1.1 Initialization
+
+
@@ -147,10 +153,10 @@ Let’s compare the ideal case (zero stiffness in rotation and infinite stif
-1.1 Initialization
Let’s initialize all the stages with default parameters. @@ -128,8 +134,8 @@ initializeMirror(); Let’s consider the heaviest mass which should we the most problematic with it comes to the flexible joints.
-
initializeSample('mass', 50, 'freq', 200*ones(6,1));
-initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
+initializeSample('mass', 50, 'freq', 200*ones(6,1));
+initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
-
@@ -158,8 +164,8 @@ Kt_F = 20*ones(6,1);
The stiffness and damping of the nano-hexapod’s legs are:
Kf_M = 15*ones(6,1); -Kf_F = 15*ones(6,1); -Kt_M = 20*ones(6,1); -Kt_F = 20*ones(6,1); +Kf_M = 15*ones(6,1); +Kf_F = 15*ones(6,1); +Kt_M = 20*ones(6,1); +Kt_F = 20*ones(6,1);
-
@@ -168,8 +174,8 @@ This corresponds to the optimal identified stiffness.
k_opt = 1e5; % [N/m] -c_opt = 2e2; % [N/(m/s)] +k_opt = 1e5; % [N/m] +c_opt = 2e2; % [N/(m/s)]
-
1.2.1 Direct Velocity Feedback
+
+
-1.2.1 Direct Velocity Feedback
We identify the dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness. @@ -189,8 +195,8 @@ It is shown that the adding of stiffness for the flexible joints does increase a
-
1.2.2 Primary Plant
+
+
-1.2.2 Primary Plant
Let’s now identify the dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs). @@ -210,10 +216,10 @@ The plant dynamics is not found to be changing significantly.
-
1.2.3 Conclusion
+
+
1.2.3 Conclusion
-
+
-
Considering realistic flexible joint bending stiffness for the nano-hexapod does not seems to impose any limitation on the DVF control nor on the primary control.
@@ -239,7 +245,7 @@ This will help to determine the requirements on the joint’s stiffness. Let’s consider the following bending stiffness of the flexible joints:
-
@@ -248,8 +254,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
+Ks = [1, 5, 10, 50, 100]; % [Nm/rad]
-
1.3.1 Direct Velocity Feedback
+
+
-1.3.1 Direct Velocity Feedback
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure 3. @@ -279,8 +285,8 @@ It is shown that the bending stiffness of the flexible joints does indeed change
-
1.3.2 Primary Control
+
+
-1.3.2 Primary Control
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure 5. @@ -299,10 +305,10 @@ It is shown that the bending stiffness of the flexible joints have very little i
-
1.3.3 Conclusion
+
+
1.3.3 Conclusion
-
+
-
The bending stiffness of the flexible joint does not significantly change the dynamics.
@@ -333,16 +339,16 @@ We choose realistic values of the axial stiffness of the joints:
-
Kz_F = 60e6*ones(6,1); % [N/m] -Kz_M = 60e6*ones(6,1); % [N/m] -Cz_F = 1*ones(6,1); % [N/(m/s)] -Cz_M = 1*ones(6,1); % [N/(m/s)] +Ka_F = 60e6*ones(6,1); % [N/m] +Ka_M = 60e6*ones(6,1); % [N/m] +Ca_F = 1*ones(6,1); % [N/(m/s)] +Ca_M = 1*ones(6,1); % [N/(m/s)]
-
2.1.1 Initialization
+
+
-2.1.1 Initialization
Let’s initialize all the stages with default parameters. @@ -363,15 +369,15 @@ initializeMirror(); Let’s consider the heaviest mass which should we the most problematic with it comes to the flexible joints.
-
initializeSample('mass', 50, 'freq', 200*ones(6,1));
-initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
+initializeSample('mass', 50, 'freq', 200*ones(6,1));
+initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60);
-
2.1.2 Direct Velocity Feedback
+
+
-2.1.2 Direct Velocity Feedback
The dynamics from actuators force \(\tau_i\) to relative motion sensors \(d\mathcal{L}_i\) with and without considering the flexible joint stiffness are identified. @@ -390,11 +396,11 @@ The obtained dynamics are shown in Figure 6.
-
2.1.3 Primary Plant
+
+
-
2.1.3 Primary Plant
-
@@ -415,10 +421,10 @@ The dynamics is compare with and without the joint flexibility in Figure
Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6); +Kdvf = 5e3*s/(1+s/2/pi/1e3)*eye(6);
-
2.1.4 Conclusion
+
+
2.1.4 Conclusion
-
+
-
For the realistic value of the flexible joint axial stiffness, the dynamics is not much impact, and this should not be a problem for control.
@@ -439,7 +445,7 @@ We wish now to see what is the impact of the axial stiffness of the flexi Let’s consider the following values for the axial stiffness:
-
@@ -448,8 +454,8 @@ We also consider here a nano-hexapod with the identified optimal actuator stiffn
Kzs = [1e4, 1e5, 1e6, 1e7, 1e8, 1e9]; % [N/m]
+Kas = [1e4, 1e5, 1e6, 1e7, 1e8, 1e9]; % [N/m]
-
2.2.1 Direct Velocity Feedback
+
+
-2.2.1 Direct Velocity Feedback
The dynamics from the actuators to the relative displacement sensor in each leg is identified and shown in Figure 8. @@ -491,8 +497,8 @@ It can be seen that very little active damping can be achieve for axial stiffnes
-
2.2.2 Primary Control
+
+
-2.2.2 Primary Control
The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for the primary controller designed in the frame of the legs) is shown in Figure 11. @@ -508,10 +514,10 @@ The dynamics from \(\bm{\tau}^\prime\) to \(\bm{\epsilon}_{\mathcal{X}_n}\) (for
-
2.3 Conclusion
+
+
2.3 Conclusion
-
+
-The axial stiffness of the flexible joints should be maximized.
@@ -533,14 +539,14 @@ We may interpolate the results and say that the axial joint stiffness should be
-Subsystems used for the Simscape Models
@@ -28,173 +28,173 @@
-3 Conclusion
+
+
3 Conclusion
-
+
+
+
+
In this study we considered the bending, torsional and axial stiffnesses of the flexible joints used for the nano-hexapod.
@@ -575,10 +581,80 @@ As there is generally a trade-off between bending stiffness and axial stiffness,
+
4 Designed Flexible Joints
+
+
+
+
+
+4.1 Initialization
+
+
++Let’s initialize all the stages with default parameters. +
+
+
+
+initializeGround(); +initializeGranite(); +initializeTy(); +initializeRy(); +initializeRz(); +initializeMicroHexapod(); +initializeAxisc('type', 'none'); +initializeMirror('type', 'none'); +initializeMirror(); ++
+Let’s consider the heaviest mass which should we the most problematic with it comes to the flexible joints. +
+
+
+
+initializeSample('mass', 50, 'freq', 200*ones(6,1)); +initializeReferences('Rz_type', 'rotating-not-filtered', 'Rz_period', 60); ++
+
+
+flex_joint = load('./mat/flexor_025.mat', 'int_xyz', 'int_i', 'n_xyz', 'n_i', 'nodes', 'M', 'K'); +apa = load('./mat/APA300ML_simplified_model.mat'); ++
+
+
+initializeNanoHexapod('actuator', 'amplified', ... + 'ke', apa.ke, 'ka', apa.ka, 'k1', apa.k1, 'c1', apa.c1, 'F_gain', apa.F_gain, ... + 'type_M', 'spherical_3dof', ... + 'Kr_M', flex_joint.K(1,1)*ones(6,1), ... + 'Ka_M', flex_joint.K(3,3)*ones(6,1), ... + 'Kf_M', flex_joint.K(4,4)*ones(6,1), ... + 'Kt_M', flex_joint.K(6,6)*ones(6,1), ... + 'type_F', 'spherical_3dof', ... + 'Kr_F', flex_joint.K(1,1)*ones(6,1), ... + 'Ka_F', flex_joint.K(3,3)*ones(6,1), ... + 'Kf_F', flex_joint.K(4,4)*ones(6,1), ... + 'Kt_F', flex_joint.K(6,6)*ones(6,1)); ++
+
+initializeNanoHexapod(); ++
+
+4.2 Direct Velocity Feedback
+
+
+4.3 Integral Force Feedback
+
-
diff --git a/docs/simscape_subsystems.html b/docs/simscape_subsystems.html
index f9bb5f5..02e8983 100644
--- a/docs/simscape_subsystems.html
+++ b/docs/simscape_subsystems.html
@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
-
+
Created: 2020-05-05 mar. 11:50
+Created: 2020-11-03 mar. 09:45
- 1. Simscape Configuration
- 2. Logging Configuration
- 3. Ground
- 4. Granite
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Granite Type -
- Material and Geometry -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. -
- Save the Structure +
- Material and Geometry +
- Stiffness and Damping properties +
- Equilibrium position of the each joint. +
- Save the Structure
- - 5. Translation Stage +
- 5. Translation Stage
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Translation Stage Type -
- Material and Geometry -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. -
- Save the Structure +
- Material and Geometry +
- Stiffness and Damping properties +
- Equilibrium position of the each joint. +
- Save the Structure
- - 6. Tilt Stage +
- 6. Tilt Stage
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Tilt Type -
- Material and Geometry -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. -
- Save the Structure +
- Material and Geometry +
- Stiffness and Damping properties +
- Equilibrium position of the each joint. +
- Save the Structure
- - 7. Spindle +
- 7. Spindle
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Spindle Type -
- Material and Geometry -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. -
- Save the Structure +
- Material and Geometry +
- Stiffness and Damping properties +
- Equilibrium position of the each joint. +
- Save the Structure
- - 8. Micro Hexapod +
- 8. Micro Hexapod
- 9. Center of gravity compensation
- 10. Mirror
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Mirror Type
- Mass and Inertia -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. +
- Stiffness and Damping properties +
- Equilibrium position of the each joint.
- Geometry -
- Save the Structure +
- Save the Structure
- - 11. Nano Hexapod +
- 11. Nano Hexapod
- 12. Sample
-
-
- Simscape Model -
- Function description -
- Optional Parameters -
- Structure initialization +
- Simscape Model +
- Function description +
- Optional Parameters +
- Structure initialization
- Add Sample Type -
- Material and Geometry +
- Material and Geometry
- Compute the Inertia -
- Stiffness and Damping properties -
- Equilibrium position of the each joint. -
- Save the Structure +
- Stiffness and Damping properties +
- Equilibrium position of the each joint. +
- Save the Structure
- 13. Initialize Controller
- 14. Generate Reference Signals
-
-
- Function Declaration and Documentation -
- Optional Parameters +
- Function Declaration and Documentation +
- Optional Parameters
- Initialize Parameters -
- Translation Stage -
- Tilt Stage -
- Spindle -
- Micro Hexapod +
- Translation Stage +
- Tilt Stage +
- Spindle +
- Micro Hexapod
- Axis Compensation -
- Nano Hexapod -
- Save +
- Nano Hexapod +
- Save
- 15. Initialize Disturbances
- 16. Initialize Position Errors
- 17. Z-Axis Geophone @@ -254,31 +254,31 @@ These functions are defined below.
