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Thomas Dehaeze 2020-07-08 18:08:42 +02:00
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@ -566,6 +566,8 @@ While having very different implementations, both proposed modifications are ver
Future work will focus on the experimental validation of the proposed active damping techniques.
The Matlab code that was used for this study is available under a MIT License and archived in Zenodo cite:dehaeze20_activ_dampin_rotat_posit_platf.
* Acknowledgment
:PROPERTIES:
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% Created 2020-07-08 mer. 18:02
% Created 2020-07-08 mer. 18:07
% Intended LaTeX compiler: pdflatex
\documentclass{ISMA_USD2020}
\usepackage[utf8]{inputenc}
@ -58,7 +58,7 @@ The results reveal that, despite their different implementations, both modified
}
\section{Introduction}
\label{sec:org639dbba}
\label{sec:orgc580a8f}
\label{sec:introduction}
There is an increasing need to reduce the undesirable vibration of many sensitive equipment.
A common method to reduce vibration is to mount the sensitive equipment on a suspended platform which attenuates the vibrations above the frequency of the suspension modes.
@ -78,7 +78,7 @@ Section \ref{sec:iff_kp} proposes to add springs in parallel with the force sens
Section \ref{sec:comparison} compares both proposed modifications to the classical IFF in terms of damping authority and closed-loop system behavior.
\section{Dynamics of Rotating Platforms}
\label{sec:orgea844f7}
\label{sec:orgf7cef1f}
\label{sec:dynamics}
In order to study how the rotation does affect the use of IFF, a model of a suspended platform on top of a rotating stage is used.
Figure \ref{fig:system} represents the model schematically which is the simplest in which gyroscopic forces can be studied.
@ -225,7 +225,7 @@ For \(\Omega > \omega_0\), the low frequency pair of complex conjugate poles \(p
\end{figure}
\section{Decentralized Integral Force Feedback}
\label{sec:org7bfaed6}
\label{sec:orgcb8c9c7}
\label{sec:iff}
In order to apply IFF to the system, force sensors are added in series with the two actuators (Figure \ref{fig:system_iff}).
As this study focuses on decentralized control, two identical controllers \(K_F\) are used to feedback each of the sensed force to its associated actuator and no attempt is made to counteract the interactions in the system.
@ -322,7 +322,7 @@ In order to apply Decentralized IFF on rotating platforms, two solutions are pro
The first one consists of slightly modifying the control law (Section \ref{sec:iff_hpf}) while the second one consists of adding springs in parallel with the force sensors (Section \ref{sec:iff_kp}).
\section{Integral Force Feedback with High Pass Filter}
\label{sec:org380bd8d}
\label{sec:org0b913ec}
\label{sec:iff_hpf}
As was explained in the previous section, the instability comes in part from the high gain at low frequency caused by the pure integrators.
@ -393,7 +393,7 @@ Three regions can be observed:
\end{itemize}
\section{Integral Force Feedback with Parallel Springs}
\label{sec:org93348b6}
\label{sec:org082b3c2}
\label{sec:iff_kp}
In this section additional springs in parallel with the force sensors are added to counteract the negative stiffness induced by the rotation.
Such springs are schematically shown in Figure \ref{fig:system_parallel_springs} where \(k_a\) is the stiffness of the actuator and \(k_p\) the stiffness in parallel with the actuator and force sensor.
@ -494,7 +494,7 @@ This is confirmed in Figure \ref{fig:mod_iff_damping_kp} where the attainable cl
\end{minipage}
\section{Comparison and Discussion}
\label{sec:org5f56e74}
\label{sec:org1f46ad4}
\label{sec:comparison}
Two modifications to adapt the IFF control strategy to rotating platforms have been proposed in Sections \ref{sec:iff_hpf} and \ref{sec:iff_kp}.
These two methods are now compared in terms of added damping, closed-loop compliance and transmissibility.
@ -554,7 +554,7 @@ On can see in Figure \ref{fig:comp_transmissibility} that the problem of the deg
The addition of the HPF or the use of the parallel stiffness permit to limit the degradation of the compliance as compared with classical IFF (Figure \ref{fig:comp_compliance}).
\section{Conclusion}
\label{sec:org6ee721e}
\label{sec:org071db57}
\label{sec:conclusion}
Due to gyroscopic effects, decentralized IFF with pure integrators was shown not to be stable when applied to rotating platforms.
@ -572,8 +572,10 @@ While having very different implementations, both proposed modifications are ver
Future work will focus on the experimental validation of the proposed active damping techniques.
The Matlab code that was used for this study is available under a MIT License and archived in Zenodo \cite{dehaeze20_activ_dampin_rotat_posit_platf}.
\section*{Acknowledgment}
\label{sec:orgd2f72ff}
\label{sec:orgd8daf24}
This research benefited from a FRIA grant from the French Community of Belgium.
\bibliography{ref.bib}