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Update initialization

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Thomas Dehaeze
2020-02-11 15:21:39 +01:00
parent e1cd9b0aa8
commit 2082bbd580
8 changed files with 64 additions and 26 deletions
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13
active-damping.org
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@@ -21,7 +21,6 @@
:END:
* Introduction :ignore:
The following decentralized active damping techniques are briefly studied:
- Inertial Control (proportional feedback of the absolute velocity): Section [[sec:active_damping_inertial]]
- Integral Force Feedback: Section [[sec:active_damping_iff]]
@@ -54,7 +53,8 @@ The following decentralized active damping techniques are briefly studied:
** Identification of the Dynamics
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -283,10 +283,12 @@ The root locus is shown in figure [[fig:root_locus_inertial_rot_stiffness]] and
** Identification of the Dynamics with perfect Joints
We first initialize the Stewart platform without joint stiffness.
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeAmplifiedStrutDynamics(stewart);
stewart = initializeJointDynamics(stewart, 'disable', true);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
@@ -316,7 +318,7 @@ And we identify the dynamics from force actuators to force sensors.
The transfer function from actuator forces to force sensors is shown in Figure [[fig:iff_plant_coupling]].
#+begin_src matlab :exports none
freqs = logspace(1, 3, 1000);
freqs = logspace(1, 4, 1000);
figure;
@@ -514,7 +516,8 @@ The root locus is shown in figure [[fig:root_locus_iff_rot_stiffness]] and the o
** Identification of the Dynamics with perfect Joints
We first initialize the Stewart platform without joint stiffness.
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);

3
control-study.org
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@@ -69,7 +69,8 @@
** Initialize the Stewart platform
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);

43
cubic-configuration.org
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@@ -56,7 +56,8 @@ We create a cubic Stewart platform (figure [[fig:3d-cubic-stewart-aligned]]) in
The Jacobian matrix is estimated at the location of the center of the cube.
#+begin_src matlab
stewart = initializeFramesPositions('H', 100e-3, 'MO_B', -50e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 100e-3, 'MO_B', -50e-3);
stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
@@ -99,7 +100,8 @@ We create a cubic Stewart platform with center of the cube located at the center
The Jacobian matrix is not estimated at the location of the center of the cube.
#+begin_src matlab
stewart = initializeFramesPositions('H', 100e-3, 'MO_B', 0);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 100e-3, 'MO_B', 0);
stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
@@ -142,7 +144,8 @@ The Jacobian is estimated at the cube center.
[[file:./figs/3d-cubic-stewart-misaligned.png]]
#+begin_src matlab
stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -40e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 80e-3, 'MO_B', -40e-3);
stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
@@ -188,7 +191,8 @@ The center height of the Stewart platform is then at $z = \frac{175-75}{2} = 50$
The center of the cube from the top platform is at $z = 110 - 175 = -65$.
#+begin_src matlab
stewart = initializeFramesPositions('H', 80e-3, 'MO_B', -40e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 80e-3, 'MO_B', -40e-3);
stewart = generateCubicConfiguration(stewart, 'Hc', 100e-3, 'FOc', 50e-3, 'FHa', 0, 'MHb', 0);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart, 'Ki', ones(6,1));
@@ -237,7 +241,8 @@ This is possible, to do so:
It is possible to have small cube, but then to configuration is a little bit strange.
#+begin_src matlab
stewart = initializeFramesPositions('H', 100e-3, 'MO_B', 50e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 100e-3, 'MO_B', 50e-3);
FOc = stewart.H + stewart.MO_B(3);
Hc = 2*(stewart.H + stewart.MO_B(3));
stewart = generateCubicConfiguration(stewart, 'Hc', Hc, 'FOc', FOc, 'FHa', 10e-3, 'MHb', 10e-3);
@@ -368,7 +373,7 @@ This Matlab function is accessible [[file:src/generateCubicConfiguration.m][here
%
% Inputs:
% - stewart - A structure with the following fields
% - H [1x1] - Total height of the platform [m]
% - geometry.H [1x1] - Total height of the platform [m]
% - args - Can have the following fields:
% - Hc [1x1] - Height of the "useful" part of the cube [m]
% - FOc [1x1] - Height of the center of the cube with respect to {F} [m]
@@ -377,8 +382,8 @@ This Matlab function is accessible [[file:src/generateCubicConfiguration.m][here
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
% - Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
% - platform_F.Fa [3x6] - Its i'th column is the position vector of joint ai with respect to {F}
% - platform_M.Mb [3x6] - Its i'th column is the position vector of joint bi with respect to {M}
#+end_src
*** Documentation
@@ -403,6 +408,15 @@ This Matlab function is accessible [[file:src/generateCubicConfiguration.m][here
end
#+end_src
*** Check the =stewart= structure elements
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
assert(isfield(stewart.geometry, 'H'), 'stewart.geometry should have attribute H')
H = stewart.geometry.H;
#+end_src
*** Position of the Cube
:PROPERTIES:
:UNNUMBERED: t
@@ -437,8 +451,17 @@ We can compute the vector of each leg ${}^{C}\hat{\bm{s}}_{i}$ (unit vector from
We now which to compute the position of the joints $a_{i}$ and $b_{i}$.
#+begin_src matlab
stewart.Fa = CCf + [0; 0; args.FOc] + ((args.FHa-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
stewart.Mb = CCf + [0; 0; args.FOc-stewart.H] + ((stewart.H-args.MHb-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
Fa = CCf + [0; 0; args.FOc] + ((args.FHa-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
Mb = CCf + [0; 0; args.FOc-H] + ((H-args.MHb-(args.FOc-args.Hc/2))./CSi(3,:)).*CSi;
#+end_src
*** Populate the =stewart= structure
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
stewart.platform_F.Fa = Fa;
stewart.platform_M.Mb = Mb;
#+end_src
* Bibliography :ignore:

12
dynamics-study.org
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@@ -41,7 +41,8 @@
** test
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -129,7 +130,8 @@ Estimation of the transfer function from $\mathcal{\bm{F}}$ to $\mathcal{\bm{X}}
** Compare external forces and forces applied by the actuators
Initialization of the Stewart platform.
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -194,7 +196,8 @@ Seems quite similar.
** Comparison of the static transfer function and the Compliance matrix
Initialization of the Stewart platform.
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -257,7 +260,8 @@ The low frequency transfer function matrix from $\mathcal{\bm{F}}$ to $\mathcal{
** Transfer function from forces applied in the legs to the displacement of the legs
Initialization of the Stewart platform.
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);

9
identification.org
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@@ -65,7 +65,8 @@ An important difference from basic Simulink models is that the states in a physi
** Initialize the Stewart Platform
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -120,7 +121,8 @@ An important difference from basic Simulink models is that the states in a physi
** Initialize the Stewart Platform
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
@@ -354,7 +356,8 @@ Save the movie of the mode shape.
** Initialize the Stewart Platform
#+begin_src matlab
stewart = initializeFramesPositions();
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);

9
kinematic-study.org
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@@ -226,7 +226,8 @@ This will also gives us the range for which the approximate forward kinematic is
*** Stewart architecture definition
We first define some general Stewart architecture.
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStewartPose(stewart);
@@ -331,7 +332,8 @@ This is what is analyzed in this section.
** Stewart architecture definition
Let's first define the Stewart platform architecture that we want to study.
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStewartPose(stewart);
@@ -487,7 +489,8 @@ However, for small displacements, we can use the Jacobian as an approximate solu
** Stewart architecture definition
Let's first define the Stewart platform architecture that we want to study.
#+begin_src matlab
stewart = initializeFramesPositions('H', 90e-3, 'MO_B', 45e-3);
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStewartPose(stewart);

1
simscape-model.org
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@@ -131,6 +131,7 @@ There is two main types of inertial sensor that can be used to measure the absol
Both inertial sensors are described bellow.
* Other Elements
** Z-Axis Geophone
*** Working Principle
From the schematic of the Z-axis geophone shown in Figure [[fig:z_axis_geophone]], we can write the transfer function from the support velocity $\dot{w}$ to the relative velocity of the inertial mass $\dot{d}$:

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simulink/stewart_active_damping.slx
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