-
Function description
-
+
+
-Function description
+
-
function [] = initializeSimscapeConfiguration(args) +function [] = initializeSimscapeConfiguration(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.gravity logical {mustBeNumericOrLogical} = true
-end
+ args.gravity logical {mustBeNumericOrLogical} = true
+end
-
Structure initialization
-
+
+
-
Structure initialization
+conf_simscape = struct();@@ -286,25 +286,25 @@ end
-
Add Type
-
+
+
-Add Type
+
-
if args.gravity +if args.gravity conf_simscape.type = 1; -else +else conf_simscape.type = 2; -end +end
-
Save the Structure
-
+
+
@@ -319,32 +319,32 @@ end
-Save the Structure
+
-
save('./mat/conf_simscape.mat', 'conf_simscape');
+save('./mat/conf_simscape.mat', 'conf_simscape');
-
Function description
-
+
+
-Function description
+
-
function [] = initializeLoggingConfiguration(args) +function [] = initializeLoggingConfiguration(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none'
- args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
-end
+ args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none'
+ args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
+end
-
Structure initialization
-
+
+
-
Structure initialization
+conf_log = struct();@@ -352,18 +352,18 @@ end
-
Add Type
-
+
-
+
@@ -379,11 +379,11 @@ end
Add Type
+
-
switch args.log - case 'none' +switch args.log + case 'none' conf_log.type = 0; - case 'all' + case 'all' conf_log.type = 1; - case 'forces' + case 'forces' conf_log.type = 2; -end +end
-
Save the Structure
-
+
+
@@ -398,9 +398,9 @@ end
-Save the Structure
+
-
save('./mat/conf_log.mat', 'conf_log');
+save('./mat/conf_log.mat', 'conf_log');
-
Simscape Model
-
+
+
-Simscape Model
+The model of the Ground is composed of:
@@ -425,32 +425,32 @@ The model of the Ground is composed of:
-
Function description
-
+
+
-Function description
+
-
function [ground] = initializeGround(args) +function [ground] = initializeGround(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid'})} = 'rigid'
- args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) % Rotation point for the ground motion [m]
-end
+ args.type char {mustBeMember(args.type,{'none', 'rigid'})} = 'rigid'
+ args.rot_point (3,1) double {mustBeNumeric} = zeros(3,1) % Rotation point for the ground motion [m]
+end
-
Structure initialization
-
+
+
-Structure initialization
+
First, we initialize the granite structure.
granite structure.
-
-Add Type
-
+
+
@@ -483,8 +483,8 @@ end
We set the shape and density of the ground solid element.
@@ -500,14 +500,14 @@ ground.density = 2800; % [kg/m3]
Add Type
+
-
switch args.type - case 'none' +switch args.type + case 'none' ground.type = 0; - case 'rigid' + case 'rigid' ground.type = 1; -end +end
-
ground.shape = [2, 2, 0.5]; % [m] -ground.density = 2800; % [kg/m3] +ground.shape = [2, 2, 0.5]; % [m] +ground.density = 2800; % [kg/m3]
-
Save the Structure
-
+
+
@@ -522,9 +522,9 @@ The
-Save the Structure
+
The ground structure is saved.
-
save('./mat/stages.mat', 'ground', '-append');
+save('./mat/stages.mat', 'ground', '-append');
ground structure is saved.
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the granite is composed of:
@@ -553,38 +553,39 @@ The outputsample_pos corresponds to the impact point of the X-ray.
-
Function description
-
+
+
-Function description
+
-
function [granite] = initializeGranite(args) +function [granite] = initializeGranite(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible'
- args.Foffset logical {mustBeNumericOrLogical} = false
- args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
- args.K (3,1) double {mustBeNumeric, mustBeNonnegative} = [4e9; 3e8; 8e8] % [N/m]
- args.C (3,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5] % [N/(m/s)]
- args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m]
- args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m]
- args.z0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Z direction [m]
-end
+ args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'modal-analysis', 'init'})} = 'flexible'
+ args.Foffset logical {mustBeNumericOrLogical} = false
+ args.density (1,1) double {mustBeNumeric, mustBeNonnegative} = 2800 % Density [kg/m3]
+ args.K (3,1) double {mustBeNumeric, mustBeNonnegative} = [4e9; 3e8; 8e8] % [N/m]
+ args.C (3,1) double {mustBeNumeric, mustBeNonnegative} = [4.0e5; 1.1e5; 9.0e5] % [N/(m/s)]
+ args.x0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the X direction [m]
+ args.y0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Y direction [m]
+ args.z0 (1,1) double {mustBeNumeric} = 0 % Rest position of the Joint in the Z direction [m]
+ args.sample_pos (1,1) double {mustBeNumeric} = 0.8 % Height of the measurment point [m]
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the granite structure.
granite structure.
Add Granite Type
-
switch args.type - case 'none' +switch args.type + case 'none' granite.type = 0; - case 'rigid' + case 'rigid' granite.type = 1; - case 'flexible' + case 'flexible' granite.type = 2; - case 'modal-analysis' + case 'modal-analysis' granite.type = 3; - case 'init' + case 'init' granite.type = 4; -end +end
-
Material and Geometry
-
+
+
-Material and Geometry
+Properties of the Material and link to the geometry of the granite.
-
@@ -632,63 +633,63 @@ granite.STEP = './STEPS/granite/granite.STEP';
Z-offset for the initial position of the sample with respect to the granite top surface.
granite.density = args.density; % [kg/m3] -granite.STEP = './STEPS/granite/granite.STEP'; +granite.density = args.density; % [kg/m3] +granite.STEP = './STEPS/granite/granite.STEP';
-
granite.sample_pos = 0.8; % [m]
+granite.sample_pos = args.sample_pos; % [m]
-
Stiffness and Damping properties
-
+
+
-Stiffness and Damping properties
+
-
granite.K = args.K; % [N/m] -granite.C = args.C; % [N/(m/s)] +granite.K = args.K; % [N/m] +granite.C = args.C; % [N/(m/s)]
-
Equilibrium position of the each joint.
-
+
+
-Equilibrium position of the each joint.
+
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fgm');
- granite.Deq = -Fgm'./granite.K;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fgm');
+ granite.Deq = -Fgm'./granite.K;
+else
granite.Deq = zeros(6,1);
-end
+end
-
Save the Structure
-
+
-
+
Save the Structure
+
The granite structure is saved.
-
save('./mat/stages.mat', 'granite', '-append');
+save('./mat/stages.mat', 'granite', '-append');
-
5 Translation Stage
+
+
5 Translation Stage
-
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the Translation stage consist of:
@@ -718,32 +719,32 @@ It is used to impose the motion in the Y direction
-
Function description
-
+
+
-Function description
+
-
function [ty] = initializeTy(args) +function [ty] = initializeTy(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
- args.Foffset logical {mustBeNumericOrLogical} = false
-end
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
+ args.Foffset logical {mustBeNumericOrLogical} = false
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the ty structure.
ty structure.
Add Translation Stage Type
-
switch args.type - case 'none' +switch args.type + case 'none' ty.type = 0; - case 'rigid' + case 'rigid' ty.type = 1; - case 'flexible' + case 'flexible' ty.type = 2; - case 'modal-analysis' + case 'modal-analysis' ty.type = 3; - case 'init' + case 'init' ty.type = 4; -end +end
-
Material and Geometry
-
+
+
-Material and Geometry
+Define the density of the materials as well as the geometry (STEP files).
-
% Ty Granite frame -ty.granite_frame.density = 7800; % [kg/m3] => 43kg -ty.granite_frame.STEP = './STEPS/Ty/Ty_Granite_Frame.STEP'; +% Ty Granite frame +ty.granite_frame.density = 7800; % [kg/m3] => 43kg +ty.granite_frame.STEP = './STEPS/Ty/Ty_Granite_Frame.STEP'; -% Guide Translation Ty -ty.guide.density = 7800; % [kg/m3] => 76kg -ty.guide.STEP = './STEPS/ty/Ty_Guide.STEP'; +% Guide Translation Ty +ty.guide.density = 7800; % [kg/m3] => 76kg +ty.guide.STEP = './STEPS/ty/Ty_Guide.STEP'; -% Ty - Guide_Translation12 -ty.guide12.density = 7800; % [kg/m3] -ty.guide12.STEP = './STEPS/Ty/Ty_Guide_12.STEP'; +% Ty - Guide_Translation12 +ty.guide12.density = 7800; % [kg/m3] +ty.guide12.STEP = './STEPS/Ty/Ty_Guide_12.STEP'; -% Ty - Guide_Translation11 -ty.guide11.density = 7800; % [kg/m3] -ty.guide11.STEP = './STEPS/ty/Ty_Guide_11.STEP'; +% Ty - Guide_Translation11 +ty.guide11.density = 7800; % [kg/m3] +ty.guide11.STEP = './STEPS/ty/Ty_Guide_11.STEP'; -% Ty - Guide_Translation22 -ty.guide22.density = 7800; % [kg/m3] -ty.guide22.STEP = './STEPS/ty/Ty_Guide_22.STEP'; +% Ty - Guide_Translation22 +ty.guide22.density = 7800; % [kg/m3] +ty.guide22.STEP = './STEPS/ty/Ty_Guide_22.STEP'; -% Ty - Guide_Translation21 -ty.guide21.density = 7800; % [kg/m3] -ty.guide21.STEP = './STEPS/Ty/Ty_Guide_21.STEP'; +% Ty - Guide_Translation21 +ty.guide21.density = 7800; % [kg/m3] +ty.guide21.STEP = './STEPS/Ty/Ty_Guide_21.STEP'; -% Ty - Plateau translation -ty.frame.density = 7800; % [kg/m3] -ty.frame.STEP = './STEPS/ty/Ty_Stage.STEP'; +% Ty - Plateau translation +ty.frame.density = 7800; % [kg/m3] +ty.frame.STEP = './STEPS/ty/Ty_Stage.STEP'; -% Ty Stator Part -ty.stator.density = 5400; % [kg/m3] -ty.stator.STEP = './STEPS/ty/Ty_Motor_Stator.STEP'; +% Ty Stator Part +ty.stator.density = 5400; % [kg/m3] +ty.stator.STEP = './STEPS/ty/Ty_Motor_Stator.STEP'; -% Ty Rotor Part -ty.rotor.density = 5400; % [kg/m3] -ty.rotor.STEP = './STEPS/ty/Ty_Motor_Rotor.STEP'; +% Ty Rotor Part +ty.rotor.density = 5400; % [kg/m3] +ty.rotor.STEP = './STEPS/ty/Ty_Motor_Rotor.STEP';
-
Stiffness and Damping properties
-
+
+
-Stiffness and Damping properties
+
-
ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad] -ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; % [N/(m/s), N*m/(rad/s)] +ty.K = [2e8; 1e8; 2e8; 6e7; 9e7; 6e7]; % [N/m, N*m/rad] +ty.C = [8e4; 5e4; 8e4; 2e4; 3e4; 2e4]; % [N/(m/s), N*m/(rad/s)]
-
Equilibrium position of the each joint.
