The theory of controls is a branch of science and technology which studies how to drive a given dynamical system. This is generally characterized by inputs and outputs and the former can be manipulated to obtain a desired output, which is chosen by a reference setpoint. The design and the technology involved depends on the system, but in general they imply a sensing section, a software section which can modify some features of the input and a feedback section to check that the manipulation of the input signal gave the output as set by the reference.
The theory of controls is a branch of science and technology which studies how to drive a given dynamical system. This is generally characterized by inputs and outputs and the former can be manipulated to obtain a desired output, which is chosen by a reference setpoint. The design and the technology involved depends on the system, but in general they imply a sensing section, a software section which can modify some features of the input and a feedback section to check that the manipulation of the input signal gives the output as set by the reference.
\subsection{Principles: control loops}
\subsection{Principles: control loops}
The collection of all the sections forms a control loop and controls the behaviour of a given variable under exam. Control loops can be:
The collection of all the sections forms a control loop and manages the behaviour of a given variable under exam. Control loops can be:
\begin{itemize}
\begin{itemize}
\item{Open-loop}: the control action is independent from the output.
\item{Open-loop}: the control action is independent from the output.
\item{Closed-loop}: the control action depends on the desired output conditions. This kind of loop uses feedback loops, that assure the process is correctly going on, i.e. the value of the variable under exam is that of setpoint.
\item{Closed-loop}: the control action depends on the desired output conditions. This kind of loop uses feedback loops, that assure that the process is correctly going on, i.e. the value of the variable under exam is that of the setpoint.
\end{itemize}
\end{itemize}
\noindent
\noindent
...
@@ -15,16 +15,17 @@ In order to design a control loop, we need to build all the subsystems up: the m
...
@@ -15,16 +15,17 @@ In order to design a control loop, we need to build all the subsystems up: the m
\subsection{How to: block diagrams}
\subsection{How to: block diagrams}
Block diagrams are useful graphical instruments to describe, study and build a control loop. Each element of the control system is represented by a block and each block is joined by lines with arrows showing the sequence of controls. Following the logical steps stated before, we can then draw the block diagram of a basic system to be controlled:
Block diagrams are useful graphical instruments to describe, study and build a control loop. Each element of the control system is represented by a block and each block is joined by lines with arrows showing the sequence of controls. Following the logical steps stated before, we can then draw the block diagram of a basic system to be controlled as in Fig. \ref{blockB}.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.8]{images/block.png}
\includegraphics[scale=0.8]{images/block.png}
\caption[Basic block diagram of a control loop.]{Basic block diagram of a control loop. The setpoint is injected as an input.}
\caption[Basic block diagram of a control loop.]{Basic block diagram of a control loop. The setpoint is injected as an input.}
\label{blockB}
\end{figure}
\end{figure}
\noindent
\noindent
Every variable under interest at the output of each block can be evaluated by \textit{solving} the diagram.
Every variable under interest at the output of each block can be evaluated by \textit{solving} the diagram. Referring to Fig. \ref{blockB}, solving a block diagram means solving the system of equations involving the variable under exam and each block. The product of the components of the block diagram give the total gain of the loop (see following sections).
\section{Control analysis}
\section{Control analysis}
Once the control loop has been schematically drafted, it needs to be finalized: the software section implies instructions. These are given by a computation of the transfer functions of the whole system, which gives the response in the frequency domain of the output to a given input. The computed (and measured) transfer function will then be modified with suitable filters to make the output adjust to the reference setpoint.
Once the control loop has been schematically drafted, it needs to be finalized: the software section implies instructions. These are given by a computation of the transfer functions of the whole system, which gives the response in the frequency domain of the output to a given input. The computed (and measured) transfer function will then be modified with suitable filters to make the output adjust to the reference setpoint.
...
@@ -46,7 +47,7 @@ T(s) = \dfrac{Y(s)}{X(s)}
...
@@ -46,7 +47,7 @@ T(s) = \dfrac{Y(s)}{X(s)}
\end{equation}
\end{equation}
\noindent
\noindent
and so the output is characterized by the product between the transfer function and the input signal in the Laplace domain, which is the Laplace transform of the convolution of the two functions in the time domain\footnote{An interesting demonstration of this statement can be found ....}.\\
and so the output is characterized by the product between the transfer function and the input signal in the Laplace domain, which is the Laplace transform of the convolution of the two functions in the time domain\footnote{An interesting demonstration of this statement can be found in \cite{wiki}}.\\
Since, in general, a function can be written as a product of polynomials, the transfer function is also in the form:
Since, in general, a function can be written as a product of polynomials, the transfer function is also in the form:
\begin{equation}
\begin{equation}
...
@@ -75,7 +76,7 @@ and the phase is $\varphi$ = arg(T(s)).\\
...
@@ -75,7 +76,7 @@ and the phase is $\varphi$ = arg(T(s)).\\
In the frame of control loops, the transfer function is given by the gain contributions of all the subsystems of the loop.
In the frame of control loops, the transfer function is given by the gain contributions of all the subsystems of the loop.
\subsection{Phase and magnitude interpretation: the Bode plot}
\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 in expressed in dB = 20$\log_{10}(x)$ and it is computes as the absolute value of the transfer function:
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:
where G$_{OL}$ is the open-loop gain and also a pole for this relation. This means that if G$_{OL}$ = -1, G$_{CL}$ diverges and the loop is unstable. On the phase plot, we will have that $\varphi$ = -180$^{\circ}$. In general, when the trace on the phase plot approaches this value at certain frequencies, it means that the loop that we are building is unstable in that region.
where G$_{OL}$ is the open-loop gain and also a pole for this relation. This means that if G$_{OL}$ = -1, G$_{CL}$ diverges and the loop is unstable. On the phase plot, we will have that $\varphi$ = -180$^{\circ}$. In general, when the trace on the phase plot approaches this value at certain frequencies, it means that the loop that we are building is unstable in that region.
\subsection{Spectral density}
\subsection{Spectral density}
Spectral densities are views of a signal in a frequency spectrum. It is a useful instrument to detect effects on the signal during processing, like peaks due to harmonics, or resonances. The physical parameter used in this study is the power spectral density, which measures the power of a signal as a function of frequency and has units of W/Hz$^{-1}$. When there is no direct power associated to the measurement (like in case of Volts) the units are in terms of the square of the signal per Hz. In some cases, an Amplitude Spectral Density (ASD), defined as the square root of the power spectral density, is used when the shape of the signal is quite constant; in this case the units are in the form of 1/Hz$^{-1/2}$ and the variations in the ASD will then be proportional to the variations of the signal itself.
