1 Undamped System
+1 Undamped System
@@ -435,12 +444,12 @@ The performance of this undamped system will be compared with the damped system
1.1 Identification of the dynamics for Active Damping
+1.1 Identification of the dynamics for Active Damping
1.1.1 Initialize the Simulation
+1.1.1 Initialize the Simulation
We initialize all the stages with the default parameters. @@ -470,7 +479,7 @@ initializeSample('mass', 50); We set the references to zero.
initializeReferences(); +initializeReferences('Rz_type', 'rotating', 'Ry_period', 1);
1.1.2 Identification
+1.1.2 Identification
First, we identify the dynamics of the system using the linearize function.
@@ -513,7 +522,7 @@ io(io_i) = linio([mdl, '/Micro-Station'], 3,
1.1.3 Obtained Plants for Active Damping
+1.1.3 Obtained Plants for Active Damping
load('./active_damping/mat/undamped_plants.mat', 'G_iff', 'G_dvf', 'G_ine'); ++
1.2 Tomography Experiment
+1.2 Tomography Experiment
1.2.1 Simulation
+1.2.1 Simulation
We initialize elements for the tomography experiment. @@ -610,8 +624,8 @@ Finally, we save the simulation results for further analysis
1.2.2 Results
+1.2.2 Results
We load the results of tomography experiments. @@ -623,14 +637,14 @@ t = linspace(0, 3, length(En(:,1)));
2 Integral Force Feedback
+2 Integral Force Feedback
@@ -657,12 +671,12 @@ Integral Force Feedback is applied on the simscape model.
2.1 Control Design
+2.1 Control Design
2.1.1 Plant
+2.1.1 Plant
Let’s load the previously indentified undamped plant: @@ -673,11 +687,11 @@ Let’s load the previously indentified undamped plant:
-Let’s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure 6). +Let’s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure 6).
-
2.1.2 Control Design
+2.1.2 Control Design
The controller for each pair of actuator/sensor is: @@ -697,11 +711,11 @@ The controller for each pair of actuator/sensor is:
-The corresponding loop gains are shown in figure 7. +The corresponding loop gains are shown in figure 7.
-
2.1.3 Diagonal Controller
+2.1.3 Diagonal Controller
We create the diagonal controller and we add a minus sign as we have a positive @@ -731,22 +745,21 @@ We save the controller for further analysis.
2.1.4 IFF with High Pass Filter
+2.1.4 IFF with High Pass Filter
w_hpf = 2*pi*10; % Cut-off frequency for the high pass filter [rad/s] -w_lpf = 2*pi*200; % Cut-off frequency for the low pass filter [rad/s] -K_iff = 2*pi*200/s * (s/w_hpf)/(s/w_hpf + 1) * 1/(s/w_lpf + 1); +K_iff = 2*pi*200/s * (s/w_hpf)/(s/w_hpf + 1);
-The corresponding loop gains are shown in figure 8. +The corresponding loop gains are shown in figure 8.
-
2.2 Tomography Experiment
+2.2 Tomography Experiment
2.2.1 Simulation with IFF Controller
+2.2.1 Simulation with IFF Controller
We initialize elements for the tomography experiment. @@ -825,8 +838,8 @@ save('./active_damping/mat/tomo_exp.mat',
2.2.2 Simulation with IFF Controller with added High Pass Filter
+2.2.2 Simulation with IFF Controller with added High Pass Filter
We initialize elements for the tomography experiment. @@ -874,8 +887,8 @@ save('./active_damping/mat/tomo_exp.mat',
2.2.3 Compare with Undamped system
+2.2.3 Compare with Undamped system
We load the results of tomography experiments. @@ -887,21 +900,21 @@ t = linspace(0, 3, length(En(:,1)));
2.3 Conclusion
+2.3 Conclusion
@@ -928,11 +941,11 @@ Integral Force Feedback:
3 Direct Velocity Feedback
+3 Direct Velocity Feedback
@@ -946,12 +959,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
3.1 Control Design
+3.1 Control Design
3.1.1 Plant
+3.1.1 Plant
Let’s load the undamped plant: @@ -962,11 +975,11 @@ Let’s load the undamped plant:
-Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure 12). +Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure 12).
-
3.1.2 Control Design
+3.1.2 Control Design
The Direct Velocity Feedback is defined below. @@ -987,11 +1000,11 @@ A Low pass Filter is added to make the controller transfer function proper.
-The obtained loop gains are shown in figure 13. +The obtained loop gains are shown in figure 13.
-
3.1.3 Diagonal Controller
+3.1.3 Diagonal Controller
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture. @@ -1021,12 +1034,12 @@ We save the controller for further analysis.
3.2 Tomography Experiment
+3.2 Tomography Experiment
3.2.1 Initialize the Simulation
+3.2.1 Initialize the Simulation
We initialize elements for the tomography experiment.
@@ -1047,8 +1060,8 @@ save('./mat/controllers.mat',
-
We change the simulation stop time.
@@ -1079,8 +1092,8 @@ save('./active_damping/mat/tomo_exp.mat',
We load the results of tomography experiments.