-
+
+
-Equilibrium position of the each joint.
+
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Ftym');
- ty.Deq = -Ftym'./ty.K;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Ftym');
+ ty.Deq = -Ftym'./ty.K;
+else
ty.Deq = zeros(6,1);
-end
+end
-
Save the Structure
-
+
-
+
Save the Structure
+
The ty structure is saved.
-
save('./mat/stages.mat', 'ty', '-append');
+save('./mat/stages.mat', 'ty', '-append');
-
6 Tilt Stage
+
+
6 Tilt Stage
-
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the Tilt stage is composed of:
@@ -902,33 +903,33 @@ The Ry motion is imposed by the input.
-
Function description
-
+
+
-Function description
+
-
function [ry] = initializeRy(args) +function [ry] = initializeRy(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
- args.Foffset logical {mustBeNumericOrLogical} = false
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
+ args.Foffset logical {mustBeNumericOrLogical} = false
args.Ry_init (1,1) double {mustBeNumeric} = 0
-end
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the ry structure.
ry structure.
Add Tilt Type
-
switch args.type - case 'none' +switch args.type + case 'none' ry.type = 0; - case 'rigid' + case 'rigid' ry.type = 1; - case 'flexible' + case 'flexible' ry.type = 2; - case 'modal-analysis' + case 'modal-analysis' ry.type = 3; - case 'init' + case 'init' ry.type = 4; -end +end
-
Material and Geometry
-
+
+
-Material and Geometry
+Properties of the Material and link to the geometry of the Tilt stage.
-
@@ -990,20 +991,20 @@ ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP';
Z-Offset so that the center of rotation matches the sample center;
% Ry - Guide for the tilt stage -ry.guide.density = 7800; % [kg/m3] -ry.guide.STEP = './STEPS/ry/Tilt_Guide.STEP'; +% Ry - Guide for the tilt stage +ry.guide.density = 7800; % [kg/m3] +ry.guide.STEP = './STEPS/ry/Tilt_Guide.STEP'; -% Ry - Rotor of the motor -ry.rotor.density = 2400; % [kg/m3] -ry.rotor.STEP = './STEPS/ry/Tilt_Motor_Axis.STEP'; +% Ry - Rotor of the motor +ry.rotor.density = 2400; % [kg/m3] +ry.rotor.STEP = './STEPS/ry/Tilt_Motor_Axis.STEP'; -% Ry - Motor -ry.motor.density = 3200; % [kg/m3] -ry.motor.STEP = './STEPS/ry/Tilt_Motor.STEP'; +% Ry - Motor +ry.motor.density = 3200; % [kg/m3] +ry.motor.STEP = './STEPS/ry/Tilt_Motor.STEP'; -% Ry - Plateau Tilt -ry.stage.density = 7800; % [kg/m3] -ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP'; +% Ry - Plateau Tilt +ry.stage.density = 7800; % [kg/m3] +ry.stage.STEP = './STEPS/ry/Tilt_Stage.STEP';
-
ry.z_offset = 0.58178; % [m]
+ry.z_offset = 0.58178; % [m]
-
ry.Ry_init = args.Ry_init; % [rad]
+ry.Ry_init = args.Ry_init; % [rad]
-
Stiffness and Damping properties
-
+
+
-
Stiffness and Damping properties
+ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8]; ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4]; @@ -1012,46 +1013,46 @@ ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4];
-
Equilibrium position of the each joint.
-
+
+
-Equilibrium position of the each joint.
+
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fym');
- ry.Deq = -Fym'./ry.K;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fym');
+ ry.Deq = -Fym'./ry.K;
+else
ry.Deq = zeros(6,1);
-end
+end
-
Save the Structure
-
+
-
+
Save the Structure
+
The ry structure is saved.
-
save('./mat/stages.mat', 'ry', '-append');
+save('./mat/stages.mat', 'ry', '-append');
-
7 Spindle
+
+
7 Spindle
-
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the Spindle is composed of:
@@ -1077,32 +1078,32 @@ The Simscape model of the Spindle is composed of:
-
Function description
-
+
+
-Function description
+
-
function [rz] = initializeRz(args) +function [rz] = initializeRz(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
- args.Foffset logical {mustBeNumericOrLogical} = false
-end
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible'
+ args.Foffset logical {mustBeNumericOrLogical} = false
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the rz structure.
rz structure.
Add Spindle Type
-
switch args.type - case 'none' +switch args.type + case 'none' rz.type = 0; - case 'rigid' + case 'rigid' rz.type = 1; - case 'flexible' + case 'flexible' rz.type = 2; - case 'modal-analysis' + case 'modal-analysis' rz.type = 3; - case 'init' + case 'init' rz.type = 4; -end +end
-
Material and Geometry
-
+
+
-Material and Geometry
+Properties of the Material and link to the geometry of the spindle.
-
% Spindle - Slip Ring -rz.slipring.density = 7800; % [kg/m3] -rz.slipring.STEP = './STEPS/rz/Spindle_Slip_Ring.STEP'; +% Spindle - Slip Ring +rz.slipring.density = 7800; % [kg/m3] +rz.slipring.STEP = './STEPS/rz/Spindle_Slip_Ring.STEP'; -% Spindle - Rotor -rz.rotor.density = 7800; % [kg/m3] -rz.rotor.STEP = './STEPS/rz/Spindle_Rotor.STEP'; +% Spindle - Rotor +rz.rotor.density = 7800; % [kg/m3] +rz.rotor.STEP = './STEPS/rz/Spindle_Rotor.STEP'; -% Spindle - Stator -rz.stator.density = 7800; % [kg/m3] -rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP'; +% Spindle - Stator +rz.stator.density = 7800; % [kg/m3] +rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP';
-
Stiffness and Damping properties
-
+
+
-
Stiffness and Damping properties
+rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7]; rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4]; @@ -1168,46 +1169,46 @@ rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4];
-
Equilibrium position of the each joint.
-
+
+
-Equilibrium position of the each joint.
+
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fzm');
- rz.Deq = -Fzm'./rz.K;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fzm');
+ rz.Deq = -Fzm'./rz.K;
+else
rz.Deq = zeros(6,1);
-end
+end
-
Save the Structure
-
+
-
+
Save the Structure
+
The rz structure is saved.
-
save('./mat/stages.mat', 'rz', '-append');
+save('./mat/stages.mat', 'rz', '-append');
-
8 Micro Hexapod
+
+
8 Micro Hexapod
-
-
Simscape Model
-
+
+
-
Simscape Model
+
@@ -1224,77 +1225,77 @@ The rz structure is saved.
-
Function description
-
+
+
-Function description
+
-
function [micro_hexapod] = initializeMicroHexapod(args) +function [micro_hexapod] = initializeMicroHexapod(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init', 'compliance'})} = 'flexible'
- % initializeFramesPositions
- args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
- args.MO_B (1,1) double {mustBeNumeric} = 270e-3
- % generateGeneralConfiguration
- args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
- args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e-3
- args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
- args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e-3
- args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e-3
- args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
- % initializeStrutDynamics
- args.Ki (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e7*ones(6,1)
- args.Ci (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3*ones(6,1)
- % initializeCylindricalPlatforms
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init', 'compliance'})} = 'flexible'
+ % initializeFramesPositions
+ args.H (1,1) double {mustBeNumeric, mustBePositive} = 350e-3
+ args.MO_B (1,1) double {mustBeNumeric} = 270e-3
+ % generateGeneralConfiguration
+ args.FH (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
+ args.FR (1,1) double {mustBeNumeric, mustBePositive} = 175.5e-3
+ args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
+ args.MH (1,1) double {mustBeNumeric, mustBePositive} = 45e-3
+ args.MR (1,1) double {mustBeNumeric, mustBePositive} = 118e-3
+ args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
+ % initializeStrutDynamics
+ args.Ki (6,1) double {mustBeNumeric, mustBeNonnegative} = 2e7*ones(6,1)
+ args.Ci (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.4e3*ones(6,1)
+ % initializeCylindricalPlatforms
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 10
- args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
- args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e-3
+ args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
+ args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 207.5e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 10
- args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
- args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
- % initializeCylindricalStruts
+ args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 26e-3
+ args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
+ % initializeCylindricalStruts
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 1
- args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
- args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
+ args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
+ args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 1
- args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
- args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
- % inverseKinematics
+ args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
+ args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 25e-3
+ % inverseKinematics
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
- % Force that stiffness of each joint should apply at t=0
- args.Foffset logical {mustBeNumericOrLogical} = false
-end
+ % Force that stiffness of each joint should apply at t=0
+ args.Foffset logical {mustBeNumericOrLogical} = false
+end
-
Function content
-
+
+
-
Function content
+stewart = initializeStewartPlatform(); stewart = initializeFramesPositions(stewart, ... - 'H', args.H, ... - 'MO_B', args.MO_B); + 'H', args.H, ... + 'MO_B', args.MO_B); stewart = generateGeneralConfiguration(stewart, ... - 'FH', args.FH, ... - 'FR', args.FR, ... - 'FTh', args.FTh, ... - 'MH', args.MH, ... - 'MR', args.MR, ... - 'MTh', args.MTh); + 'FH', args.FH, ... + 'FR', args.FR, ... + 'FTh', args.FTh, ... + 'MH', args.MH, ... + 'MR', args.MR, ... + 'MTh', args.MTh); stewart = computeJointsPose(stewart);@@ -1302,42 +1303,42 @@ stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, ... - 'K', args.Ki, ... - 'C', args.Ci); + 'K', args.Ki, ... + 'C', args.Ci); stewart = initializeJointDynamics(stewart, ... - 'type_F', 'universal_p', ... - 'type_M', 'spherical_p'); + 'type_F', 'universal_p', ... + 'type_M', 'spherical_p');
stewart = initializeCylindricalPlatforms(stewart, ... - 'Fpm', args.Fpm, ... - 'Fph', args.Fph, ... - 'Fpr', args.Fpr, ... - 'Mpm', args.Mpm, ... - 'Mph', args.Mph, ... - 'Mpr', args.Mpr); + 'Fpm', args.Fpm, ... + 'Fph', args.Fph, ... + 'Fpr', args.Fpr, ... + 'Mpm', args.Mpm, ... + 'Mph', args.Mph, ... + 'Mpr', args.Mpr); stewart = initializeCylindricalStruts(stewart, ... - 'Fsm', args.Fsm, ... - 'Fsh', args.Fsh, ... - 'Fsr', args.Fsr, ... - 'Msm', args.Msm, ... - 'Msh', args.Msh, ... - 'Msr', args.Msr); + 'Fsm', args.Fsm, ... + 'Fsh', args.Fsh, ... + 'Fsr', args.Fsr, ... + 'Msm', args.Msm, ... + 'Msh', args.Msh, ... + 'Msr', args.Msr); stewart = computeJacobian(stewart); stewart = initializeStewartPose(stewart, ... - 'AP', args.AP, ... - 'ARB', args.ARB); + 'AP', args.AP, ... + 'ARB', args.ARB);
-
@@ -1345,49 +1346,49 @@ stewart = initializeStewartPose(stewart, ...
