#+TITLE: Subsystems used for the Simscape Models :DRAWER: #+STARTUP: overview #+PROPERTY: header-args:matlab :session *MATLAB* #+PROPERTY: header-args:matlab+ :comments org #+PROPERTY: header-args:matlab+ :results none #+PROPERTY: header-args:matlab+ :exports both #+PROPERTY: header-args:matlab+ :eval no-export #+PROPERTY: header-args:matlab+ :output-dir figs #+PROPERTY: header-args:matlab+ :tangle no #+PROPERTY: header-args:matlab+ :mkdirp yes #+PROPERTY: header-args:shell :eval no-export #+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/org/}{config.tex}") #+PROPERTY: header-args:latex+ :imagemagick t :fit yes #+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 #+PROPERTY: header-args:latex+ :imoutoptions -quality 100 #+PROPERTY: header-args:latex+ :results raw replace :buffer no #+PROPERTY: header-args:latex+ :eval no-export #+PROPERTY: header-args:latex+ :exports both #+PROPERTY: header-args:latex+ :mkdirp yes #+PROPERTY: header-args:latex+ :output-dir figs :END: * Introduction :ignore: The full Simscape Model is represented in Figure [[fig:simscape_picture]]. #+name: fig:simscape_picture #+caption: Screenshot of the Multi-Body Model representation [[file:figs/images/simscape_picture.png]] This model is divided into multiple subsystems that are independent. These subsystems are saved in separate files and imported in the main file using a block balled "subsystem reference". Each stage is configured (geometry, mass properties, dynamic properties ...) using one function. These functions are defined below. * Simscape Configuration :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeSimscapeConfiguration.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializeSimscapeConfiguration(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments args.gravity logical {mustBeNumericOrLogical} = true end #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab conf_simscape = struct(); #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab if args.gravity conf_simscape.type = 1; else conf_simscape.type = 2; end #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab save('./mat/conf_simscape.mat', 'conf_simscape'); #+end_src * Logging Configuration :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeLoggingConfiguration.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializeLoggingConfiguration(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments args.log char {mustBeMember(args.log,{'none', 'all', 'forces'})} = 'none' args.Ts (1,1) double {mustBeNumeric, mustBePositive} = 1e-3 end #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab conf_log = struct(); #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.log case 'none' conf_log.type = 0; case 'all' conf_log.type = 1; case 'forces' conf_log.type = 2; end #+end_src ** Sampling Time :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab conf_log.Ts = args.Ts; #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab save('./mat/conf_log.mat', 'conf_log'); #+end_src * Ground :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeGround.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The model of the Ground is composed of: - A *Cartesian* joint that is used to simulation the ground motion - A solid that represents the ground on which the granite is located #+name: fig:simscape_model_ground #+attr_org: :width 800 #+caption: Simscape model for the Ground [[file:figs/images/simscape_model_ground.png]] #+name: fig:simscape_picture_ground #+attr_org: :width 800 #+caption: Simscape picture for the Ground [[file:figs/images/simscape_picture_ground.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [ground] = initializeGround(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =granite= structure. #+begin_src matlab ground = struct(); #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' ground.type = 0; case 'rigid' ground.type = 1; end #+end_src ** Ground Solid properties :PROPERTIES: :UNNUMBERED: t :END: We set the shape and density of the ground solid element. #+begin_src matlab ground.shape = [2, 2, 0.5]; % [m] ground.density = 2800; % [kg/m3] #+end_src ** Rotation Point :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab ground.rot_point = args.rot_point; #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =ground= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'ground', '-append'); #+end_src * Granite :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeGranite.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the granite is composed of: - A cartesian joint such that the granite can vibrations along x, y and z axis - A solid The output =sample_pos= corresponds to the impact point of the X-ray. #+name: fig:simscape_model_granite #+attr_org: :width 800 #+caption: Simscape model for the Granite [[file:figs/images/simscape_model_granite.png]] #+name: fig:simscape_picture_granite #+attr_org: :width 800 #+caption: Simscape picture for the Granite [[file:figs/images/simscape_picture_granite.