diff --git a/active_damping/index.html b/active_damping/index.html index 9d62bf6..f2af323 100644 --- a/active_damping/index.html +++ b/active_damping/index.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Active Damping applied on the Simscape Model @@ -247,31 +247,16 @@ for the JavaScript code in this tag. } /*]]>*///--> - - + +
@@ -284,110 +269,116 @@ for the JavaScript code in this tag.

Table of Contents

-First, in section 1, we will looked at the undamped system. +First, in section 1, we will looked at the undamped system.

Then, we will compare three active damping techniques:

@@ -426,30 +417,24 @@ The disturbances are:

  • Motion errors of all the stages
    • -
    -

    1 Undamped System

    +
    +

    1 Undamped System

    - +

    -
    -

    -All the files (data and Matlab scripts) are accessible here. -

    - -

    We first look at the undamped system. The performance of this undamped system will be compared with the damped system using various techniques.

    -
    -

    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. @@ -479,7 +464,12 @@ initializeSample('mass', 50); We set the references to zero.

    -
    initializeReferences('Rz_type', 'rotating', 'Ry_period', 1);
+
    initializeReferences();
+
    
+
    + +
    +
    initializeDisturbances('enable', false);
    @@ -500,8 +490,8 @@ save('./mat/controllers.mat', -

    1.1.2 Identification

    +
    +

    1.1.2 Identification

    First, we identify the dynamics of the system using the linearize function. @@ -522,7 +512,7 @@ io(io_i) = linio([mdl, '/Micro-Station'], 3, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; %% Run the linearization -G = linearize(mdl, io, 1, options); +G = linearize(mdl, io, 0.5, options); G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... @@ -550,8 +540,8 @@ And we save them for further analysis.

    -
    -

    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');
@@ -559,21 +549,21 @@ And we save them for further analysis.
    -
    +

    nass_active_damping_iff_plant.png

    Figure 1: G_iff: IFF Plant (png, pdf)

    -
    +

    nass_active_damping_ine_plant.png

    Figure 2: G_dvf: Plant for Direct Velocity Feedback (png, pdf)

    -
    +

    nass_active_damping_inertial_plant.png

    Figure 3: G_ine: Inertial Feedback Plant (png, pdf)

    @@ -582,12 +572,12 @@ And we save them for further analysis.
    -
    -

    1.2 Tomography Experiment

    +
    +

    1.2 Tomography Experiment

    -
    -

    1.2.1 Simulation

    +
    +

    1.2.1 Simulation

    We initialize elements for the tomography experiment. @@ -624,8 +614,8 @@ Finally, we save the simulation results for further analysis

    -
    -

    1.2.2 Results

    +
    +

    1.2.2 Results

    We load the results of tomography experiments. @@ -637,14 +627,14 @@ t = linspace(0, 3, length(En(:,1)));

    -
    +

    nass_act_damp_undamped_sim_tomo_trans.png

    Figure 4: Position Error during tomography experiment - Translations (png, pdf)

    -
    +

    nass_act_damp_undamped_sim_tomo_rot.png

    Figure 5: Position Error during tomography experiment - Rotations (png, pdf)

    @@ -654,11 +644,347 @@ t = linspace(0, 3, length(En(:,1)));
    -
    -

    2 Integral Force Feedback

    +
    +

    2 Variability of the system dynamics for Active Damping

    - + +

    +

    +The goal of this section is to study how the dynamics of the Active Damping plants are changing with the experimental conditions. +These experimental conditions are: +

    +
      +
    • The mass of the sample (section 2.1)
      • +
    • The spindle angle with a null rotating speed (section 2.2)
      • +
    • The spindle rotation speed (section 2.3)
      • +
    • The tilt angle (section 2.4)
      • +
    • The scans of the translation stage (section 2.5)
      • +
    + +

    +For the identification of the dynamics, the system is simulation for \(\approx 0.5s\) before the linearization is performed. +This is done in order for the transient phase to be over. +

    +
    + +
    +

    2.1 Variation of the Sample Mass

    +
    +

    + +

    +

    +For all the identifications, the disturbances are disabled and no controller are used. +

    +

    +We identify the dynamics for the following sample mass. +

    +
    +
    masses = [1, 10, 50]; % [kg]
+
    +
    + +
    +

    act_damp_variability_iff_sample_mass.png +

    +

    Figure 6: Variability of the IFF plant with the Sample Mass (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_sample_mass.png +

    +

    Figure 7: Variability of the DVF plant with the Sample Mass (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_sample_mass.png +

    +

    Figure 8: Variability of the Inertial plant with the Sample Mass (png, pdf)

    +
    +
    +
    + +
    +

    2.2 Variation of the Spindle Angle

    +
    +

    + +

    +

    +We identify the dynamics for the following Spindle angles. +

    +
    +
    Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
+
    +
    + +
    +

    act_damp_variability_iff_spindle_angle.png +

    +

    Figure 9: Variability of the IFF plant with the Spindle Angle (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_spindle_angle.png +

    +

    Figure 10: Variability of the DVF plant with the Spindle Angle (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_spindle_angle.png +

    +

    Figure 11: Variability of the Inertial plant with the Spindle Angle (png, pdf)

    +
    +
    +
    + +
    +

    2.3 Variation of the Spindle Rotation Speed

    +
    +

    + +

    +

    +We identify the dynamics for the following Spindle rotation periods. +

    +
    +
    Rz_periods = [60, 6, 2, 1]; % [s]
+
    +
    + +

    +The identification of the dynamics is done at the same Spindle angle position. +

    +
    +
    +

    2.3.1 Dynamics of the Active Damping plants

    +
    + +
    +

    act_damp_variability_iff_spindle_speed.png +

    +

    Figure 12: Variability of the IFF plant with the Spindle rotation speed (png, pdf)

    +
    + + +
    +

    act_damp_variability_iff_spindle_speed_zoom.png +

    +

    Figure 13: Variability of the IFF plant with the Spindle rotation speed (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_spindle_speed.png +

    +

    Figure 14: Variability of the DVF plant with the Spindle rotation speed (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_spindle_speed_zoom.png +

    +

    Figure 15: Variability of the DVF plant with the Spindle rotation speed (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_spindle_speed.png +

    +

    Figure 16: Variability of the Inertial plant with the Spindle rotation speed (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_spindle_speed_zoom.png +

    +

    Figure 17: Variability of the Inertial plant with the Spindle rotation speed (png, pdf)

    +
    +
    +
    + +
    +

    2.3.2 Variation of the poles and zeros with the Spindle rotation frequency

    +
    + +
    +

    campbell_diagram_spindle_rotation.png +

    +

    Figure 18: Evolution of the pole with respect to the spindle rotation speed (png, pdf)

    +
    + + +
    +

    variation_zeros_active_damping_plants.png +

    +

    Figure 19: Evolution of the zero with respect to the spindle rotation speed (png, pdf)

    +
    +
    +
    +
    + +
    +

    2.4 Variation of the Tilt Angle

    +
    +

    + +

    +

    +We identify the dynamics for the following Tilt stage angles. +

    +
    +
    Ry_amplitudes = [-3*pi/180, 3*pi/180]; % [rad]
+
    +
    + +
    +

    act_damp_variability_iff_tilt_angle.png +

    +

    Figure 20: Variability of the IFF plant with the Tilt stage Angle (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_tilt_angle.png +

    +

    Figure 21: Variability of the DVF plant with the Tilt Angle (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_tilt_angle.png +

    +

    Figure 22: Variability of the Inertial plant with the Tilt Angle (png, pdf)

    +
    +
    +
    + +
    +

    2.5 Scans of the Translation Stage

    +
    +

    + +

    +

    +We want here to verify if the dynamics used for Active damping is varying when using the translation stage for scans. +

    +

    +We initialize the translation stage reference to be a sinus with an amplitude of 5mm and a period of 1s (Figure 23). +

    +
    +
    initializeReferences('Dy_type', 'sinusoidal', ...
+                     'Dy_amplitude', 5e-3, ... % [m]
+                     'Dy_period', 1); % [s]
+
    +
    + + +
    +

    ty_scanning_reference_sinus.png +

    +

    Figure 23: Reference path for the translation stage (png, pdf)

    +
    + +

    +We identify the dynamics at different positions (times) when scanning with the Translation stage. +

    +
    +
    t_lin = [0.5, 0.75, 1, 1.25];
+
    +
    + +
    +

    act_damp_variability_iff_ty_scans.png +

    +

    Figure 24: Variability of the IFF plant at different Ty scan positions (png, pdf)

    +
    + + +
    +

    act_damp_variability_dvf_ty_scans.png +

    +

    Figure 25: Variability of the DVF plant at different Ty scan positions (png, pdf)

    +
    + + +
    +

    act_damp_variability_ine_ty_scans.png +

    +

    Figure 26: Variability of the Inertial plant at different Ty scan positions (png, pdf)

    +
    +
    +
    + +
    +

    2.6 Conclusion

    +
    + + + +++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Table 1: Conclusion on the variability of the system dynamics for active damping
     Change of Dynamics
    Sample MassLarge
    Spindle AngleSmall
    Spindle Rotation SpeedFirst resonance is split in two resonances
    Tilt AngleNegligible
    Translation Stage scansNegligible
    + +

    +Also, for the Inertial Sensor, a RHP zero may appear when the spindle is rotating fast. +

    + +
    +

    +When using either a force sensor or a relative motion sensor for active damping, the only “parameter” that induce a large change for the dynamics to be controlled is the sample mass. +Thus, the developed damping techniques should be robust to variations of the sample mass. +

    + +
    +
    +
    +
    + +
    +

    3 Integral Force Feedback

    +
    +

    +

    @@ -671,13 +997,13 @@ Integral Force Feedback is applied on the simscape model.

    -
    -

    2.1 Control Design

    -
    +
    +

    3.1 Control Design

    +
    -
    -

    2.1.1 Plant

    -
    +
    +

    3.1.1 Plant

    +

    Let’s load the previously indentified undamped plant:

    @@ -687,21 +1013,21 @@ 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 27).

