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Vibration Isolation
Project
Objective
The objective to be achieved is the isolation from
environmental vibration of the LEGO® platform from
the myphotonics project.
This must be done with low cost
instrumentation in order to fit the
purpose of OpenAdaptronik project.
Michelson-Interferometer
Optische Pinzette
Zweistrahl-Interferometer
LEGO® platform
Simple Vibration Problem – Skyhook Solution
A solution to this problem is the adoption of an
active damping system.
Skyhook control is a feedback velocity control
widely use in vibration isolation for a vehicle.
It simply introduce into the system a force
proportional to the speed of the mass to be
isolated changing the damping of the system
only form the point of view of the mass and not
from the one of the incoming disturbance.
Equation of motion:
𝑚 𝑥 + 𝑟 𝑥 + 𝑘𝑥 = 𝒇 + 𝑟 𝑥 𝑝 + 𝑘𝑥 𝑝 𝑚 𝑥 + 𝑟 𝑥 + 𝑘𝑥 = −𝑲 𝑥 + 𝑟 𝑥 𝑝 + 𝑘𝑥 𝑝
Choosing: 𝐾 = 2𝑚 𝑒 𝜔0 − 𝑟
the best attenuation at the
resonance frequency is obtained
𝐺 𝑠𝑦𝑠𝐶 =
𝑟𝑠 + 𝑘
𝑚 𝑒 𝑠2 + 𝑟 + 𝑲 𝑠 + 𝑘
1. Amplitude attenuation at
the resonance frequency
2. Amplitude attenuation at
frequencies higher then
the resonance
It’s now possible to calculate the mode shapes of the structure ϕ , visualize them and comparing with the results
obtained directly by the software implemented in the Laser Vibrometer used for the measurements.
• Left side: 1st and 2nd eigenmodes reconstructed.
• Right side: 1st and 2nd eigenmodes from L.V.
From left to right and up to down : eigenmodes
reconstructed 3,4,5,6,7,8.
Preliminary Measurements - Modal Analysis
Real System
It is now possible to pass to the analysis of the real configuration of the problem.
The connections between the plate and the actuators are made by other LEGO® bricks. They are glued on the
actuator side and the connection on the plate side is left free in order to have the possibility to easily remove the
LEGO® plate and to not modify the structure.
ϕ
𝜗
𝑥 𝑝1 𝑥 𝑝2
𝑥 𝑝3
𝑓𝑐1
𝑓𝑐2
𝑓𝑐3
k
k
kr
r
r
𝑧𝑐
𝑙 𝑥
𝑙 𝑦
𝑚 𝑒 ; 𝐽φ ; 𝐽ϑ
1
4
3
2
x
yz
 Four actuators are attached on the base of the plate in a
symmetric way and for sensors (accelerometers) are
placed on the top of the plate in a position
corresponding to the center of the actuators.
 In this way is possible to reach a symmetric behavior of
the system.
Actuators Location and Mounting
• In the figure is reported a scheme of the
considered system in which is possible to see
the forces exercised by the four actuators and
the incoming disturbances for each one.
• From now on the moving part of the actuators
are considered integrated with the LEGO® plate
and the mechanical and electrical parameters
are considered equal for each actuator. Scheme of the final configuration
Decentralized control vs. MIMO control
Decentralized MIMO
Simplified system: 4 independent control loops
No significant performance reduction by decentralized approach
Real System – Sampling Effect
A sampling frequency of 10 kHz is definitively to high for implementing a control on a low cost control board so
the effect of sampling is experimentally studied.
In the two figures the centralized and decentralized controls effects are compared for two different sampling
frequencies, 1 kHz and 0.5 kHz.
10 kHz 1 kHz 0,5 kHz
Lower sampling rate causes higher delays in the loop
Smaller stability margin  Lower performance
 Analog control circuit preferred to avoid effects of DAC/ADC
Real System – Experimental Results
The results obtained were done hammering the upper surface of the structure because for the best case experiment
it will be needed four shakers, one for each actuator, capable of carrying at least one quarter the weight of the
entire structure.
Transmissibility Measurement set-up
The transmissibility between the accelerometer on the base (cyan arrow) and the accelerometer of the center of the
plate (red arrow) is measured hammering the base.
Despite the high noise, it is possible to see in the controlled transfer function a reduction of the incoming
disturbance in the controlled frequency region and also a gradually phase shift.