Equilibrium position of the each joint.
stewart = initializeInertialSensor(stewart, 'type', 'none'); +stewart = initializeInertialSensor(stewart, 'type', 'none');
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fhm');
- stewart.actuators.dLeq = -Fhm'./args.Ki;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fhm');
+ stewart.actuators.dLeq = -Fhm'./args.Ki;
+else
stewart.actuators.dLeq = zeros(6,1);
-end
+end
-
Add Type
-
+
+
-Add Type
+
-
switch args.type - case 'none' +switch args.type + case 'none' stewart.type = 0; - case 'rigid' + case 'rigid' stewart.type = 1; - case 'flexible' + case 'flexible' stewart.type = 2; - case 'modal-analysis' + case 'modal-analysis' stewart.type = 3; - case 'init' + case 'init' stewart.type = 4; - case 'compliance' + case 'compliance' stewart.type = 5; -end +end
-
Save the Structure
-
+
+
@@ -1402,9 +1403,9 @@ save('./mat/stages.mat', 'micro_hexapod', '-append');
-Save the Structure
+
The micro_hexapod structure is saved.
micro_hexapod = stewart;
-save('./mat/stages.mat', 'micro_hexapod', '-append');
+save('./mat/stages.mat', 'micro_hexapod', '-append');
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the Center of gravity compensator is composed of:
@@ -1429,31 +1430,31 @@ The Simscape model of the Center of gravity compensator is composed of:
-
Function description
-
+
+
-Function description
+
-
function [axisc] = initializeAxisc(args) +function [axisc] = initializeAxisc(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
-end
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible'
+end
-
Structure initialization
-
+
+
-Structure initialization
+
First, we initialize the axisc structure.
axisc structure.
-
Add Type
-
+
+
-Add Type
+
-
switch args.type - case 'none' +switch args.type + case 'none' axisc.type = 0; - case 'rigid' + case 'rigid' axisc.type = 1; - case 'flexible' + case 'flexible' axisc.type = 2; -end +end
-
Material and Geometry
-
+
+
-Material and Geometry
+Properties of the Material and link to the geometry files.
-
% Structure -axisc.structure.density = 3400; % [kg/m3] -axisc.structure.STEP = './STEPS/axisc/axisc_structure.STEP'; +% Structure +axisc.structure.density = 3400; % [kg/m3] +axisc.structure.STEP = './STEPS/axisc/axisc_structure.STEP'; -% Wheel -axisc.wheel.density = 2700; % [kg/m3] -axisc.wheel.STEP = './STEPS/axisc/axisc_wheel.STEP'; +% Wheel +axisc.wheel.density = 2700; % [kg/m3] +axisc.wheel.STEP = './STEPS/axisc/axisc_wheel.STEP'; -% Mass -axisc.mass.density = 7800; % [kg/m3] -axisc.mass.STEP = './STEPS/axisc/axisc_mass.STEP'; +% Mass +axisc.mass.density = 7800; % [kg/m3] +axisc.mass.STEP = './STEPS/axisc/axisc_mass.STEP'; -% Gear -axisc.gear.density = 7800; % [kg/m3] -axisc.gear.STEP = './STEPS/axisc/axisc_gear.STEP'; +% Gear +axisc.gear.density = 7800; % [kg/m3] +axisc.gear.STEP = './STEPS/axisc/axisc_gear.STEP';
-
Save the Structure
-
+
+
@@ -1530,9 +1531,9 @@ The
-Save the Structure
+
The axisc structure is saved.
-
save('./mat/stages.mat', 'axisc', '-append');
+save('./mat/stages.mat', 'axisc', '-append');
axisc structure is saved.
-
Simscape Model
-
+
+
-Simscape Model
+
The Simscape Model of the mirror is just a solid body.
The output mirror_center corresponds to the center of the Sphere and is the point of measurement for the metrology
@@ -1554,35 +1555,35 @@ The output mirror_center corresponds to the center of the Sphere an
-
Function description
-
+
+
-Function description
+
-
function [] = initializeMirror(args) +function [] = initializeMirror(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'rigid'
- args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
- args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45 % [deg]
- args.mass (1,1) double {mustBeNumeric, mustBePositive} = 10 % [kg]
- args.freq (6,1) double {mustBeNumeric, mustBeNonnegative} = 200*ones(6,1) % [Hz]
-end
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'rigid'
+ args.shape char {mustBeMember(args.shape,{'spherical', 'conical'})} = 'spherical'
+ args.angle (1,1) double {mustBeNumeric, mustBePositive} = 45 % [deg]
+ args.mass (1,1) double {mustBeNumeric, mustBePositive} = 10 % [kg]
+ args.freq (6,1) double {mustBeNumeric, mustBeNonnegative} = 200*ones(6,1) % [Hz]
+end
-
Structure initialization
-
+
+
@@ -1621,23 +1622,23 @@ mirror.freq = args.freq;
-Structure initialization
+
First, we initialize the mirror structure.
mirror structure.
Add Mirror Type
-
switch args.type - case 'none' +switch args.type + case 'none' mirror.type = 0; - case 'rigid' + case 'rigid' mirror.type = 1; - case 'flexible' + case 'flexible' mirror.type = 2; -end +end
-
Stiffness and Damping properties
-
+
+
-Stiffness and Damping properties
+mirror.K = zeros(6,1); -mirror.K(1:3) = mirror.mass * (2*pi*mirror.freq(1:3)).^2; +mirror.K(1:3) = mirror.mass * (2*pi*mirror.freq(1:3)).^2; mirror.C = zeros(6,1); -mirror.C(1:3) = 0.2 * sqrt(mirror.K(1:3).*mirror.mass); +mirror.C(1:3) = 0.2 * sqrt(mirror.K(1:3).*mirror.mass);
-
Equilibrium position of the each joint.
-
+
+
-
Equilibrium position of the each joint.
+mirror.Deq = zeros(6,1);@@ -1652,30 +1653,30 @@ mirror.C(1:3) = 0.2 * sqrt(mirror.K(1:3).*mirror.mass); We define the geometrical values.
-
mirror.h = 0.05; % Height of the mirror [m] +mirror.h = 0.05; % Height of the mirror [m] -mirror.thickness = 0.025; % Thickness of the plate supporting the sample [m] +mirror.thickness = 0.02; % Thickness of the plate supporting the sample [m] -mirror.hole_rad = 0.125; % radius of the hole in the mirror [m] +mirror.hole_rad = 0.125; % radius of the hole in the mirror [m] -mirror.support_rad = 0.1; % radius of the support plate [m] +mirror.support_rad = 0.1; % radius of the support plate [m] -% point of interest offset in z (above the top surfave) [m] -switch args.type - case 'none' - mirror.jacobian = 0.20; - case 'rigid' - mirror.jacobian = 0.20 - mirror.h; - case 'flexible' - mirror.jacobian = 0.20 - mirror.h; -end +% point of interest offset in z (above the top surfave) [m] +switch args.type + case 'none' + mirror.jacobian = 0.205; + case 'rigid' + mirror.jacobian = 0.205 - mirror.h; + case 'flexible' + mirror.jacobian = 0.205 - mirror.h; +end -mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m] +mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m]
-
@@ -1685,8 +1686,8 @@ We first start with the internal part.
mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point +mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
mirror.shape = [... - mirror.support_rad+5e-3 mirror.h-mirror.thickness - mirror.hole_rad mirror.h-mirror.thickness; ... + mirror.support_rad+5e-3 mirror.h-mirror.thickness + mirror.hole_rad mirror.h-mirror.thickness; ... mirror.hole_rad 0; ... mirror.rad 0 ... ]; @@ -1697,17 +1698,17 @@ We first start with the internal part. Then, we define the reflective used part of the mirror.-@@ -1715,37 +1716,37 @@ end Finally, we close the shape.if strcmp(args.shape, 'spherical') - mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm] +if strcmp(args.shape, 'spherical') + mirror.sphere_radius = sqrt((mirror.jacobian+mirror.h)^2+mirror.rad^2); % Radius of the sphere [mm] - for z = linspace(0, mirror.h, 101) - mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z]; - end -elseif strcmp(args.shape, 'conical') - mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.angle) mirror.h]; -else - error('Shape should be either conical or spherical'); -end + for z = linspace(0, mirror.h, 101) + mirror.shape = [mirror.shape; sqrt(mirror.sphere_radius^2-(z-mirror.jacobian-mirror.h)^2) z]; + end +elseif strcmp(args.shape, 'conical') + mirror.shape = [mirror.shape; mirror.rad+mirror.h/tand(args.angle) mirror.h]; +else + error('Shape should be either conical or spherical'); +end-mirror.shape = [mirror.shape; mirror.support_rad+5e-3 mirror.h]; +mirror.shape = [mirror.shape; mirror.support_rad+5e-3 mirror.h];
-
Save the Structure
-
+
-
+
Save the Structure
+
The mirror structure is saved.
-
save('./mat/stages.mat', 'mirror', '-append');
+save('./mat/stages.mat', 'mirror', '-append');
-
11 Nano Hexapod
+
+
11 Nano Hexapod
-
-
Simscape Model
-
+
+
-
Simscape Model
+
@@ -1762,153 +1763,159 @@ The mirror structure is saved.