Spectral densities are views of a signal in a frequency spectrum. It is a useful instrument to detect effects on the signal during processing, like peaks due to harmonics, or resonances. The physical parameter used in this study is the power spectral density, which measures the power of a signal as a function of frequency and has units of W/Hz$^{-1/2}$. When there is no direct power associated to the measurement (like in case of Volts) the units are in terms of the square of the signal per Hz. In some cases, an Amplitude Spectral Density (ASD), defined as the square root of the power spectral density, is used when the shape of the signal is quite constant; in this case the units are in the form of 1/Hz$^{-1/2}$ and the variations in the ASD will then be proportional to the variations of the signal itself.
\subsection{Coherence}
\subsection{Coherence}
The coherence is a statistic relation between two signals or data sets x and y. It is defined as the ration between the cross spectral density of the two functions and the product of the spectral densities of each function:
The coherence is a statistic relation between two signals or data sets x and y. It is defined as the ratio between the cross spectral density of the two functions and the product of the spectral densities of each function:
\chapter{Reducing differential motion of aLIGO seismic platforms}
\chapter{Reducing differential motion of aLIGO seismic platforms}
\label{CPSdiff}
\label{CPSdiff}
During 2019, I spent some months working on LIGO Hanford site (Washington, USA). This experience allowed me to be critically involved in the complicated life of a gravitational-wave interferometer. In particular, I was given the opportunity to study how to improve LIGO performances at low-frequency, focussing on the reduction of seismic motion of the platforms where the optics live.\\
During 2019, I spent some months working on LIGO Hanford site (Washington, USA). This experience allowed me to be critically involved in the complicated life of a gravitational-wave interferometer. In particular, I was given the opportunity to study how to improve LIGO performances at low-frequency, focussing on the reduction of seismic motion of the platforms where the optics live.\\
In this chapter I will demonstrate how we can modify the software set up of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC.\\
In this chapter I will demonstrate how we can modify the software set up of LIGO in order to obtain different and possibly better performances for seismic motion stabilization, faster and longer locking mode and, ultimately, gravitational waves detections. The detailed computations included in this chapter are original and partially presented to the LIGO community and stored in LIGO DCC\cite{proposal}\cite{technote1}.\\
This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB and completed at UoB during 2020.\\
This work has been developed in collaboration with LIGO Hanford and LIGO Livingston laboratories, Stanford University, MIT and UoB and completed at UoB during 2020.\\
This chapter is partially including some technical notes I shared with LIGO collaboration and the contents of this study have been presented at conferences and workshops.\\
This chapter is partially including some technical notes I shared with LIGO collaboration and the contents of this study have been presented at conferences and workshops\cite{chiatalk}.\\
Essential information about the sections of LIGO involved in this study has been exposed in detail in Chapter \ref{LIGO}.
Essential information about the sections of LIGO involved in this study has been exposed in detail in Chapter \ref{LIGO}.
\section{Motivation: Duty cycle on LIGO}
\section{Motivation: Duty cycle on LIGO}
Lock loss events are the main sources of preventing continuous observations for long periods of time: when light loses resonance in the cavities, a lock loss happens and the control system of the optical cavities are under effort to restore stabilization. This means that during lock loss the interferometer is no longer able to be stable and the observing time is interrupted.\\
Lock loss events are the main sources of preventing continuous observations for long periods of time: when light loses resonance in the cavities, a lock loss happens and the control system of the optical cavities are under effort to restore stabilization. This means that during lock loss the interferometer is no longer able to be stable and the observing time is interrupted\cite{biscans}.\\
Duty cycle is one of the main topic where commissioners focus on before starting an observing run. It is needed not only to observe more gravitational waves, but also to identify noise sources and improve sensitivity.\\
Duty cycle is one of the main topic where commissioners focus on before starting an observing run\cite{biscans}\cite{kisseltalk1}. It is needed not only to observe more gravitational waves, but also to identify noise sources and improve sensitivity \cite{biscanstalk}.\\
Since the number of detected events over a time period N(t) is proportional to the volume of Universe under observation V, the observing time t and the rate R of astrophysical sources that can occur in a certain volume:
Since the number of detected events over a time period N(t) is proportional to the volume of Universe under observation V, the observing time t and the rate R of astrophysical sources that can occur in a certain volume:
\begin{equation}
\begin{equation}
...
@@ -40,60 +40,61 @@ N(t) = R\cdot V\cdot t,
...
@@ -40,60 +40,61 @@ N(t) = R\cdot V\cdot t,
\end{equation}\\
\end{equation}\\
it can be seen that increasing the observing time towards a given direction, will increase the number of detected events.\\
it can be seen that increasing the observing time towards a given direction, will increase the number of detected events.\\
\noindent
\noindent
Other ways to spend time to improve duty cycle is instead to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth.
Other ways to spend time to improve duty cycle is instead to increase the observable volume: this can be achieved by spending time on hardware to improve sensitivity on a given frequency bandwidth\cite{kisseltalk1}.
\caption[LHO duty cycle during O3b]{Example of duty cycle for Hanford Observatory, during O3b.}
\caption[LHO duty cycle during O3b]{Example of duty cycle for Hanford Observatory, during O3b (Figure taken from \cite{kisseltalk1}) For almost 20\% of the running time the detector was not locked, which means that it was not observing. It is important to minimise this number, so more gravitational waves can be detected.}
\label{duty}
\label{duty}
\end{figure}
\end{figure}
\subsection{Differential motion between chambers}
\subsection{Differential motion between chambers}
We have seen that among the noise sources which contribute to lock loss events there is the ground motion, including earthquakes and microseismic events. \\
We have seen that among the noise sources which contribute to lock loss events there is the ground motion, including earthquakes and microseismic events. \\
In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential motion with respect to each other. It is reasonable to think that if the chambers have a synchronized motion, the whole interferometer will move following the ground motion, and not being affected by it. This would in principle help the cavities to be stable and maintain resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times.\\
In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential motion with respect to each other\cite{technote1}. It is reasonable to think that if the chambers have a synchronized motion, the whole interferometer will move following the ground motion, and not being affected by it. This would in principle help the cavities to be stable and maintain resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times \cite{biswas}.\\
On another side, reducing the differential motion between the chambers means to reduce a source of noise at low frequency (5-30 Hz), as we will show in the next section: this would improve the sensitivity of the interferometer.
On another side, reducing the differential motion between the chambers means to reduce a source of noise at low frequency (5-30 Hz), as we will show in the next section: this would improve the sensitivity of the interferometer.
\subsection{ISI stabilization}
\subsection{ISI stabilization}
Differential motion affects the ISI of the HAM and BSC chambers in the CS: these are then the platforms that we want to stabilize. Several sensors are responsible for sensing the seismic motion, in all degrees of freedom of each stage. They are T240, L4C, GS13, OSEMs and CPS.
