-
-
- 1. System Kinematics +
- 1. System Kinematics -
- 2. Open Loop System Identification +
- 2. Open Loop System Identification -
- 3. Active Damping Plant (Strain gauges) +
- 3. Open-Loop Noise Budgeting -
- 4. Active Damping Plant (Force Sensors) +
- 4. Active Damping Plant (Strain gauges) -
- 5. HAC-LAC (IFF) architecture +
- 5. Active Damping Plant (Force Sensors) + +
- 6. HAC-LAC (IFF) architecture +
-
-
- Section 1: the kinematics of the DCM is presented, and Jacobian matrices which are used to solve the inverse and forward kinematics are computed. -
- Section 2: the system dynamics is identified in the absence of control. -
- Section 3: it is studied whether if the strain gauges fixed to the piezoelectric actuators can be used to actively damp the plant. -
- Section 4: piezoelectric force sensors are added in series with the piezoelectric actuators and are used to actively damp the plant using the Integral Force Feedback (IFF) control strategy. -
- Section 5: the High Authority Control - Low Authority Control (HAC-LAC) strategy is tested on the Simscape model. +
- Section 1: the kinematics of the DCM is presented, and Jacobian matrices which are used to solve the inverse and forward kinematics are computed. +
- Section 2: the system dynamics is identified in the absence of control. +
- Section 3: an open-loop noise budget is performed. +
- Section 4: it is studied whether if the strain gauges fixed to the piezoelectric actuators can be used to actively damp the plant. +
- Section 5: piezoelectric force sensors are added in series with the piezoelectric actuators and are used to actively damp the plant using the Integral Force Feedback (IFF) control strategy. +
- Section 6: the High Authority Control - Low Authority Control (HAC-LAC) strategy is tested on the Simscape model.
1. System Kinematics
+1. System Kinematics
-1.1. Bragg Angle
+1.1. Bragg Angle
%% Tested bragg angles -bragg = linspace(5, 80, 1000); % Bragg angle [deg] -d_off = 10.5e-3; % Wanted offset between x-rays [m] --
+There is a simple relation eq:bragg_angle_formula between: +
+-
+
- \(d_{\text{off}}\) is the wanted offset between the incident x-ray and the output x-ray +
- \(\theta_b\) is the bragg angle +
- \(d_z\) is the corresponding distance between the first and second crystals +
%% Vertical Jack motion as a function of Bragg angle -dz = d_off./(2*cos(bragg*pi/180)); --
+This relation is shown in Figure 1. +
-
Figure 1: Jack motion as a function of Bragg angle
+The required jack stroke is approximately 25mm. +
+%% Required Jack stroke ans = 1e3*(dz(end) - dz(1)) @@ -144,34 +160,34 @@ dz = d_off./(2*
1.2. Kinematics (111 Crystal)
+1.2. Kinematics (111 Crystal)
The reference frame is taken at the center of the 111 second crystal.
1.2.1. Interferometers - 111 Crystal
+1.2.1. Interferometers - 111 Crystal
Three interferometers are pointed to the bottom surface of the 111 crystal.
-The position of the measurement points are shown in Figure 2 as well as the origin where the motion of the crystal is computed. +The position of the measurement points are shown in Figure 2 as well as the origin where the motion of the crystal is computed.
-
Figure 2: Bottom view of the second crystal 111. Position of the measurement points.
-The inverse kinematics consisting of deriving the interferometer measurements from the motion of the crystal (see Figure 3): +The inverse kinematics consisting of deriving the interferometer measurements from the motion of the crystal (see Figure 3):
\begin{equation} \begin{bmatrix} @@ -185,7 +201,7 @@ d_z \\ r_y \\ r_x \end{equation} -
Figure 3: Inverse Kinematics - Interferometers
@@ -193,7 +209,7 @@ d_z \\ r_y \\ r_x-From the Figure 2, the inverse kinematics can be solved as follow (for small motion): +From the Figure 2, the inverse kinematics can be solved as follow (for small motion):
\begin{equation} \bm{J}_{s,111} @@ -213,7 +229,7 @@ J_s_111 = [1, 0.07, -0.015
+
+
+
+