-
Function description
-
+
+
-Function description
+
-
function [nano_hexapod] = initializeNanoHexapod(args) +function [nano_hexapod] = initializeNanoHexapod(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'init'})} = 'flexible'
- % initializeFramesPositions
- args.H (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
- args.MO_B (1,1) double {mustBeNumeric} = 175e-3
- % generateGeneralConfiguration
- args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
- args.FR (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
- args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
- args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
- args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
- args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
- % initializeStrutDynamics
- args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz', 'amplified'})} = 'piezo'
+ args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'init'})} = 'flexible'
+ % initializeFramesPositions
+ args.H (1,1) double {mustBeNumeric, mustBePositive} = 95e-3
+ args.MO_B (1,1) double {mustBeNumeric} = 170e-3
+ % generateGeneralConfiguration
+ args.FH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+ args.FR (1,1) double {mustBeNumeric, mustBePositive} = 100e-3
+ args.FTh (6,1) double {mustBeNumeric} = [-10, 10, 120-10, 120+10, 240-10, 240+10]*(pi/180)
+ args.MH (1,1) double {mustBeNumeric, mustBePositive} = 15e-3
+ args.MR (1,1) double {mustBeNumeric, mustBePositive} = 90e-3
+ args.MTh (6,1) double {mustBeNumeric} = [-60+10, 60-10, 60+10, 180-10, 180+10, -60-10]*(pi/180)
+ % initializeStrutDynamics
+ args.actuator char {mustBeMember(args.actuator,{'piezo', 'lorentz', 'amplified'})} = 'piezo'
args.k1 (1,1) double {mustBeNumeric} = 1e6
args.ke (1,1) double {mustBeNumeric} = 5e6
args.ka (1,1) double {mustBeNumeric} = 60e6
args.c1 (1,1) double {mustBeNumeric} = 10
- args.ce (1,1) double {mustBeNumeric} = 10
- args.ca (1,1) double {mustBeNumeric} = 10
- args.k (1,1) double {mustBeNumeric} = -1
- args.c (1,1) double {mustBeNumeric} = -1
- % initializeJointDynamics
- args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof'})} = 'universal'
- args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'spherical_3dof'})} = 'spherical'
- args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
- args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
- args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
- args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
- args.Kz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
- args.Cz_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
- args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
- args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
- args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
- args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
- args.Kz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 60e6*ones(6,1)
- args.Cz_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e2*ones(6,1)
- % initializeCylindricalPlatforms
+ args.F_gain (1,1) double {mustBeNumeric} = 1
+ args.k (1,1) double {mustBeNumeric} = -1
+ args.c (1,1) double {mustBeNumeric} = -1
+ % initializeJointDynamics
+ args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'universal'
+ args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'spherical'
+ args.Ka_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
+ args.Ca_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+ args.Kr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
+ args.Cr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+ args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
+ args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
+ args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
+ args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
+ args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
+ args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
+ args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
+ args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
+ args.Ka_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
+ args.Ca_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+ args.Kr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
+ args.Cr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
+ % initializeCylindricalPlatforms
args.Fpm (1,1) double {mustBeNumeric, mustBePositive} = 1
- args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
- args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
+ args.Fph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
+ args.Fpr (1,1) double {mustBeNumeric, mustBePositive} = 150e-3
args.Mpm (1,1) double {mustBeNumeric, mustBePositive} = 1
- args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
- args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 120e-3
- % initializeCylindricalStruts
+ args.Mph (1,1) double {mustBeNumeric, mustBePositive} = 10e-3
+ args.Mpr (1,1) double {mustBeNumeric, mustBePositive} = 120e-3
+ % initializeCylindricalStruts
args.Fsm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
- args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
- args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
+ args.Fsh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
+ args.Fsr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
args.Msm (1,1) double {mustBeNumeric, mustBePositive} = 0.1
- args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
- args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
- % inverseKinematics
+ args.Msh (1,1) double {mustBeNumeric, mustBePositive} = 50e-3
+ args.Msr (1,1) double {mustBeNumeric, mustBePositive} = 5e-3
+ % inverseKinematics
args.AP (3,1) double {mustBeNumeric} = zeros(3,1)
args.ARB (3,3) double {mustBeNumeric} = eye(3)
- % Equilibrium position of each leg
+ % Equilibrium position of each leg
args.dLeq (6,1) double {mustBeNumeric} = zeros(6,1)
- % Force that stiffness of each joint should apply at t=0
- args.Foffset logical {mustBeNumericOrLogical} = false
-end
+ % Force that stiffness of each joint should apply at t=0
+ args.Foffset logical {mustBeNumericOrLogical} = false
+end
-
Function content
-
+
+
-Function content
+stewart = initializeStewartPlatform(); -stewart = initializeFramesPositions(stewart, 'H', args.H, 'MO_B', args.MO_B); +stewart = initializeFramesPositions(stewart, 'H', args.H, 'MO_B', args.MO_B); -stewart = generateGeneralConfiguration(stewart, 'FH', args.FH, 'FR', args.FR, 'FTh', args.FTh, 'MH', args.MH, 'MR', args.MR, 'MTh', args.MTh); +stewart = generateGeneralConfiguration(stewart, 'FH', args.FH, 'FR', args.FR, 'FTh', args.FTh, 'MH', args.MH, 'MR', args.MR, 'MTh', args.MTh); stewart = computeJointsPose(stewart);
-
if args.k > 0 && args.c > 0
- stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', args.c*ones(6,1));
-elseif args.k > 0
- stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', 1.5*sqrt(args.k)*ones(6,1));
-elseif strcmp(args.actuator, 'piezo')
- stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e7*ones(6,1), 'C', 1e2*ones(6,1));
-elseif strcmp(args.actuator, 'lorentz')
- stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e4*ones(6,1), 'C', 1e2*ones(6,1));
-elseif strcmp(args.actuator, 'amplified')
- stewart = initializeStrutDynamics(stewart, 'type', 'amplified', ...
- 'k1', args.k1*ones(6,1), ...
- 'c1', args.c1*ones(6,1), ...
- 'ka', args.ka*ones(6,1), ...
- 'ca', args.ca*ones(6,1), ...
- 'ke', args.ke*ones(6,1), ...
- 'ce', args.ce*ones(6,1));
-else
- error('args.actuator should be piezo, lorentz or amplified');
-end
+if args.k > 0 && args.c > 0
+ stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', args.c*ones(6,1));
+elseif args.k > 0
+ stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', args.k*ones(6,1), 'C', 1.5*sqrt(args.k)*ones(6,1));
+elseif strcmp(args.actuator, 'piezo')
+ stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e7*ones(6,1), 'C', 1e2*ones(6,1));
+elseif strcmp(args.actuator, 'lorentz')
+ stewart = initializeStrutDynamics(stewart, 'type', 'classical', 'K', 1e4*ones(6,1), 'C', 1e2*ones(6,1));
+elseif strcmp(args.actuator, 'amplified')
+ stewart = initializeStrutDynamics(stewart, 'type', 'amplified', ...
+ 'k1', args.k1*ones(6,1), ...
+ 'c1', args.c1*ones(6,1), ...
+ 'ka', args.ka*ones(6,1), ...
+ 'ke', args.ke*ones(6,1), ...
+ 'F_gain', args.F_gain*ones(6,1));
+else
+ error('args.actuator should be piezo, lorentz or amplified');
+end
stewart = initializeJointDynamics(stewart, ... - 'type_F', args.type_F, ... - 'type_M', args.type_M, ... - 'Kf_M' , args.Kf_M, ... - 'Cf_M' , args.Cf_M, ... - 'Kt_M' , args.Kt_M, ... - 'Ct_M' , args.Ct_M, ... - 'Kz_M' , args.Kz_M, ... - 'Cz_M' , args.Cz_M, ... - 'Kf_F' , args.Kf_F, ... - 'Cf_F' , args.Cf_F, ... - 'Kt_F' , args.Kt_F, ... - 'Ct_F' , args.Ct_F, ... - 'Kz_F' , args.Kz_F, ... - 'Cz_F' , args.Cz_F); + 'type_F', args.type_F, ... + 'type_M', args.type_M, ... + 'Kf_M', args.Kf_M, ... + 'Cf_M', args.Cf_M, ... + 'Kt_M', args.Kt_M, ... + 'Ct_M', args.Ct_M, ... + 'Kf_F', args.Kf_F, ... + 'Cf_F', args.Cf_F, ... + 'Kt_F', args.Kt_F, ... + 'Ct_F', args.Ct_F, ... + 'Ka_F', args.Ka_F, ... + 'Ca_F', args.Ca_F, ... + 'Kr_F', args.Kr_F, ... + 'Cr_F', args.Cr_F, ... + 'Ka_M', args.Ka_M, ... + 'Ca_M', args.Ca_M, ... + 'Kr_M', args.Kr_M, ... + 'Cr_M', args.Cr_M);
-
stewart = initializeCylindricalPlatforms(stewart, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr); +stewart = initializeCylindricalPlatforms(stewart, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr); -stewart = initializeCylindricalStruts(stewart, 'Fsm', args.Fsm, 'Fsh', args.Fsh, 'Fsr', args.Fsr, 'Msm', args.Msm, 'Msh', args.Msh, 'Msr', args.Msr); +stewart = initializeCylindricalStruts(stewart, 'Fsm', args.Fsm, 'Fsh', args.Fsh, 'Fsr', args.Fsr, 'Msm', args.Msm, 'Msh', args.Msh, 'Msr', args.Msr); stewart = computeJacobian(stewart); -stewart = initializeStewartPose(stewart, 'AP', args.AP, 'ARB', args.ARB); +stewart = initializeStewartPose(stewart, 'AP', args.AP, 'ARB', args.ARB);
-
@@ -1917,42 +1924,42 @@ Equilibrium position of the each joint.
stewart = initializeInertialSensor(stewart, 'type', 'accelerometer'); +stewart = initializeInertialSensor(stewart, 'type', 'accelerometer');
-if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fnm');
- stewart.actuators.dLeq = -Fnm'./stewart.Ki;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fnm');
+ stewart.actuators.dLeq = -Fnm'./stewart.Ki;
+else
stewart.actuators.dLeq = args.dLeq;
-end
+end
-
Add Type
-
+
+
-Add Type
+
-
switch args.type - case 'none' +switch args.type + case 'none' stewart.type = 0; - case 'rigid' + case 'rigid' stewart.type = 1; - case 'flexible' + case 'flexible' stewart.type = 2; - case 'init' + case 'init' stewart.type = 4; -end +end
-
Save the Structure
-
+
+
@@ -1967,9 +1974,9 @@ save('./mat/stages.mat', 'nano_hexapod', '-append');
-Save the Structure
+nano_hexapod = stewart;
-save('./mat/stages.mat', 'nano_hexapod', '-append');
+save('./mat/stages.mat', 'nano_hexapod', '-append');
-
Simscape Model
-
+
+
-Simscape Model
+The Simscape model of the sample environment is composed of:
@@ -1997,37 +2004,37 @@ This could be the case for cable forces for instance.