Differential motion affects the ISI of the HAM and BSC chambers in the CS: these are then the platforms that we want to stabilize. Several sensors are responsible for sensing the seismic motion, in all degrees of freedom of each stage. They are T240, L4C, GS13, OSEMs and CPS\cite{kisselthesis}.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.9]{images/isi.png}
\includegraphics[scale=0.9]{images/isi.png}
\caption[Example of ISI scheme]{Example of ISI scheme.}
\caption[Example of ISI scheme]{Example of ISI inertial sensor scheme (figure taken from \cite{adl2}). All the main inertial sensors involved in the seismic isolation are shown in their locations. The CPSs are position sensors located between stages to measure the relative position.}
\label{isi}
\label{isi}
\end{figure}
\end{figure}
\noindent
\noindent
In particular, CPS sensors are placed in every chambers at all stages: it is easy to compare motion between HAM and BSC chambers through the signal of a device sensing the same motion on every chamber.\\
In particular, CPS sensors are placed in every chambers at all stages: it is easy to compare motion between HAM and BSC chambers through the signal of a device sensing the same motion on every chamber\cite{kisseltalk2}.\\
The idea which should stabilize ISIs to follow the ground motion is to lock the chambers to each other, in order to make them move on a synchronized way, following a common motion given by a driver chamber (or block of chambers).
The idea which should stabilize ISIs to follow the ground motion is to lock the chambers to each other, in order to make them move on a synchronized way, following a common motion given by a driver chamber (or block of chambers).
\paragraph*{Role of the mode cleaner}
\paragraph*{Role of the mode cleaner}
We started our design on chambers of x arm. Along this direction, the Input Mode Cleaner (IMC) lies totally on HAM2 and HAM3 platforms: it can be used as a reference, or witness, of the motion between chambers, once they are locked together.\\
We started our design on the chambers on the x arm. Along this direction, the Input Mode Cleaner (IMC) lies totally on HAM2 and HAM3 platforms: it can be used as a reference, or witness, of the motion between chambers, once they are locked together.\\
%\begin{figure}[h!]
%\begin{figure}[h!]
%\centering
%\centering
%\includegraphics[scale=0.8]{images/IMC.png}
%\includegraphics[scale=0.8]{images/IMC.png}
%\caption[Optical layout of the HAM2 and HAM3 chambers]{Optical layout of the HAM2 and HAM3 chambers.}
%\caption[Optical layout of the HAM2 and HAM3 chambers]{Optical layout of the HAM2 and HAM3 chambers.}
%\label{imc}
%\label{imc}
%\end{figure}\\
%\end{figure}\\
\noindent
\noindent
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and they also can be used to lock the chambers with each other.
In the next section we will demonstrate that CPS are good witnesses to sense differential motion and they also can be used to lock the chambers with each other.
\section{Sensing differential motion via CPS}
\section{Sensing differential motion via CPS}
Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. On HAM chambers, they are are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers, they also measure the relative motion between Stage 1 and Stage 2. Plots is Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors are reliable for this measurement, and they put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on x arm is more relatively stable and can be used as driver for the other chambers, with the mode cleaner acting as witness.\\
The Capacitive Position Sensors (CPS) measure the relative motion between two stages of the isolation system. Referring to Fig. \ref{isi}, on HAM chambers they are are set between HEPI and ground, and between Stage 1 and HEPI. On BSC chambers they also measure the relative motion between Stage 1 and Stage 2. The plots is Fig. \ref{diff} show the differential motion seen by the CPS between BSC and HAM chambers: the sensors are reliable for this measurement, and they put in evidence that the HAM chambers have a more synchronized motion with respect to the motion between HAM and BSC and BSCs only. This means that the block of HAM chambers on x arm is more relatively stable and can be used as driver for the other chambers, with the mode cleaner acting as witness. We then projected the CPS of the x axis chambers to the suspension point in order to obtain PRCL and IMCL traces like as they would be sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum.
\caption[CPS differential motion]{CPS differential motion between the HAM and BSC chambers along x axis. ISIs move in common, particularly in the same building. This can be confirmed by noting that the difference between two chambers is much lower than individual chambers.}
\caption[CPS differential motion]{CPS differential motion between the HAM and BSC chambers along x axis. ISIs move in common, particularly in the same building. This can be confirmed by noting that the difference between two chambers is much lower than individual chambers.}
\label{diff}
\label{diff}
\end{figure}
\end{figure}
\newpage
\noindent
\noindent
We projected the CPS of the x axis chambers to the suspension point in order to obtain PRCL and IMCL traces sensed by the CPS. For BSCs, we decided to sum the contributions of the CPSs on stage 1 and stage 2 and to project this sum.\\
One of the main differences between the behaviour of CPS IMCL and CPS PRCL, is that the former is obviously involving only the HAM chambers. Since HAM2 and HAM3 have a very good common motion, IMCL can be considered more stable with respect to PRCL, which instead involves also BSCs. Indeed, CPS PRCL is following the only BSCs at frequencies below 0.02 Hz (\ref{sus}).\\
One of the main differences between the behaviour of CPS IMCL and CPS PRCL, is that the former is obviously involving only the HAM chambers. Since HAM2 and HAM3 have a very good common motion, IMCL can be considered more stable with respect to PRCL, which instead involves also BSCs. Indeed, CPS PRCL is following the only BSCs at frequencies below 0.02 Hz.\\
\noindent
Fig. \ref{sus} shows plots of PRCL and ICML by CPS projection to suspoint. These projections indicate that reducing the differential motion as seen by the CPSs will help to reduce the residual motion seen by the optical cavities.\\
Fig. \ref{sus} shows the plots of PRCL and ICML as sensed by CPS projection to the suspension point. These projections indicate that reducing the differential motion as seen by the CPSs will help to reduce the residual motion seen by the optical cavities.\\
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
...
@@ -104,9 +105,9 @@ Fig. \ref{sus} shows plots of PRCL and ICML by CPS projection to suspoint. These
...
