Add few comments on simscape multibody

.SimulinkProject/Root.type.Files/identification.type.File.xml

@@ -1,2 +1,2 @@
 <?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="hac_lac" Type="Relative" />
+<Info />

.SimulinkProject/Root.type.Files/identification.type.File/1.type.DIR_SIGNIFIER.xml

@@ -1,2 +1,2 @@
 <?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="control" Type="Relative" />
+<Info />

.SimulinkProject/Root.type.ProjectPath/0ae7cdd8-73c1-44a2-bc58-56fac4006009.type.Reference.xml

@@ -1,2 +0,0 @@
-<?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="nass_library" Type="Relative" />

.SimulinkProject/Root.type.ProjectPath/1809d361-dc3d-4fcb-8b9b-833180e2f6fc.type.Reference.xml

@@ -1,2 +0,0 @@
-<?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="active_damping" Type="Relative" />

.SimulinkProject/Root.type.ProjectPath/7e53593c-166d-46eb-8350-609f08763240.type.Reference.xml

@@ -1,2 +0,0 @@
-<?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="analysis" Type="Relative" />

.SimulinkProject/Root.type.ProjectPath/a3b2491b-7b63-4e77-b2a4-97d4753c1df9.type.Reference.xml

@@ -1,2 +0,0 @@
-<?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="initialize" Type="Relative" />

.SimulinkProject/Root.type.ProjectPath/d03bc20c-98e3-4ed4-a859-51e1f5a18637.type.Reference.xml

@@ -1,2 +0,0 @@
-<?xml version='1.0' encoding='UTF-8'?>
-<Info Ref="demonstration" Type="Relative" />

identification/index.org

@@ -41,6 +41,21 @@
 #+PROPERTY: header-args:latex+ :output-dir figs
 :END:
 
+* Introduction                                                       :ignore:
+The goal here is to make an identification of the micro-station in order to compare the model with the measurements on the real micro-station.
+
+In order to do so:
+- Decide where to virtually excite the station and where to measure its motion
+- Extract transfer functions from the excitation forces to the measured motion
+- Compare those transfer functions with the modal analysis
+
+For the excitation, we can choose the same excitation points as the one used for the modal test.
+For the measurement points, we can choose the Center of Mass of each solid body.
+The center of mass of each solid body is not easily defined using Simscape.
+Indeed, we can define the center of mass of any solid body but not of multiple solid bodies. However, one solid body is composed of multiple STEP files.
+One solution could be to use one STEP file for one solid body.
+However, the position of the center of mass can be exported using simulink and then defined on Simscape.
+
 * ZIP file containing the data and matlab files                      :ignore:
 #+begin_src bash :exports none :results none
   if [ matlab/identification_micro_station.m -nt data/identification_micro_station.zip ]; then
@@ -56,9 +71,25 @@
   All the files (data and Matlab scripts) are accessible [[file:data/identification_micro_station.zip][here]].
 #+end_note
 
+* Matlab Init                                               :noexport:ignore:
+#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
+  <<matlab-dir>>
+#+end_src
+
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+end_src
 
 * Identification of the micro-station
+#+begin_src matlab
+  simulinkproject('../');
+#+end_src
+
+#+begin_src matlab
+  open sim_micro_station_id.slx
+#+end_src
 
 * Plot the obtained transfer functions
 
 * Compare with the modal measurements
+* Modal Identification of the micro station

index.org

@@ -64,12 +64,10 @@ The project can be opened using the =simulinkproject= function:
 When the project opens, a startup script is ran.
 The startup script is defined below and is exported to the =project_startup.m= script.
 #+begin_src matlab :eval no :tangle src/project_startup.m
-  %%
   freqs = logspace(-1, 3, 1000);
   save_fig = false;
   save('./mat/config.mat', 'freqs', 'save_fig');
 
-  %%
   project = simulinkproject;
   projectRoot = project.RootFolder;
 
@@ -89,11 +87,107 @@ When the project closes, it runs the =project_shutdown.m= script defined below.
 
 The project also permits to automatically add defined folder to the path when the project is opened.
 
-* Notes
+* Simscape Model
-Step files are exported from SolidWorks and imported into Simscape.
+A [[https://.mathworks.com/products/simscape.html][simscape]] model permits to model multi-physics systems.
-Each step file is then considered as a solid body.
-Inertia and mass matrices are computed from the density of the material and the geometry as defined by the step file.
 