-
Function description
-
+
+
-Function description
+
-
function [sample] = initializeSample(args) +function [sample] = initializeSample(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'init'})} = 'flexible'
- args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m]
- args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m]
- args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
- args.freq (6,1) double {mustBeNumeric, mustBePositive} = 100*ones(6,1) % [Hz]
- args.offset (1,1) double {mustBeNumeric} = 0 % [m]
- args.Foffset logical {mustBeNumericOrLogical} = false
-end
+ args.type char {mustBeMember(args.type,{'rigid', 'flexible', 'none', 'init'})} = 'flexible'
+ args.radius (1,1) double {mustBeNumeric, mustBePositive} = 0.1 % [m]
+ args.height (1,1) double {mustBeNumeric, mustBePositive} = 0.3 % [m]
+ args.mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
+ args.freq (6,1) double {mustBeNumeric, mustBePositive} = 100*ones(6,1) % [Hz]
+ args.offset (1,1) double {mustBeNumeric} = 0 % [m]
+ args.Foffset logical {mustBeNumericOrLogical} = false
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the sample structure.
sample structure.
Add Sample Type
-
switch args.type - case 'none' +switch args.type + case 'none' sample.type = 0; - case 'rigid' + case 'rigid' sample.type = 1; - case 'flexible' + case 'flexible' sample.type = 2; - case 'init' + case 'init' sample.type = 3; -end +end
-
Material and Geometry
-
+
+
@@ -2077,17 +2084,17 @@ sample.offset = args.offset; % [m]
-Material and Geometry
+We define the geometrical parameters of the sample as well as its mass and position.
-
sample.radius = args.radius; % [m] -sample.height = args.height; % [m] -sample.mass = args.mass; % [kg] -sample.offset = args.offset; % [m] +sample.radius = args.radius; % [m] +sample.height = args.height; % [m] +sample.mass = args.mass; % [kg] +sample.offset = args.offset; % [m]
Compute the Inertia
-
sample.inertia = [1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ... - 1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ... - 1/2 * sample.mass * sample.radius^2]; +sample.inertia = [1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ... + 1/12 * sample.mass * (3*sample.radius^2 + sample.height^2); ... + 1/2 * sample.mass * sample.radius^2];
-
Stiffness and Damping properties
-
+
+
-
Stiffness and Damping properties
+sample.K = zeros(6, 1); sample.C = zeros(6, 1); @@ -2098,8 +2105,8 @@ sample.C = zeros(6, 1); Translation Stiffness and Damping:-@@ -2107,36 +2114,36 @@ sample.C(1:3) = 0.1 * sqrt(sample.K(1:3)*sample.mass); % [N/(m/s)] Rotational Stiffness and Damping:sample.K(1:3) = sample.mass .* (2*pi * args.freq(1:3)).^2; % [N/m] -sample.C(1:3) = 0.1 * sqrt(sample.K(1:3)*sample.mass); % [N/(m/s)] +sample.K(1:3) = sample.mass .* (2*pi * args.freq(1:3)).^2; % [N/m] +sample.C(1:3) = 0.1 * sqrt(sample.K(1:3)*sample.mass); % [N/(m/s)]-sample.K(4:6) = sample.inertia .* (2*pi * args.freq(4:6)).^2; % [N/m] -sample.C(4:6) = 0.1 * sqrt(sample.K(4:6).*sample.inertia); % [N/(m/s)] +sample.K(4:6) = sample.inertia .* (2*pi * args.freq(4:6)).^2; % [N/m] +sample.C(4:6) = 0.1 * sqrt(sample.K(4:6).*sample.inertia); % [N/(m/s)]
-
Equilibrium position of the each joint.
-
+
+
-Equilibrium position of the each joint.
+
-
if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
- load('mat/Foffset.mat', 'Fsm');
- sample.Deq = -Fsm'./sample.K;
-else
+if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init')
+ load('mat/Foffset.mat', 'Fsm');
+ sample.Deq = -Fsm'./sample.K;
+else
sample.Deq = zeros(6,1);
-end
+end
-
Save the Structure
-
+
+
@@ -2151,31 +2158,31 @@ The
-Save the Structure
+
The sample structure is saved.
-
save('./mat/stages.mat', 'sample', '-append');
+save('./mat/stages.mat', 'sample', '-append');
sample structure is saved.
-
Function Declaration and Documentation
-
+
+
-Function Declaration and Documentation
+
-
function [] = initializeController(args) +function [] = initializeController(args)
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
-end
+ args.type char {mustBeMember(args.type,{'open-loop', 'iff', 'dvf', 'hac-dvf', 'ref-track-L', 'ref-track-iff-L', 'cascade-hac-lac', 'hac-iff', 'stabilizing'})} = 'open-loop'
+end
-
Structure initialization
-
+
+
-
Structure initialization
+
First, we initialize the controller structure.
controller structure.
Controller Type
-
switch args.type - case 'open-loop' +switch args.type + case 'open-loop' controller.type = 1; - controller.name = 'Open-Loop'; - case 'dvf' + controller.name = 'Open-Loop'; + case 'dvf' controller.type = 2; - controller.name = 'Decentralized Direct Velocity Feedback'; - case 'iff' + controller.name = 'Decentralized Direct Velocity Feedback'; + case 'iff' controller.type = 3; - controller.name = 'Decentralized Integral Force Feedback'; - case 'hac-dvf' + controller.name = 'Decentralized Integral Force Feedback'; + case 'hac-dvf' controller.type = 4; - controller.name = 'HAC-DVF'; - case 'ref-track-L' + controller.name = 'HAC-DVF'; + case 'ref-track-L' controller.type = 5; - controller.name = 'Reference Tracking in the frame of the legs'; - case 'ref-track-iff-L' + controller.name = 'Reference Tracking in the frame of the legs'; + case 'ref-track-iff-L' controller.type = 6; - controller.name = 'Reference Tracking in the frame of the legs + IFF'; - case 'cascade-hac-lac' + controller.name = 'Reference Tracking in the frame of the legs + IFF'; + case 'cascade-hac-lac' controller.type = 7; - controller.name = 'Cascade Control + HAC-LAC'; - case 'hac-iff' + controller.name = 'Cascade Control + HAC-LAC'; + case 'hac-iff' controller.type = 8; - controller.name = 'HAC-IFF'; - case 'stabilizing' + controller.name = 'HAC-IFF'; + case 'stabilizing' controller.type = 9; - controller.name = 'Stabilizing Controller'; -end + controller.name = 'Stabilizing Controller'; +end
-
Save the Structure
-
+
+
@@ -2246,56 +2253,56 @@ The
-Save the Structure
+
The controller structure is saved.
-
save('./mat/controller.mat', 'controller');
+save('./mat/controller.mat', 'controller');
controller structure is saved.
-
Function Declaration and Documentation
-
+
+
-Function Declaration and Documentation
+
-
function [ref] = initializeReferences(args) +function [ref] = initializeReferences(args)
-
Optional Parameters
-
+
+
@@ -2306,159 +2313,159 @@ end
-Optional Parameters
+arguments
- % Sampling Frequency [s]
- args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
- % Maximum simulation time [s]
+ % Sampling Frequency [s]
+ args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3
+ % Maximum simulation time [s]
args.Tmax (1,1) double {mustBeNumeric, mustBePositive} = 100
- % Either "constant" / "triangular" / "sinusoidal"
- args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
- % Amplitude of the displacement [m]
+ % Either "constant" / "triangular" / "sinusoidal"
+ args.Dy_type char {mustBeMember(args.Dy_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
+ % Amplitude of the displacement [m]
args.Dy_amplitude (1,1) double {mustBeNumeric} = 0
- % Period of the displacement [s]
+ % Period of the displacement [s]
args.Dy_period (1,1) double {mustBeNumeric, mustBePositive} = 1
- % Either "constant" / "triangular" / "sinusoidal"
- args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
- % Amplitude [rad]
+ % Either "constant" / "triangular" / "sinusoidal"
+ args.Ry_type char {mustBeMember(args.Ry_type,{'constant', 'triangular', 'sinusoidal'})} = 'constant'
+ % Amplitude [rad]
args.Ry_amplitude (1,1) double {mustBeNumeric} = 0
- % Period of the displacement [s]
+ % Period of the displacement [s]
args.Ry_period (1,1) double {mustBeNumeric, mustBePositive} = 1
- % Either "constant" / "rotating"
- args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating', 'rotating-not-filtered'})} = 'constant'
- % Initial angle [rad]
+ % Either "constant" / "rotating"
+ args.Rz_type char {mustBeMember(args.Rz_type,{'constant', 'rotating', 'rotating-not-filtered'})} = 'constant'
+ % Initial angle [rad]
args.Rz_amplitude (1,1) double {mustBeNumeric} = 0
- % Period of the rotating [s]
+ % Period of the rotating [s]
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1
- % For now, only constant is implemented
- args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
- % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
+ % For now, only constant is implemented
+ args.Dh_type char {mustBeMember(args.Dh_type,{'constant'})} = 'constant'
+ % Initial position [m,m,m,rad,rad,rad] of the top platform (Pitch-Roll-Yaw Euler angles)
args.Dh_pos (6,1) double {mustBeNumeric} = zeros(6, 1), ...