@@ -104,9 +105,9 @@ Fig. \ref{sus} shows plots of PRCL and ICML by CPS projection to suspoint. These
\end{figure}
\end{figure}
\section{Locking chambers via CPS}
\section{Locking chambers via CPS}
In the previous section we demonstrated that CPSs are good sensors for differential motion and can be used to monitor chamber motions at lower frequencies. Given that and remembering the aim of stabilize the motion of the chambers making them moving in sync, it is possible to use the CPSs to lock HAM2 and HAM3 together, HAM4 and HAM5 together, BSCs in the Corner Station together and BSCs hosting the ETMs together. This will stabilize the ISI differential motion with respect to a driving chamber.\\
In the previous section we demonstrated that the CPSs are good sensors for differential motion and that they can be used to monitor the chamber motion at lower frequencies. That said, and remembering the aim of stabilizing the motion of the chambers making them moving in sync, it is possible to use the CPSs to lock HAM2 and HAM3 together, HAM4 and HAM5 together, BSCs in the Corner Station together and BSCs hosting the ETMs together (refer to Chapter \ref{LIGO} for the location of these chambers). This will stabilize the ISI differential motion with respect to a driving chamber.\\
Since we saw that HAM2 and HAM3 show a very good common motion and that we can use the IMC as a witness of it, our first step has been to lock the HAM2 and HAM3 chambers together by feeding HAM3 a calculated differential CPS signal. This is done in practice with an additive offset to the setpoint of the HAM3 isolation control loop.\\
Since we saw that HAM2 and HAM3 show a very good common motion and that we can use the IMC as a witness of it, our first step is locking the HAM2 and HAM3 chambers together by feeding HAM3 a calculated differential CPS signal. This is done in practice with an additive offset to the setpoint of the HAM3 isolation control loop \cite{technote2}.\\
The block diagram in Fig. \ref{ham2b}, shows the structure of HAM2, where the signals from $d_{2}$ and $i_{2}$ represent the offsets given by CPS and inertial sensors.\\
The block diagram in Fig. \ref{ham2b}, shows the structure of HAM2, where the signals from $d_{2}$ and $i_{2}$ represent the offsets given by CPS and inertial sensors\footnote{For a summary on control loops, general design and feature and how to solve a block diagram, refer to Appendix \ref{B}.}.\\
At low frequency the CPS noise is negligible because its contribution is about 10$^3$ times lower than the microseismic peak.\\
At low frequency the CPS noise is negligible because its contribution is about 10$^3$ times lower than the microseismic peak.\\
General block diagrams notations are listed in Tab. \ref{tab1}\\
General block diagrams notations are listed in Tab. \ref{tab1}\\
...
@@ -139,8 +140,8 @@ $x_{p}$ & plant motion\\
...
@@ -139,8 +140,8 @@ $x_{p}$ & plant motion\\
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1]{images/ham2B.PNG}
\includegraphics[scale=0.8]{images/ham2B.PNG}
\caption[HAM2 simplified block diagram]{Simplified block diagram for HAM2 chamber as it is at present on LIGO.}
\caption[HAM2 simplified block diagram]{Simplified block diagram for HAM2 chamber as it is at present on LIGO\cite{technote2}.}
\label{ham2b}
\label{ham2b}
\end{figure}
\end{figure}
...
@@ -179,15 +180,16 @@ After some manipulations, and remembering that L$_2$ + H$_2$ = 1, we obtain:\\
...
@@ -179,15 +180,16 @@ After some manipulations, and remembering that L$_2$ + H$_2$ = 1, we obtain:\\
The result in Eq. \ref{d2} is the signal to subtract to HAM3 in order to feed HAM3 a CPS differential motion; it is added to HAM3 as in the block diagram in Fig. \ref{ham3b} for HAM3. In the original configuration, without any feeding into HAM3 the block diagrams for both chambers would be identical. In this new configuration instead, there is no sensor correction and ground noise on HAM3 because they both come from the contribution from HAM2, which is the offset $d_{2}$ added to HAM3.\\
The result in Eq. \ref{d2} is the signal to subtract to HAM3 in order to feed HAM3 a CPS differential motion; it is added to HAM3 as in the block diagram in Fig. \ref{ham3b} for HAM3. In the original configuration, without any feeding into HAM3, the block diagrams for both chambers would be identical. In this new configuration instead, there is no sensor correction and ground noise on HAM3 because they both come from the contribution from HAM2, which is the offset $d_{2}$ added to HAM3.\\
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1]{images/ham3B.PNG}
\includegraphics[scale=0.8]{images/ham3B.PNG}
\caption[HAM3 simplified block diagram with HAM2 offset]{Simplified block diagram for HAM3 in the new configuration where this chamber is now connected to HAM2: d$_{2}$ is the offset coming from HAM2.}
\caption[HAM3 simplified block diagram with HAM2 offset]{Simplified block diagram for HAM3 in the new configuration where this chamber is now connected to HAM2: d$_{2}$ is the offset coming from HAM2\cite{technote2}.}
\label{ham3b}
\label{ham3b}
\end{figure}
\end{figure}
\noindent
\noindent
We then want to know the reaction on HAM3 plant in this configuration, in order to compute differential motion between plants on both chambers.\\
We then want to know the reaction on HAM3 plant in this configuration, in order to compute the differential motion between plants on both chambers.\\
Following the usual notations and the block diagram of HAM3:\\
Following the usual notations and the block diagram of HAM3:\\
which is what we expect to be the signal of the differential motion sensed by the CPSs. In order to see this signal, we need to put in practice the modifications of the filters involved in the loop, as shown in the following section.
\section{Analysis of feasibility}
\section{Analysis of feasibility}
Next step is to study how to modify the low and high pass filters in order to obtain the best performances from each one in the new configuration of chambers. To do this, we are going to change the blending filters, i.e. those filters whose combination gives the best performance of the set low+high pass filters.\\
The next step is to study how to modify the low and high pass filters in order to obtain the best performances from each one in the new configuration of the chambers \cite{technote3}. To do this, we are going to change the blending filters, i.e. those filters whose combination gives the best performance of the set low+high pass filters.\\
If by definition we have L+H=1, we can write it also as:
If by definition we have L+H=1, we can write it also as:
According to the values of l and h we have different order of magnitudes of the binomials, which can be solved for the real part.\\
According to the values of \textit{l} and \textit{h} we have different order of magnitudes of the binomials, which can be solved for the real part.\\
\noindent
\noindent
In our case, we have two main contributions given by inertial sensors and CPS. We will apply the high-pass filter to the GS13 and the low-pass one to the CPS.\\
In our case, we have two main contributions given by inertial sensors and the CPS. We will apply the high-pass filter to the GS13 and the low-pass one to the CPS.\\
To do this, we need the specific contributions for each chamber to be specified, with all the components well defined. So for example, in the case of the CPS contribution, we need to define the tilt component, the CPS noise and the ground motion, which will take part into the platform motion as seen by the CPS sensor. This is because these components are independent from each other and will need to be summed in quadrature.\\
To do this, we need that the specific contributions for each chamber are specified, with all the components well defined. For example, in the case of the CPS contribution, we need to define the tilt component, the CPS noise and the ground motion, which will take part into the platform motion as seen by the CPS sensor. This is because these components are independent from each other and will need to be summed in quadrature.\\
Besides, as we saw in the previous computations, we will need to apply filters: the Sensor Correction filter will be the one used on LIGO and shown in Fig. \ref{SC}; the high- and low- pass filters will be find through blending several possible filters across a certain number of l and h order of magnitude, as introduced before. The best blended filter will be given by a combination of two l and h values at a specific blending frequency.\\
Besides, as we saw in the previous computations, we will need to apply filters: the Sensor Correction filter will be the one used on LIGO and shown in Fig. \ref{SC}; the high- and low- pass filters will be found through blending several possible filters across a certain number of \textit{l} and \textit{h} order of magnitudes, as introduced before. The best blended filter will be given by a combination of two \textit{l} and \textit{h} values at a specific blending frequency.\\
At the end of the analysis for each chamber (HAM and BSC) in isolation, we will connect the chambers via CPS and look at the results.\\
At the end of the analysis for each chamber (HAM and BSC) in isolation, we will connect the chambers via CPS and look at the results.\\
All this analysis has been performed through Matlab software.\\
All this analysis has been performed through Matlab software.\\
...
