diff --git a/active_damping/index.html b/active_damping/index.html index c8f60b3..a58e314 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 @@ -284,101 +284,101 @@ 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:

@@ -417,11 +417,11 @@ The disturbances are:

  • Motion errors of all the stages
    • -
    -

    1 Undamped System

    +
    +

    1 Undamped System

    - +

    @@ -435,12 +435,12 @@ The performance of this undamped system will be compared with the damped system

    -
    -

    1.1 Identification of the dynamics for Active Damping

    +
    +

    1.1 Identification of the dynamics for Active Damping

    -
    -

    1.1.1 Initialize the Simulation

    +
    +

    1.1.1 Initialize the Simulation

    We initialize all the stages with the default parameters. @@ -491,8 +491,8 @@ save('./mat/controllers.mat', -

    1.1.2 Identification

    +
    +

    1.1.2 Identification

    First, we identify the dynamics of the system using the linearize function. @@ -541,25 +541,25 @@ And we save them for further analysis.

    -
    -

    1.1.3 Obtained Plants for Active Damping

    +
    +

    1.1.3 Obtained Plants for Active Damping

    -
    +

    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: Inertial Feedback Plant (png, pdf)

    @@ -568,12 +568,12 @@ 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. @@ -610,8 +610,8 @@ Finally, we save the simulation results for further analysis

    -
    -

    1.2.2 Results

    +
    +

    1.2.2 Results

    We load the results of tomography experiments. @@ -623,14 +623,14 @@ 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)

    @@ -640,11 +640,11 @@ t = linspace(0, 3, length(En(:,1)));
    -
    -

    2 Integral Force Feedback

    +
    +

    2 Integral Force Feedback

    - +

    @@ -657,12 +657,12 @@ Integral Force Feedback is applied on the simscape model.

    -
    -

    2.1 Control Design

    +
    +

    2.1 Control Design

    -
    -

    2.1.1 Plant

    +
    +

    2.1.1 Plant

    Let’s load the previously indentified undamped plant: @@ -673,11 +673,11 @@ Let’s load the previously indentified undamped plant:

    -Let’s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure 6). +Let’s look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor (figure 6).

    -
    +

    iff_plant.png

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

    @@ -685,8 +685,8 @@ Let’s look at the transfer function from actuator forces in the nano-hexap
    -
    -

    2.1.2 Control Design

    +
    +

    2.1.2 Control Design

    The controller for each pair of actuator/sensor is: @@ -697,11 +697,11 @@ The controller for each pair of actuator/sensor is:

    -The corresponding loop gains are shown in figure 7. +The corresponding loop gains are shown in figure 7.

    -
    +

    iff_open_loop.png

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

    @@ -709,8 +709,8 @@ The corresponding loop gains are shown in figure 7.
    -
    -

    2.1.3 Diagonal Controller

    +
    +

    2.1.3 Diagonal Controller

    We create the diagonal controller and we add a minus sign as we have a positive @@ -731,8 +731,8 @@ We save the controller for further analysis.

    -
    -

    2.1.4 IFF with High Pass Filter

    +
    +

    2.1.4 IFF with High Pass Filter

    w_hpf = 2*pi*10; % Cut-off frequency for the high pass filter [rad/s]
@@ -743,10 +743,10 @@ K_iff = 2*pi
 
 
    
-The corresponding loop gains are shown in figure 8.
+The corresponding loop gains are shown in figure 8.
 
    
 
-
    
+
    
 
    iff_hpf_open_loop.png
 
    
 
    Figure 8: Loop Gain for the Integral Force Feedback with an High pass filter (png, pdf)
    
@@ -772,12 +772,12 @@ We save the controller for further analysis.
 
