From 148dcd63a9ac42b593c60832f33e9d9d2a7d2b63 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Fri, 14 Jun 2013 07:14:10 -0400 Subject: [PATCH] pyafm/auxiliary.tex: Bring in some text and figures from my oral Back in 2007-07-01 ;). --- src/pyafm/auxiliary.tex | 66 ++++++++++++++++++++++++++++++++++++++++- 1 file changed, 65 insertions(+), 1 deletion(-) diff --git a/src/pyafm/auxiliary.tex b/src/pyafm/auxiliary.tex index 2282527..80a409f 100644 --- a/src/pyafm/auxiliary.tex +++ b/src/pyafm/auxiliary.tex @@ -83,6 +83,16 @@ phase). \subsection{stepper} \label{sec:pyafm:stepper} +Because of thermal drift and mechanical instability, the distance +between the tip and the surface changes significantly over time. When +the distance change exceeds the range of the piezo scanner, the +stepper motor must be engaged to reposition the AFM tip relative to +the sample. The earlier LabVIEW software (\cref{sec:labview}) lacked +the ability to control the motor on its own, so it would pause roughly +every half hour and prompt the operator to make the necessary manual +adjustments. Automatic motor control allows the system to run longer +without interrupts, facilitating the collection of large data sets. + The \stepper\ package provides Python control of stepper motors\cite{jones95}. The package is mostly concerned with the maintenance of internal motor state: @@ -101,7 +111,61 @@ maintenance of internal motor state: Actualizing the motor control signal is left up to the caller, in this case \pyafm. -TODO: backlash and step-size graphics. +We verified the stability and reproducibility of the microscopic +movement of the motor by making several approach-retreat cycles from +the surface of $\sim$70 steps which resulted in the data displayed in +\cref{fig.stepper:backlash}. We also measured the distance the +surface moved with every step by determining the change in deflection +voltage as a function of peizo position as we stepped the AFM tip +closer the the surface. Our stepsize data is displayed in +\cref{fig:stepper:step-size}. + +The motor is very consistent when approaching the surface, which +indicates that our control software is operating correctly. However, +the motor exhibits some hysteretic behavior on a scale of $\sim$46 +steps, which is almost certainly due to \emph{backlash}, or slack in +the motor--surface coupling machinery. The first 46 steps in a new +direction take the slack out of the coupling, and further steps move +the tip relative to the surface. The problem can be avoided entirely +by simply replacing ``backwards motion by one step'' with ``backwards +motion by 60 steps and forward motion by 59 steps''. + +One issue raised by backlash is that it might be the source of some of +our surface drift, as the drive-chain relaxes towards some central +value and pulls the surface with it. By oscillating into our eventual +position, we could perhaps settle the system at the beginning, +reducing the need for adjustments later on. While this is not a +problem for the current unfolding experiments, it could be an issue +for longer unfolding-refolding experiments. + +\begin{figure} + \begin{center} + \subfloat[][]{\label{fig:stepper:backlash} + \asyinclude{figures/stepper/backlash}} + \hspace{\stretch{1}} + \subfloat[][]{\label{fig:stepper:step-size} + \asyinclude{figures/stepper/step-size}} + \caption{\protect\subref{fig:stepper:backlash} Stepper motor + reproducibility, stability, and backlash. The data are from a + single continuous counterclockwise trace of 14 approach-retreat + cycles. The jump from about $(18, -6)$ to $(17, -0.4)$ is the + snap-off effect, where short-range attractive interactions + between the tip and the sample---due to surface wetting in + air---require the tip to be actively pulled off surface. Signal + noise is comparable to that expected by drift. + \protect\subref{fig:stepper:step-size} Motor step size + calibration. The stepper gradually stepped closer to the + surface, feeling forward with the piezo after each step. + Successive motor positions yield traces $a$, $b$, $c$, $d$, and + $e$. As the motor moves the sample closer, less piezo movement + is required to approach to same deflection level. The average + spacing between the traces is roughly $170\U{nm}$. Traces $c$ + and $d$ have regions of negative deflection because the tip no + longer retracts far enough from the surface to break free of the + snap-off effect. There is no backlash because the data were + taken during a single approach.\label{fig:stepper}} + \end{center} +\end{figure} \subsection{pypid} \label{sec:pyafm:pypid} -- 2.26.2