@@ -288,7 +293,7 @@ To calculate the platform motion of the BSC, we used data from the ITMX ISI alon
...
@@ -288,7 +293,7 @@ To calculate the platform motion of the BSC, we used data from the ITMX ISI alon
\begin{equation}
\begin{equation}
T240_{inj} = \sqrt{{BSC\theta_p}^2+{N_{T240}}^2}.
T240_{inj} = \sqrt{{BSC\theta_p}^2+{N_{T240}}^2}.
\end{equation}\\
\end{equation}\\
Figure \ref{t240_inj} shows the T240 signal and its contributors:
Figure \ref{t240_inj} shows the T240 signal and its contributors.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
...
@@ -302,7 +307,7 @@ The inertial contribution for HAM chambers is computed in a similar way: the sen
...
@@ -302,7 +307,7 @@ The inertial contribution for HAM chambers is computed in a similar way: the sen
\begin{equation}
\begin{equation}
GS13_{inj}= \sqrt{{HAM\theta_p}^2+{N_{GS13}}^2}.
GS13_{inj}= \sqrt{{HAM\theta_p}^2+{N_{GS13}}^2}.
\end{equation}\\
\end{equation}\\
Figure \ref{gs13_inj} shows the GS13 signal and its contributors:
Figure \ref{gs13_inj} shows the GS13 signal and its contributors.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
...
@@ -312,7 +317,7 @@ Figure \ref{gs13_inj} shows the GS13 signal and its contributors:
...
@@ -312,7 +317,7 @@ Figure \ref{gs13_inj} shows the GS13 signal and its contributors:
\end{figure}
\end{figure}
\subsection{Blending filters}
\subsection{Blending filters}
In order to compute platform motions for single chambers in isolation and, later, locked together via CPS, we need low- and high- pass filters. Many possible blended filters have been found for different combinations of order of magnitude and blending frequency: plots in Fig. \ref{blend} show the velocity rms for every combination.
In order to compute the platform motion for the single chambers in isolation and, later, locked together via CPS, we need the low- and high- pass filters. Many possible blended filters have been found for different combinations of order of magnitudes and blending frequency: the plots in Fig. \ref{blend} show the velocity rms for every combination.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
...
@@ -323,7 +328,7 @@ In order to compute platform motions for single chambers in isolation and, later
...
@@ -323,7 +328,7 @@ In order to compute platform motions for single chambers in isolation and, later
\end{figure}
\end{figure}
\noindent
\noindent
The best combination has been found computing the orders and the blending frequency which give the minimum of the cost. The optimized blending filter has been then built using the best values of l and h orders and blending frequency. The cost is given by:
The best combination has been found computing the orders and the blending frequency which give the minimum of the cost. The optimized blending filter has been then built using the best values of \textit{l} and \textit{h} orders and blending frequency. The cost is given by:
@@ -339,7 +344,7 @@ Fig. \ref{cost} shows the cost and its rms obtained with the best blending filte
...
@@ -339,7 +344,7 @@ Fig. \ref{cost} shows the cost and its rms obtained with the best blending filte
\end{figure}
\end{figure}
\subsection{Locking chambers}
\subsection{Locking chambers}
With these elements, we can proceed with the analysis of the behaviour of the chambers when locked via CPS. We refer to HAM2 and HAM3 chambers, since in the previous sections we made the computations for these chambers. Reminding that the equations we need are:
With these elements, we can proceed with the analysis of the behaviour of the chambers when locked via CPS. We refer to HAM2 and HAM3 chambers, since in the previous sections we made the computations for these chambers. We recall here that the equations we need are:
For the analysis of this section, we need to know which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. Since we know that the ground motion is the same everywhere in the Corner Station, the terms involving $x_g$ are coherent. Noises are instead, by definition, independent from each other.\\
For the analysis of this section, we need to know which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. Since we know that the ground motion is the same everywhere in the Corner Station, the terms involving $x_g$ are coherent. Noises are instead, by definition, independent from each other.\\
The previous equations then become:
The previous equations then become:
\begin{equation}
\begin{equation}
...
@@ -379,37 +386,36 @@ Since L$_3$ = L$_2$ and H$_2$=H$_3$:
...
@@ -379,37 +386,36 @@ Since L$_3$ = L$_2$ and H$_2$=H$_3$:
Plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in isolation, and Fig. \ref{cpsdiff} shows motions of the chambers when locked to each other and their differential motion. The improvement of the differential motion is evident below 0.1 Hz, but it is not convenient above this frequency: in this case, further studies of the blending filters involved could help to find a compromise.
The plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in isolation, and Fig. \ref{cpsdiff} shows motions of the chambers when locked to each other and their differential motion. The improvement of the differential motion is evident below 0.1 Hz, but it is not convenient above this frequency: in this case, further studies of the blending filters involved could help to find a compromise.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.3]{images/diffham.png}
\includegraphics[scale=0.3]{images/diffham.png}
\caption[Ham chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference.}
\caption[Ham chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference. The purple trace is the differential motion between HAM2 and HAM3 that we are interested in reducing.}
\label{diffham}
\label{diffham}
\end{figure}
\end{figure}
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.5]{images/cpsdiff.png}
\includegraphics[scale=0.5]{images/cpsdiff.png}
\caption[HAM chambers in CPS locking condition]{HAM chambers in CPS locking condition: the plot shows the motion of each chamber, where HAM3 depends on HAM2, through CPS locking, and the differential motion between them. There is an improvement of the differential motion in the new configuration (purple trace) with respect to the situation in isolation (green dotted trace) by a factor of 3 in order of magnitude below 0.1 Hz.}
\caption[HAM chambers in CPS locking condition]{HAM chambers in CPS locking condition: the plot shows the motion of each chamber, where HAM3 depends on HAM2, through CPS locking, and the differential motion between them. There is an improvement of the differential motion in the new configuration (purple trace) with respect to the situation in isolation (green dashed trace) by a factor of 3 in order of magnitude below 0.1 Hz.}
\label{cpsdiff}
\label{cpsdiff}
\end{figure}
\end{figure}
\section{Inertial sensors locking}
\section{Inertial sensors locking}
\subsection{Locking chambers via inertial sensors}
In the frame of ISI stabilization from ground motion, the inertial sensors could also be used for the same purpose to lock chambers, in addition to CPS locking \cite{technote3}. This means that HAM3 will be fed by the inertial sensors signal coming from HAM2.\\
In the frame of ISI stabilization from ground motion, the inertial sensors could also be used for the same purpose to lock chambers, in addition to CPS locking. This means that HAM3 will be fed by the inertial sensors signal coming from HAM2.\\
Signals from inertial sensors are represented by i$_2$ and i$_3$ notations in Fig. \ref{ham2b} and \ref{ham3b}. However, adding the signal i$_2$ to HAM3 implies that the block diagram will be modified as in Fig. \ref{ham3bi}.
