[WIP] Add Amplified piezo and Variant subsystems

This commit is contained in:
Thomas Dehaeze 2020-02-10 18:17:37 +01:00
parent 214cacf0e9
commit 2231aa53ce
14 changed files with 693 additions and 333 deletions

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@ -0,0 +1,39 @@
function [stewart] = initializeAmplifiedStrutDynamics(stewart, args)
% initializeAmplifiedStrutDynamics - Add Stiffness and Damping properties of each strut
%
% Syntax: [stewart] = initializeAmplifiedStrutDynamics(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Ksi [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Csi [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kdi [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - Cdi [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - Ki [6x1] - Total Stiffness of each strut [N/m]
% - Ci [6x1] - Total Damping of each strut [N/(m/s)]
% - Ksi [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Csi [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kdi [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - Cdi [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
arguments
stewart
args.Kdi (6,1) double {mustBeNumeric, mustBeNonnegative} = 5e6*ones(6,1)
args.Cdi (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ksi (6,1) double {mustBeNumeric, mustBeNonnegative} = 15e6*ones(6,1)
args.Csi (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
end
stewart.Ksi = args.Ksi;
stewart.Csi = args.Csi;
stewart.Kdi = args.Kdi;
stewart.Cdi = args.Cdi;
stewart.Ki = args.Ksi + args.Kdi;
stewart.Ci = args.Csi + args.Cdi;
stewart.actuator_type = 2;

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@ -21,3 +21,5 @@ end
stewart.Ki = args.Ki;
stewart.Ci = args.Ci;
stewart.actuator_type = 1;

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@ -288,6 +288,15 @@ Let's now move a little bit the top platform and re-display the configuration:
This Matlab function is accessible [[file:src/initializeFramesPositions.m][here]].
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
#+name: fig:stewart-frames-position
#+caption: Definition of the position of the frames
[[file:figs/stewart-frames-position.png]]
*** Function description
:PROPERTIES:
:UNNUMBERED: t
@ -311,15 +320,6 @@ This Matlab function is accessible [[file:src/initializeFramesPositions.m][here]
% - FO_A [3x1] - Position of {A} with respect to {F} [m]
#+end_src
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
#+name: fig:stewart-frames-position
#+caption: Definition of the position of the frames
[[file:figs/stewart-frames-position.png]]
*** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
@ -362,31 +362,6 @@ This Matlab function is accessible [[file:src/initializeFramesPositions.m][here]
This Matlab function is accessible [[file:src/generateGeneralConfiguration.m][here]].
*** Function description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
function [stewart] = generateGeneralConfiguration(stewart, args)
% generateGeneralConfiguration - Generate a Very General Configuration
%
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
%
% Inputs:
% - args - Can have the following fields:
% - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
% - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m]
% - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
% - MH [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
% - FR [1x1] - Radius of the position of the mobile joints in the X-Y [m]
% - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
%
% 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}
#+end_src
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
@ -442,6 +417,31 @@ The radius of the circles can be chosen as well as the angles where the joints a
#+RESULTS:
[[file:figs/stewart_bottom_plate.png]]
*** Function description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
function [stewart] = generateGeneralConfiguration(stewart, args)
% generateGeneralConfiguration - Generate a Very General Configuration
%
% Syntax: [stewart] = generateGeneralConfiguration(stewart, args)
%
% Inputs:
% - args - Can have the following fields:
% - FH [1x1] - Height of the position of the fixed joints with respect to the frame {F} [m]
% - FR [1x1] - Radius of the position of the fixed joints in the X-Y [m]
% - FTh [6x1] - Angles of the fixed joints in the X-Y plane with respect to the X axis [rad]
% - MH [1x1] - Height of the position of the mobile joints with respect to the frame {M} [m]
% - FR [1x1] - Radius of the position of the mobile joints in the X-Y [m]
% - MTh [6x1] - Angles of the mobile joints in the X-Y plane with respect to the X axis [rad]
%
% 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}
#+end_src
*** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
@ -483,6 +483,15 @@ The radius of the circles can be chosen as well as the angles where the joints a
This Matlab function is accessible [[file:src/computeJointsPose.m][here]].