@@ -1092,21 +1105,21 @@ t = linspace(0, 3, length(En(:,1)));
@@ -1131,11 +1144,11 @@ Direct Velocity Feedback:
@@ -1148,12 +1161,12 @@ In Inertial Control, a feedback is applied between the measured absolute
Let’s load the undamped plant:
@@ -1164,11 +1177,11 @@ Let’s load the undamped plant:
-Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure 17).
+Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure 17).
-The controller is defined below and the obtained loop gain is shown in figure 18.
+The controller is defined below and the obtained loop gain is shown in figure 18.
Figure 18: Loop Gain for Inertial Control (png, pdf)
We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1219,12 +1232,12 @@ We save the controller for further analysis.
We initialize elements for the tomography experiment.
@@ -1245,8 +1258,8 @@ save('./mat/controllers.mat',
-
We change the simulation stop time.
@@ -1277,8 +1290,8 @@ save('./active_damping/mat/tomo_exp.mat',
We load the results of tomography experiments.
@@ -1290,21 +1303,21 @@ t = linspace(0, 3, length(En_ine(:,1)));
@@ -1326,16 +1339,191 @@ Inertial Control:
+All the files (data and Matlab scripts) are accessible here.
+
+For all the identifications, the disturbances are disabled and no controller are used.
+
+We identify the dynamics for the following sample mass.
+
+We identify the dynamics for the following Spindle angles.
+
+We identify the dynamics for the following Spindle rotation periods.
+
+We identify the dynamics for the following Tilt stage angles.
+ Figure 22: Sensitivity to ground motion in the Z direction on the Z motion error (png, pdf) Figure 37: Sensitivity to ground motion in the Z direction on the Z motion error (png, pdf) Figure 23: Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (png, pdf) Figure 38: Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (png, pdf) Figure 24: Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (png, pdf) Figure 39: Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (png, pdf) Figure 27: Plant for the \(z\) direction for different active damping technique used (png, pdf) Figure 42: Plant for the \(z\) direction for different active damping technique used (png, pdf)
Window used for Figure 30: PSD of the translation errors for applied Active Damping techniques (png, pdf) Figure 45: PSD of the translation errors in the X direction for applied Active Damping techniques (png, pdf) Figure 31: PSD of the rotation errors for applied Active Damping techniques (png, pdf) Figure 46: PSD of the rotation errors in the X direction for applied Active Damping techniques (png, pdf)
@@ -1487,9 +1675,9 @@ This Matlab function is accessible h
We initialize all the stages with the default parameters.
Created: 2020-01-20 lun. 17:45 Created: 2020-01-21 mar. 17:283.2.2 Simulation
+3.2.2 Simulation
3.2.3 Compare with Undamped system
+3.2.3 Compare with Undamped system
3.3 Conclusion
+3.3 Conclusion
4 Inertial Control
+4 Inertial Control
4.1 Control Design
+4.1 Control Design
4.1.1 Plant
+4.1.1 Plant
4.1.2 Control Design
+4.1.2 Control Design
4.1.3 Diagonal Controller
+4.1.3 Diagonal Controller
4.2 Tomography Experiment
+4.2 Tomography Experiment
4.2.1 Initialize the Simulation
+4.2.1 Initialize the Simulation
4.2.2 Simulation
+4.2.2 Simulation
4.2.3 Compare with Undamped system
+4.2.3 Compare with Undamped system
4.3 Conclusion
+4.3 Conclusion
5 Comparison
+5 Variability of the system dynamics for Active Damping
5.1 Variation of the Sample Mass
+masses = [1, 10, 50]; % [kg]
+
+5.2 Variation of the Spindle Angle
+Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
+
+5.3 Variation of the Spindle Rotation Speed
+Rz_periods = [60, 10, 1]; % [s]
+
+5.4 Variation of the Tilt Angle
+Ry_amplitudes = [0, 3*pi/180]; % [rad]
+
+5.5 Conclusion
+6 Comparison
+
-5.1 Load the plants
-6.1 Load the plants
+load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_ine', 'G_dvf');
@@ -1343,81 +1531,81 @@ Inertial Control:
5.2 Sensitivity to Disturbance
-6.2 Sensitivity to Disturbance
+
5.3 Damped Plant
-6.3 Damped Plant
+
5.4 Tomography Experiment
-6.4 Tomography Experiment
+5.4.1 Load the Simulation Data
-6.4.1 Load the Simulation Data
+load('./active_damping/mat/tomo_exp.mat', 'En', 'En_iff_hpf', 'En_dvf', 'En_ine');
En_iff = En_iff_hpf;
@@ -1427,9 +1615,9 @@ t = linspace(0, 3, length(En(:,1)));
5.4.2 Frequency Domain Analysis
-6.4.2 Frequency Domain Analysis
+pwelch function.
6 Useful Functions
-7 Useful Functions
+6.1 prepareTomographyExperiment
-7.1 prepareTomographyExperiment
+Function Description
-Function Description
+function [] = prepareTomographyExperiment(args)
@@ -1497,9 +1685,9 @@ This Matlab function is accessible h
Optional Parameters
-Optional Parameters
+arguments
args.nass_actuator char {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo'
@@ -1511,9 +1699,9 @@ This Matlab function is accessible h
Initialize the Simulation
-Initialize the Simulation
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