    -
    +

    iff_plant.png

    -

    Figure 6: Transfer function from forces applied in the legs to force sensor (png, pdf)

    +

    Figure 27: Transfer function from forces applied in the legs to force sensor (png, pdf)

    -
    -

    2.1.2 Control Design

    -
    +
    +

    3.1.2 Control Design

    +

    The controller for each pair of actuator/sensor is:

    @@ -711,21 +1037,21 @@ 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 28.

    -
    +

    iff_open_loop.png

    -

    Figure 7: Loop Gain for the Integral Force Feedback (png, pdf)

    +

    Figure 28: Loop Gain for the Integral Force Feedback (png, pdf)

    -
    -

    2.1.3 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. @@ -745,9 +1071,9 @@ We save the controller for further analysis.

    -
    -

    2.1.4 IFF with High Pass Filter

    -
    +
    +

    3.1.4 IFF with High Pass Filter

    +
    w_hpf = 2*pi*10; % Cut-off frequency for the high pass filter [rad/s]
 
@@ -756,13 +1082,13 @@ K_iff = 2*pi
 
 
    
-The corresponding loop gains are shown in figure 8.
+The corresponding loop gains are shown in figure 29.
 
    
 
-
    
+
    
 
    iff_hpf_open_loop.png
 
    
-
    Figure 8: Loop Gain for the Integral Force Feedback with an High pass filter (png, pdf)
    
+
    Figure 29: Loop Gain for the Integral Force Feedback with an High pass filter (png, pdf)
    
 
    
 
 
    
@@ -785,13 +1111,13 @@ We save the controller for further analysis.
    -
    -

    2.2 Tomography Experiment

    -
    +
    +

    3.2 Tomography Experiment

    +
    -
    -

    2.2.1 Simulation with IFF Controller

    -
    +
    +

    3.2.1 Simulation with IFF Controller

    +

    We initialize elements for the tomography experiment.

    @@ -838,9 +1164,9 @@ save('./active_damping/mat/tomo_exp.mat',
    -
    -

    2.2.2 Simulation with IFF Controller with added High Pass Filter

    -
    +
    +

    3.2.2 Simulation with IFF Controller with added High Pass Filter

    +

    We initialize elements for the tomography experiment.

    @@ -887,9 +1213,9 @@ save('./active_damping/mat/tomo_exp.mat',
    -
    -

    2.2.3 Compare with Undamped system

    -
    +
    +

    3.2.3 Compare with Undamped system

    +

    We load the results of tomography experiments.

    @@ -900,32 +1226,32 @@ t = linspace(0, 3, length(En(:,1)));
    -
    +

    nass_act_damp_iff_sim_tomo_xy.png

    -

    Figure 9: Position Error during tomography experiment - XY Motion (png, pdf)

    +

    Figure 30: Position Error during tomography experiment - XY Motion (png, pdf)

    -
    +

    nass_act_damp_iff_sim_tomo_trans.png

    -

    Figure 10: Position Error during tomography experiment - Translations (png, pdf)

    +

    Figure 31: Position Error during tomography experiment - Translations (png, pdf)

    -
    +

    nass_act_damp_iff_sim_tomo_rot.png

    -

    Figure 11: Position Error during tomography experiment - Rotations (png, pdf)

    +

    Figure 32: Position Error during tomography experiment - Rotations (png, pdf)

    -
    -

    2.3 Conclusion

    -
    +
    +

    3.3 Conclusion

    +

    Integral Force Feedback: @@ -941,11 +1267,11 @@ Integral Force Feedback:

    -
    -

    3 Direct Velocity Feedback

    -
    +
    +

    4 Direct Velocity Feedback

    +

    - +

    @@ -959,13 +1285,13 @@ The actuator displacement can be measured with a capacitive sensor for instance.

    -
    -

    3.1 Control Design

    -
    +
    +

    4.1 Control Design

    +
    -
    -

    3.1.1 Plant

    -
    +
    +

    4.1.1 Plant

    +

    Let’s load the undamped plant:

    @@ -975,21 +1301,21 @@ 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 33).

    -
    +

    dvf_plant.png

    -

    Figure 12: Transfer function from forces applied in the legs to leg displacement sensor (png, pdf)

    +

    Figure 33: Transfer function from forces applied in the legs to leg displacement sensor (png, pdf)

    -
    -

    3.1.2 Control Design

    -
    +
    +

    4.1.2 Control Design

    +

    The Direct Velocity Feedback is defined below. A Low pass Filter is added to make the controller transfer function proper. @@ -1000,21 +1326,21 @@ 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 34.

    -
    +

    dvf_open_loop.png

    -

    Figure 13: Loop Gain for the Integral Force Feedback (png, pdf)

    +

    Figure 34: Loop Gain for the Integral Force Feedback (png, pdf)

    -
    -

    3.1.3 Diagonal Controller

    -
    +
    +

    4.1.3 Diagonal Controller

    +

    We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.

    @@ -1034,13 +1360,13 @@ We save the controller for further analysis.
    -
    -

    3.2 Tomography Experiment

    -
    +
    +

    4.2 Tomography Experiment

    +
    -
    -

    3.2.1 Initialize the Simulation

    -
    +
    +

    4.2.1 Initialize the Simulation

    +

    We initialize elements for the tomography experiment.

    @@ -1060,9 +1386,9 @@ save('./mat/controllers.mat', -

    3.2.2 Simulation

    -
    +
    +

    4.2.2 Simulation

    +

    We change the simulation stop time.

    @@ -1092,9 +1418,9 @@ save('./active_damping/mat/tomo_exp.mat',
    -
    -

    3.2.3 Compare with Undamped system

    -
    +
    +

    4.2.3 Compare with Undamped system

    +

    We load the results of tomography experiments.

    @@ -1105,32 +1431,32 @@ t = linspace(0, 3, length(En(:,1)));
    -
    +

    nass_act_damp_dvf_sim_tomo_xy.png

    -

    Figure 14: Position Error during tomography experiment - XY Motion (png, pdf)

    +

    Figure 35: Position Error during tomography experiment - XY Motion (png, pdf)

    -
    +

    nass_act_damp_dvf_sim_tomo_trans.png

    -

    Figure 15: Position Error during tomography experiment - Translations (png, pdf)

    +

    Figure 36: Position Error during tomography experiment - Translations (png, pdf)

    -
    +

    nass_act_damp_dvf_sim_tomo_rot.png

    -

    Figure 16: Position Error during tomography experiment - Rotations (png, pdf)

    +

    Figure 37: Position Error during tomography experiment - Rotations (png, pdf)

    -
    -

    3.3 Conclusion

    -
    +
    +

    4.3 Conclusion

    +

    Direct Velocity Feedback: @@ -1144,11 +1470,11 @@ Direct Velocity Feedback:

    -
    -

    4 Inertial Control

    -
    +
    +

    5 Inertial Control

    +

    - +

    @@ -1161,13 +1487,13 @@ In Inertial Control, a feedback is applied between the measured absolute

    -
    -

    4.1 Control Design

    -
    +
    +

    5.1 Control Design

    +
    -
    -

    4.1.1 Plant

    -
    +
    +

    5.1.1 Plant

    +

    Let’s load the undamped plant:

    @@ -1177,23 +1503,23 @@ 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 38).

    -
    +

    ine_plant.png

    -

    Figure 17: Transfer function from forces applied in the legs to leg velocity sensor (png, pdf)

    +

    Figure 38: Transfer function from forces applied in the legs to leg velocity sensor (png, pdf)

    -
    -

    4.1.2 Control Design

    -
    +
    +

    5.1.2 Control Design

    +

    -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 39.

    @@ -1202,17 +1528,17 @@ The controller is defined below and the obtained loop gain is shown in figure -
    +

    ine_open_loop_gain.png

    -

    Figure 18: Loop Gain for Inertial Control (png, pdf)

    +

    Figure 39: Loop Gain for Inertial Control (png, pdf)

    -
    -

    4.1.3 Diagonal Controller

    -
    +
    +

    5.1.3 Diagonal Controller

    +

    We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.

    @@ -1232,13 +1558,13 @@ We save the controller for further analysis.
    -
    -

    4.2 Tomography Experiment

    -
    +
    +

    5.2 Tomography Experiment

    +
    -
    -

    4.2.1 Initialize the Simulation

    -
    +
    +

    5.2.1 Initialize the Simulation

    +

    We initialize elements for the tomography experiment.

    @@ -1258,9 +1584,9 @@ save('./mat/controllers.mat', -

    4.2.2 Simulation

    -
    +
    +

    5.2.2 Simulation

    +

    We change the simulation stop time.

    @@ -1290,9 +1616,9 @@ save('./active_damping/mat/tomo_exp.mat',
    -
    -

    4.2.3 Compare with Undamped system

    -
    +
    +

    5.2.3 Compare with Undamped system

    +

    We load the results of tomography experiments.

    @@ -1303,32 +1629,32 @@ t = linspace(0, 3, length(En_ine(:,1)));
    -
    +

    nass_act_damp_ine_sim_tomo_xy.png

    -

    Figure 19: Position Error during tomography experiment - XY Motion (png, pdf)

    +

    Figure 40: Position Error during tomography experiment - XY Motion (png, pdf)

    -
    +

    nass_act_damp_ine_sim_tomo_trans.png

    -

    Figure 20: Position Error during tomography experiment - Translations (png, pdf)

    +

    Figure 41: Position Error during tomography experiment - Translations (png, pdf)

    -
    +

    nass_act_damp_ine_sim_tomo_rot.png

    -

    Figure 21: Position Error during tomography experiment - Rotations (png, pdf)

    +

    Figure 42: Position Error during tomography experiment - Rotations (png, pdf)

    -
    -

    4.3 Conclusion

    -
    +
    +

    5.3 Conclusion

    +

    Inertial Control: @@ -1339,190 +1665,15 @@ Inertial Control:

    -
    -

    5 Variability of the system dynamics for Active Damping

    -
    -

    - -

    -
    -

    -All the files (data and Matlab scripts) are accessible here. -

    - -
    -
    - -
    -

    5.1 Variation of the Sample Mass

    -
    -

    -For all the identifications, the disturbances are disabled and no controller are used. -

    -

    -We identify the dynamics for the following sample mass. -

    -
    -
    masses = [1, 10, 50]; % [kg]
-
    -
    - -
    -

    act_damp_variability_iff_sample_mass.png -

    -

    Figure 22: Variability of the IFF plant with the Sample Mass (png, pdf)