- % For now, only constant is implemented
- args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
- % Initial position of the two masses
- args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
- % For now, only constant is implemented
- args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
- % Initial position [m,m,m,rad,rad,rad] of the top platform
+ % For now, only constant is implemented
+ args.Rm_type char {mustBeMember(args.Rm_type,{'constant'})} = 'constant'
+ % Initial position of the two masses
+ args.Rm_pos (2,1) double {mustBeNumeric} = [0; pi]
+ % For now, only constant is implemented
+ args.Dn_type char {mustBeMember(args.Dn_type,{'constant'})} = 'constant'
+ % Initial position [m,m,m,rad,rad,rad] of the top platform
args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1)
-end
+end
Initialize Parameters
-
%% Set Sampling Time +%% Set Sampling Time Ts = args.Ts; Tmax = args.Tmax; -%% Low Pass Filter to filter out the references -s = zpk('s'); -w0 = 2*pi*10; +%% Low Pass Filter to filter out the references +s = zpk('s'); +w0 = 2*pi*10; xi = 1; -H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2); +H_lpf = 1/(1 + 2*xi/w0*s + s^2/w0^2);
-
Translation Stage
-
+
+
-Translation Stage
+
-
%% Translation stage - Dy -t = 0:Ts:Tmax; % Time Vector [s] +%% 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 +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 + % 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 + 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);
-
Tilt Stage
-
+
+
-Tilt Stage
+
-
%% Tilt Stage - Ry -t = 0:Ts:Tmax; % Time Vector [s] +%% 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 + % 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 = 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);
-
Spindle
-
+
+
-Spindle
+
-
%% Spindle - Rz -t = 0:Ts:Tmax; % Time Vector [s] +%% Spindle - Rz +t = 0:Ts:Tmax; % Time Vector [s] Rz = zeros(length(t), 1); Rzd = zeros(length(t), 1); Rzdd = zeros(length(t), 1); -switch args.Rz_type - case 'constant' - Rz(:) = args.Rz_amplitude; - Rzd(:) = 0; - Rzdd(:) = 0; - case 'rotating-not-filtered' - Rz(:) = 2*pi/args.Rz_period*t; +switch args.Rz_type + case 'constant' + Rz(:) = args.Rz_amplitude; + Rzd(:) = 0; + Rzdd(:) = 0; + case 'rotating-not-filtered' + Rz(:) = 2*pi/args.Rz_period*t; - % The signal is filtered out - Rz(:) = 2*pi/args.Rz_period*t; - Rzd(:) = 2*pi/args.Rz_period; - Rzdd(:) = 0; + % The signal is filtered out + Rz(:) = 2*pi/args.Rz_period*t; + Rzd(:) = 2*pi/args.Rz_period; + Rzdd(:) = 0; - % We add the angle offset - Rz = Rz + args.Rz_amplitude; + % We add the angle offset + Rz = Rz + args.Rz_amplitude; - case 'rotating' - Rz(:) = 2*pi/args.Rz_period*t; + case 'rotating' + Rz(:) = 2*pi/args.Rz_period*t; - % The signal is filtered out + % The signal is filtered out Rz = lsim(H_lpf, Rz, t); - Rzd = lsim(H_lpf*s, Rz, t); - Rzdd = lsim(H_lpf*s^2, Rz, t); + Rzd = lsim(H_lpf*s, Rz, t); + Rzdd = lsim(H_lpf*s^2, Rz, t); - % We add the angle offset - Rz = Rz + args.Rz_amplitude; - otherwise - warning('Rz_type is not set correctly'); -end + % We add the angle offset + Rz = Rz + args.Rz_amplitude; + otherwise + warning('Rz_type is not set correctly'); +end -Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd); +Rz = struct('time', t, 'signals', struct('values', Rz), 'deriv', Rzd, 'dderiv', Rzdd);
-
Micro Hexapod
-
+
+
@@ -2493,29 +2500,29 @@ Dhl = struct('time', t, 'signals', struct('values', Dhl));
-Micro Hexapod
+
-
%% Micro-Hexapod +%% Micro-Hexapod t = [0, Ts]; Dh = zeros(length(t), 6); Dhl = zeros(length(t), 6); -switch args.Dh_type - case 'constant' +switch args.Dh_type + case 'constant' Dh = [args.Dh_pos, args.Dh_pos]; - load('mat/stages.mat', 'micro_hexapod'); + load('mat/stages.mat', 'micro_hexapod'); AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)]; @@ -2466,24 +2473,24 @@ switch args.Dh_type ty = args.Dh_pos(5); tz = args.Dh_pos(6); - ARB = [cos(tz) -sin(tz) 0; + ARB = [cos(tz) -sin(tz) 0; sin(tz) cos(tz) 0; - 0 0 1]*... + 0 0 1]*... [ cos(ty) 0 sin(ty); 0 1 0; - -sin(ty) 0 cos(ty)]*... + -sin(ty) 0 cos(ty)]*... [1 0 0; - 0 cos(tx) -sin(tx); + 0 cos(tx) -sin(tx); 0 sin(tx) cos(tx)]; - [~, Dhl] = inverseKinematics(micro_hexapod, 'AP', AP, 'ARB', ARB); + [~, Dhl] = inverseKinematics(micro_hexapod, 'AP', AP, 'ARB', ARB); Dhl = [Dhl, Dhl]; - otherwise - warning('Dh_type is not set correctly'); -end + otherwise + warning('Dh_type is not set correctly'); +end -Dh = struct('time', t, 'signals', struct('values', Dh)); -Dhl = struct('time', t, 'signals', struct('values', Dhl)); +Dh = struct('time', t, 'signals', struct('values', Dh)); +Dhl = struct('time', t, 'signals', struct('values', Dhl));
Axis Compensation
-
%% Axis Compensation - Rm +%% Axis Compensation - Rm t = [0, Ts]; Rm = [args.Rm_pos, args.Rm_pos]; -Rm = struct('time', t, 'signals', struct('values', Rm)); +Rm = struct('time', t, 'signals', struct('values', Rm));
-
Nano Hexapod
-
+
+
-Nano Hexapod
+
-
%% Nano-Hexapod +%% Nano-Hexapod t = [0, Ts]; Dn = zeros(length(t), 6); -switch args.Dn_type - case 'constant' +switch args.Dn_type + case 'constant' Dn = [args.Dn_pos, args.Dn_pos]; - load('mat/stages.mat', 'nano_hexapod'); + load('mat/stages.mat', 'nano_hexapod'); AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)]; @@ -2523,36 +2530,36 @@ switch args.Dn_type ty = args.Dn_pos(5); tz = args.Dn_pos(6); - ARB = [cos(tz) -sin(tz) 0; + ARB = [cos(tz) -sin(tz) 0; sin(tz) cos(tz) 0; - 0 0 1]*... + 0 0 1]*... [ cos(ty) 0 sin(ty); 0 1 0; - -sin(ty) 0 cos(ty)]*... + -sin(ty) 0 cos(ty)]*... [1 0 0; - 0 cos(tx) -sin(tx); + 0 cos(tx) -sin(tx); 0 sin(tx) cos(tx)]; - [~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB); + [~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB); Dnl = [Dnl, Dnl]; - otherwise - warning('Dn_type is not set correctly'); -end + otherwise + warning('Dn_type is not set correctly'); +end -Dn = struct('time', t, 'signals', struct('values', Dn)); -Dnl = struct('time', t, 'signals', struct('values', Dnl)); +Dn = struct('time', t, 'signals', struct('values', Dn)); +Dnl = struct('time', t, 'signals', struct('values', Dnl));
-
Save
-
+
+
@@ -2567,43 +2574,43 @@ end
-Save
+
-
%% Save
- save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'args', 'Ts');
-end
+ %% Save
+ save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'args', 'Ts');
+end
-
Function Declaration and Documentation
-
+
+
-Function Declaration and Documentation
+
-
function [] = initializeDisturbances(args) -% initializeDisturbances - Initialize the disturbances -% -% Syntax: [] = initializeDisturbances(args) -% -% Inputs: -% - args - +function [] = initializeDisturbances(args) +% initializeDisturbances - Initialize the disturbances +% +% Syntax: [] = initializeDisturbances(args) +% +% Inputs: +% - args -
-
Optional Parameters
-
+
+
@@ -2614,7 +2621,7 @@ end
@@ -2647,49 +2654,49 @@ Ts = 1/Fs; % Sampling Time [s]
@@ -2699,21 +2706,21 @@ end
@@ -2723,21 +2730,21 @@ end
@@ -2747,21 +2754,21 @@ end
@@ -2782,22 +2789,22 @@ Fd = u;
-Optional Parameters
+arguments
- % Global parameter to enable or disable the disturbances
- args.enable logical {mustBeNumericOrLogical} = true
- % Ground Motion - X direction
- args.Dwx logical {mustBeNumericOrLogical} = true
- % Ground Motion - Y direction
- args.Dwy logical {mustBeNumericOrLogical} = true
- % Ground Motion - Z direction
- args.Dwz logical {mustBeNumericOrLogical} = true
- % Translation Stage - X direction
- args.Fty_x logical {mustBeNumericOrLogical} = true
- % Translation Stage - Z direction
- args.Fty_z logical {mustBeNumericOrLogical} = true
- % Spindle - Z direction
- args.Frz_z logical {mustBeNumericOrLogical} = true
-end
+ % Global parameter to enable or disable the disturbances
+ args.enable logical {mustBeNumericOrLogical} = true
+ % Ground Motion - X direction
+ args.Dwx logical {mustBeNumericOrLogical} = true
+ % Ground Motion - Y direction
+ args.Dwy logical {mustBeNumericOrLogical} = true
+ % Ground Motion - Z direction
+ args.Dwz logical {mustBeNumericOrLogical} = true
+ % Translation Stage - X direction
+ args.Fty_x logical {mustBeNumericOrLogical} = true
+ % Translation Stage - Z direction
+ args.Fty_z logical {mustBeNumericOrLogical} = true
+ % Spindle - Z direction
+ args.Frz_z logical {mustBeNumericOrLogical} = true
+end
Load Data
-
@@ -2630,13 +2637,13 @@ We remove the first frequency point that usually is very large.
We define some parameters that will be used in the algorithm.