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
#+name: fig:stewart-struts
#+caption: Position and orientation of the struts
[[file:figs/stewart-struts.png]]
*** Function description
:PROPERTIES:
:UNNUMBERED: t
@ -514,15 +523,6 @@ This Matlab function is accessible [[file:src/computeJointsPose.m][here]].
% - MRb [3x3x6] - The i'th 3x3 array is the rotation matrix to orientate the top of the i'th strut from {M}
#+end_src
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
#+name: fig:stewart-struts
#+caption: Position and orientation of the struts
[[file:figs/stewart-struts.png]]
*** Compute the position of the Joints
:PROPERTIES:
:UNNUMBERED: t
@ -805,6 +805,50 @@ This Matlab function is accessible [[file:src/initializeCylindricalStruts.m][her
This Matlab function is accessible [[file:src/initializeStrutDynamics.m][here]].
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
#+name: fig:piezoelectric_stack
#+attr_html: :width 500px
#+caption: Example of a piezoelectric stach actuator (PI)
[[file:figs/piezoelectric_stack.jpg]]
A simplistic model of such amplified actuator is shown in Figure [[fig:actuator_model_simple]] where:
- $k_{i}$ represent the vertical stiffness of the actuator
- $F_{i}$ represents the force applied by the actuator
- $F_{m,i}$ represents the total measured force
- $v_{m,i}$ represents the absolute velocity of the top part of the actuator
- $d_{m,i}$ represents the total relative displacement of the actuator
#+begin_src latex :file actuator_model_simple.pdf :post pdf2svg(file=*this*, ext="png") :exports results
\begin{tikzpicture}
\draw (-1, 0) -- (1, 0);
% Spring, Damper, and Actuator
\draw[spring] (-1, 0) -- (-1, 1.5) node[midway, left=0.1]{$k_{i}$};
\draw[damper] ( 0, 0) -- ( 0, 1.5) node[midway, left=0.2]{$c_{i}$};
\draw[actuator] ( 1, 0) -- ( 1, 1.5) node[midway, left=0.1](F){$F_{i}$};
\node[forcesensor={2}{0.2}] (fsens) at (0, 1.5){};
\node[left] at (fsens.west) {$F_{m,i}$};
\draw[dashed] (1, 0) -- ++(0.4, 0);
\draw[dashed] (1, 1.7) -- ++(0.4, 0);
\draw[->] (0, 1.7)node[]{$\bullet$} -- ++(0, 0.5) node[right]{$v_{m,i}$};
\draw[<->] (1.4, 0) -- ++(0, 1.7) node[midway, right]{$d_{m,i}$};
\end{tikzpicture}
#+end_src
#+name: fig:actuator_model_simple
#+caption: Simple model of an Actuator
#+RESULTS:
[[file:figs/actuator_model_simple.png]]
*** Function description
:PROPERTIES:
:UNNUMBERED: t
@ -845,6 +889,127 @@ This Matlab function is accessible [[file:src/initializeStrutDynamics.m][here]].
#+begin_src matlab
stewart.Ki = args.Ki;
stewart.Ci = args.Ci;
stewart.actuator_type = 1;
#+end_src
** =initializeAmplifiedStrutDynamics=: Add Stiffness and Damping properties of each strut for an amplified piezoelectric actuator
:PROPERTIES:
:header-args:matlab+: :tangle src/initializeAmplifiedStrutDynamics.m
:header-args:matlab+: :comments none :mkdirp yes :eval no
:END:
<<sec:initializeAmplifiedStrutDynamics>>
This Matlab function is accessible [[file:src/initializeAmplifiedStrutDynamics.m][here]].
*** Documentation
:PROPERTIES:
:UNNUMBERED: t
:END:
An amplified piezoelectric actuator is shown in Figure [[fig:cedrat_apa95ml]].