    -
    - - -
    -

    act_damp_variability_dvf_sample_mass.png -

    -

    Figure 23: Variability of the DVF plant with the Sample Mass (png, pdf)

    -
    - - -
    -

    act_damp_variability_ine_sample_mass.png -

    -

    Figure 24: Variability of the Inertial plant with the Sample Mass (png, pdf)

    -
    -
    -
    - -
    -

    5.2 Variation of the Spindle Angle

    -
    -

    -We identify the dynamics for the following Spindle angles. -

    -
    -
    Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad]
-
    -
    - -
    -

    act_damp_variability_iff_spindle_angle.png -

    -

    Figure 25: Variability of the IFF plant with the Spindle Angle (png, pdf)

    -
    - - -
    -

    act_damp_variability_dvf_spindle_angle.png -

    -

    Figure 26: Variability of the DVF plant with the Spindle Angle (png, pdf)

    -
    - - -
    -

    act_damp_variability_ine_spindle_angle.png -

    -

    Figure 27: Variability of the Inertial plant with the Spindle Angle (png, pdf)

    -
    -
    -
    - -
    -

    5.3 Variation of the Spindle Rotation Speed

    -
    -

    -We identify the dynamics for the following Spindle rotation periods. -

    -
    -
    Rz_periods = [60, 10, 1]; % [s]
-
    -
    - -
    -

    act_damp_variability_iff_spindle_speed.png -

    -

    Figure 28: Variability of the IFF plant with the Spindle rotation speed (png, pdf)

    -
    - - -
    -

    act_damp_variability_iff_spindle_speed_zoom.png -

    -

    Figure 29: Variability of the IFF plant with the Spindle rotation speed (png, pdf)

    -
    - - -
    -

    act_damp_variability_dvf_spindle_speed.png -

    -

    Figure 30: Variability of the DVF plant with the Spindle rotation speed (png, pdf)

    -
    - - -
    -

    act_damp_variability_dvf_spindle_speed_zoom.png -

    -

    Figure 31: Variability of the DVF plant with the Spindle rotation speed (png, pdf)

    -
    - - -
    -

    act_damp_variability_ine_spindle_speed.png -

    -

    Figure 32: Variability of the Inertial plant with the Spindle rotation speed (png, pdf)

    -
    - - -
    -

    act_damp_variability_ine_spindle_speed_zoom.png -

    -

    Figure 33: Variability of the Inertial plant with the Spindle rotation speed (png, pdf)

    -
    -
    -
    - -
    -

    5.4 Variation of the Tilt Angle

    -
    -

    -We identify the dynamics for the following Tilt stage angles. -

    -
    -
    Ry_amplitudes = [0, 3*pi/180]; % [rad]
-
    -
    - -
    -

    act_damp_variability_iff_tilt_angle.png -

    -

    Figure 34: Variability of the IFF plant with the Spindle Angle (png, pdf)

    -
    - - -
    -

    act_damp_variability_dvf_tilt_angle.png -

    -

    Figure 35: Variability of the DVF plant with the Spindle Angle (png, pdf)

    -
    - - -
    -

    act_damp_variability_ine_tilt_angle.png -

    -

    Figure 36: Variability of the Inertial plant with the Spindle Angle (png, pdf)

    -
    -
    -
    - -
    -

    5.5 Conclusion

    -
    -
    - -
    -

    6 Comparison

    +
    +

    6 Comparison

    - +

    -
    -

    6.1 Load the plants

    +
    +

    6.1 Load the plants

    load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_ine', 'G_dvf');
@@ -1531,80 +1682,80 @@ We identify the dynamics for the following Tilt stage angles.
    -
    -

    6.2 Sensitivity to Disturbance

    +
    +

    6.2 Sensitivity to Disturbance

    -
    +

    sensitivity_comp_ground_motion_z.png

    -

    Figure 37: Sensitivity to ground motion in the Z direction on the Z motion error (png, pdf)

    +

    Figure 43: Sensitivity to ground motion in the Z direction on the Z motion error (png, pdf)

    -
    +

    sensitivity_comp_direct_forces_z.png

    -

    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 44: Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (png, pdf)

    -
    +

    sensitivity_comp_spindle_z.png

    -

    Figure 39: Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (png, pdf)

    +

    Figure 45: Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (png, pdf)

    -
    +

    sensitivity_comp_ty_z.png

    -

    Figure 40: Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (png, pdf)

    +

    Figure 46: Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (png, pdf)

    -
    +

    sensitivity_comp_ty_x.png

    -

    Figure 41: Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (png, pdf)

    +

    Figure 47: Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (png, pdf)

    -
    -

    6.3 Damped Plant

    +
    +

    6.3 Damped Plant

    -
    +

    plant_comp_damping_z.png

    -

    Figure 42: Plant for the \(z\) direction for different active damping technique used (png, pdf)

    +

    Figure 48: Plant for the \(z\) direction for different active damping technique used (png, pdf)

    -
    +

    plant_comp_damping_x.png

    -

    Figure 43: Plant for the \(x\) direction for different active damping technique used (png, pdf)

    +

    Figure 49: Plant for the \(x\) direction for different active damping technique used (png, pdf)

    -
    +

    plant_comp_damping_coupling.png

    -

    Figure 44: Comparison of one off-diagonal plant for different damping technique applied (png, pdf)

    +

    Figure 50: Comparison of one off-diagonal plant for different damping technique applied (png, pdf)

    -
    -

    6.4 Tomography Experiment

    +
    +

    6.4 Tomography Experiment

    -
    -

    6.4.1 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');
@@ -1615,8 +1766,8 @@ t = linspace(0, 3, length(En(:,1)));
    -
    -

    6.4.2 Frequency Domain Analysis

    +
    +

    6.4.2 Frequency Domain Analysis

    Window used for pwelch function. @@ -1628,46 +1779,46 @@ han_win = hanning(ceil(length(En(:, 1)) -

    +

    act_damp_tomo_exp_comp_psd_trans.png

    -

    Figure 45: PSD of the translation errors in the X direction for applied Active Damping techniques (png, pdf)

    +

    Figure 51: PSD of the translation errors in the X direction for applied Active Damping techniques (png, pdf)

    -
    +

    act_damp_tomo_exp_comp_psd_rot.png

    -

    Figure 46: PSD of the rotation errors in the X direction for applied Active Damping techniques (png, pdf)

    +

    Figure 52: PSD of the rotation errors in the X direction for applied Active Damping techniques (png, pdf)

    -
    +

    act_damp_tomo_exp_comp_cps_trans.png

    -

    Figure 47: CPS of the translation errors in the X direction for applied Active Damping techniques (png, pdf)

    +

    Figure 53: CPS of the translation errors in the X direction for applied Active Damping techniques (png, pdf)

    -
    +

    act_damp_tomo_exp_comp_cps_rot.png

    -

    Figure 48: CPS of the rotation errors in the X direction for applied Active Damping techniques (png, pdf)

    +

    Figure 54: CPS of the rotation errors in the X direction for applied Active Damping techniques (png, pdf)

    -
    -

    7 Useful Functions

    +
    +

    7 Useful Functions

    -
    -

    7.1 prepareTomographyExperiment

    +
    +

    7.1 prepareTomographyExperiment

    - +

    @@ -1675,9 +1826,9 @@ This Matlab function is accessible h

    -
    -

    Function Description

    -
    +
    +

    Function Description

    +
    function [] = prepareTomographyExperiment(args)
    @@ -1685,9 +1836,9 @@ This Matlab function is accessible     h
    -
    -

    Optional Parameters

    -
    +
    +

    Optional Parameters

    +
    arguments
     args.nass_actuator       char   {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo'
@@ -1699,9 +1850,9 @@ This Matlab function is accessible h
    -
    -

    Initialize the Simulation

    -
    +
    +

    Initialize the Simulation

    +

    We initialize all the stages with the default parameters.