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [granite] = initializeGranite(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =granite= structure. #+begin_src matlab granite = struct(); #+end_src ** Add Granite Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' granite.type = 0; case 'rigid' granite.type = 1; case 'flexible' granite.type = 2; case 'modal-analysis' granite.type = 3; case 'init' granite.type = 4; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: Properties of the Material and link to the geometry of the granite. #+begin_src matlab granite.density = args.density; % [kg/m3] granite.STEP = './STEPS/granite/granite.STEP'; #+end_src Z-offset for the initial position of the sample with respect to the granite top surface. #+begin_src matlab granite.sample_pos = 0.8; % [m] #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab granite.K = args.K; % [N/m] granite.C = args.C; % [N/(m/s)] #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =granite= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'granite', '-append'); #+end_src * Translation Stage :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeTy.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the Translation stage consist of: - One rigid body for the fixed part of the translation stage - One rigid body for the moving part of the translation stage - Four 6-DOF Joints that only have some rigidity in the X and Z directions. The rigidity in rotation comes from the fact that we use multiple joints that are located at different points - One 6-DOF joint that represent the Actuator. It is used to impose the motion in the Y direction - One 6-DOF joint to inject force disturbance in the X and Z directions #+name: fig:simscape_model_ty #+ATTR_ORG: :width 800 #+caption: Simscape model for the Translation Stage [[file:figs/images/simscape_model_ty.png]] #+name: fig:simscape_picture_ty #+attr_org: :width 800 #+caption: Simscape picture for the Translation Stage [[file:figs/images/simscape_picture_ty.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [ty] = initializeTy(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' args.Foffset logical {mustBeNumericOrLogical} = false end #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =ty= structure. #+begin_src matlab ty = struct(); #+end_src ** Add Translation Stage Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' ty.type = 0; case 'rigid' ty.type = 1; case 'flexible' ty.type = 2; case 'modal-analysis' ty.type = 3; case 'init' ty.type = 4; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: Define the density of the materials as well as the geometry (STEP files). #+begin_src matlab % 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'; % 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_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 - 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 Rotor Part ty.rotor.density = 5400; % [kg/m3] ty.rotor.STEP = './STEPS/ty/Ty_Motor_Rotor.STEP'; #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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)] #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =ty= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'ty', '-append'); #+end_src * Tilt Stage :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeRy.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the Tilt stage is composed of: - Two solid bodies for the two part of the stage - *Four* 6-DOF joints to model the flexibility of the stage. These joints are virtually located along the rotation axis and are connecting the two solid bodies. These joints have some translation stiffness in the u-v-w directions aligned with the joint. The stiffness in rotation between the two solids is due to the fact that the 4 joints are connecting the two solids are different locations - A Bushing Joint used for the Actuator. The Ry motion is imposed by the input. #+name: fig:simscape_model_ry #+attr_org: :width 800 #+caption: Simscape model for the Tilt Stage [[file:figs/images/simscape_model_ry.png]] #+name: fig:simscape_picture_ry #+attr_org: :width 800 #+caption: Simscape picture for the Tilt Stage [[file:figs/images/simscape_picture_ry.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [ry] = initializeRy(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments 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_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =ry= structure. #+begin_src matlab ry = struct(); #+end_src ** Add Tilt Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' ry.type = 0; case 'rigid' ry.type = 1; case 'flexible' ry.type = 2; case 'modal-analysis' ry.type = 3; case 'init' ry.type = 4; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: Properties of the Material and link to the geometry of the Tilt stage. #+begin_src matlab % 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 - 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'; #+end_src Z-Offset so that the center of rotation matches the sample center; #+begin_src matlab ry.z_offset = 0.58178; % [m] #+end_src #+begin_src matlab ry.Ry_init = args.Ry_init; % [rad] #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab ry.K = [3.8e8; 4e8; 3.8e8; 1.2e8; 6e4; 1.2e8]; ry.C = [1e5; 1e5; 1e5; 3e4; 1e3; 3e4]; #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =ry= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'ry', '-append'); #+end_src * Spindle :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeRz.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the Spindle is composed of: - Two rigid bodies: the stator and the rotor - A Bushing Joint that is used both as the actuator (the Rz motion is imposed by the input) and as the force perturbation in the Z direction. - The Bushing joint has some flexibility in the X-Y-Z directions as well as in Rx and Ry rotations #+name: fig:simscape_model_rz #+attr_org: :width 800 #+caption: Simscape model for the Spindle [[file:figs/images/simscape_model_rz.png]] #+name: fig:simscape_picture_rz #+attr_org: :width 800 #+caption: Simscape picture for the Spindle [[file:figs/images/simscape_picture_rz.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [rz] = initializeRz(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible', 'modal-analysis', 'init'})} = 'flexible' args.Foffset logical {mustBeNumericOrLogical} = false end #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =rz= structure. #+begin_src matlab rz = struct(); #+end_src ** Add Spindle Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' rz.type = 0; case 'rigid' rz.type = 1; case 'flexible' rz.type = 2; case 'modal-analysis' rz.type = 3; case 'init' rz.type = 4; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: Properties of the Material and link to the geometry of the spindle. #+begin_src matlab % 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 - Stator rz.stator.density = 7800; % [kg/m3] rz.stator.STEP = './STEPS/rz/Spindle_Stator.STEP'; #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab rz.K = [7e8; 7e8; 2e9; 1e7; 1e7; 1e7]; rz.C = [4e4; 4e4; 7e4; 1e4; 1e4; 1e4]; #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =rz= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'rz', '-append'); #+end_src * Micro Hexapod :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeMicroHexapod.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: #+name: fig:simscape_model_micro_hexapod #+attr_org: :width 800 #+caption: Simscape model for the Micro-Hexapod [[file:figs/images/simscape_model_micro_hexapod.png]] #+name: fig:simscape_picture_micro_hexapod #+attr_org: :width 800 #+caption: Simscape picture for the Micro-Hexapod [[file:figs/images/simscape_picture_micro_hexapod.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [micro_hexapod] = initializeMicroHexapod(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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.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.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.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.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.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 #+end_src ** Function content :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab micro_hexapod = initializeFramesPositions('H', args.H, 'MO_B', args.MO_B); micro_hexapod = generateGeneralConfiguration(micro_hexapod, 'FH', args.FH, 'FR', args.FR, 'FTh', args.FTh, 'MH', args.MH, 'MR', args.MR, 'MTh', args.MTh); micro_hexapod = computeJointsPose(micro_hexapod); micro_hexapod = initializeStrutDynamics(micro_hexapod, 'Ki', args.Ki, 'Ci', args.Ci); micro_hexapod = initializeCylindricalPlatforms(micro_hexapod, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr); micro_hexapod = initializeCylindricalStruts(micro_hexapod, 'Fsm', args.Fsm, 'Fsh', args.Fsh, 'Fsr', args.Fsr, 'Msm', args.Msm, 'Msh', args.Msh, 'Msr', args.Msr); micro_hexapod = computeJacobian(micro_hexapod); [Li, dLi] = inverseKinematics(micro_hexapod, 'AP', args.AP, 'ARB', args.ARB); micro_hexapod.Li = Li; micro_hexapod.dLi = dLi; #+end_src Equilibrium position of the each joint. #+begin_src matlab if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') load('mat/Foffset.mat', 'Fhm'); micro_hexapod.dLeq = -Fhm'./args.Ki; else micro_hexapod.dLeq = zeros(6,1); end #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' micro_hexapod.type = 0; case 'rigid' micro_hexapod.type = 1; case 'flexible' micro_hexapod.type = 2; case 'modal-analysis' micro_hexapod.type = 3; case 'init' micro_hexapod.type = 4; case 'compliance' micro_hexapod.type = 5; end #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =micro_hexapod= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'micro_hexapod', '-append'); #+end_src * Center of gravity compensation :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeAxisc.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the Center of gravity compensator is composed of: - One main solid that is connected to two other solids (the masses to position of center of mass) through two revolute joints - The angle of both revolute joints is set by the input #+name: fig:simscape_model_axisc #+attr_org: :width 800 #+caption: Simscape model for the Center of Mass compensation system [[file:figs/images/simscape_model_axisc.png]] #+name: fig:simscape_picture_axisc #+attr_org: :width 800 #+caption: Simscape picture for the Center of Mass compensation system [[file:figs/images/simscape_picture_axisc.