Signals from inertial sensors are represented by i$_2$ and i$_3$ notations in Fig. \ref{ham2b} and \ref{ham3b}. However, adding the signal i$_2$ to HAM3 implies that the block diagram will be modified as in Fig. \ref{ham3bi}.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1]{images/ham3Bi.png}
\includegraphics[scale=0.8]{images/ham3Bi.png}
\caption[Inertial sensor locking setup]{New setup of HAM3 chamber fed by CPS and inertial sensor signals from HAM2.}
\caption[Inertial sensor locking setup]{New setup of HAM3 chamber fed by CPS and inertial sensor signals from HAM2.}
\label{ham3bi}
\label{ham3bi}
\end{figure}
\end{figure}
\noindent
\noindent
Following a similar path for the math in this configuration of i$_2$ signal from HAM2:\\
Following a similar path for the math for this configuration of i$_2$ signal from HAM2:\\
The computation of the differential motion between HAM2 nad HAM3 in the conditions where the two ISIs are connected both via CPS and inertial sensors, shows that there is no contribution from the sensor correction and from the ground noise.\\
The computation of the differential motion between HAM2 and HAM3 in the conditions where the two ISIs are connected both via CPS and inertial sensors shows that there is no contribution from the sensor correction and from the ground noise.\\
Besides, it is worth notice that if L$_2$ = L$_3$, also H$_2$=H$_3$ by definition and the differential motion is:\\
Besides, it is worth notice that if L$_2$ = L$_3$, also H$_2$=H$_3$ by definition and the differential motion is:\\
\begin{equation}
\begin{equation}
\centering
\centering
...
@@ -461,55 +467,58 @@ which is exactly the solution that we would obtain if the differential motion wa
...
@@ -461,55 +467,58 @@ which is exactly the solution that we would obtain if the differential motion wa
\section{Test on LIGO Hanford and LSC signals optimization}
\section{Test on LIGO Hanford and LSC signals optimization}
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.\\
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 so a more detailed and precise study for the choice of the blending filters involved is essential to get the expected improvements; however the preliminary tests at LHO showed an improvement of a factor of 3 at 60 mHz, 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.
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 interested 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.\\
\begin{figure}
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1.15]{images/isi_sup.png}
\includegraphics[scale=1.15]{images/isi_sup.png}
\caption[ISI motion suppression]{Screenshot from LHO CDS showing a quick measurement with the chambers in the CS were locked: the witness is the IMC and we monitored also the ground motion to make sure that no important variations were happening at the moment of the measurement. The green traces represents the motion before the locking, while we took two measurement after the locking (blue and pink) to validate the test. \textbf{Left:} motion of the suspension point of the M2 and M3 optics (lying on HAM3 and HAM2 respectively). \textbf{Right:} ground motion and IMC cavity motion before (green) and after the locking mode (blue and pink).}
\caption[ISI motion suppression]{Screenshot from LHO CDS showing a quick measurement with the chambers in the CS were locked: the witness is the IMC and we monitored also the ground motion to make sure that no important variations were happening at the moment of the measurement. The green traces represents the motion before the locking, while we took two measurement after the locking (blue and pink) to validate the test. \textbf{Left:} motion of the suspension point of the M2 and M3 optics (lying on HAM3 and HAM2 respectively). \textbf{Right:} ground motion and IMC cavity motion before (green) and after the locking mode (blue and pink).}
\label{isitest}
\end{figure}
\end{figure}
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1.2]{images/darm.png}
\includegraphics[scale=1.2]{images/darm.png}
\caption[DARM improvement with locked chambers]{Screenshot taken from LHO CDS when a quick measurement of DARM reaction to the lock of all the chambers has been taken. The result is encouraging because it shows an improvement of the signal below 0.1 Hz.}
\caption[DARM improvement with locked chambers]{Screenshot taken from LHO CDS when a quick measurement of DARM reaction to the lock of all the chambers has been taken. The result is encouraging because it shows an improvement of the signal below 0.1 Hz.}
\label{darmtest}
\end{figure}
\end{figure}
\noindent
\noindent
With the obtained results, a positive consequence of this work might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal.
With this in mind, a positive consequence of this effect might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. It might be convenient to make the optics of the LS cavities, lying on the platforms and subjected to the ISI motion, be controlled by the ISI itself. This ideas has been developed and tested at LHO and is exposed in the following section.
\subsection{LSC offloading}
\subsection{LSC offloading}
We saw that the cavities (and the optical signals) in LIGO are affected by the ISI motion, simply because they lie on them. Given the work done with the CPSs to suppress the ISI motion, we should see an improvement on LSC signals. This is not immediate, though, nor trivial, because the optics are just set on the optical bench, without any communication with the ISI. The motion of the optics on the chambers due to other factors than seismic is not seen by the platforms: if we could connect this motion to the platform via software, this would make the optics and the platform more dependent on each other. This means that we can control the stabilization of the cavity lengths also with the ISIs.\\
We saw that the cavities (and the optical signals) in LIGO are affected by the ISI motion, simply because they lie on them. Given the work done with the CPSs to suppress the ISI motion, we should see an improvement on LSC signals. This is not immediate, though, nor trivial, because the optics are just set on the optical bench, without any communication with the ISI. Despite there is a sort of benefit as testified by Fig. \ref{darmtest}, the motion of the optics on the chambers due to other factors than seismic noise is not seen by the platforms: if we could connect this motion to the platform via software, this would make the optics and the platform more dependent on each other. This means that we can control the stabilization of the cavity lengths also with the ISIs.\\
What we expect is a faster reach of locking and a longer state of lock of the interferometer during observing runs.\\
What we expect is a faster reach of locking and a longer state of lock of the interferometer during observing runs.\\
\noindent
\noindent
This work has been performed on LIGO during the commissioning break between O3a and O3b observing runs, in October 2019. The reason of this choice is that we needed the interferometer to \textit{not} be observing, since we were going to modify some software structure of the instrument.\\
This work has been performed on LIGO Hanford during the commissioning break between O3a and O3b observing runs, in October and November 2019. The reason of this choice is that we needed the interferometer to \textit{not} be observing, since we were going to modify some software structure of the instrument.\\
\noindent
\noindent
Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambers and made them to move in sync. So they can be considered as a whole block. The IMC is entirely lying on HAM2 and HAM3, and it is straightforward to use it as a witness: to make this real, we need to feed the HAM2-HAM3 block with IMCL. This will lock the cavity signal to the HAM2-HAM3 block. The same feeding will be performed with PRCL, SRCL, DARM and MICH cavities, which optics lie on the other chambers, in and out the corner station. Fig. \ref{chamb} illustrates the chambers and the locations of the cavities of interest.