    @@ -1755,7 +1906,7 @@ save('./mat/controllers.mat',

    Author: Dehaeze Thomas

    -

    Created: 2020-01-21 mar. 17:28

    +

    Created: 2020-02-04 mar. 16:13

    diff --git a/active_damping/index.org b/active_damping/index.org index e4b210c..e8c2b5d 100644 --- a/active_damping/index.org +++ b/active_damping/index.org @@ -65,20 +65,6 @@ The disturbances are: :END: <> -** ZIP file containing the data and matlab files :ignore: -#+begin_src bash :exports none :results none - if [ matlab/undamped_system.m -nt data/undamped_system.zip ]; then - cp matlab/undamped_system.m undamped_system.m; - zip data/undamped_system \ - undamped_system.m - rm undamped_system.m; - fi -#+end_src - -#+begin_note - All the files (data and Matlab scripts) are accessible [[file:data/undamped_system.zip][here]]. -#+end_note - ** Introduction :ignore: We first look at the undamped system. The performance of this undamped system will be compared with the damped system using various techniques. @@ -369,6 +355,1316 @@ We load the results of tomography experiments. #+CAPTION: Position Error during tomography experiment - Rotations ([[./figs/nass_act_damp_undamped_sim_tomo_rot.png][png]], [[./figs/nass_act_damp_undamped_sim_tomo_rot.pdf][pdf]]) [[file:figs/nass_act_damp_undamped_sim_tomo_rot.png]] +* Variability of the system dynamics for Active Damping +:PROPERTIES: +:header-args:matlab+: :tangle matlab/act_damp_variability_plant.m +:header-args:matlab+: :comments org :mkdirp yes +:END: +<> + +** Introduction :ignore: +The goal of this section is to study how the dynamics of the Active Damping plants are changing with the experimental conditions. +These experimental conditions are: +- The mass of the sample (section [[sec:variability_sample_mass]]) +- The spindle angle with a null rotating speed (section [[sec:variability_spindle_angle]]) +- The spindle rotation speed (section [[sec:variability_rotation_speed]]) +- The tilt angle (section [[sec:variability_tilt_angle]]) +- The scans of the translation stage (section [[sec:variability_ty_scans]]) + +For the identification of the dynamics, the system is simulation for $\approx 0.5s$ before the linearization is performed. +This is done in order for the transient phase to be over. + +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); + addpath('active_damping/src/'); +#+end_src + +#+begin_src matlab + open('active_damping/matlab/sim_nass_active_damping.slx') + load('mat/conf_simscape.mat'); +#+end_src + +** Variation of the Sample Mass +<> +*** Introduction :ignore: +For all the identifications, the disturbances are disabled and no controller are used. + +*** Initialize the Simulation :noexport: +We initialize all the stages with the default parameters. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); +#+end_src + +No disturbances. +#+begin_src matlab + initializeDisturbances('enable', false); +#+end_src + +The nano-hexapod is a piezoelectric hexapod. +#+begin_src matlab + initializeNanoHexapod('actuator', 'piezo'); +#+end_src + +We set the references to zero. +#+begin_src matlab + initializeReferences(); +#+end_src + +And all the controllers are set to 0. +#+begin_src matlab + K = tf(zeros(6)); + save('./mat/controllers.mat', 'K', '-append'); + K_ine = tf(zeros(6)); + save('./mat/controllers.mat', 'K_ine', '-append'); + K_iff = tf(zeros(6)); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_dvf = tf(zeros(6)); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +*** Identification :ignore: +#+begin_src matlab :exports none + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nass_active_damping'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; +#+end_src + +We identify the dynamics for the following sample mass. +#+begin_src matlab + masses = [1, 10, 50]; % [kg] +#+end_src + +#+begin_src matlab :exports none + Gm = {zeros(length(masses))}; + Gm_iff = {zeros(length(masses))}; + Gm_dvf = {zeros(length(masses))}; + Gm_ine = {zeros(length(masses))}; + + for i = 1:length(masses) + initializeSample('mass', masses(i)); + + %% Run the linearization + G = linearize(mdl, io, 0.3, options); + G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; + G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... + 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... + 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; + Gm(i) = {G}; + Gm_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gm_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gm_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + end +#+end_src + +#+begin_src matlab :exports none + save('./active_damping/mat/plants_variable.mat', 'masses', 'Gm_iff', 'Gm_dvf', 'Gm_ine', '-append'); +#+end_src + +*** Plots :ignore: +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'masses', 'Gm_iff', 'Gm_dvf', 'Gm_ine'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gm_iff) + plot(freqs, abs(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gm_iff) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_sample_mass +#+CAPTION: Variability of the IFF plant with the Sample Mass ([[./figs/act_damp_variability_iff_sample_mass.png][png]], [[./figs/act_damp_variability_iff_sample_mass.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_sample_mass.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + + for i = 1:length(Gm_dvf) + plot(freqs, abs(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gm_dvf) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_sample_mass +#+CAPTION: Variability of the DVF plant with the Sample Mass ([[./figs/act_damp_variability_dvf_sample_mass.png][png]], [[./figs/act_damp_variability_dvf_sample_mass.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_sample_mass.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gm_ine) + plot(freqs, abs(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gm_ine) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_sample_mass +#+CAPTION: Variability of the Inertial plant with the Sample Mass ([[./figs/act_damp_variability_ine_sample_mass.png][png]], [[./figs/act_damp_variability_ine_sample_mass.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_sample_mass.png]] + +** Variation of the Spindle Angle +<> +*** Introduction :ignore: +*** Initialize the Simulation :noexport: +We initialize all the stages with the default parameters. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); +#+end_src + +No disturbances. +#+begin_src matlab + initializeDisturbances('enable', false); +#+end_src + +The nano-hexapod is a piezoelectric hexapod. +#+begin_src matlab + initializeNanoHexapod('actuator', 'piezo'); + initializeSample('mass', 50); +#+end_src + +And all the controllers are set to 0. +#+begin_src matlab + K = tf(zeros(6)); + save('./mat/controllers.mat', 'K', '-append'); + K_ine = tf(zeros(6)); + save('./mat/controllers.mat', 'K_ine', '-append'); + K_iff = tf(zeros(6)); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_dvf = tf(zeros(6)); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +*** Identification :ignore: +#+begin_src matlab :exports none + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nass_active_damping'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; +#+end_src + +We identify the dynamics for the following Spindle angles. +#+begin_src matlab + Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad] +#+end_src + +#+begin_src matlab :exports none + Ga = {zeros(length(Rz_amplitudes))}; + Ga_iff = {zeros(length(Rz_amplitudes))}; + Ga_dvf = {zeros(length(Rz_amplitudes))}; + Ga_ine = {zeros(length(Rz_amplitudes))}; + + for i = 1:length(Rz_amplitudes) + initializeReferences('Rz_type', 'constant', 'Rz_amplitude', Rz_amplitudes(i)) + + %% Run the linearization + G = linearize(mdl, io, 0.3, options); + G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; + G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... + 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... + 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; + Ga(i) = {G}; + Ga_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Ga_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Ga_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + end +#+end_src + +#+begin_src matlab :exports none + save('./active_damping/mat/plants_variable.mat', 'Rz_amplitudes', 'Ga_iff', 'Ga_dvf', 'Ga_ine', '-append'); +#+end_src + +*** Plots :ignore: +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'Rz_amplitudes', 'Ga_iff', 'Ga_dvf', 'Ga_ine'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Ga_iff) + plot(freqs, abs(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Ga_iff) + plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_spindle_angle +#+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_spindle_angle.png][png]], [[./figs/act_damp_variability_iff_spindle_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_spindle_angle.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + + for i = 1:length(Ga_dvf) + plot(freqs, abs(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Ga_dvf) + plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_spindle_angle +#+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_spindle_angle.png][png]], [[./figs/act_damp_variability_dvf_spindle_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_spindle_angle.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Ga_ine) + plot(freqs, abs(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Ga_ine) + plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); + end + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_spindle_angle +#+CAPTION: Variability of the Inertial plant with the Spindle Angle ([[./figs/act_damp_variability_ine_spindle_angle.png][png]], [[./figs/act_damp_variability_ine_spindle_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_spindle_angle.png]] + +** Variation of the Spindle Rotation Speed +<> +*** Introduction :ignore: +*** Initialize the Simulation :noexport: +We initialize all the stages with the default parameters. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); +#+end_src + +No disturbances. +#+begin_src matlab + initializeDisturbances('enable', false); +#+end_src + +The nano-hexapod is a piezoelectric hexapod. +#+begin_src matlab + initializeNanoHexapod('actuator', 'piezo'); + initializeSample('mass', 50); +#+end_src + +And all the controllers are set to 0. +#+begin_src matlab + K = tf(zeros(6)); + save('./mat/controllers.mat', 'K', '-append'); + K_ine = tf(zeros(6)); + save('./mat/controllers.mat', 'K_ine', '-append'); + K_iff = tf(zeros(6)); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_dvf = tf(zeros(6)); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +*** Identification :ignore: +#+begin_src matlab :exports none + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nass_active_damping'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; +#+end_src + +We identify the dynamics for the following Spindle rotation periods. +#+begin_src matlab + Rz_periods = [60, 6, 2, 1]; % [s] +#+end_src + +The identification of the dynamics is done at the same Spindle angle position. + +#+begin_src matlab :exports none + Gw = {zeros(length(Rz_periods))}; + Gw_iff = {zeros(length(Rz_periods))}; + Gw_dvf = {zeros(length(Rz_periods))}; + Gw_ine = {zeros(length(Rz_periods))}; + + for i = 1:length(Rz_periods) + initializeReferences('Rz_type', 'rotating', ... + 'Rz_period', Rz_periods(i), ... % Rotation period [s] + 'Rz_amplitude', -0.5*(2*pi/Rz_periods(i))); % Angle offset [rad] + + load('mat/nass_references.mat', 'Rz'); % We load the reference for the Spindle + [~, i_end] = min(abs(Rz.signals.values)); % Obtain the indice where the spindle angle is zero + t_sim = Rz.time(i_end) % Simulation time before identification [s] + + %% Run the linearization + G = linearize(mdl, io, t_sim, options); + G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; + G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... + 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... + 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; + + Gw(i) = {G}; + Gw_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gw_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gw_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + end +#+end_src + +#+begin_src matlab :exports none + save('./active_damping/mat/plants_variable.mat', 'Rz_periods', 'Gw_iff', 'Gw_dvf', 'Gw_ine', '-append'); +#+end_src + +*** Dynamics of the Active Damping plants +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'Rz_periods', 'Gw_iff', 'Gw_dvf', 'Gw_ine'); + load('./active_damping/mat/undamped_plants.mat', 'G_iff', 'G_dvf', 'G_ine'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 10000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gw_iff) + plot(freqs, abs(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gw_iff) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', 'No Rotation'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_spindle_speed +#+CAPTION: Variability of the IFF plant with the Spindle rotation speed ([[./figs/act_damp_variability_iff_spindle_speed.png][png]], [[./figs/act_damp_variability_iff_spindle_speed.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_spindle_speed.png]] + +#+begin_src matlab :exports none + xlim([20, 30]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_spindle_speed_zoom +#+CAPTION: Variability of the IFF plant with the Spindle rotation speed ([[./figs/act_damp_variability_iff_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_iff_spindle_speed_zoom.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_spindle_speed_zoom.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 5000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + + for i = 1:length(Gw_dvf) + plot(freqs, abs(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gw_dvf) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', 'No Rotation'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_spindle_speed +#+CAPTION: Variability of the DVF plant with the Spindle rotation speed ([[./figs/act_damp_variability_dvf_spindle_speed.png][png]], [[./figs/act_damp_variability_dvf_spindle_speed.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_spindle_speed.png]] + +#+begin_src matlab :exports none + xlim([20, 30]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_spindle_speed_zoom +#+CAPTION: Variability of the DVF plant with the Spindle rotation speed ([[./figs/act_damp_variability_dvf_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_dvf_spindle_speed_zoom.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_spindle_speed_zoom.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 5000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gw_ine) + plot(freqs, abs(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gw_ine) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', 'No Rotation'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_spindle_speed +#+CAPTION: Variability of the Inertial plant with the Spindle rotation speed ([[./figs/act_damp_variability_ine_spindle_speed.png][png]], [[./figs/act_damp_variability_ine_spindle_speed.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_spindle_speed.png]] + +#+begin_src matlab :exports none + xlim([20, 30]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_spindle_speed_zoom +#+CAPTION: Variability of the Inertial plant with the Spindle rotation speed ([[./figs/act_damp_variability_ine_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_ine_spindle_speed_zoom.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_spindle_speed_zoom.png]] + +*** Variation of the poles and zeros with the Spindle rotation frequency +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'Rz_periods', 'Gw_iff', 'Gw_dvf', 'Gw_ine'); + load('./active_damping/mat/undamped_plants.mat', 'G_iff', 'G_dvf', 'G_ine'); +#+end_src + + +#+begin_src matlab :exports none + figure; + + subplot(1,2,1); + hold on; + for i = 1:length(Gw_iff) + G_poles = pole(Gw_iff{i}('Fnlm1', 'Fnl1')); + plot(1/Rz_periods(i), real(G_poles(imag(G_poles)<2*pi*30 & imag(G_poles)>2*pi*22)), 'kx'); + end + G_poles = pole(G_iff('Fnlm1', 'Fnl1')); + plot(0, real(G_poles(imag(G_poles)<2*pi*30 & imag(G_poles)>2*pi*22)), 'kx'); + hold off; + ylim([-inf, 0]); + xlabel('Rotation Speed [Hz]'); + ylabel('Real Part'); + + subplot(1,2,2); + hold on; + for i = 1:length(Gw_iff) + G_poles = pole(Gw_iff{i}('Fnlm1', 'Fnl1')); + plot(1/Rz_periods(i), imag(G_poles(imag(G_poles)<2*pi*30 & imag(G_poles)>2*pi*22)), 'kx'); + end + G_poles = pole(G_iff('Fnlm1', 'Fnl1')); + plot(0, imag(G_poles(imag(G_poles)<2*pi*30 & imag(G_poles)>2*pi*22)), 'kx'); + hold off; + ylim([0, inf]); + xlabel('Rotation Speed [Hz]'); + ylabel('Imaginary Part'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/campbell_diagram_spindle_rotation.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:campbell_diagram_spindle_rotation +#+CAPTION: Evolution of the pole with respect to the spindle rotation speed ([[./figs/campbell_diagram_spindle_rotation.png][png]], [[./figs/campbell_diagram_spindle_rotation.pdf][pdf]]) +[[file:figs/campbell_diagram_spindle_rotation.png]] + +#+begin_src matlab :exports none + figure; + + subplot(1,2,1); + hold on; + for i = 1:length(Gw_ine) + set(gca,'ColorOrderIndex',1); + G_zeros = zero(Gw_ine{i}('Vnlm1', 'Fnl1')); + plot(1/Rz_periods(i), real(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + + set(gca,'ColorOrderIndex',2); + G_zeros = zero(Gw_iff{i}('Fnlm1', 'Fnl1')); + plot(1/Rz_periods(i), real(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + + set(gca,'ColorOrderIndex',3); + G_zeros = zero(Gw_dvf{i}('Dnlm1', 'Fnl1')); + plot(1/Rz_periods(i), real(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + end + hold off; + xlabel('Rotation Speed [Hz]'); + ylabel('Real Part'); + + subplot(1,2,2); + hold on; + for i = 1:length(Gw_ine) + set(gca,'ColorOrderIndex',1); + G_zeros = zero(Gw_ine{i}('Vnlm1', 'Fnl1')); + p_ine = plot(1/Rz_periods(i), imag(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + + set(gca,'ColorOrderIndex',2); + G_zeros = zero(Gw_iff{i}('Fnlm1', 'Fnl1')); + p_iff = plot(1/Rz_periods(i), imag(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + + set(gca,'ColorOrderIndex',3); + G_zeros = zero(Gw_dvf{i}('Dnlm1', 'Fnl1')); + p_dvf = plot(1/Rz_periods(i), imag(G_zeros(imag(G_zeros)<2*pi*25 & imag(G_zeros)>2*pi*22)), 'o'); + end + hold off; + xlabel('Rotation Speed [Hz]'); + ylabel('Imaginary Part'); + legend([p_ine p_iff p_dvf],{'Inertial Sensor','Force Sensor', 'Relative Motion Sensor'}, 'location', 'southwest'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/variation_zeros_active_damping_plants.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:variation_zeros_active_damping_plants +#+CAPTION: Evolution of the zero with respect to the spindle rotation speed ([[./figs/variation_zeros_active_damping_plants.png][png]], [[./figs/variation_zeros_active_damping_plants.pdf][pdf]]) +[[file:figs/variation_zeros_active_damping_plants.png]] + +** Variation of the Tilt Angle +<> +*** Introduction :ignore: +*** Initialize the Simulation :noexport: +We initialize all the stages with the default parameters. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); +#+end_src + +No disturbances. +#+begin_src matlab + initializeDisturbances('enable', false); +#+end_src + +The nano-hexapod is a piezoelectric hexapod. +#+begin_src matlab + initializeNanoHexapod('actuator', 'piezo'); + initializeSample('mass', 50); +#+end_src + +And all the controllers are set to 0. +#+begin_src matlab + K = tf(zeros(6)); + save('./mat/controllers.mat', 'K', '-append'); + K_ine = tf(zeros(6)); + save('./mat/controllers.mat', 'K_ine', '-append'); + K_iff = tf(zeros(6)); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_dvf = tf(zeros(6)); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +*** Identification :ignore: +#+begin_src matlab :exports none + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nass_active_damping'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; +#+end_src + +We identify the dynamics for the following Tilt stage angles. +#+begin_src matlab + Ry_amplitudes = [-3*pi/180, 3*pi/180]; % [rad] +#+end_src + +#+begin_src matlab :exports none + Gy = {zeros(length(Ry_amplitudes))}; + Gy_iff = {zeros(length(Ry_amplitudes))}; + Gy_dvf = {zeros(length(Ry_amplitudes))}; + Gy_ine = {zeros(length(Ry_amplitudes))}; + + for i = 1:length(Ry_amplitudes) + initializeReferences('Ry_type', 'constant', 'Ry_amplitude', Ry_amplitudes(i)) + + %% Run the linearization + G = linearize(mdl, io, 0.3, options); + G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; + G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... + 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... + 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; + Gy(i) = {G}; + Gy_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gy_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + Gy_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; + end +#+end_src + +#+begin_src matlab :exports none + save('./active_damping/mat/plants_variable.mat', 'Ry_amplitudes', 'Gy_iff', 'Gy_dvf', 'Gy_ine', '-append'); +#+end_src + +*** Plots :ignore: +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'Ry_amplitudes', 'Gy_iff', 'Gy_dvf', 'Gy_ine'); + load('./active_damping/mat/undamped_plants.mat', 'G_iff', 'G_dvf', 'G_ine'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gy_iff) + plot(freqs, abs(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gy_iff) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_tilt_angle +#+CAPTION: Variability of the IFF plant with the Tilt stage Angle ([[./figs/act_damp_variability_iff_tilt_angle.png][png]], [[./figs/act_damp_variability_iff_tilt_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_tilt_angle.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + + for i = 1:length(Gy_dvf) + plot(freqs, abs(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gy_dvf) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_tilt_angle +#+CAPTION: Variability of the DVF plant with the Tilt Angle ([[./figs/act_damp_variability_dvf_tilt_angle.png][png]], [[./figs/act_damp_variability_dvf_tilt_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_tilt_angle.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gy_ine) + plot(freqs, abs(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gy_ine) + plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_tilt_angle +#+CAPTION: Variability of the Inertial plant with the Tilt Angle ([[./figs/act_damp_variability_ine_tilt_angle.png][png]], [[./figs/act_damp_variability_ine_tilt_angle.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_tilt_angle.png]] + +** Scans of the Translation Stage +<> +*** Introduction :ignore: +We want here to verify if the dynamics used for Active damping is varying when using the translation stage for scans. + +*** Initialize the Simulation :noexport: +We initialize all the stages with the default parameters. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); +#+end_src + +No disturbances. +#+begin_src matlab + initializeDisturbances('enable', false); +#+end_src + +The nano-hexapod is a piezoelectric hexapod and the mass of the sample is set to 50kg. +#+begin_src matlab + initializeNanoHexapod('actuator', 'piezo'); + initializeSample('mass', 50); +#+end_src + +And all the controllers are set to 0. +#+begin_src matlab + K = tf(zeros(6)); + save('./mat/controllers.mat', 'K', '-append'); + K_ine = tf(zeros(6)); + save('./mat/controllers.mat', 'K_ine', '-append'); + K_iff = tf(zeros(6)); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_dvf = tf(zeros(6)); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +*** Identification :ignore: +#+begin_src matlab :exports none + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nass_active_damping'; + + %% Input/Output definition + clear io; io_i = 1; + io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; + io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; +#+end_src + +We initialize the translation stage reference to be a sinus with an amplitude of 5mm and a period of 1s (Figure [[fig:ty_scanning_reference_sinus]]). +#+begin_src matlab + initializeReferences('Dy_type', 'sinusoidal', ... + 'Dy_amplitude', 5e-3, ... % [m] + 'Dy_period', 1); % [s] +#+end_src + +#+begin_src matlab :exports none + load('mat/nass_references.mat', 'Dy'); + figure; + plot(Dy.time, Dy.signals.values); + xlabel('Time [s]'); ylabel('Dy - Position [m]'); + xlim([0, 2]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/ty_scanning_reference_sinus.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:ty_scanning_reference_sinus +#+CAPTION: Reference path for the translation stage ([[./figs/ty_scanning_reference_sinus.png][png]], [[./figs/ty_scanning_reference_sinus.pdf][pdf]]) +[[file:figs/ty_scanning_reference_sinus.png]] + +We identify the dynamics at different positions (times) when scanning with the Translation stage. +#+begin_src matlab + t_lin = [0.5, 0.75, 1, 1.25]; +#+end_src + +#+begin_src matlab :exports none + Gty = {zeros(length(t_lin))}; + Gty_iff = {zeros(length(t_lin))}; + Gty_dvf = {zeros(length(t_lin))}; + Gty_ine = {zeros(length(t_lin))}; + + %% Run the linearization + G = linearize(mdl, io, t_lin, options); + G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; + G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... + 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... + 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; + + for i = 1:length(t_lin) + Gty(i) = {G(:,:,i)}; + Gty_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}, i))}; + Gty_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}, i))}; + Gty_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}, i))}; + end +#+end_src + +#+begin_src matlab :exports none + Gty_tlin = t_lin; + save('./active_damping/mat/plants_variable.mat', 'Gty_tlin', 'Dy', 'Gty_iff', 'Gty_dvf', 'Gty_ine', '-append'); +#+end_src + +*** Plots :ignore: +#+begin_src matlab :exports none + load('./active_damping/mat/plants_variable.mat', 'Gty_tlin', 'Dy', 'Gty_iff', 'Gty_dvf', 'Gty_ine'); + load('./active_damping/mat/undamped_plants.mat', 'G_iff', 'G_dvf', 'G_ine'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gty_iff) + plot(freqs, abs(squeeze(freqresp(Gty_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gty_iff) + [~, i_t] = min(abs(Dy.time - Gty_tlin(i))); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gty_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Dy = %.0f$ [mm]', 1e3*Dy.signals.values(i_t))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_iff_ty_scans.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_iff_ty_scans +#+CAPTION: Variability of the IFF plant at different Ty scan positions ([[./figs/act_damp_variability_iff_ty_scans.png][png]], [[./figs/act_damp_variability_iff_ty_scans.pdf][pdf]]) +[[file:figs/act_damp_variability_iff_ty_scans.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + + for i = 1:length(Gty_dvf) + plot(freqs, abs(squeeze(freqresp(Gty_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gty_dvf) + [~, i_t] = min(abs(Dy.time - Gty_tlin(i))); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gty_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Dy = %.0f$ [mm]', 1e3*Dy.signals.values(i_t))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_ty_scans.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_dvf_ty_scans +#+CAPTION: Variability of the DVF plant at different Ty scan positions ([[./figs/act_damp_variability_dvf_ty_scans.png][png]], [[./figs/act_damp_variability_dvf_ty_scans.pdf][pdf]]) +[[file:figs/act_damp_variability_dvf_ty_scans.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + for i = 1:length(Gty_ine) + plot(freqs, abs(squeeze(freqresp(Gty_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); + end + plot(freqs, abs(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + hold on; + for i = 1:length(Gty_ine) + [~, i_t] = min(abs(Dy.time - Gty_tlin(i))); + plot(freqs, 180/pi*angle(squeeze(freqresp(Gty_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Dy = %.0f$ [mm]', 1e3*Dy.signals.values(i_t))); + end + plot(freqs, 180/pi*angle(squeeze(freqresp(G_ine('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'k--', 'DisplayName', '$Ry = 0$ [deg]'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + legend('location', 'southwest'); + + linkaxes([ax1,ax2],'x'); + xlim([freqs(1), freqs(end)]); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/act_damp_variability_ine_ty_scans.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") +<> +#+end_src + +#+NAME: fig:act_damp_variability_ine_ty_scans +#+CAPTION: Variability of the Inertial plant at different Ty scan positions ([[./figs/act_damp_variability_ine_ty_scans.png][png]], [[./figs/act_damp_variability_ine_ty_scans.pdf][pdf]]) +[[file:figs/act_damp_variability_ine_ty_scans.png]] + +** Conclusion + +#+name: tab:active_damping_plant_variability +#+caption: Conclusion on the variability of the system dynamics for active damping +| | | +| | *Change of Dynamics* | +|---------------------------+--------------------------------------------| +| *Sample Mass* | Large | +| *Spindle Angle* | Small | +| *Spindle Rotation Speed* | First resonance is split in two resonances | +| *Tilt Angle* | Negligible | +| *Translation Stage scans* | Negligible | + +Also, for the Inertial Sensor, a RHP zero may appear when the spindle is rotating fast. + +#+begin_important + When using either a force sensor or a relative motion sensor for active damping, the only "parameter" that induce a large change for the dynamics to be controlled is the *sample mass*. + Thus, the developed damping techniques should be robust to variations of the sample mass. +#+end_important + * Integral Force Feedback :PROPERTIES: :header-args:matlab+: :tangle matlab/iff.m @@ -1941,941 +3237,6 @@ We load the results of tomography experiments. Inertial Control: #+end_important -* Variability of the system dynamics for Active Damping -:PROPERTIES: -:header-args:matlab+: :tangle matlab/act_damp_variability_plant.m -:header-args:matlab+: :comments org :mkdirp yes -:END: -<> - -** ZIP file containing the data and matlab files :ignore: -#+begin_src bash :exports none :results none -if [ matlab/act_damp_variability_plant.m -nt data/act_damp_variability_plant.zip ]; then -cp matlab/act_damp_variability_plant.m act_damp_variability_plant.m; -zip data/act_damp_variability_plant \ -act_damp_variability_plant.m -rm act_damp_variability_plant.m; -fi -#+end_src - -#+begin_note -All the files (data and Matlab scripts) are accessible [[file:data/act_damp_variability_plant.zip][here]]. -#+end_note - -** Introduction :ignore: -** Matlab Init :noexport:ignore: -#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) - <> -#+end_src - -#+begin_src matlab :exports none :results silent :noweb yes - <> -#+end_src - -#+begin_src matlab :tangle no - simulinkproject('../'); - addpath('active_damping/src/'); -#+end_src - -#+begin_src matlab - open('active_damping/matlab/sim_nass_active_damping.slx') - load('mat/conf_simscape.mat'); -#+end_src - -** Variation of the Sample Mass -*** Introduction :ignore: -For all the identifications, the disturbances are disabled and no controller are used. - -*** Initialize the Simulation :noexport: -We initialize all the stages with the default parameters. -#+begin_src matlab - initializeGround(); - initializeGranite(); - initializeTy(); - initializeRy(); - initializeRz(); - initializeMicroHexapod(); - initializeAxisc(); - initializeMirror(); -#+end_src - -No disturbances. -#+begin_src matlab - initializeDisturbances('enable', false); -#+end_src - -The nano-hexapod is a piezoelectric hexapod. -#+begin_src matlab - initializeNanoHexapod('actuator', 'piezo'); -#+end_src - -We set the references to zero. -#+begin_src matlab - initializeReferences(); -#+end_src - -And all the controllers are set to 0. -#+begin_src matlab - K = tf(zeros(6)); - save('./mat/controllers.mat', 'K', '-append'); - K_ine = tf(zeros(6)); - save('./mat/controllers.mat', 'K_ine', '-append'); - K_iff = tf(zeros(6)); - save('./mat/controllers.mat', 'K_iff', '-append'); - K_dvf = tf(zeros(6)); - save('./mat/controllers.mat', 'K_dvf', '-append'); -#+end_src - -*** Identification :ignore: -#+begin_src matlab :exports none - %% Options for Linearized - options = linearizeOptions; - options.SampleTime = 0; - - %% Name of the Simulink File - mdl = 'sim_nass_active_damping'; - - %% Input/Output definition - clear io; io_i = 1; - io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; -#+end_src - -We identify the dynamics for the following sample mass. -#+begin_src matlab - masses = [1, 10, 50]; % [kg] -#+end_src - -#+begin_src matlab :exports none - Gm = {zeros(length(masses))}; - Gm_iff = {zeros(length(masses))}; - Gm_dvf = {zeros(length(masses))}; - Gm_ine = {zeros(length(masses))}; - - for i = 1:length(masses) - initializeSample('mass', masses(i)); - - %% Run the linearization - G = linearize(mdl, io, 0.1, options); - G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; - G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... - 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... - 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; - Gm(i) = {G}; - Gm_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gm_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gm_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - end -#+end_src - -#+begin_src matlab :exports none - save('./active_damping/mat/plants_variable.mat', 'masses', 'Gm_iff', 'Gm_dvf', 'Gm_ine', '-append'); -#+end_src - -*** Plots :ignore: -#+begin_src matlab :exports none - load('./active_damping/mat/plants_variable.mat', 'masses', 'Gm_iff', 'Gm_dvf', 'Gm_ine'); -#+end_src - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gm_iff) - plot(freqs, abs(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gm_iff) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_iff_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_iff_sample_mass -#+CAPTION: Variability of the IFF plant with the Sample Mass ([[./figs/act_damp_variability_iff_sample_mass.png][png]], [[./figs/act_damp_variability_iff_sample_mass.pdf][pdf]]) -[[file:figs/act_damp_variability_iff_sample_mass.