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [axisc] = initializeAxisc(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments args.type char {mustBeMember(args.type,{'none', 'rigid', 'flexible'})} = 'flexible' end #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =axisc= structure. #+begin_src matlab axisc = struct(); #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' axisc.type = 0; case 'rigid' axisc.type = 1; case 'flexible' axisc.type = 2; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: Properties of the Material and link to the geometry files. #+begin_src matlab % 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'; % 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'; #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =axisc= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'axisc', '-append'); #+end_src * Mirror :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeMirror.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: 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 #+name: fig:simscape_model_mirror #+attr_org: :width 800 #+caption: Simscape model for the Mirror [[file:figs/images/simscape_model_mirror.png]] #+name: fig:simscape_picture_mirror #+attr_org: :width 800 #+caption: Simscape picture for the Mirror [[file:figs/images/simscape_picture_mirror.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializeMirror(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =mirror= structure. #+begin_src matlab mirror = struct(); #+end_src ** Add Mirror Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' mirror.type = 0; case 'rigid' mirror.type = 1; case 'flexible' mirror.type = 2; end #+end_src ** Mass and Inertia :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab mirror.mass = args.mass; mirror.freq = args.freq; #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab mirror.K = zeros(6,1); 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); #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab mirror.Deq = zeros(6,1); #+end_src ** Geometry :PROPERTIES: :UNNUMBERED: t :END: We define the geometrical values. #+begin_src matlab mirror.h = 0.05; % Height of the mirror [m] mirror.thickness = 0.025; % Thickness of the plate supporting the sample [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] % 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 mirror.rad = 0.180; % radius of the mirror (at the bottom surface) [m] #+end_src #+begin_src matlab mirror.cone_length = mirror.rad*tand(args.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point #+end_src Now we define the Shape of the mirror. We first start with the internal part. #+begin_src matlab mirror.shape = [... mirror.support_rad+5e-3 mirror.h-mirror.thickness mirror.hole_rad mirror.h-mirror.thickness; ... mirror.hole_rad 0; ... mirror.rad 0 ... ]; #+end_src Then, we define the reflective used part of the mirror. #+begin_src matlab 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 #+end_src Finally, we close the shape. #+begin_src matlab mirror.shape = [mirror.shape; mirror.support_rad+5e-3 mirror.h]; #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =mirror= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'mirror', '-append'); #+end_src * Nano Hexapod :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeNanoHexapod.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: #+name: fig:simscape_model_nano_hexapod #+attr_org: :width 800 #+caption: Simscape model for the Nano Hexapod [[file:figs/images/simscape_model_nano_hexapod.png]] #+name: fig:simscape_picture_nano_hexapod #+attr_org: :width 800 #+caption: Simscape picture for the Nano Hexapod [[file:figs/images/simscape_picture_nano_hexapod.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [nano_hexapod] = initializeNanoHexapod(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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'})} = 'piezo' args.k (1,1) double {mustBeNumeric} = -1 args.c (1,1) double {mustBeNumeric} = -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.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.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.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.AP (3,1) double {mustBeNumeric} = zeros(3,1) args.ARB (3,3) double {mustBeNumeric} = eye(3) % 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 #+end_src ** Function content :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab nano_hexapod = initializeFramesPositions('H', args.H, 'MO_B', args.MO_B); nano_hexapod = generateGeneralConfiguration(nano_hexapod, 'FH', args.FH, 'FR', args.FR, 'FTh', args.FTh, 'MH', args.MH, 'MR', args.MR, 'MTh', args.MTh); nano_hexapod = computeJointsPose(nano_hexapod); #+end_src #+begin_src matlab if args.k > 0 && args.c > 0 nano_hexapod = initializeStrutDynamics(nano_hexapod, 'Ki', args.k*ones(6,1), 'Ci', args.c*ones(6,1)); elseif args.k > 0 nano_hexapod = initializeStrutDynamics(nano_hexapod, 'Ki', args.k*ones(6,1), 'Ci', 1.5*sqrt(args.k)*ones(6,1)); elseif strcmp(args.actuator, 'piezo') nano_hexapod = initializeStrutDynamics(nano_hexapod, 'Ki', 1e7*ones(6,1), 'Ci', 1e2*ones(6,1)); elseif strcmp(args.actuator, 'lorentz') nano_hexapod = initializeStrutDynamics(nano_hexapod, 'Ki', 1e4*ones(6,1), 'Ci', 1e2*ones(6,1)); else error('args.actuator should be piezo or lorentz'); end #+end_src #+begin_src matlab nano_hexapod = initializeCylindricalPlatforms(nano_hexapod, 'Fpm', args.Fpm, 'Fph', args.Fph, 'Fpr', args.Fpr, 'Mpm', args.Mpm, 'Mph', args.Mph, 'Mpr', args.Mpr); nano_hexapod = initializeCylindricalStruts(nano_hexapod, 'Fsm', args.Fsm, 'Fsh', args.Fsh, 'Fsr', args.Fsr, 'Msm', args.Msm, 'Msh', args.Msh, 'Msr', args.Msr); nano_hexapod = computeJacobian(nano_hexapod); [Li, dLi] = inverseKinematics(nano_hexapod, 