Piezo actuators as orbit correctors. Jürgen Pfingstner 25 th of June 2009. Principle and Motivation. 1.) Corrector coil as orbit corrector. 3.) Actuated quadrupoles as orbit corrector. d. 2.) Action of a displaced quadrupoles. Advantages : Simpler magnet design
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1.) Corrector coil as orbit corrector
3.) Actuated quadrupoles as orbit corrector
d
2.) Action of a displaced quadrupoles
d
d
Quadrupole (magnet)
Dipole (magnet)
Piezo actuator
“Complete” electromechanical model of a piezo cristall [1], [2]:
Simple electromechanical model of a piezo cristall [1], [3]:
M = mmagnet+ mpiezo_eff
Fp
Hysteresis
Fe
Piezo
material
k
d
Fp
uin
xabs
kT
qp ← y
uin
Tem
up
L+x
C
xgm
up → Fp
Fp
Fe
Mechanical model
Electrical model
2nd Newton’s law:
State space representation
Laplace transformation
2 measurements:
y1 … Length of the piezo (xabs – xgm)
y2 … vertical acceleration of the magnet ( )
… resonance frequency
… damping factor
… voltage to length conversion
Based on the ground motion models of A. Sery and O. Napoly [4]:
Noise of the sensors:
Cap. distance sensor
E509 (PI)
umeas
uin
Amplifier
E503 (PI)
Piezo act.
P753 (PI)
Passive noise filter
Remaining meas. noise level : app. 3nm rms
Simulation delivers the ‘same’ curves
> Reality and model fit very well
3.) Piezo amplifier
1.) Resonance frequency of a piezo actuator
The eigenfrequency can be calculated [3] as:
… Spring constant of the piezo
P225.40 (high load)
… Effective mass of the piezo
… Biggest CLIC QP (1.9m)
on 3 actuators
2.) Damping factor of a piezo actuator
gm(t)
FF
Gd
n(t)


r(t)
x(t)
y(t)
u(t)
C
+
+
+
+
+
k