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - - for i = 1:length(Gm_dvf) - plot(freqs, abs(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gm_dvf) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_dvf_sample_mass -#+CAPTION: Variability of the DVF plant with the Sample Mass ([[./figs/act_damp_variability_dvf_sample_mass.png][png]], [[./figs/act_damp_variability_dvf_sample_mass.pdf][pdf]]) -[[file:figs/act_damp_variability_dvf_sample_mass.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gm_ine) - plot(freqs, abs(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gm_ine) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gm_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$M = %.0f$ [kg]', masses(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_ine_sample_mass.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_ine_sample_mass -#+CAPTION: Variability of the Inertial plant with the Sample Mass ([[./figs/act_damp_variability_ine_sample_mass.png][png]], [[./figs/act_damp_variability_ine_sample_mass.pdf][pdf]]) -[[file:figs/act_damp_variability_ine_sample_mass.png]] - -** Variation of the Spindle Angle -*** Introduction :ignore: -*** Initialize the Simulation :noexport: -We initialize all the stages with the default parameters. -#+begin_src matlab - initializeGround(); - initializeGranite(); - initializeTy(); - initializeRy(); - initializeRz(); - initializeMicroHexapod(); - initializeAxisc(); - initializeMirror(); -#+end_src - -No disturbances. -#+begin_src matlab - initializeDisturbances('enable', false); -#+end_src - -The nano-hexapod is a piezoelectric hexapod. -#+begin_src matlab - initializeNanoHexapod('actuator', 'piezo'); - initializeSample('mass', 50); -#+end_src - -And all the controllers are set to 0. -#+begin_src matlab - K = tf(zeros(6)); - save('./mat/controllers.mat', 'K', '-append'); - K_ine = tf(zeros(6)); - save('./mat/controllers.mat', 'K_ine', '-append'); - K_iff = tf(zeros(6)); - save('./mat/controllers.mat', 'K_iff', '-append'); - K_dvf = tf(zeros(6)); - save('./mat/controllers.mat', 'K_dvf', '-append'); -#+end_src - -*** Identification :ignore: -#+begin_src matlab :exports none - %% Options for Linearized - options = linearizeOptions; - options.SampleTime = 0; - - %% Name of the Simulink File - mdl = 'sim_nass_active_damping'; - - %% Input/Output definition - clear io; io_i = 1; - io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; -#+end_src - -We identify the dynamics for the following Spindle angles. -#+begin_src matlab - Rz_amplitudes = [0, pi/4, pi/2, pi]; % [rad] -#+end_src - -#+begin_src matlab :exports none - Ga = {zeros(length(Rz_amplitudes))}; - Ga_iff = {zeros(length(Rz_amplitudes))}; - Ga_dvf = {zeros(length(Rz_amplitudes))}; - Ga_ine = {zeros(length(Rz_amplitudes))}; - - for i = 1:length(Rz_amplitudes) - initializeReferences('Rz_type', 'constant', 'Rz_amplitude', Rz_amplitudes(i)) - - %% Run the linearization - G = linearize(mdl, io, 0.1, options); - G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; - G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... - 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... - 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; - Ga(i) = {G}; - Ga_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Ga_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Ga_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - end -#+end_src - -#+begin_src matlab :exports none - save('./active_damping/mat/plants_variable.mat', 'Rz_amplitudes', 'Ga_iff', 'Ga_dvf', 'Ga_ine', '-append'); -#+end_src - -*** Plots :ignore: -#+begin_src matlab :exports none - load('./active_damping/mat/plants_variable.mat', 'Rz_amplitudes', 'Ga_iff', 'Ga_dvf', 'Ga_ine'); -#+end_src - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Ga_iff) - plot(freqs, abs(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Ga_iff) - plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_iff_spindle_angle -#+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_spindle_angle.png][png]], [[./figs/act_damp_variability_iff_spindle_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_iff_spindle_angle.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - - for i = 1:length(Ga_dvf) - plot(freqs, abs(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Ga_dvf) - plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_dvf_spindle_angle -#+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_spindle_angle.png][png]], [[./figs/act_damp_variability_dvf_spindle_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_dvf_spindle_angle.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Ga_ine) - plot(freqs, abs(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Ga_ine) - plot(freqs, 180/pi*angle(squeeze(freqresp(Ga_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [deg]', Rz_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_ine_spindle_angle -#+CAPTION: Variability of the Inertial plant with the Spindle Angle ([[./figs/act_damp_variability_ine_spindle_angle.png][png]], [[./figs/act_damp_variability_ine_spindle_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_ine_spindle_angle.png]] - -** Variation of the Spindle Rotation Speed -*** Introduction :ignore: -*** Initialize the Simulation :noexport: -We initialize all the stages with the default parameters. -#+begin_src matlab - initializeGround(); - initializeGranite(); - initializeTy(); - initializeRy(); - initializeRz(); - initializeMicroHexapod(); - initializeAxisc(); - initializeMirror(); -#+end_src - -No disturbances. -#+begin_src matlab - initializeDisturbances('enable', false); -#+end_src - -The nano-hexapod is a piezoelectric hexapod. -#+begin_src matlab - initializeNanoHexapod('actuator', 'piezo'); - initializeSample('mass', 50); -#+end_src - -And all the controllers are set to 0. -#+begin_src matlab - K = tf(zeros(6)); - save('./mat/controllers.mat', 'K', '-append'); - K_ine = tf(zeros(6)); - save('./mat/controllers.mat', 'K_ine', '-append'); - K_iff = tf(zeros(6)); - save('./mat/controllers.mat', 'K_iff', '-append'); - K_dvf = tf(zeros(6)); - save('./mat/controllers.mat', 'K_dvf', '-append'); -#+end_src - -*** Identification :ignore: -#+begin_src matlab :exports none - %% Options for Linearized - options = linearizeOptions; - options.SampleTime = 0; - - %% Name of the Simulink File - mdl = 'sim_nass_active_damping'; - - %% Input/Output definition - clear io; io_i = 1; - io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; -#+end_src - -We identify the dynamics for the following Spindle rotation periods. -#+begin_src matlab - Rz_periods = [60, 10, 1]; % [s] -#+end_src - -The goal is to identify the dynamics: -- after the transient phase -- at the same spindle angle - -#+begin_src matlab - Gw = {zeros(length(Rz_periods))}; - Gw_iff = {zeros(length(Rz_periods))}; - Gw_dvf = {zeros(length(Rz_periods))}; - Gw_ine = {zeros(length(Rz_periods))}; - - for i = 1:length(Rz_periods) - initializeReferences('Rz_type', 'rotating', ... - 'Rz_period', Rz_periods(i), ... % Rotation period [s] - 'Rz_amplitude', -0.5*(2*pi/Rz_periods(i))); % Angle offset [rad] - - load('mat/nass_references.mat', 'Rz'); % We load the reference for the Spindle - [~, i_end] = min(abs(Rz.signals.values)); % Obtain the indice where the spindle angle is zero - t_sim = Rz.time(i_end) % Simulation time before identification [s] - - %% Run the linearization - G = linearize(mdl, io, t_sim, options); - G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; - G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... - 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... - 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; - - Gw(i) = {G}; - Gw_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gw_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gw_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - end -#+end_src - -#+begin_src matlab :exports none - save('./active_damping/mat/plants_variable.mat', 'Rz_periods', 'Gw_iff', 'Gw_dvf', 'Gw_ine', '-append'); -#+end_src - -*** Plots :ignore: -#+begin_src matlab :exports none - load('./active_damping/mat/plants_variable.mat', 'Rz_periods', 'Gw_iff', 'Gw_dvf', 'Gw_ine'); -#+end_src - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 5000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gw_iff) - plot(freqs, abs(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gw_iff) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_iff_spindle_speed -#+CAPTION: Variability of the IFF plant with the Spindle rotation speed ([[./figs/act_damp_variability_iff_spindle_speed.png][png]], [[./figs/act_damp_variability_iff_spindle_speed.pdf][pdf]]) -[[file:figs/act_damp_variability_iff_spindle_speed.png]] - -#+begin_src matlab :exports none - xlim([10, 30]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_iff_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_iff_spindle_speed_zoom -#+CAPTION: Variability of the IFF plant with the Spindle rotation speed ([[./figs/act_damp_variability_iff_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_iff_spindle_speed_zoom.pdf][pdf]]) -[[file:figs/act_damp_variability_iff_spindle_speed_zoom.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 5000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - - for i = 1:length(Gw_dvf) - plot(freqs, abs(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gw_dvf) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_dvf_spindle_speed -#+CAPTION: Variability of the DVF plant with the Spindle rotation speed ([[./figs/act_damp_variability_dvf_spindle_speed.png][png]], [[./figs/act_damp_variability_dvf_spindle_speed.pdf][pdf]]) -[[file:figs/act_damp_variability_dvf_spindle_speed.png]] - -#+begin_src matlab :exports none - xlim([10, 30]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_dvf_spindle_speed_zoom -#+CAPTION: Variability of the DVF plant with the Spindle rotation speed ([[./figs/act_damp_variability_dvf_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_dvf_spindle_speed_zoom.pdf][pdf]]) -[[file:figs/act_damp_variability_dvf_spindle_speed_zoom.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 5000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gw_ine) - plot(freqs, abs(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gw_ine) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gw_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Rz = %.0f$ [rpm]', 60/Rz_periods(i))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_speed.