    
 
    
 
-
    
-
    2.2 Tomography Experiment
    
+
    
+
    2.2 Tomography Experiment
    
 
    
 
    
-
    
-
    2.2.1 Simulation with IFF Controller
    
+
    
+
    2.2.1 Simulation with IFF Controller
    
 
    
 
    
 We initialize elements for the tomography experiment.
@@ -825,8 +825,8 @@ save('./active_damping/mat/tomo_exp.mat', 
 
    
 
-
    
-
    2.2.2 Simulation with IFF Controller with added High Pass Filter
    
+
    
+
    2.2.2 Simulation with IFF Controller with added High Pass Filter
    
 
    
 
    
 We initialize elements for the tomography experiment.
@@ -874,8 +874,8 @@ save('./active_damping/mat/tomo_exp.mat', 
 
    
 
-
    
-
    2.2.3 Compare with Undamped system
    
+
    
+
    2.2.3 Compare with Undamped system
    
 
    
 
    
 We load the results of tomography experiments.
@@ -887,21 +887,21 @@ 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)
    
 
    
 
 
-
    
+
    
 
    nass_act_damp_iff_sim_tomo_trans.png
 
    
 
    Figure 10: 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)
    
@@ -910,8 +910,8 @@ t = linspace(0, 3, length(En(:,1)));
 
    
 
    
 
-
    
-
    2.3 Conclusion
    
+
    
+
    2.3 Conclusion
    
 
    
 
    
 
    
@@ -928,11 +928,11 @@ Integral Force Feedback:
 
    
 
    
 
-
    
-
    3 Direct Velocity Feedback
    
+
    
+
    3 Direct Velocity Feedback
    
 
    
 
    
-
+
 
    
 
    
 
    
@@ -946,12 +946,12 @@ The actuator displacement can be measured with a capacitive sensor for instance.
 
    
 
    
 
-
    
-
    3.1 Control Design
    
+
    
+
    3.1 Control Design
    
 
    
 
    
-
    
-
    3.1.1 Plant
    
+
    
+
    3.1.1 Plant
    
 
    
 
    
 Let’s load the undamped plant:
@@ -962,11 +962,11 @@ Let’s load the undamped plant:
 
    
 
 
    
-Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure 12).
+Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor (figure 12).
 
    
 
 
-
    
+
    
 
    dvf_plant.png
 
    
 
    Figure 12: Transfer function from forces applied in the legs to leg displacement sensor (png, pdf)
    
@@ -974,8 +974,8 @@ Let’s look at the transfer function from actuator forces in the nano-hexap
 
    
 
    
 
-
    
-
    3.1.2 Control Design
    
+
    
+
    3.1.2 Control Design
    
 
    
 
    
 The Direct Velocity Feedback is defined below.
@@ -987,11 +987,11 @@ A Low pass Filter is added to make the controller transfer function proper.
 
    
 
 
    
-The obtained loop gains are shown in figure 13.
+The obtained loop gains are shown in figure 13.
 
    
 
 
-
    
+
    
 
    dvf_open_loop.png
 
    
 
    Figure 13: Loop Gain for the Integral Force Feedback (png, pdf)
    
@@ -999,8 +999,8 @@ The obtained loop gains are shown in figure 13.
 
    
 
    
 
-
    
-
    3.1.3 Diagonal Controller
    
+
    
+
    3.1.3 Diagonal Controller
    
 
    
 
    
 We create the diagonal controller and we add a minus sign as we have a positive feedback architecture.
@@ -1021,12 +1021,12 @@ We save the controller for further analysis.
 
    
 
    
 
-
    
-
    3.2 Tomography Experiment
    
+
    
+
    3.2 Tomography Experiment
    
 
    
 
    
-
    
-
    3.2.1 Initialize the Simulation
    
+
    
+
    3.2.1 Initialize the Simulation
    
 
    
 
    
 We initialize elements for the tomography experiment.
@@ -1047,8 +1047,8 @@ save('./mat/controllers.mat', 
-
    3.2.2 Simulation
    
+
    
+
    3.2.2 Simulation
    
 
    
 
    
 We change the simulation stop time.
@@ -1079,8 +1079,8 @@ save('./active_damping/mat/tomo_exp.mat', 
 
    
 