'AP', args.AP, 'ARB', args.ARB); nano_hexapod.Li = Li; nano_hexapod.dLi = dLi; #+end_src Equilibrium position of the each joint. #+begin_src matlab if args.Foffset && ~strcmp(args.type, 'none') && ~strcmp(args.type, 'rigid') && ~strcmp(args.type, 'init') load('mat/Foffset.mat', 'Fnm'); nano_hexapod.dLeq = -Fnm'./nano_hexapod.Ki; else nano_hexapod.dLeq = args.dLeq; end #+end_src ** Add Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' nano_hexapod.type = 0; case 'rigid' nano_hexapod.type = 1; case 'flexible' nano_hexapod.type = 2; case 'init' nano_hexapod.type = 4; end #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab save('./mat/stages.mat', 'nano_hexapod', '-append'); #+end_src * Sample :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeSample.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Simscape Model :PROPERTIES: :UNNUMBERED: t :END: The Simscape model of the sample environment is composed of: - A rigid transform that can be used to translate the sample (position offset) - A cartesian joint to add some flexibility to the sample environment mount - A solid that represent the sample - An input is added to apply some external forces and torques at the center of the sample environment. This could be the case for cable forces for instance. #+name: fig:simscape_model_sample #+attr_org: :width 800 #+caption: Simscape model for the Sample [[file:figs/images/simscape_model_sample.png]] #+name: fig:simscape_picture_sample #+attr_org: :width 800 #+caption: Simscape picture for the Sample [[file:figs/images/simscape_picture_sample.png]] ** Function description :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [sample] = initializeSample(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =sample= structure. #+begin_src matlab sample = struct(); #+end_src ** Add Sample Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'none' sample.type = 0; case 'rigid' sample.type = 1; case 'flexible' sample.type = 2; case 'init' sample.type = 3; end #+end_src ** Material and Geometry :PROPERTIES: :UNNUMBERED: t :END: We define the geometrical parameters of the sample as well as its mass and position. #+begin_src matlab sample.radius = args.radius; % [m] sample.height = args.height; % [m] sample.mass = args.mass; % [kg] sample.offset = args.offset; % [m] #+end_src ** Compute the Inertia :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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]; #+end_src ** Stiffness and Damping properties :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab sample.K = zeros(6, 1); sample.C = zeros(6, 1); #+end_src Translation Stiffness and Damping: #+begin_src matlab 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)] #+end_src Rotational Stiffness and Damping: #+begin_src matlab 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)] #+end_src ** Equilibrium position of the each joint. :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =sample= structure is saved. #+begin_src matlab save('./mat/stages.mat', 'sample', '-append'); #+end_src * Initialize Controller :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeController.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Function Declaration and Documentation :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializeController(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =controller= structure. #+begin_src matlab controller = struct(); #+end_src ** Controller Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab switch args.type case 'open-loop' controller.type = 1; controller.name = 'Open-Loop'; case 'dvf' controller.type = 2; controller.name = 'Decentralized Direct Velocity Feedback'; case 'iff' controller.type = 3; controller.name = 'Decentralized Integral Force Feedback'; case 'hac-dvf' controller.type = 4; 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.type = 6; 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.type = 8; controller.name = 'HAC-IFF'; case 'stabilizing' controller.type = 9; controller.name = 'Stabilizing Controller'; end #+end_src ** Save the Structure :PROPERTIES: :UNNUMBERED: t :END: The =controller= structure is saved. #+begin_src matlab save('./mat/controller.mat', 'controller'); #+end_src * Generate Reference Signals :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeReferences.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> ** Function Declaration and Documentation :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [ref] = initializeReferences(args) #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab arguments % 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] args.Dy_amplitude (1,1) double {mustBeNumeric} = 0 % 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] args.Ry_amplitude (1,1) double {mustBeNumeric} = 0 % 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] args.Rz_amplitude (1,1) double {mustBeNumeric} = 0 % 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) 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 args.Dn_pos (6,1) double {mustBeNumeric} = zeros(6,1) end #+end_src ** Initialize Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Set Sampling Time Ts = args.Ts; Tmax = args.Tmax; %% 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); #+end_src ** Translation