@@ -108,7 +108,7 @@ X_{err} = IN + G \cdot X_{err} = \dfrac{IN}{1-G}.
\end{equation}
\noindent
The term 1/(1+G) is called \textit{closed loop gain}.
The term 1/(1-G) is called \textit{closed loop gain}.
\subsection{Phase and magnitude interpretation: the Bode plot}
The Bode plot is a graph representing the response in frequency of the magnitude and phase of the system under exam. It is largely used to define the marginal conditions for the stability of the loop. The magnitude is expressed in dB = 20$\log_{10}(x)$ and it is computed as the absolute value of the transfer function:
@@ -20,7 +20,7 @@ This detection has been the result of a wide scientific collaboration which effo
\end{figure}
\section{LIGO duty cycle}
The efficiency of the instrument was show in Fig. \ref{duty}, and the upper chart is reported here.
The efficiency of the instrument was shown in Fig. \ref{duty}, and the upper chart is reported here.
\begin{figure}[h!]
\centering
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...
@@ -52,7 +52,7 @@ Other definitions and details about duty cycle and performance of the instrument
\section{The PRCL suspension filters}
The transfer function of the suspensions of the PRCL cavity illustrated in the block diagram of Chapter 5, are shown in the plot \ref{prclm1}. The complicated shape of this functions makes difficult to manually solve the PRCL block diagram and simulate the motion of the optics. To solve the diagram, the Mathematica software has been used.
The transfer function of the suspensions of the PR cavities, illustrated in the block diagram \ref{prcl} in Chapter 5, are shown in the plot \ref{prclm1}. The complicated shape of this functions makes difficult to manually solve the PRCL block diagram and simulate the motion of the optics. To solve the diagram, the Mathematica software has been used and several tests have been tried to look for the best filters and their effects (as reported on LHO logbook posts 52623, 53160, 53442, 53442).
\begin{figure}[h!]
\centering
...
...
@@ -61,8 +61,7 @@ The transfer function of the suspensions of the PRCL cavity illustrated in the b
\label{prclm1}
\end{figure}
%\section{CPS and LSC offloading tests at LIGO: some references}
%During the study for the CPS and LSC offloading exposed in Chapter 5, several tests and changes in the models of LHO and LLO have been carried on. The details of those tests are reported in the SEI, LHO and LLO logbooks: here some useful references are reported.
@@ -462,7 +462,7 @@ which is exactly the solution that we would obtain if the differential motion wa
During the 2019 commissioning break, in collaboration with LIGO Livingston Observatory, we tried to apply the new CPS configuration in order to obtain improvements in ISI motion and LSC signals at LIGO Hanford.\\
This test has been performed before the detailed analysis exposed previously and hence a more detailed and precise study for the choice of the blending filters involved is essential to get the expected enhancements. However the preliminary tests at LHO showed an improvement of a factor of 3 at 60 mHz (Fig. \ref{isitest}), as detected by the IMC sensors, and an encouraging result detected by DARM cavity below 0.1 Hz when all the chambers inside and outside the CS were locked (Fig. \ref{darmtest}).
\noindent
This is an interesting result that shows that with the implementation of the correct filters as shown in the analysis it is possible to reduce the differential motion of the platforms.\\
This is an interesting result that shows that with the implementation of the correct filters as shown in the analysis it is possible to reduce the differential motion of the platforms. Some effects of this configuration have been testified even by IMCL, during a measurement in on/off offloading, reported in the LHO logbook post 52690. Other tests looking at the effect on the LSC cavities are reported in post 52729 of LHO logbook.\\