-
    
-
    3.2.3 Compare with Undamped system
    
+
    
+
    3.2.3 Compare with Undamped system
    
 
    
 
    
 We load the results of tomography experiments.
@@ -1092,21 +1092,21 @@ 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)
    
 
    
 
 
-
    
+
    
 
    nass_act_damp_dvf_sim_tomo_trans.png
 
    
 
    Figure 15: 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)
    
@@ -1115,8 +1115,8 @@ t = linspace(0, 3, length(En(:,1)));
 
    
 
    
 
-
    
-
    3.3 Conclusion
    
+
    
+
    3.3 Conclusion
    
 
    
 
    
 
    
@@ -1131,11 +1131,11 @@ Direct Velocity Feedback:
 
    
 
    
 
-
    
-
    4 Inertial Control
    
+
    
+
    4 Inertial Control
    
 
    
 
    
-
+
 
    
 
    
 
    
@@ -1148,12 +1148,12 @@ In Inertial Control, a feedback is applied between the measured absolute
 
    
 
    
 
-
    
-
    4.1 Control Design
    
+
    
+
    4.1 Control Design
    
 
    
 
    
-
    
-
    4.1.1 Plant
    
+
    
+
    4.1.1 Plant
    
 
    
 
    
 Let’s load the undamped plant:
@@ -1164,11 +1164,11 @@ Let’s load the undamped plant:
 
    
 
 
    
-Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure 17).
+Let’s look at the transfer function from actuator forces in the nano-hexapod to the measured velocity of the nano-hexapod platform in the direction of the corresponding actuator for all 6 pairs of actuator/sensor (figure 17).
 
    
 
 
-
    
+
    
 
    ine_plant.png
 
    
 
    Figure 17: Transfer function from forces applied in the legs to leg velocity sensor (png, pdf)
    
@@ -1176,11 +1176,11 @@ Let’s look at the transfer function from actuator forces in the nano-hexap
 
    
 
    
 
-
    
-
    4.1.2 Control Design
    
+
    
+
    4.1.2 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 18.
 
    
 
 
    
@@ -1189,7 +1189,7 @@ 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)
    
@@ -1197,8 +1197,8 @@ The controller is defined below and the obtained loop gain is shown in figure 
 
    
 
-
    
-
    4.1.3 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.
@@ -1219,12 +1219,12 @@ We save the controller for further analysis.
 
    
 
    
 
-
    
-
    4.2 Tomography Experiment
    
+
    
+
    4.2 Tomography Experiment
    
 
    
 
    
-
    
-
    4.2.1 Initialize the Simulation
    
+
    
+
    4.2.1 Initialize the Simulation
    
 
    
 
    
 We initialize elements for the tomography experiment.
@@ -1245,8 +1245,8 @@ save('./mat/controllers.mat', 
-
    4.2.2 Simulation
    
+
    
+
    4.2.2 Simulation
    
 
    
 
    
 We change the simulation stop time.
@@ -1277,8 +1277,8 @@ save('./active_damping/mat/tomo_exp.mat', 
 
    
 
-
    
-
    4.2.3 Compare with Undamped system
    
+
    
+
    4.2.3 Compare with Undamped system
    
 
    
 
    
 We load the results of tomography experiments.
@@ -1290,21 +1290,21 @@ t = linspace(0, 3, length(En_ine(:,1)));
 
    
 
 
-
    
+
 
 
-
    
+
    
 
    nass_act_damp_ine_sim_tomo_trans.png
 
    
 
    Figure 20: 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)
    
@@ -1313,8 +1313,8 @@ t = linspace(0, 3, length(En_ine(:,1)));
 
    
 
    
 
-
    
-
    4.3 Conclusion
    
+
    
+
    4.3 Conclusion
    
 
    
 
    
 
    
@@ -1326,15 +1326,15 @@ Inertial Control:
 
    
 
    
 
-
    
-
    5 Comparison
    
+
    
+
    5 Comparison
    
 
    
 
    
-
+
 
    
 
    
-
    
-
    5.1 Load the plants
    
+
    
+
    5.1 Load the plants
    
 
    