To lock the LSC signals to ISIs, we need to do something similar to what we did with the HAM chambers: we need to connect via software two different setups which do not talk to each other. We decided to start from the Power Recycling Cavity Length (PRCL) because we locked HAM2 and HAM3 chambers, so it was natural to start to lock the cavities on the x axis.\\
Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambers and made them to move in sync. So they can be considered as a whole block. The IMC is entirely lying on HAM2 and HAM3, and it is straightforward to use it as a witness: to make this real, we need to feed the HAM2-HAM3 block with IMCL. This will lock the cavity signal to the HAM2-HAM3 block. The same feeding will be performed with PRCL, SRCL, DARM and MICH cavities, which optics lie on the other chambers, in and out the corner station. Fig. \ref{chamb} illustrates the chambers and the locations of the cavities of interest in this study.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.3]{images/chambs.pdf}
\includegraphics[scale=0.3]{images/chambs.pdf}
\caption[Sketch of the blocks and the locations of the cavities]{Sketch of the blocks and the locations of the PRC and IMC cavities (not in scale). the HSTS suspensions of the mode cleaner and the power recycling cavoty lie all on HAM2 and HAM3 chambers. the signal for PRCL come form the Corner Station, which can be grouped as a BSC block.}
\caption[Sketch of the blocks and the locations of the cavities]{Sketch of the blocks and the locations of the PRC and IMC cavities (not in scale). the suspensions of the mode cleaner and the power recycling cavity lie all on HAM2 and HAM3 chambers. the signal for PRCL come form the Corner Station, which can be grouped as a BSC block.}
\label{chamb}
\label{chamb}
\end{figure}
\end{figure}
\noindent
\noindent
To lock the LSC signals to ISIs, we need to do something similar to what we did with the HAM chambers: we need to connect via software two different setups which do not talk to each other. We decided to start from the Power Recycling Cavity Length (PRCL) because we locked HAM2 and HAM3 chambers, so it was natural to start to lock the cavities on the x axis.\\
The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the software for PRCL, since the job involved the request of permissions to modify the structure of the interferometer and the synchronization with the job of other people working on different parts of LIGO. Moreover, during the commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time.
The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the software for PRCL, since the job involved the request of permissions to modify the structure of the interferometer and the synchronization with the job of other people working on different parts of LIGO. Moreover, during commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time.
\paragraph{The Power Recycling Cavity Length (PRCL)}
\paragraph{The Power Recycling Cavity Length (PRCL)}
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI. The block diagram in Fig. \ref{prcl} illustrate the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrate the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
The work done in this case is similar to the one done for the HAM chambers, except from the fact that a new filter need snow to be built in order to control how the ISI affect the motion of the PRC optics.
The work done in this case is similar to the one done for the HAM chambers, except from the fact that a new filter needs now to be built in order to control how the ISI affect the motion of the PRC optics.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.7]{images/PRCLfeed.png}
\includegraphics[scale=0.7]{images/PRCLfeed.png}
\caption[Block diagram of PRCL locked to the ISI]{Block diagram of PRCL locked to the ISI. This drawing highlights the details of the PRCL cavity sections involved in active control. In the standard diagram, only the PRCL sections would be involved, while now the cavity is connected via software to the ISI. The LSCfilter block is the crossover filter between the cavity and the ISI (and the connection between them is enabled by a switcher) while the ISItoM3 block represents the plant block of the suspension point of M3 after the connection.}
\caption[Block diagram of PRCL locked to the ISI]{Block diagram of PRCL locked to the ISI. This drawing highlights the details of the PRCL cavity sections involved in active control. In the standard diagram, only the PRCL sections would be involved, while now the cavity is connected via software to the ISI. The LSCfilter block is the crossover filter between the cavity and the ISI (and the connection between them is enabled by a switcher) while the ISItoM3 block represents the plant block of the suspension point of M3 after the connection. The blocks in pink represents the 3 stages of optics involved in the HSTS suspension and the controller already existing on LIGO.}
\label{prcl}
\label{prcl}
\end{figure}
\end{figure}
\noindent
\noindent
This block diagram has been solved with Mathematica in order to find the correct crossoover filters to add. The system was simulated via Matlab and includes information from calibration filter modules, PRM control filters, and HSTS models via the calibration filters. This is needed to simulate the addition of the ISI as a PRCL actuator. The aim was to offload low-frequencies to the ISI and hence we needed to decide the best configuration of gains and offsets of the crossover filter.\\
This block diagram has been solved with Mathematica in order to find the correct crossover filters to add. The system was simulated via Matlab and includes information from calibration filter modules, PRM control filters, and HSTS models via the calibration filters. This is needed to simulate the addition of the ISI as a PRCL actuator. The aim is to offload low-frequencies to the ISI and hence we need to decide the best configuration of gains and offsets of the crossover filter.\\
After every simulation which could possibly work for the system, we locked the interferometer and took a measurement of the PRM suspension point. The plot in Fig. \ref{prcltest} shows a comparison between the simulation and the actual measured PRCL signal: the test is positive because the two traces differ by only a factor of 2. This result has been obtained implementing the filter in Fig. \ref{prclfilter}. The test shows that the offloading works as expected and that the PRCL signal can be driven (and hence controlled) by the ISI. Further studies of the crossover filters might improve the results.
After every simulation which could possibly work for the system, we locked the interferometer and took a measurement of the PRM suspension point. The plot in Fig. \ref{prcltest} shows a comparison between the simulation and the actual measured PRCL signal: the outcome is positive because the two traces differ by only a factor of 2, which says that the crossover filter should be adjusted by a factor of 2 to match the real signal. This result has been obtained implementing the filter in Fig. \ref{prclfilter}. The test shows that the offloading works as expected and that the PRCL signal can be driven (and hence controlled) by the ISI.
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=0.4]{images/PRM.png}
\includegraphics[scale=0.4]{images/PRM.png}
...
@@ -525,8 +534,8 @@ After every simulation which could possibly work for the system, we locked the i
...
@@ -525,8 +534,8 @@ After every simulation which could possibly work for the system, we locked the i
\end{figure}
\end{figure}
\section*{Conclusions}
\section*{Conclusions}
This study is promising to provide a significant contribution to the improvement of LIGO LSC signals and the detector stability when it is running in observing mode. The tests at LHO demonstrated that the experiment succeeded in lowering the seismic motion of the platforms by a factor of 3 at low frequencies and that also the DARM signal benefited from it. The simulations have shown that it is possible to reduce the differential motion of the chambers by a factor of 3 in order of magnitude. The test on the Power Recycling Cavity Length highlighted that the signal can be controlled by the ISI according with the software simulations.\\
This study is promising to provide a significant contribution to the improvement of LIGO LSC signals and the detector stability when it is running in observing mode. The tests at LHO demonstrated that the experiment succeeded in lowering the seismic motion of the platforms by a factor of 3 at low frequencies and that also the DARM signal benefited from it. The simulations have shown that it is possible to reduce the differential motion of the chambers by a factor of 3 in order of magnitude below 0.1 Hz. The test on the Power Recycling Cavity Length highlighted that the signal can be controlled by the ISI according with the software simulations.\\
As we saw, the implications go straight to the basics of the instrument: a more stable detector produces a less noisy signal which can last longer into the cavities, assuring a longer observing time and giving the possibility to detect more gravitational waves and in lower ranges of frequency.