load('./mat/dist_psd.mat', 'dist_f');
+load('./mat/dist_psd.mat', 'dist_f');
-
Fs = 2*dist_f.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz] -N = 2*length(dist_f.f); % Number of Samples match the one of the wanted PSD -T0 = N/Fs; % Signal Duration [s] -df = 1/T0; % Frequency resolution of the DFT [Hz] - % Also equal to (dist_f.f(2)-dist_f.f(1)) -t = linspace(0, T0, N+1)'; % Time Vector [s] -Ts = 1/Fs; % Sampling Time [s] +Fs = 2*dist_f.f(end); % Sampling Frequency of data is twice the maximum frequency of the PSD vector [Hz] +N = 2*length(dist_f.f); % Number of Samples match the one of the wanted PSD +T0 = N/Fs; % Signal Duration [s] +df = 1/T0; % Frequency resolution of the DFT [Hz] + % Also equal to (dist_f.f(2)-dist_f.f(1)) +t = linspace(0, T0, N+1)'; % Time Vector [s] +Ts = 1/Fs; % Sampling Time [s]
phi = dist_f.psd_gm; -C = zeros(N/2,1); -for i = 1:N/2 - C(i) = sqrt(phi(i)*df); -end +C = zeros(N/2,1); +for i = 1:N/2 + C(i) = sqrt(phi(i)*df); +end
-
if args.Dwx && args.enable - rng(111); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - Dwx = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m] -else +if args.Dwx && args.enable + rng(111); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + Dwx = N/sqrt(2)*ifft(Cx); % Ground Motion - x direction [m] +else Dwx = zeros(length(t), 1); -end +end
-
if args.Dwy && args.enable - rng(112); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - Dwy = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m] -else +if args.Dwy && args.enable + rng(112); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + Dwy = N/sqrt(2)*ifft(Cx); % Ground Motion - y direction [m] +else Dwy = zeros(length(t), 1); -end +end
-
if args.Dwy && args.enable - rng(113); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - Dwz = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m] -else +if args.Dwy && args.enable + rng(113); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + Dwz = N/sqrt(2)*ifft(Cx); % Ground Motion - z direction [m] +else Dwz = zeros(length(t), 1); -end +end
Translation Stage - X direction
-
if args.Fty_x && args.enable - phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate - C = zeros(N/2,1); - for i = 1:N/2 - C(i) = sqrt(phi(i)*df); - end - rng(121); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty x [N] +if args.Fty_x && args.enable + phi = dist_f.psd_ty; % TODO - we take here the vertical direction which is wrong but approximate + C = zeros(N/2,1); + for i = 1:N/2 + C(i) = sqrt(phi(i)*df); + end + rng(121); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty x [N] Fty_x = u; -else +else Fty_x = zeros(length(t), 1); -end +end
Translation Stage - Z direction
-
if args.Fty_z && args.enable +if args.Fty_z && args.enable phi = dist_f.psd_ty; - C = zeros(N/2,1); - for i = 1:N/2 - C(i) = sqrt(phi(i)*df); - end - rng(122); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty z [N] + C = zeros(N/2,1); + for i = 1:N/2 + C(i) = sqrt(phi(i)*df); + end + rng(122); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + u = N/sqrt(2)*ifft(Cx); % Disturbance Force Ty z [N] Fty_z = u; -else +else Fty_z = zeros(length(t), 1); -end +end
Spindle - Z direction
-
if args.Frz_z && args.enable +if args.Frz_z && args.enable phi = dist_f.psd_rz; - C = zeros(N/2,1); - for i = 1:N/2 - C(i) = sqrt(phi(i)*df); - end - rng(131); - theta = 2*pi*rand(N/2,1); % Generate random phase [rad] - Cx = [0 ; C.*complex(cos(theta),sin(theta))]; - Cx = [Cx; flipud(conj(Cx(2:end)))];; - u = N/sqrt(2)*ifft(Cx); % Disturbance Force Rz z [N] + C = zeros(N/2,1); + for i = 1:N/2 + C(i) = sqrt(phi(i)*df); + end + rng(131); + theta = 2*pi*rand(N/2,1); % Generate random phase [rad] + Cx = [0 ; C.*complex(cos(theta),sin(theta))]; + Cx = [Cx; flipud(conj(Cx(2:end)))];; + u = N/sqrt(2)*ifft(Cx); % Disturbance Force Rz z [N] Frz_z = u; -else +else Frz_z = zeros(length(t), 1); -end +end
Set initial value to zero
-
Dwx = Dwx - Dwx(1); -Dwy = Dwy - Dwy(1); -Dwz = Dwz - Dwz(1); -Fty_x = Fty_x - Fty_x(1); -Fty_z = Fty_z - Fty_z(1); -Frz_z = Frz_z - Frz_z(1); +Dwx = Dwx - Dwx(1); +Dwy = Dwy - Dwy(1); +Dwz = Dwz - Dwz(1); +Fty_x = Fty_x - Fty_x(1); +Fty_z = Fty_z - Fty_z(1); +Frz_z = Frz_z - Frz_z(1);
-
Save
-
+
+
@@ -2812,41 +2819,41 @@ Frz_z = Frz_z - Frz_z(1);
-Save
+
-
save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't', 'args');
+save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't', 'args');
-
Function Declaration and Documentation
-
+
+
-Function Declaration and Documentation
+
-
function [] = initializePosError(args) -% initializePosError - Initialize the position errors -% -% Syntax: [] = initializePosError(args) -% -% Inputs: -% - args - +function [] = initializePosError(args) +% initializePosError - Initialize the position errors +% +% Syntax: [] = initializePosError(args) +% +% Inputs: +% - args -
-
Optional Parameters
-
+
+
-Optional Parameters
+arguments
- args.error logical {mustBeNumericOrLogical} = false
- args.Dy (1,1) double {mustBeNumeric} = 0 % [m]
- args.Ry (1,1) double {mustBeNumeric} = 0 % [m]
- args.Rz (1,1) double {mustBeNumeric} = 0 % [m]
-end
+ args.error logical {mustBeNumericOrLogical} = false
+ args.Dy (1,1) double {mustBeNumeric} = 0 % [m]
+ args.Ry (1,1) double {mustBeNumeric} = 0 % [m]
+ args.Rz (1,1) double {mustBeNumeric} = 0 % [m]
+end
-
Structure initialization
-
+Stewart Platform - Simscape Model
@@ -36,159 +36,150 @@
-
+
@@ -2883,11 +2890,11 @@ pos_error.Rz = args.Rz;
-Structure initialization
+
First, we initialize the pos_error structure.
pos_error structure.
Type
-
if args.error +if args.error pos_error.type = 1; -else +else pos_error.type = 0; -end +end
-
Save
-
+
@@ -2961,7 +2968,7 @@ end
+
@@ -2902,24 +2909,24 @@ pos_error.Rz = args.Rz;
@@ -2933,27 +2940,27 @@ end
Save
+
-
save('./mat/pos_error.mat', 'pos_error');
+save('./mat/pos_error.mat', 'pos_error');
-
function [geophone] = initializeZAxisGeophone(args) +function [geophone] = initializeZAxisGeophone(args) arguments - args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg] - args.freq (1,1) double {mustBeNumeric, mustBePositive} = 1 % [Hz] - end + args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg] + args.freq (1,1) double {mustBeNumeric, mustBePositive} = 1 % [Hz] + end - %% + %% geophone.m = args.mass; - %% The Stiffness is set to have the damping resonance frequency - geophone.k = geophone.m * (2*pi*args.freq)^2; + %% The Stiffness is set to have the damping resonance frequency + geophone.k = geophone.m * (2*pi*args.freq)^2; - %% We set the damping value to have critical damping - geophone.c = 2*sqrt(geophone.m * geophone.k); + %% We set the damping value to have critical damping + geophone.c = 2*sqrt(geophone.m * geophone.k); - %% Save - save('./mat/geophone_z_axis.mat', 'geophone'); -end + %% Save + save('./mat/geophone_z_axis.mat', 'geophone'); +end
-
function [accelerometer] = initializeZAxisAccelerometer(args) +function [accelerometer] = initializeZAxisAccelerometer(args) arguments - args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg] - args.freq (1,1) double {mustBeNumeric, mustBePositive} = 5e3 % [Hz] - end + args.mass (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 % [kg] + args.freq (1,1) double {mustBeNumeric, mustBePositive} = 5e3 % [Hz] + end - %% + %% accelerometer.m = args.mass; - %% The Stiffness is set to have the damping resonance frequency - accelerometer.k = accelerometer.m * (2*pi*args.freq)^2; + %% The Stiffness is set to have the damping resonance frequency + accelerometer.k = accelerometer.m * (2*pi*args.freq)^2; - %% We set the damping value to have critical damping - accelerometer.c = 2*sqrt(accelerometer.m * accelerometer.k); + %% We set the damping value to have critical damping + accelerometer.c = 2*sqrt(accelerometer.m * accelerometer.k); - %% Gain correction of the accelerometer to have a unity gain until the resonance - accelerometer.gain = -accelerometer.k/accelerometer.m; + %% Gain correction of the accelerometer to have a unity gain until the resonance + accelerometer.gain = -accelerometer.k/accelerometer.m; - %% Save - save('./mat/accelerometer_z_axis.mat', 'accelerometer'); -end + %% Save + save('./mat/accelerometer_z_axis.mat', 'accelerometer'); +end
-
diff --git a/docs/stewart_platform.html b/docs/stewart_platform.html
index 65a8a51..9faff69 100644
--- a/docs/stewart_platform.html
+++ b/docs/stewart_platform.html
@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
-
+
Created: 2020-07-31 ven. 17:58
+Created: 2020-11-03 mar. 09:45
- 1.
initializeStewartPlatform: Initialize the Stewart Platform structure - 2.
initializeFramesPositions: Initialize the positions of frames {A}, {B}, {F} and {M} - 3.
generateGeneralConfiguration: Generate a Very General Configuration - 4.
computeJointsPose: Compute the Pose of the Joints-
-
- Documentation -
- Function description -
- Check the
stewartstructure elements
+ - Documentation +
- Function description +
- Check the
stewartstructure elements - Compute the position of the Joints
- Compute the strut length and orientation
- Compute the orientation of the Joints -
- Populate the
stewartstructure
+ - Populate the
stewartstructure
- 5.
initializeStewartPose: Determine the initial stroke in each leg to have the wanted pose - 6.
initializeCylindricalPlatforms: Initialize the geometry of the Fixed and Mobile Platforms - 7.
initializeCylindricalStruts: Define the inertia of cylindrical struts - 8.
initializeStrutDynamics: Add Stiffness and Damping properties of each strut
- - 9.
initializeAmplifiedStrutDynamics: Add Stiffness and Damping properties of each strut for an amplified piezoelectric actuator + - 9.
initializeJointDynamics: Add Stiffness and Damping properties for spherical joints -
- - 10.
initializeJointDynamics: Add Stiffness and Damping properties for spherical joints -
- - 11.
initializeInertialSensor: Initialize the inertial sensor in each strut + - 10.
initializeInertialSensor: Initialize the inertial sensor in each strut
- - 12.
displayArchitecture: 3D plot of the Stewart platform architecture + - 11.
displayArchitecture: 3D plot of the Stewart platform architecture-
-
- Function description -
- Optional Parameters -
- Check the
stewartstructure elements
+ - Function description +
- Optional Parameters +
- Check the
stewartstructure elements - Figure Creation, Frames and Homogeneous transformations
- Fixed Base elements
- Mobile Platform elements
- Legs -
- 12.1. Figure parameters -
- 12.2. Subplots +
- 11.1. Figure parameters +
- 11.2. Subplots
- - 13.
describeStewartPlatform: Display some text describing the current defined Stewart Platform + - 12.
describeStewartPlatform: Display some text describing the current defined Stewart Platform
- - 14.
generateCubicConfiguration: Generate a Cubic Configuration + - 13.
generateCubicConfiguration: Generate a Cubic Configuration-
-
- Function description -
- Documentation -
- Optional Parameters -
- Check the
stewartstructure elements
+ - Function description +
- Documentation +
- Optional Parameters +
- Check the
stewartstructure elements - Position of the Cube -
- Compute the pose -
- Populate the
stewartstructure
+ - Compute the pose +
- Populate the
stewartstructure
- - 15.
computeJacobian: Compute the Jacobian Matrix + - 14.
computeJacobian: Compute the Jacobian Matrix
- - 16.
inverseKinematics: Compute Inverse Kinematics + - 15.
inverseKinematics: Compute Inverse Kinematics
- - 17.
forwardKinematicsApprox: Compute the Approximate Forward Kinematics + - 16.
forwardKinematicsApprox: Compute the Approximate Forward Kinematics
@@ -274,11 +265,11 @@ This Matlab function is accessible
-
Documentation
-
+
+
Documentation
+
-
+
-
-
Function description
-
+
+
Function description
+
-
function [stewart] = initializeStewartPlatform() -% initializeStewartPlatform - Initialize the stewart structure -% -% Syntax: [stewart] = initializeStewartPlatform(args) -% -% Outputs: -% - stewart - A structure with the following sub-structures: -% - platform_F - -% - platform_M - -% - joints_F - -% - joints_M - -% - struts_F - -% - struts_M - -% - actuators - -% - geometry - -% - properties - +