• Replace the RCP system by the control system of the SISO isolation demo:
– Low cost sensors
– Analog PID controllers
– Low cost amplifiers
Next steps

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Presentation statusmeeting 2017_05

  • 2. Objective The objective to be achieved is the isolation from environmental vibration of the LEGO® platform from the myphotonics project. This must be done with low cost instrumentation in order to fit the purpose of OpenAdaptronik project. Michelson-Interferometer Optische Pinzette Zweistrahl-Interferometer LEGO® platform
  • 3. Simple Vibration Problem – Skyhook Solution A solution to this problem is the adoption of an active damping system. Skyhook control is a feedback velocity control widely use in vibration isolation for a vehicle. It simply introduce into the system a force proportional to the speed of the mass to be isolated changing the damping of the system only form the point of view of the mass and not from the one of the incoming disturbance. Equation of motion: 𝑚 𝑥 + 𝑟 𝑥 + 𝑘𝑥 = 𝒇 + 𝑟 𝑥 𝑝 + 𝑘𝑥 𝑝 𝑚 𝑥 + 𝑟 𝑥 + 𝑘𝑥 = −𝑲 𝑥 + 𝑟 𝑥 𝑝 + 𝑘𝑥 𝑝 Choosing: 𝐾 = 2𝑚 𝑒 𝜔0 − 𝑟 the best attenuation at the resonance frequency is obtained 𝐺 𝑠𝑦𝑠𝐶 = 𝑟𝑠 + 𝑘 𝑚 𝑒 𝑠2 + 𝑟 + 𝑲 𝑠 + 𝑘 1. Amplitude attenuation at the resonance frequency 2. Amplitude attenuation at frequencies higher then the resonance
  • 4. It’s now possible to calculate the mode shapes of the structure ϕ , visualize them and comparing with the results obtained directly by the software implemented in the Laser Vibrometer used for the measurements. • Left side: 1st and 2nd eigenmodes reconstructed. • Right side: 1st and 2nd eigenmodes from L.V. From left to right and up to down : eigenmodes reconstructed 3,4,5,6,7,8. Preliminary Measurements - Modal Analysis
  • 5. Real System It is now possible to pass to the analysis of the real configuration of the problem. The connections between the plate and the actuators are made by other LEGO® bricks. They are glued on the actuator side and the connection on the plate side is left free in order to have the possibility to easily remove the LEGO® plate and to not modify the structure. ϕ 𝜗 𝑥 𝑝1 𝑥 𝑝2 𝑥 𝑝3 𝑓𝑐1 𝑓𝑐2 𝑓𝑐3 k k kr r r 𝑧𝑐 𝑙 𝑥 𝑙 𝑦 𝑚 𝑒 ; 𝐽φ ; 𝐽ϑ 1 4 3 2 x yz  Four actuators are attached on the base of the plate in a symmetric way and for sensors (accelerometers) are placed on the top of the plate in a position corresponding to the center of the actuators.  In this way is possible to reach a symmetric behavior of the system. Actuators Location and Mounting • In the figure is reported a scheme of the considered system in which is possible to see the forces exercised by the four actuators and the incoming disturbances for each one. • From now on the moving part of the actuators are considered integrated with the LEGO® plate and the mechanical and electrical parameters are considered equal for each actuator. Scheme of the final configuration
  • 6. Decentralized control vs. MIMO control Decentralized MIMO Simplified system: 4 independent control loops No significant performance reduction by decentralized approach
  • 7. Real System – Sampling Effect A sampling frequency of 10 kHz is definitively to high for implementing a control on a low cost control board so the effect of sampling is experimentally studied. In the two figures the centralized and decentralized controls effects are compared for two different sampling frequencies, 1 kHz and 0.5 kHz. 10 kHz 1 kHz 0,5 kHz Lower sampling rate causes higher delays in the loop Smaller stability margin  Lower performance  Analog control circuit preferred to avoid effects of DAC/ADC
  • 8. Real System – Experimental Results The results obtained were done hammering the upper surface of the structure because for the best case experiment it will be needed four shakers, one for each actuator, capable of carrying at least one quarter the weight of the entire structure. Transmissibility Measurement set-up The transmissibility between the accelerometer on the base (cyan arrow) and the accelerometer of the center of the plate (red arrow) is measured hammering the base. Despite the high noise, it is possible to see in the controlled transfer function a reduction of the incoming disturbance in the controlled frequency region and also a gradually phase shift.
  • 9. • Replace the RCP system by the control system of the SISO isolation demo: – Low cost sensors – Analog PID controllers – Low cost amplifiers Next steps