As we saw, the implications go straight to the basics of the instrument: a more stable detector produces a less noisy signal which can last longer into the cavities, assuring a longer observing time and giving the possibility to detect more gravitational waves and in lower ranges of frequency\cite{lantztalk}\cite{jenne}.
LIGO Livingston site has also actuated a similar process, following the progression at LHO during the work on site in 2019. Due to the limited time of the commissioning break, it was not possible to take further measurements of ISI motion and LSC signals, especially with an accurate study of the blending filters. However, since the software skeleton of the new configuration has been built and installed on both LIGO CDSs, further studies and tests were due in 2020 to complete the last steps and test it fully on the interferometer. The results make the experiment worthy of future developments and we are confident that these tests could be carried out in the coming months.
LIGO Livingston site has also actuated a similar process, following the progression at LHO during the work on site in 2019\cite{llo}. Due to the limited time of the commissioning break, it was not possible to take further measurements of ISI motion and LSC signals, especially with an accurate study of the blending filters. However, since the software skeleton of the new configuration has been built and installed on both LIGO CDSs, further studies and tests were due in 2020 to complete the last steps and test it fully on the interferometer. The results make the experiment worthy of future developments and we are confident that these tests could be carried out in the coming months.
@@ -112,6 +112,7 @@ RIN = Relative Intensity Noise\\
...
@@ -112,6 +112,7 @@ RIN = Relative Intensity Noise\\
SC = Sensor Correction\\
SC = Sensor Correction\\
SR = Signal Recycling\\
SR = Signal Recycling\\
SRCL = Signal Recycling Cavity Length\\
SRCL = Signal Recycling Cavity Length\\
STS = \\
TEC = Thermo-Electric Controller\\
TEC = Thermo-Electric Controller\\
UoB = University of Birmingham\\
UoB = University of Birmingham\\
...
@@ -214,31 +215,40 @@ Beginning of Gravitational Wave Astronomy}
...
@@ -214,31 +215,40 @@ Beginning of Gravitational Wave Astronomy}
%cpsdiff
%cpsdiff
\bibitem{biscans} S. Biscans et al., \textit{Control strategy to limit duty cycle impact of earthquakes on the LIGO gravitational-wave detectors}, arXiv:1707.03466, 2017
\bibitem{proposal} C. Di Fronzo et al., \textit{Proposal for an experiment at LHO: Locking PRCL to IMCL}, proposal, 2019, DCC T1900656-v2
\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020
\bibitem{technote1} C. Di Fronzo et al., \textit{Reducing differential motion using CPS sensors}, technical note, 2019, DCC T1900777-v1
\bibitem{kisseltalk} J. Kissel, \textit{Advanced LIGO Active Seismic Isolation}, talk, 2011
\bibitem{chiatalk} C. Di Fronzo, \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals}, talk, LVK September 2020
\bibitem{lantztech} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, technical note, 2018, DCC T1800066-v2
\bibitem{biscans} S. Biscans et al., \textit{Control strategy to limit duty cycle impact of earthquakes on the LIGO gravitational-wave detectors}, arXiv:1707.03466, 2017
\bibitem{hammodel} S. Cooper et al., \textit{Ham ISI Model}, technical note, 2018
\bibitem{kisseltalk1} J. Kissel, \textit{On Relaxing Our Demand for Single IFO Duty Cycle}, talk, 2019, DCC G1901125-v1
\bibitem{biscanstalk} S. Biscans, \textit{Global seismic control}, talk, GWADW 2019
\bibitem{biswas} A. Biswas et al., \textit{New methods to assess the impact of seismic events on LIGO detector duty cycle}, 2019, arXiv:1910.12143
\bibitem{kisselthesis} J. Kissel, \textit{Calibrating and improving the sensitivity of the LIGO detectors}, PhD thesis, 2010
\bibitem{kisselthesis} J. Kissel, \textit{Calibrating and improving the sensitivity of the LIGO detectors}, PhD thesis, 2010
\bibitem{proposal} C. Di Fronzo et al., \textit{Proposal for an experiment at LHO: Locking PRCL to IMCL}, proposal, 2019, DCC T1900656-v2
\bibitem{technote1} C. Di Fronzo et al., \textit{Reducing differential motion using CPS sensors}, technical note, 2019, DCC T1900777-v1
\bibitem{kisseltalk2} J. Kissel, \textit{Advanced LIGO Active Seismic Isolation}, talk, 2011
\bibitem{technote2} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals: block diagrams and maths}, technical note, 2020, DCC T2000108-v1
\bibitem{technote2} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals: block diagrams and maths}, technical note, 2020, DCC T2000108-v1
\bibitem{technote3} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals:analysis of feasibility}, technical note, 2020, DCC T2000365-v2
\bibitem{technote3} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals:analysis of feasibility}, technical note, 2020, DCC T2000365-v2
\bibitem{chiatalk} C. Di Fronzo, \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals}, talk, LVK September 2020
\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020
\bibitem{jenne} J. Driggers, \textit{Noise Cancellation for Gravitational Wave Detectors}, PhD thesis, 2016
\bibitem{llo} A. Pele' et al., \textit{ECR: Differential CPS and cavity offload}, proposal, 2019, DCC E1900330-v1
\bibitem{llo} A. Pele' et al., \textit{ECR: Differential CPS and cavity offload}, proposal, 2019, DCC E1900330-v1
\bibitem{jenne} J. Driggers, \textit{Noise Cancellation for Gravitational Wave Detectors}, PhD thesis, 2016
\bibitem{lantztech} B. Lantz et al., \textit{Estimates of HAM-ISI motion for A+}, technical note, 2018, DCC T1800066-v2
\bibitem{hammodel} S. Cooper et al., \textit{Ham ISI Model}, technical note, 2018
%6D
%6D
...
@@ -258,6 +268,14 @@ Beginning of Gravitational Wave Astronomy}
...
@@ -258,6 +268,14 @@ Beginning of Gravitational Wave Astronomy}
\bibitem{freise} Andreas Freise, \textit{The Next Generation of Interferometry: Multi-Frequency Optical Modelling, Control Concepts and Implementation}, Appendix B \textit{Control loops}, PhD thesis, 2003
