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Update flexible Stewart platform

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Thomas Dehaeze
2020-09-01 13:19:26 +02:00
parent 1fd35e9449
commit 8173db25fb
14 changed files with 3095 additions and 1567 deletions
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@@ -1168,45 +1168,20 @@ An amplified piezoelectric actuator is shown in Figure [[fig:cedrat_apa95ml]].
#+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:
- $K_{r}$ represent the vertical stiffness when the piezoelectric stack is removed
- $K_{a}$ 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
A simplistic model of such amplified actuator is shown in Figure [[fig:souleille18_model_piezo]] where the parameters are described in Table [[tab:parameters_amplified_piezo]].
#+begin_src latex :file iff_1dof.pdf
\begin{tikzpicture}
% Ground
\draw (-1.2, 0) -- (1, 0);
#+name: tab:parameters_amplified_piezo
#+caption: Parameters used for the model of the APA 100M
| | Meaning |
|-------+----------------------------------------------------------------|
| $k_e$ | Stiffness used to adjust the pole of the isolator |
| $k_1$ | Stiffness of the metallic suspension when the stack is removed |
| $k_a$ | Stiffness of the actuator |
| $c_1$ | Added viscous damping |
% 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) {$F_{m}$};
% Spring, Damper, and Actuator
\draw[spring] (-0.4, 0) -- (-0.4, 1) node[midway, right=0.1]{$K_{a}$};
\draw[actuator={0.4}{0.2}] (0.4, 0) -- (0.4, 1) node[midway, right=0.1]{$F$};
\draw[spring] (-1, 0) -- (-1, 1.4) node[midway, left=0.1]{$K_{r}$};
\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]{$v_{m}$};
\draw[<->] (1.4, 0) -- ++(0, 1.4) node[midway, right]{$d_{m}$};
\end{tikzpicture}
#+end_src
#+name: fig:amplified_piezo_model
#+caption: Model of an amplified actuator
#+RESULTS:
[[file:figs/iff_1dof.png]]
#+name: fig:souleille18_model_piezo
#+caption: Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator
[[file:./figs/souleille18_model_piezo.png]]
*** Function description
:PROPERTIES:
@@ -1220,20 +1195,20 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
%
% Inputs:
% - args - Structure with the following fields:
% - Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - Kr [6x1] - Vertical (residual) stiffness when the piezoelectric stack is removed [N/m]
% - Cr [6x1] - Vertical (residual) damping when the piezoelectric stack is removed [N/(m/s)]
% - Ka [6x1] - Stiffness of the actuator [N/m]
% - Ke [6x1] - Stiffness used to adjust the pole of the isolator [N/m]
% - K1 [6x1] - Stiffness of the metallic suspension when the stack is removed [N/m]
% - C1 [6x1] - Added viscous damping [N/(m/s)]
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
% - actuators.type = 2
% - actuators.K [6x1] - Total Stiffness of each strut [N/m]
% - actuators.C [6x1] - Total Damping of each strut [N/(m/s)]
% - actuators.Ka [6x1] - Vertical stiffness contribution of the piezoelectric stack [N/m]
% - actuators.Ca [6x1] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - actuators.Kr [6x1] - Vertical stiffness when the piezoelectric stack is removed [N/m]
% - actuators.Cr [6x1] - Vertical damping when the piezoelectric stack is removed [N/(m/s)]
% - actuators.Ka [6x1] - Stiffness of the actuator [N/m]
% - actuators.Ke [6x1] - Stiffness used to adjust the pole of the isolator [N/m]
% - actuators.K1 [6x1] - Stiffness of the metallic suspension when the stack is removed [N/m]
% - actuators.C1 [6x1] - Added viscous damping [N/(m/s)]
#+end_src
*** Optional Parameters
@@ -1243,10 +1218,10 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
#+begin_src matlab
arguments
stewart
args.Kr (6,1) double {mustBeNumeric, mustBeNonnegative} = 5e6*ones(6,1)
args.Cr (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ka (6,1) double {mustBeNumeric, mustBeNonnegative} = 15e6*ones(6,1)
args.Ca (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ke (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.5e6*ones(6,1)
args.Ka (6,1) double {mustBeNumeric, mustBeNonnegative} = 43e6*ones(6,1)
args.K1 (6,1) double {mustBeNumeric, mustBeNonnegative} = 0.4e6*ones(6,1)
args.C1 (6,1) double {mustBeNumeric, mustBeNonnegative} = 10*ones(6,1)
end
#+end_src
@@ -1255,8 +1230,8 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
:UNNUMBERED: t
:END:
#+begin_src matlab
K = args.Ka + args.Kr;
C = args.Ca + args.Cr;
K = args.K1 + args.Ka.*args.Ke./(args.Ka + args.Ke);
C = args.C1;
#+end_src
*** Populate the =stewart= structure
@@ -1267,10 +1242,9 @@ A simplistic model of such amplified actuator is shown in Figure [[fig:amplified
stewart.actuators.type = 2;
stewart.actuators.Ka = args.Ka;
stewart.actuators.Ca = args.Ca;
stewart.actuators.Kr = args.Kr;
stewart.actuators.Cr = args.Cr;
stewart.actuators.Ke = args.Ke;
stewart.actuators.K1 = args.K1;
stewart.actuators.C1 = args.C1;
stewart.actuators.K = K;