 
    
 
    load('./active_damping/mat/plants.mat', 'G', 'G_iff', 'G_ine', 'G_dvf');
@@ -1343,11 +1343,11 @@ Inertial Control:
 
    
 
    
 
-
    
-
    5.2 Sensitivity to Disturbance
    
+
    
+
    5.2 Sensitivity to Disturbance
    
 
    
 
-
    
+
    
 
    sensitivity_comp_ground_motion_z.png
 
    
 
    Figure 22: Sensitivity to ground motion in the Z direction on the Z motion error (png, pdf)
    
@@ -1355,21 +1355,21 @@ Inertial Control:
 
 
 
-
    
+
    
 
    sensitivity_comp_direct_forces_z.png
 
    
 
    Figure 23: Compliance in the Z direction: Sensitivity of direct forces applied on the sample in the Z direction on the Z motion error (png, pdf)
    
 
    
 
 
-
    
+
    
 
    sensitivity_comp_spindle_z.png
 
    
 
    Figure 24: Sensitivity to forces applied in the Z direction by the Spindle on the Z motion error (png, pdf)
    
 
    
 
 
-
    
+
    
 
    sensitivity_comp_ty_z.png
 
    
 
    Figure 25: Sensitivity to forces applied in the Z direction by the Y translation stage on the Z motion error (png, pdf)
    
@@ -1377,7 +1377,7 @@ Inertial Control:
 
 
 
-
    
+
    
 
    sensitivity_comp_ty_x.png
 
    
 
    Figure 26: Sensitivity to forces applied in the X direction by the Y translation stage on the X motion error (png, pdf)
    
@@ -1385,25 +1385,25 @@ Inertial Control:
 
    
 
    
 
-
    
-
    5.3 Damped Plant
    
+
    
+
    5.3 Damped Plant
    
 
    
 
-
    
+
    
 
    plant_comp_damping_z.png
 
    
 
    Figure 27: Plant for the \(z\) direction for different active damping technique used (png, pdf)
    
 
    
 
 
-
    
+
    
 
    plant_comp_damping_x.png
 
    
 
    Figure 28: Plant for the \(x\) direction for different active damping technique used (png, pdf)
    
 
    
 
 
-
    
+
    
 
    plant_comp_damping_coupling.png
 
    
 
    Figure 29: Comparison of one off-diagonal plant for different damping technique applied (png, pdf)
    
@@ -1411,12 +1411,12 @@ Inertial Control:
 
    
 
    
 
-
    
-
    5.4 Tomography Experiment
    
+
    
+
    5.4 Tomography Experiment
    
 
    
 
    
-
    
-
    5.4.1 Load the Simulation Data
    
+
    
+
    5.4.1 Load the Simulation Data
    
 
    
 
    
 
    load('./active_damping/mat/tomo_exp.mat', 'En', 'En_iff_hpf', 'En_dvf', 'En_ine');
@@ -1427,8 +1427,8 @@ t = linspace(0, 3, length(En(:,1)));
 
    
 
    
 
-
    
-
    5.4.2 Frequency Domain Analysis
    
+
    
+
    5.4.2 Frequency Domain Analysis
    
 
    
 
    
 Window used for pwelch function.
@@ -1440,28 +1440,28 @@ han_win = hanning(ceil(length(En(:, 1))
 
 
-
    
+
    
 
    act_damp_tomo_exp_comp_psd_trans.png
 
    
 
    Figure 30: PSD of the translation errors for applied Active Damping techniques (png, pdf)
    
 
    
 
 
-
    
+
    
 
    act_damp_tomo_exp_comp_psd_rot.png
 
    
 
    Figure 31: PSD of the rotation errors for applied Active Damping techniques (png, pdf)
    
 
    
 
 
-
    
+
    
 
    act_damp_tomo_exp_comp_cps_trans.png
 
    
 
    Figure 32: CPS of the translation errors for applied Active Damping techniques (png, pdf)
    
 
    
 
 
-