+[[https://mathworks.com/products/simmechanics.html][Simscape Multibody]] permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
+
+** Solid bodies
+Each solid body is represented by a [[https://mathworks.com/help/physmod/sm/ref/solid.html][solid block]].
+The geometry of the solid body can be imported using a =step= file. The properties of the solid body such as its mass, center of mass and moment of inertia can be derived from its density and its geometry as defined by the =step= file. They also can be set by hand.
+
+** Frames
+Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
+
+They can be defined from the solid body geometry, or using the [[https://mathworks.com/help/physmod/sm/ref/rigidtransform.html][rigid transform block]].
+
+** Joints
+Solid Bodies are connected with joints (between frames of the two solid bodies).
+
+There are various types of joints that are all described [[https://mathworks.com/help/physmod/sm/ug/joints.html][here]].
+
+#+name: tab:joint_dof
+#+caption: Degrees of freedom associated with each joint
+| Joint Block       | Translational DOFs | Rotational DOFs |
+|-------------------+--------------------+-----------------|
+| 6-DOF             |                  3 |               3 |
+| Bearing           |                  1 |               3 |
+| Bushing           |                  3 |               3 |
+| Cartesian         |                  3 |               0 |
+| Constant Velocity |                  0 |               2 |
+| Cylindrical       |                  1 |               1 |
+| Gimbal            |                  0 |               3 |
+| Leadscrew         |        1 (coupled) |     1 (coupled) |
+| Pin Slot          |                  1 |               1 |
+| Planar            |                  2 |               1 |
+| Prismatic         |                  1 |               0 |
+| Rectangular       |                  2 |               0 |
+| Revolute          |                  0 |               1 |
+| Spherical         |                  1 |               3 |
+| Telescoping       |                  1 |               3 |
+| Universal         |                  0 |               2 |
+| Weld              |                  0 |               0 |
+
+Joint blocks are assortments of joint primitives:
+- *Prismatic*: allows translation along a single standard axis: =Px=, =Py=, =Pz=
+- *Revolute*: allows rotation about a single standard axis: =Rx=, =Ry=, =Rz=
+- *Spherical*: allow rotation about any 3D axis: =S=
+- *Lead Screw*: allows coupled rotation and translation on a standard axis: =LSz=
+- *Constant Velocity*: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: =CV=
+
+#+name: tab:joint_primitive
+#+caption: Joint primitives for each joint type
+| Joint Block       | Px | Py | Pz | Rx | Ry | Rz | S | CV | LSz |
+|-------------------+----+----+----+----+----+----+---+----+-----|
+| 6-DOF             | x  | x  | x  |    |    |    | x |    |     |
+| Bearing           |    |    | x  | x  | x  | x  |   |    |     |
+| Bushing           | x  | x  | x  | x  | x  | x  |   |    |     |
+| Cartesian         | x  | x  | x  |    |    |    |   |    |     |
+| Constant Velocity |    |    |    |    |    |    |   | x  |     |
+| Cylindrical       |    |    | x  |    |    | x  |   |    |     |
+| Gimbal            |    |    |    | x  | x  | x  |   |    |     |
+| Leadscrew         |    |    |    |    |    |    |   |    | x   |
+| Pin Slot          | x  |    |    |    |    | x  |   |    |     |
+| Planar            | x  | x  |    |    |    | x  |   |    |     |
+| Prismatic         |    |    | x  |    |    |    |   |    |     |
+| Rectangular       | x  | x  |    |    |    |    |   |    |     |
+| Revolute          |    |    |    |    |    | x  |   |    |     |
+| Spherical         |    |    |    |    |    |    | x |    |     |
+| Telescoping       |    |    | x  |    |    |    | x |    |     |
+| Universal         |    |    |    | x  | x  |    |   |    |     |
+| Weld              |    |    |    |    |    |    |   |    |     |
+
+For each of the joint primitive, we can specify the dynamical properties:
+- The *spring stiffness*: either linear or rotational one
+- The *damping coefficient*
+
+For the actuation, we can either specify the motion or the force:
+- the force applied in the corresponding DOF is provided by the input
+- the motion is provided by the input
+
+A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
+
+Composite Force/Torque sensing:
+- Constraint force
+- Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.
+
+** Measurements
+A transform sensor block measures the spatial relationship between two frames: the base =B= and the follower =F=.
+
+It can give the rotational and translational position, velocity and acceleration.
+
+The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is =world=.
+
+If we want to simulate an *inertial sensor*, we just have to choose =B= to be the =world= frame.
+
+*Force sensors* are included in the joints blocks.
+
+** Excitation
+We can apply *external forces* to the model by using an [[https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html][external force and torque block]].
+
+Internal force, acting reciprocally between base and following origins is implemented using the [[https://mathworks.com/help/physmod/sm/ref/internalforce.html][internal force block]] even though it is usually included in one joint block.
+
+* Notes
 ** Simscape files for identification
 |------------------------+----+----+----+------+------|
 | Simscape Name          | Ty | Ry | Rz | Hexa | NASS |