stewart.actuators.C = C;
@@ -1301,6 +1275,7 @@ This Matlab function is accessible [[file:../src/initializeFlexibleStrutDynamics
% - M [nxn] - Vertical damping contribution of the piezoelectric stack [N/(m/s)]
% - xi [1x1] - Vertical (residual) stiffness when the piezoelectric stack is removed [N/m]
% - step_file [6x1] - Vertical (residual) damping when the piezoelectric stack is removed [N/(m/s)]
% - Gf [6x1] - Gain from strain in [m] to measured [N] such that it matches
%
% Outputs:
% - stewart - updated Stewart structure with the added fields:
@@ -1318,6 +1293,7 @@ This Matlab function is accessible [[file:../src/initializeFlexibleStrutDynamics
args.H double {mustBeNumeric} = 0
args.n_xyz double {mustBeNumeric} = zeros(2,3)
args.xi double {mustBeNumeric} = 0.1
args.Gf double {mustBeNumeric} = 1
args.step_file char {} = ''
end
#+end_src
@@ -1347,6 +1323,8 @@ This Matlab function is accessible [[file:../src/initializeFlexibleStrutDynamics
stewart.actuators.step_file = args.step_file;
stewart.actuators.K = args.K(3,3); % Axial Stiffness
stewart.actuators.Gf = args.Gf;
#+end_src
** TODO =initializeJointDynamics=: Add Stiffness and Damping properties for spherical joints
@@ -1400,16 +1378,24 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
#+begin_src matlab
arguments
stewart
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'universal'
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'flexible'})} = 'spherical'
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
args.type_F char {mustBeMember(args.type_F,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'universal'
args.type_M char {mustBeMember(args.type_M,{'universal', 'spherical', 'universal_p', 'spherical_p', 'universal_3dof', 'spherical_3dof', 'flexible'})} = 'spherical'
args.Kf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
args.Kt_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 15*ones(6,1)
args.Kf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 33*ones(6,1)
args.Cf_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-4*ones(6,1)
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 20*ones(6,1)
args.Kt_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 236*ones(6,1)
args.Ct_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e-3*ones(6,1)
args.Ka_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_F (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Ka_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.2e8*ones(6,1)
args.Ca_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.Kr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1.1e7*ones(6,1)
args.Cr_M (6,1) double {mustBeNumeric, mustBeNonnegative} = 1e1*ones(6,1)
args.K_M double {mustBeNumeric} = zeros(6,6)
args.M_M double {mustBeNumeric} = zeros(6,6)
args.n_xyz_M double {mustBeNumeric} = zeros(2,3)
@@ -1439,6 +1425,10 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
stewart.joints_F.type = 4;
case 'flexible'
stewart.joints_F.type = 5;
case 'universal_3dof'
stewart.joints_F.type = 6;
case 'spherical_3dof'
stewart.joints_F.type = 7;
end
switch args.type_M
@@ -1452,6 +1442,10 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
stewart.joints_M.type = 4;
case 'flexible'
stewart.joints_M.type = 5;
case 'universal_3dof'
stewart.joints_M.type = 6;
case 'spherical_3dof'
stewart.joints_M.type = 7;
end
#+end_src
@@ -1459,26 +1453,22 @@ This Matlab function is accessible [[file:../src/initializeJointDynamics.m][here
:PROPERTIES:
:UNNUMBERED: t
:END:
Translation Stiffness
Axial and Radial (shear) Stiffness
#+begin_src matlab
stewart.joints_M.Kx = zeros(6,1);
stewart.joints_M.Ky = zeros(6,1);
stewart.joints_M.Kz = zeros(6,1);
stewart.joints_M.Ka = args.Ka_M;
stewart.joints_M.Kr = args.Kr_M;
stewart.joints_F.Kx = zeros(6,1);
stewart.joints_F.Ky = zeros(6,1);
stewart.joints_F.Kz = zeros(6,1);
stewart.joints_F.Ka = args.Ka_F;
stewart.joints_F.Kr = args.Kr_F;
#+end_src
Translation Damping
#+begin_src matlab
stewart.joints_M.Cx = zeros(6,1);
stewart.joints_M.Cy = zeros(6,1);
stewart.joints_M.Cz = zeros(6,1);
stewart.joints_M.Ca = args.Ca_M;
stewart.joints_M.Cr = args.Cr_M;
stewart.joints_F.Cx = zeros(6,1);
stewart.joints_F.Cy = zeros(6,1);
stewart.joints_F.Cz = zeros(6,1);
stewart.joints_F.Ca = args.Ca_F;
stewart.joints_F.Cr = args.Cr_F;
#+end_src
*** Add Stiffness and Damping in Rotation of each strut
@@ -1488,19 +1478,19 @@ Translation Damping
Rotational Stiffness
#+begin_src matlab
stewart.joints_M.Kf = args.Kf_M;
stewart.joints_M.Kt = args.Kf_M;
stewart.joints_M.Kt = args.Kt_M;
stewart.joints_F.Kf = args.Kf_F;
stewart.joints_F.Kt = args.Kf_F;
stewart.joints_F.Kt = args.Kt_F;
#+end_src
Rotational Damping
#+begin_src matlab
stewart.joints_M.Cf = args.Cf_M;
stewart.joints_M.Ct = args.Cf_M;
stewart.joints_M.Ct = args.Ct_M;
stewart.joints_F.Cf = args.Cf_F;
stewart.joints_F.Ct = args.Cf_F;
stewart.joints_F.Ct = args.Ct_F;
#+end_src
*** Stiffness and Mass matrices for flexible joint