115 lines
2.7 KiB
Matlab
115 lines
2.7 KiB
Matlab
% Matlab Init :noexport:ignore:
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%% dcm_kinematics.m
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% Computation of the DCM kinematics
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for data
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%% Simscape Model - Nano Hexapod
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addpath('./STEPS/')
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(1, 3, 1000);
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% Bragg Angle
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% There is a simple relation eqref:eq:bragg_angle_formula between:
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% - $d_{\text{off}}$ is the wanted offset between the incident x-ray and the output x-ray
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% - $\theta_b$ is the bragg angle
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% - $d_z$ is the corresponding distance between the first and second crystals
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% \begin{equation} \label{eq:bragg_angle_formula}
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% d_z = \frac{d_{\text{off}}}{2 \cos \theta_b}
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% \end{equation}
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%% Tested bragg angles
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bragg = linspace(5, 80, 1000); % Bragg angle [deg]
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d_off = 10.5e-3; % Wanted offset between x-rays [m]
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%% Vertical Jack motion as a function of Bragg angle
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dz = d_off./(2*cos(bragg*pi/180));
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% This relation is shown in Figure [[fig:jack_motion_bragg_angle]].
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%% Jack motion as a function of Bragg angle
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figure;
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plot(bragg, 1e3*dz)
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xlabel('Bragg angle [deg]'); ylabel('Jack Motion [mm]');
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% #+name: fig:jack_motion_bragg_angle
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% #+caption: Jack motion as a function of Bragg angle
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% #+RESULTS:
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% [[file:figs/jack_motion_bragg_angle.png]]
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% The required jack stroke is approximately 25mm.
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%% Required Jack stroke
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ans = 1e3*(dz(end) - dz(1))
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% #+name: fig:schematic_sensor_jacobian_inverse_kinematics
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% #+caption: Inverse Kinematics - Interferometers
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% #+RESULTS:
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% [[file:figs/schematic_sensor_jacobian_inverse_kinematics.png]]
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% From the Figure [[fig:sensor_111_crystal_points]], the inverse kinematics can be solved as follow (for small motion):
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% \begin{equation}
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% \bm{J}_{s,111}
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% =
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% \begin{bmatrix}
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% 1 & 0.07 & -0.015 \\
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% 1 & 0 & 0.015 \\
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% 1 & -0.07 & -0.015
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% \end{bmatrix}
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% \end{equation}
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%% Sensor Jacobian matrix for 111 crystal
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J_s_111 = [1, 0.07, -0.015
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1, 0, 0.015
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1, -0.07, -0.015];
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% #+name: fig:schematic_sensor_jacobian_inverse_kinematics
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% #+caption: Inverse Kinematics - Actuators
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% #+RESULTS:
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% [[file:figs/schematic_actuator_jacobian_inverse_kinematics.png]]
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% Based on the geometry in Figure [[fig:actuator_jacobian_111_points]], we obtain:
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% \begin{equation}
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% \bm{J}_{a,111}
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% =
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% \begin{bmatrix}
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% 1 & 0.14 & -0.1525 \\
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% 1 & 0.14 & 0.0675 \\
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% 1 & -0.14 & -0.0425
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% \end{bmatrix}
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% \end{equation}
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%% Actuator Jacobian - 111 crystal
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J_a_111 = [1, 0.14, -0.1525
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1, 0.14, 0.0675
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1, -0.14, -0.0425];
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save('mat/dcm_kinematics.mat', 'J_a_111', 'J_s_111')
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