Stage :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Translation stage - Dy t = 0:Ts:Tmax; % Time Vector [s] Dy = zeros(length(t), 1); Dyd = zeros(length(t), 1); Dydd = zeros(length(t), 1); switch args.Dy_type case 'constant' Dy(:) = args.Dy_amplitude; Dyd(:) = 0; Dydd(:) = 0; case 'triangular' % This is done to unsure that we start with no displacement Dy_raw = args.Dy_amplitude*sawtooth(2*pi*t/args.Dy_period,1/2); i0 = find(t>=args.Dy_period/4,1); Dy(1:end-i0+1) = Dy_raw(i0:end); Dy(end-i0+2:end) = Dy_raw(end); % we fix the last value % The signal is filtered out Dy = lsim(H_lpf, Dy, t); Dyd = lsim(H_lpf*s, Dy, t); Dydd = lsim(H_lpf*s^2, Dy, t); case 'sinusoidal' Dy(:) = args.Dy_amplitude*sin(2*pi/args.Dy_period*t); Dyd = args.Dy_amplitude*2*pi/args.Dy_period*cos(2*pi/args.Dy_period*t); Dydd = -args.Dy_amplitude*(2*pi/args.Dy_period)^2*sin(2*pi/args.Dy_period*t); otherwise warning('Dy_type is not set correctly'); end Dy = struct('time', t, 'signals', struct('values', Dy), 'deriv', Dyd, 'dderiv', Dydd); #+end_src ** Tilt Stage :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Tilt Stage - Ry t = 0:Ts:Tmax; % Time Vector [s] Ry = zeros(length(t), 1); Ryd = zeros(length(t), 1); Rydd = zeros(length(t), 1); switch args.Ry_type case 'constant' Ry(:) = args.Ry_amplitude; Ryd(:) = 0; Rydd(:) = 0; case 'triangular' Ry_raw = args.Ry_amplitude*sawtooth(2*pi*t/args.Ry_period,1/2); i0 = find(t>=args.Ry_period/4,1); Ry(1:end-i0+1) = Ry_raw(i0:end); Ry(end-i0+2:end) = Ry_raw(end); % we fix the last value % The signal is filtered out Ry = lsim(H_lpf, Ry, t); Ryd = lsim(H_lpf*s, Ry, t); Rydd = lsim(H_lpf*s^2, Ry, t); case 'sinusoidal' Ry(:) = args.Ry_amplitude*sin(2*pi/args.Ry_period*t); 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); #+end_src ** Spindle :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% 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; % 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; case 'rotating' Rz(:) = 2*pi/args.Rz_period*t; % 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); % 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); #+end_src ** Micro Hexapod :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Micro-Hexapod t = [0, Ts]; Dh = zeros(length(t), 6); Dhl = zeros(length(t), 6); switch args.Dh_type case 'constant' Dh = [args.Dh_pos, args.Dh_pos]; load('mat/stages.mat', 'micro_hexapod'); AP = [args.Dh_pos(1) ; args.Dh_pos(2) ; args.Dh_pos(3)]; tx = args.Dh_pos(4); ty = args.Dh_pos(5); tz = args.Dh_pos(6); ARB = [cos(tz) -sin(tz) 0; sin(tz) cos(tz) 0; 0 0 1]*... [ cos(ty) 0 sin(ty); 0 1 0; -sin(ty) 0 cos(ty)]*... [1 0 0; 0 cos(tx) -sin(tx); 0 sin(tx) cos(tx)]; [~, Dhl] = inverseKinematics(micro_hexapod, 'AP', AP, 'ARB', ARB); Dhl = [Dhl, Dhl]; 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)); #+end_src ** Axis Compensation :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Axis Compensation - Rm t = [0, Ts]; Rm = [args.Rm_pos, args.Rm_pos]; Rm = struct('time', t, 'signals', struct('values', Rm)); #+end_src ** Nano Hexapod :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Nano-Hexapod t = [0, Ts]; Dn = zeros(length(t), 6); switch args.Dn_type case 'constant' Dn = [args.Dn_pos, args.Dn_pos]; load('mat/stages.mat', 'nano_hexapod'); AP = [args.Dn_pos(1) ; args.Dn_pos(2) ; args.Dn_pos(3)]; tx = args.Dn_pos(4); ty = args.Dn_pos(5); tz = args.Dn_pos(6); ARB = [cos(tz) -sin(tz) 0; sin(tz) cos(tz) 0; 0 0 1]*... [ cos(ty) 0 sin(ty); 0 1 0; -sin(ty) 0 cos(ty)]*... [1 0 0; 0 cos(tx) -sin(tx); 0 sin(tx) cos(tx)]; [~, Dnl] = inverseKinematics(nano_hexapod, 'AP', AP, 'ARB', ARB); Dnl = [Dnl, Dnl]; 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)); #+end_src ** Save :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab %% Save save('./mat/nass_references.mat', 'Dy', 'Ry', 'Rz', 'Dh', 'Dhl', 'Rm', 'Dn', 'Dnl', 'args', 'Ts'); end #+end_src * Initialize Disturbances :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeDisturbances.m :header-args:matlab+: :comments none :mkdirp yes :header-args:matlab+: :eval no :results none :END: <> ** Function Declaration and Documentation :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializeDisturbances(args) % initializeDisturbances - Initialize the disturbances % % Syntax: [] = initializeDisturbances(args) % % Inputs: % - args - #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Load Data :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab load('./mat/dist_psd.mat', 'dist_f'); #+end_src We remove the first frequency point that usually is very large. #+begin_src matlab :exports none dist_f.f = dist_f.f(2:end); dist_f.psd_gm = dist_f.psd_gm(2:end); dist_f.psd_ty = dist_f.psd_ty(2:end); dist_f.psd_rz = dist_f.psd_rz(2:end); #+end_src ** Parameters :PROPERTIES: :UNNUMBERED: t :END: We define some parameters that will be used in the algorithm. #+begin_src matlab 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] #+end_src ** Ground Motion :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab phi = dist_f.psd_gm; C = zeros(N/2,1); for i = 1:N/2 C(i) = sqrt(phi(i)*df); end #+end_src #+begin_src matlab 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_src #+begin_src matlab 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_src #+begin_src matlab 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_src ** Translation Stage - X direction :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 Fty_x = zeros(length(t), 1); end #+end_src ** Translation Stage - Z direction :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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] Fty_z = u; else Fty_z = zeros(length(t), 1); end #+end_src ** Spindle - Z direction :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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] Frz_z = u; else Frz_z = zeros(length(t), 1); end #+end_src ** Direct Forces :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab u = zeros(length(t), 6); Fd = u; #+end_src ** Set initial value to zero :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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); #+end_src ** Save :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab save('./mat/nass_disturbances.mat', 'Dwx', 'Dwy', 'Dwz', 'Fty_x', 'Fty_z', 'Frz_z', 'Fd', 'Ts', 't', 'args'); #+end_src * Initialize Position Errors :PROPERTIES: :header-args:matlab+: :tangle ../src/initializePosError.m :header-args:matlab+: :comments none :mkdirp yes :header-args:matlab+: :eval no :results none :END: <> ** Function Declaration and Documentation :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab function [] = initializePosError(args) % initializePosError - Initialize the position errors % % Syntax: [] = initializePosError(args) % % Inputs: % - args - #+end_src ** Optional Parameters :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab 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 #+end_src ** Structure initialization :PROPERTIES: :UNNUMBERED: t :END: First, we initialize the =pos_error= structure. #+begin_src matlab pos_error = struct(); #+end_src ** Type :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab if args.error pos_error.type = 1; else pos_error.type = 0; end #+end_src ** Position Errors :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab pos_error.Dy = args.Dy; pos_error.Ry = args.Ry; pos_error.Rz = args.Rz; #+end_src ** Save :PROPERTIES: :UNNUMBERED: t :END: #+begin_src matlab save('./mat/pos_error.mat', 'pos_error'); #+end_src * Z-Axis Geophone :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeZAxisGeophone.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> #+begin_src matlab 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 %% geophone.m = args.mass; %% 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); %% Save save('./mat/geophone_z_axis.mat', 'geophone'); end #+end_src * Z-Axis Accelerometer :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeZAxisAccelerometer.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> #+begin_src matlab 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 %% accelerometer.m = args.mass; %% 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); %% 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 #+end_src * Old functions :noexport: ** Micro Hexapod :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeMicroHexapodOld.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> #+begin_src matlab function [micro_hexapod] = initializeMicroHexapod(args) arguments args.rigid logical {mustBeNumericOrLogical} = false args.AP (3,1) double {mustBeNumeric} = zeros(3,1) args.ARB (3,3) double {mustBeNumeric} = eye(3) end %% Stewart Object micro_hexapod = struct(); micro_hexapod.h = 350; % Total height of the platform [mm] micro_hexapod.jacobian = 270; % Distance from the top of the mobile platform to the Jacobian point [mm] %% Bottom Plate - Mechanical Design BP = struct(); BP.rad.int = 110; % Internal Radius [mm] BP.rad.ext = 207.5; % External Radius [mm] BP.thickness = 26; % Thickness [mm] BP.leg.rad = 175.5; % Radius where the legs articulations are positionned [mm] BP.leg.ang = 9.5; % Angle Offset [deg] BP.density = 8000; % Density of the material [kg/m^3] BP.color = [0.6 0.6 0.6]; % Color [rgb] BP.shape = [BP.rad.int BP.thickness; BP.rad.int 0; BP.rad.ext 0; BP.rad.ext BP.thickness]; %% Top Plate - Mechanical Design TP = struct(); TP.rad.int = 82; % Internal Radius [mm] TP.rad.ext = 150; % Internal Radius [mm] TP.thickness = 26; % Thickness [mm] TP.leg.rad = 118; % Radius where the legs articulations are positionned [mm] TP.leg.ang = 12.1; % Angle Offset [deg] TP.density = 8000; % Density of the material [kg/m^3] TP.color = [0.6 0.6 0.6]; % Color [rgb] TP.shape = [TP.rad.int TP.thickness; TP.rad.int 0; TP.rad.ext 0; TP.rad.ext TP.thickness]; %% Struts Leg = struct(); Leg.stroke = 10e-3; % Maximum Stroke of each leg [m] if args.rigid Leg.k.ax = 1e12; % Stiffness of each leg [N/m] else Leg.k.ax = 2e7; % Stiffness of each leg [N/m] end Leg.ksi.ax = 0.1; % Modal damping ksi = 1/2*c/sqrt(km) [] Leg.rad.bottom = 25; % Radius of the cylinder of the bottom part [mm] Leg.rad.top = 17; % Radius of the cylinder of the top part [mm] Leg.density = 8000; % Density of the material [kg/m^3] Leg.color.bottom = [0.5 0.5 0.5]; % Color [rgb] Leg.color.top = [0.5 0.5 0.5]; % Color [rgb] Leg.sphere.bottom = Leg.rad.bottom; % Size of the sphere at the end of the leg [mm] Leg.sphere.top = Leg.rad.top; % Size of the sphere at the end of the leg [mm] Leg.m = TP.density*((pi*(TP.rad.ext/1000)^2)*(TP.thickness/1000)-(pi*(TP.rad.int/1000^2))*(TP.thickness/1000))/6; % TODO [kg] Leg = updateDamping(Leg); %% Sphere SP = struct(); SP.height.bottom = 27; % [mm] SP.height.top = 27; % [mm] SP.density.bottom = 8000; % [kg/m^3] SP.density.top = 8000; % [kg/m^3] SP.color.bottom = [0.6 0.6 0.6]; % [rgb] SP.color.top = [0.6 0.6 0.6]; % [rgb] SP.k.ax = 0; % [N*m/deg] SP.ksi.ax = 10; SP.thickness.bottom = SP.height.bottom-Leg.sphere.bottom; % [mm] SP.thickness.top = SP.height.top-Leg.sphere.top; % [mm] SP.rad.bottom = Leg.sphere.bottom; % [mm] SP.rad.top = Leg.sphere.top; % [mm] SP.m = SP.density.bottom*2*pi*((SP.rad.bottom*1e-3)^2)*(SP.height.bottom*1e-3); % TODO [kg] SP = updateDamping(SP); %% Leg.support.bottom = [0 SP.thickness.bottom; 0 0; SP.rad.bottom 0; SP.rad.bottom SP.height.bottom]; Leg.support.top = [0 SP.thickness.top; 0 0; SP.rad.top 0; SP.rad.top SP.height.top]; %% micro_hexapod.BP = BP; micro_hexapod.TP = TP; micro_hexapod.Leg = Leg; micro_hexapod.SP = SP; %% micro_hexapod = initializeParameters(micro_hexapod); %% Setup equilibrium position of each leg micro_hexapod.L0 = inverseKinematicsHexapod(micro_hexapod, args.AP, args.ARB); %% Save save('./mat/stages.mat', 'micro_hexapod', '-append'); %% function [element] = updateDamping(element) field = fieldnames(element.k); for i = 1:length(field) element.c.(field{i}) = 2*element.ksi.(field{i})*sqrt(element.k.(field{i})*element.m); end end %% function [stewart] = initializeParameters(stewart) %% Connection points on base and top plate w.r.t. World frame at the center of the base plate stewart.pos_base = zeros(6, 3); stewart.pos_top = zeros(6, 3); alpha_b = stewart.BP.leg.ang*pi/180; % angle de décalage par rapport à 120 deg (pour positionner les supports bases) alpha_t = stewart.TP.leg.ang*pi/180; % +- offset angle from 120 degree spacing on top height = (stewart.h-stewart.BP.thickness-stewart.TP.thickness-stewart.Leg.sphere.bottom-stewart.Leg.sphere.top-stewart.SP.thickness.bottom-stewart.SP.thickness.top)*0.001; % TODO radius_b = stewart.BP.leg.rad*0.001; % rayon emplacement support base radius_t = stewart.TP.leg.rad*0.001; % top radius in meters for i = 1:3 % base points angle_m_b = (2*pi/3)* (i-1) - alpha_b; angle_p_b = (2*pi/3)* (i-1) + alpha_b; stewart.pos_base(2*i-1,:) = [radius_b*cos(angle_m_b), radius_b*sin(angle_m_b), 0.0]; stewart.pos_base(2*i,:) = [radius_b*cos(angle_p_b), radius_b*sin(angle_p_b), 0.0]; % top points % Top points are 60 degrees offset angle_m_t = (2*pi/3)* (i-1) - alpha_t + 2*pi/6; angle_p_t = (2*pi/3)* (i-1) + alpha_t + 2*pi/6; stewart.pos_top(2*i-1,:) = [radius_t*cos(angle_m_t), radius_t*sin(angle_m_t), height]; stewart.pos_top(2*i,:) = [radius_t*cos(angle_p_t), radius_t*sin(angle_p_t), height]; end % permute pos_top points so that legs are end points of base and top points stewart.pos_top = [stewart.pos_top(6,:); stewart.pos_top(1:5,:)]; %6th point on top connects to 1st on bottom stewart.pos_top_tranform = stewart.pos_top - height*[zeros(6, 2),ones(6, 1)]; %% leg vectors legs = stewart.pos_top - stewart.pos_base; leg_length = zeros(6, 1); leg_vectors = zeros(6, 3); for i = 1:6 leg_length(i) = norm(legs(i,:)); leg_vectors(i,:) = legs(i,:) / leg_length(i); end stewart.Leg.lenght = 1000*leg_length(1)/1.5; stewart.Leg.shape.bot = [0 0; ... stewart.Leg.rad.bottom 0; ... stewart.Leg.rad.bottom stewart.Leg.lenght; ... stewart.Leg.rad.top stewart.Leg.lenght; ... stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ... 0 0.2*stewart.Leg.lenght]; %% Calculate revolute and cylindrical axes rev1 = zeros(6, 3); rev2 = zeros(6, 3); cyl1 = zeros(6, 3); for i = 1:6 rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]); rev1(i,:) = rev1(i,:) / norm(rev1(i,:)); rev2(i,:) = - cross(rev1(i,:), leg_vectors(i,:)); rev2(i,:) = rev2(i,:) / norm(rev2(i,:)); cyl1(i,:) = leg_vectors(i,:); end %% Coordinate systems stewart.lower_leg = struct('rotation', eye(3)); stewart.upper_leg = struct('rotation', eye(3)); for i = 1:6 stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; end %% Position Matrix stewart.M_pos_base = stewart.pos_base + (height+(stewart.TP.thickness+stewart.Leg.sphere.top+stewart.SP.thickness.top+stewart.jacobian)*1e-3)*[zeros(6, 2),ones(6, 1)]; %% Compute Jacobian Matrix aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; stewart.J = getJacobianMatrix(leg_vectors', aa'); end %% function J = getJacobianMatrix(RM, M_pos_base) % RM: [3x6] unit vector of each leg in the fixed frame % M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame J = zeros(6); J(:, 1:3) = RM'; J(:, 4:6) = cross(M_pos_base, RM)'; end end #+end_src ** Cedrat Actuator :PROPERTIES: :header-args:matlab+: :tangle ../src/initializeCedratPiezo.m :header-args:matlab+: :comments none :mkdirp yes :eval no :END: <> #+begin_src matlab function [cedrat] = initializeCedratPiezo() %% Stewart Object cedrat = struct(); cedrat.k = 10e7; % Linear Stiffness of each "blade" [N/m] cedrat.ka = 10e7; % Linear Stiffness of the stack [N/m] cedrat.c = 0.1*sqrt(1*cedrat.k); % [N/(m/s)] cedrat.ca = 0.1*sqrt(1*cedrat.ka); % [N/(m/s)] cedrat.L = 80; % Total Width of the Actuator[mm] cedrat.H = 45; % Total Height of the Actuator [mm] cedrat.L2 = sqrt((cedrat.L/2)^2 + (cedrat.H/2)^2); % Length of the elipsoidal sections [mm] cedrat.alpha = 180/pi*atan2(cedrat.L/2, cedrat.H/2); % [deg] %% Save save('./mat/stages.mat', 'cedrat', '-append'); end #+end_src