achieved for active magnetic dampers obtained with the simplified model. ØThis controller does not destabilize the system, as it is the case for full suspension self-sensing configurations. 18

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CONCLUSION ØThe study of an observer-based self-sensing active magnetic damper has been presented both in simulation and experimentally. ØThe closed-loop system has good damping performances than open-loop system. ØThe modeling approach and the identification procedure have been validated experimentally comparing the openloop and the closed-loop frequency response to the model. ØThe self-sensing configuration provides good robustness performances even for relatively large parameter deviations. 20

References ØA. Tonoli, N. Amati, M. Silvagni, 2008, “Transformer Eddy Current Dampers for the Vibration Control, ” ASME J. Dyn. Syst. , Meas. , Control, 130, p. 031010. ØE. 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. ØV. P. Singh, “Mechanical Vibrations”. 21

Thank you… 22