#+name: fig:cedrat_apa95ml
#+attr_html: :width 500px
#+caption: Example of an Amplified piezoelectric actuator with an integrated displacement sensor (Cedrat Technologies)
[[file:figs/amplified_piezo_with_displacement_sensor.jpg]]
A simplistic model of such amplified actuator is shown in Figure [[fig:amplified_piezo_model]] where:
- $k_{p,i}$ represent the vertical stiffness when the piezoelectric stack is removed
- $k_{s,i}$ is the vertical stiffness contribution of the piezoelectric stack
- $F_{i}$ represents the part of the piezoelectric stack that is used as a force actuator
- $F_{m,i}$ represents the remaining part of the piezoelectric stack that is used as a force sensor
- $v_{m,i}$ represents the absolute velocity of the top part of the actuator
- $d_{m,i}$ represents the total relative displacement of the actuator
#+begin_src latex :file iff_1dof.pdf :post pdf2svg(file=*this*, ext="png") :exports results
\begin{tikzpicture}
% Ground
\draw (-1.2, 0) -- (1, 0);
% Mass
\draw (-1.2, 1.4) -- ++(2.2, 0);
\node[forcesensor={0.4}{0.4}] (fsensn) at (0, 1){};
\draw[] (-0.4, 1) -- (0.4, 1);
\node[right] at (fsensn.east) {$F_{m,i}$};
% Spring, Damper, and Actuator
\draw[spring] (-0.4, 0) -- (-0.4, 1) node[midway, right=0.1]{$k_{s,i}$};
\draw[actuator={0.4}{0.2}] (0.4, 0) -- (0.4, 1) node[midway, right=0.1]{$F_{i}$};
\draw[spring] (-1, 0) -- (-1, 1.4) node[midway, left=0.1]{$k_{p,i}$};
\draw[dashed] (1, 0) -- ++(0.4, 0);
\draw[dashed] (1, 1.4) -- ++(0.4, 0);
\draw[->] (0, 1.4)node[]{$\bullet$} -- ++(0, 0.5) node[right]{$v_{m,i}$};
\draw[<->] (1.4, 0) -- ++(0, 1.4) node[midway, right]{$d_{m,i}$};
\end{tikzpicture}
#+end_src
#+name: fig:amplified_piezo_model
#+caption: Model of an amplified actuator
#+RESULTS:
[[file:figs/iff_1dof.png]]
*** Function description
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
function [stewart] = initializeAmplifiedStrutDynamics(stewart, args)
% initializeAmplifiedStrutDynamics - Add Stiffness and Damping properties of each strut
%
% Syntax: [stewart] = initializeAmplifiedStrutDynamics(args)
%
% Inputs:
% - args - Structure with the following fields:
% - Ksi [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Csi [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kdi [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - Cdi [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - Ki [6x1] - Total Stiffness of each strut [N/m]
% - Ci [6x1] - Total Damping of each strut [N/(m/s)]
% - Ksi [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Csi [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kdi [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - Cdi [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
#+end_src
*** Optional Parameters
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
arguments
stewart
args.Kdi (6,1) double {mustBeNumeric, mustBeNonnegative} = 5e6*ones(6,1)
args.Cdi (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ksi (6,1) double {mustBeNumeric, mustBeNonnegative} = 15e6*ones(6,1)
args.Csi (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
end
#+end_src
*** Add Stiffness and Damping properties of each strut
:PROPERTIES:
:UNNUMBERED: t
:END:
#+begin_src matlab
stewart.Ksi = args.Ksi;
stewart.Csi = args.Csi;
stewart.Kdi = args.Kdi;
stewart.Cdi = args.Cdi;
stewart.Ki = args.Ksi + args.Kdi;
stewart.Ci = args.Csi + args.Cdi;
stewart.actuator_type = 2;
#+end_src
** =initializeJointDynamics=: Add Stiffness and Damping properties for spherical joints