Download Self-Sensing Active Magnetic Dampers for Vibration Control

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
 Viscoelastic and fluid film dampers.
 Passive, semi-active and active dampers.
 Electromechanical dampers
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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
Nominal model
 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
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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:
(1)
where the force can be obtained as
(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
(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
.
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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 Model
The system used is a test rig
used for static characterization
of radial magnetic bearings.
This 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
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.
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k, c, and m are determined from physical dimensions,
direct measurements, and impact response in opencircuit electromagnets conditions.
The electromechanical parameters
and
are
equal.
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 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.
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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 openloop 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…
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