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_ine_spindle_speed -#+CAPTION: Variability of the Inertial plant with the Spindle rotation speed ([[./figs/act_damp_variability_ine_spindle_speed.png][png]], [[./figs/act_damp_variability_ine_spindle_speed.pdf][pdf]]) -[[file:figs/act_damp_variability_ine_spindle_speed.png]] - -#+begin_src matlab :exports none - xlim([10, 30]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_ine_spindle_speed_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_ine_spindle_speed_zoom -#+CAPTION: Variability of the Inertial plant with the Spindle rotation speed ([[./figs/act_damp_variability_ine_spindle_speed_zoom.png][png]], [[./figs/act_damp_variability_ine_spindle_speed_zoom.pdf][pdf]]) -[[file:figs/act_damp_variability_ine_spindle_speed_zoom.png]] - -** Variation of the Tilt Angle -*** Introduction :ignore: -*** Initialize the Simulation :noexport: -We initialize all the stages with the default parameters. -#+begin_src matlab - initializeGround(); - initializeGranite(); - initializeTy(); - initializeRy(); - initializeRz(); - initializeMicroHexapod(); - initializeAxisc(); - initializeMirror(); -#+end_src - -No disturbances. -#+begin_src matlab - initializeDisturbances('enable', false); -#+end_src - -The nano-hexapod is a piezoelectric hexapod. -#+begin_src matlab - initializeNanoHexapod('actuator', 'piezo'); - initializeSample('mass', 50); -#+end_src - -And all the controllers are set to 0. -#+begin_src matlab - K = tf(zeros(6)); - save('./mat/controllers.mat', 'K', '-append'); - K_ine = tf(zeros(6)); - save('./mat/controllers.mat', 'K_ine', '-append'); - K_iff = tf(zeros(6)); - save('./mat/controllers.mat', 'K_iff', '-append'); - K_dvf = tf(zeros(6)); - save('./mat/controllers.mat', 'K_dvf', '-append'); -#+end_src - -*** Identification :ignore: -#+begin_src matlab :exports none - %% Options for Linearized - options = linearizeOptions; - options.SampleTime = 0; - - %% Name of the Simulink File - mdl = 'sim_nass_active_damping'; - - %% Input/Output definition - clear io; io_i = 1; - io(io_i) = linio([mdl, '/Fnl'], 1, 'openinput'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Dnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Fnlm'); io_i = io_i + 1; - io(io_i) = linio([mdl, '/Micro-Station'], 3, 'openoutput', [], 'Vlm'); io_i = io_i + 1; -#+end_src - -We identify the dynamics for the following Tilt stage angles. -#+begin_src matlab - Ry_amplitudes = [0, 20*pi/180]; % [rad] -#+end_src - -#+begin_src matlab :exports none - Gy = {zeros(length(Ry_amplitudes))}; - Gy_iff = {zeros(length(Ry_amplitudes))}; - Gy_dvf = {zeros(length(Ry_amplitudes))}; - Gy_ine = {zeros(length(Ry_amplitudes))}; - - for i = 1:length(Ry_amplitudes) - initializeReferences('Ry_type', 'constant', 'Ry_amplitude', Ry_amplitudes(i)) - - %% Run the linearization - G = linearize(mdl, io, 0.25, options); - G.InputName = {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}; - G.OutputName = {'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6', ... - 'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6', ... - 'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}; - Gy(i) = {G}; - Gy_iff(i) = {minreal(G({'Fnlm1', 'Fnlm2', 'Fnlm3', 'Fnlm4', 'Fnlm5', 'Fnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gy_dvf(i) = {minreal(G({'Dnlm1', 'Dnlm2', 'Dnlm3', 'Dnlm4', 'Dnlm5', 'Dnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - Gy_ine(i) = {minreal(G({'Vnlm1', 'Vnlm2', 'Vnlm3', 'Vnlm4', 'Vnlm5', 'Vnlm6'}, {'Fnl1', 'Fnl2', 'Fnl3', 'Fnl4', 'Fnl5', 'Fnl6'}))}; - end -#+end_src - -#+begin_src matlab :exports none - save('./active_damping/mat/plants_variable.mat', 'Ry_amplitudes', 'Gy_iff', 'Gy_dvf', 'Gy_ine', '-append'); -#+end_src - -*** Plots :ignore: -#+begin_src matlab :exports none - load('./active_damping/mat/plants_variable.mat', 'Ry_amplitudes', 'Gy_iff', 'Gy_dvf', 'Gy_ine'); -#+end_src - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gy_iff) - plot(freqs, abs(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gy_iff) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_iff{i}('Fnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_iff_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_iff_tilt_angle -#+CAPTION: Variability of the IFF plant with the Spindle Angle ([[./figs/act_damp_variability_iff_tilt_angle.png][png]], [[./figs/act_damp_variability_iff_tilt_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_iff_tilt_angle.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - - for i = 1:length(Gy_dvf) - plot(freqs, abs(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gy_dvf) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_dvf{i}('Dnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_dvf_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_dvf_tilt_angle -#+CAPTION: Variability of the DVF plant with the Spindle Angle ([[./figs/act_damp_variability_dvf_tilt_angle.png][png]], [[./figs/act_damp_variability_dvf_tilt_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_dvf_tilt_angle.png]] - -#+begin_src matlab :exports none - freqs = logspace(0, 3, 1000); - - figure; - - ax1 = subplot(2, 1, 1); - hold on; - for i = 1:length(Gy_ine) - plot(freqs, abs(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz')))); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); - ylabel('Amplitude [$\frac{m/s}{N}$]'); set(gca, 'XTickLabel',[]); - - ax2 = subplot(2, 1, 2); - hold on; - for i = 1:length(Gy_ine) - plot(freqs, 180/pi*angle(squeeze(freqresp(Gy_ine{i}('Vnlm1', 'Fnl1'), freqs, 'Hz'))), 'DisplayName', sprintf('$Ry = %.0f$ [deg]', Ry_amplitudes(i)*180/pi)); - end - hold off; - set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); - ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); - ylim([-180, 180]); - yticks([-180, -90, 0, 90, 180]); - legend('location', 'southwest'); - - linkaxes([ax1,ax2],'x'); - xlim([freqs(1), freqs(end)]); -#+end_src - -#+HEADER: :tangle no :exports results :results none :noweb yes -#+begin_src matlab :var filepath="figs/act_damp_variability_ine_tilt_angle.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") -<> -#+end_src - -#+NAME: fig:act_damp_variability_ine_tilt_angle -#+CAPTION: Variability of the Inertial plant with the Spindle Angle ([[./figs/act_damp_variability_ine_tilt_angle.png][png]], [[./figs/act_damp_variability_ine_tilt_angle.pdf][pdf]]) -[[file:figs/act_damp_variability_ine_tilt_angle.png]] - -** Conclusion - * Comparison <> ** Introduction :ignore: diff --git a/active_damping/mat/plants_variable.mat b/active_damping/mat/plants_variable.mat index c11bd0b..a98d7cc 100644 Binary files a/active_damping/mat/plants_variable.mat and b/active_damping/mat/plants_variable.mat differ diff --git a/active_damping/mat/undamped_plants.mat b/active_damping/mat/undamped_plants.mat index 812b563..a773304 100644 Binary files a/active_damping/mat/undamped_plants.mat and b/active_damping/mat/undamped_plants.mat differ diff --git a/active_damping/matlab/sim_nass_active_damping.slx b/active_damping/matlab/sim_nass_active_damping.slx index 22db770..52ae7e1 100644 Binary files a/active_damping/matlab/sim_nass_active_damping.slx and b/active_damping/matlab/sim_nass_active_damping.slx differ diff --git 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b/simscape_subsystems/index.org @@ -1123,36 +1123,36 @@ The =sample= structure is saved. :UNNUMBERED: t :END: #+begin_src matlab - %% Translation stage - Dy - t = 0:Ts:Tmax; % Time Vector [s] - Dy = zeros(length(t), 1); - Dyd = zeros(length(t), 1); - Dydd = zeros(length(t), 1); - switch args.Dy_type - case 'constant' - Dy(:) = args.Dy_amplitude; - Dyd(:) = 0; - Dydd(:) = 0; - case 'triangular' - % This is done to unsure that we start with no displacement - Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2); - i0 = find(t>=args.Dy_period/4,1); - Dy(1:end-i0+1) = Dy_raw(i0:end); - Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value + %% Translation stage - Dy + t = 0:Ts:Tmax; % Time Vector [s] + Dy = zeros(length(t), 1); + Dyd = zeros(length(t), 1); + Dydd = zeros(length(t), 1); + switch args.Dy_type + case 'constant' + Dy(:) = args.Dy_amplitude; + Dyd(:) = 0; + Dydd(:) = 0; + case 'triangular' + % This is done to unsure that we start with no displacement + Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2); + i0 = find(t>=args.Dy_period/4,1); + Dy(1:end-i0+1) = Dy_raw(i0:end); + Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value - % The signal is filtered out - Dy = lsim(H_lpf, Dy, t); - Dyd = lsim(H_lpf*s, Dy, t); - Dydd = lsim(H_lpf*s^2, Dy, t); - case 'sinusoidal' - Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t); - Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t); - Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t); - otherwise - warning('Dy_type is not set correctly'); - end + % The signal is filtered out + Dy = lsim(H_lpf, Dy, t); + Dyd = lsim(H_lpf*s, Dy, t); + Dydd = lsim(H_lpf*s^2, Dy, t); + case 'sinusoidal' + Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t); + Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t); + Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t); + otherwise + warning('Dy_type is not set correctly'); + end - Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd); + Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd); #+end_src ** Tilt Stage @@ -1160,37 +1160,37 @@ The =sample= structure is saved. :UNNUMBERED: t :END: #+begin_src matlab - %% Tilt Stage - Ry - t = 0:Ts:Tmax; % Time Vector [s] - Ry = zeros(length(t), 1); - Ryd = zeros(length(t), 1); - Rydd = zeros(length(t), 1); + %% Tilt Stage - Ry + t = 0:Ts:Tmax; % Time Vector [s] + Ry = zeros(length(t), 1); + Ryd = zeros(length(t), 1); + Rydd = zeros(length(t), 1); - switch args.Ry_type - case 'constant' - Ry(:) = args.Ry_amplitude; - Ryd(:) = 0; - Rydd(:) = 0; - case 'triangular' - Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2); - i0 = find(t>=args.Ry_period/4,1); - Ry(1:end-i0+1) = Ry_raw(i0:end); - Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value + switch args.Ry_type + case 'constant' + Ry(:) = args.Ry_amplitude; + Ryd(:) = 0; + Rydd(:) = 0; + case 'triangular' + Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2); + i0 = find(t>=args.Ry_period/4,1); + Ry(1:end-i0+1) = Ry_raw(i0:end); + Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value - % The signal is filtered out - Ry = lsim(H_lpf, Ry, t); - Ryd = lsim(H_lpf*s, Ry, t); - Rydd = lsim(H_lpf*s^2, Ry, t); - case 'sinusoidal' - Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t); + % The signal is filtered out + Ry = lsim(H_lpf, Ry, t); + Ryd = lsim(H_lpf*s, Ry, t); + Rydd = lsim(H_lpf*s^2, Ry, t); + case 'sinusoidal' + Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t); - Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t); - Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t); - otherwise - warning('Ry_type is not set correctly'); - end + Ryd = args.Ry_amplitude*2*pi/args.Ry_period*cos(2*pi/args.Ry_period*t); + Rydd = -args.Ry_amplitude*(2*pi/args.Ry_period)^2*sin(2*pi/args.Ry_period*t); + otherwise + warning('Ry_type is not set correctly'); + end - Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd); + Ry = struct('time', t, 'signals', struct('values', Ry), 'deriv', Ryd, 'dderiv', Rydd); #+end_src ** Spindle @@ -1273,11 +1273,11 @@ The =sample= structure is saved. :UNNUMBERED: t :END: #+begin_src matlab - %% Axis Compensation - Rm - t = [0, Ts]; + %% Axis Compensation - Rm + t = [0, Ts]; - Rm = [args.Rm_pos, args.Rm_pos]; - Rm = struct('time', t, 'signals', struct('values', Rm)); + Rm = [args.Rm_pos, args.Rm_pos]; + Rm = struct('time', t, 'signals', struct('values', Rm)); #+end_src ** Nano Hexapod @@ -1285,18 +1285,18 @@ The =sample= structure is saved. :UNNUMBERED: t :END: #+begin_src matlab - %% Nano-Hexapod - t = [0, Ts]; - Dn = zeros(length(t), 6); + %% Nano-Hexapod + t = [0, Ts]; + Dn = zeros(length(t), 6); - switch args.Dn_type - case 'constant' - Dn = [args.Dn_pos, args.Dn_pos]; - otherwise - warning('Dn_type is not set correctly'); - end + switch args.Dn_type + case 'constant' + Dn = [args.Dn_pos, args.Dn_pos]; + otherwise + warning('Dn_type is not set correctly'); + end - Dn = struct('time', t, 'signals', struct('values', Dn)); + Dn = struct('time', t, 'signals', struct('values', Dn)); #+end_src ** Save