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Update gravimeter parameters

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This commit is contained in:
Thomas Dehaeze 2020-10-05 18:06:49 +02:00
parent 2186df3f20
commit aa7613b2fc
11 changed files with 4359 additions and 4600 deletions
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2530
figs/gravimeter_analytical_system_open_loop_models.pdf
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figs/gravimeter_analytical_system_open_loop_models.png
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figs/open_loop_tf.pdf
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figs/open_loop_tf_g.pdf
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gravimeter/gravimeter.slx
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36
gravimeter/script.m
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@ -14,11 +14,11 @@ open('gravimeter.slx')
% Parameters
l = 0.5; % Length of the mass [m]
la = 0.5; % Position of Act. [m]
l = 0.5/2; % Length of the mass [m]
la = 0.5/2; % Position of Act. [m]
h = 1.7; % Height of the mass [m]
ha = 1.7; % Position of Act. [m]
h = 1.7/2; % Height of the mass [m]
ha = 1.7/2; % Position of Act. [m]
m = 400; % Mass [kg]
I = 115; % Inertia [kg m^2]
@ -33,7 +33,7 @@ g = 0; % Gravity [m/s2]
% System Identification - Without Gravity
%% Name of the Simulink File
mdl = 'gravimeter';
mdl = 'gravimeterplanarjoints2020a';
%% Input/Output definition
clear io; io_i = 1;
@ -57,12 +57,12 @@ pole(G)
% #+begin_example
% pole(G)
% ans =
% -0.000473481142385801 + 21.7596190728632i
% -0.000473481142385801 - 21.7596190728632i
% -7.49842879459177e-05 + 8.6593576906982i
% -7.49842879459177e-05 - 8.6593576906982i
% -5.15386867925747e-06 + 2.27025295182755i
% -5.15386867925747e-06 - 2.27025295182755i
% -0.000143694057817022 + 11.9872485389527i
% -0.000143694057817022 - 11.9872485389527i
% -7.49842879371933e-05 + 8.65931816830372i
% -7.49842879371933e-05 - 8.65931816830372i
% -4.25202990156283e-06 + 2.06202312114216i
% -4.25202990156283e-06 - 2.06202312114216i
% #+end_example
% The plant as 6 states as expected (2 translations + 1 rotation)
@ -104,14 +104,14 @@ pole(Gg)
% #+RESULTS:
% #+begin_example
% pole(G)
% pole(Gg)
% ans =
% -10.9848275341276 + 0i
% 10.9838836405193 + 0i
% -7.49855396089326e-05 + 8.65962885769976i
% -7.49855396089326e-05 - 8.65962885769976i
% -6.68819341967921e-06 + 0.83296042226902i
% -6.68819341967921e-06 - 0.83296042226902i
% -7.49842906813125e-05 + 8.6594885739673i
% -7.49842906813125e-05 - 8.6594885739673i
% 7.08960832564352 + 0i
% -7.08989438800737 + 0i
% 1.70627135943515 + 0i
% -1.70628118924799 + 0i
% #+end_example

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index.html
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66
index.org
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@ -47,6 +47,12 @@
:PROPERTIES:
:header-args:matlab+: :tangle gravimeter/script.m
:END:
** Introduction
#+name: fig:gravimeter_model
#+caption: Model of the gravimeter
[[file:figs/gravimeter_model.png]]
** 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>>
@ -67,11 +73,11 @@
Parameters
#+begin_src matlab
l = 0.5/2; % Length of the mass [m]
la = 0.5/2; % Position of Act. [m]
l = 1.0; % Length of the mass [m]
la = 0.5; % Position of Act. [m]
h = 1.7/2; % Height of the mass [m]
ha = 1.7/2; % Position of Act. [m]
h = 3.4; % Height of the mass [m]
ha = 1.7; % Position of Act. [m]
m = 400; % Mass [kg]
I = 115; % Inertia [kg m^2]
@ -112,12 +118,12 @@ Parameters
#+begin_example
pole(G)
ans =
-0.000143694057817022 + 11.9872485389527i
-0.000143694057817022 - 11.9872485389527i
-7.49842879371933e-05 + 8.65931816830372i
-7.49842879371933e-05 - 8.65931816830372i
-4.25202990156283e-06 + 2.06202312114216i
-4.25202990156283e-06 - 2.06202312114216i
-0.000473481142385795 + 21.7596190728632i
-0.000473481142385795 - 21.7596190728632i
-7.49842879459172e-05 + 8.6593576906982i
-7.49842879459172e-05 - 8.6593576906982i
-5.1538686792578e-06 + 2.27025295182756i
-5.1538686792578e-06 - 2.27025295182756i
#+end_example
The plant as 6 states as expected (2 translations + 1 rotation)
@ -170,12 +176,12 @@ We can now see that the system is unstable due to gravity.
#+begin_example
pole(Gg)
ans =
-7.49842906813125e-05 + 8.6594885739673i
-7.49842906813125e-05 - 8.6594885739673i
7.08960832564352 + 0i
-7.08989438800737 + 0i
1.70627135943515 + 0i
-1.70628118924799 + 0i
-10.9848275341252 + 0i
10.9838836405201 + 0i
-7.49855379478109e-05 + 8.65962885770051i
-7.49855379478109e-05 - 8.65962885770051i
-6.68819548733559e-06 + 0.832960422243848i
-6.68819548733559e-06 - 0.832960422243848i
#+end_example
#+begin_src matlab :exports none
@ -205,27 +211,6 @@ ans =
** Analytical Model
*** Parameters
Control parameters
#+begin_src matlab
g = 1e5;
g_svd = 1e5;
#+end_src
System parameters
#+begin_src matlab
l = 0.5; % Length of the mass [m]
la = 0.5; % Position of Act. [m]
h = 1.7; % Height of the mass [m]
ha = 1.7; % Position of Act. [m]
m = 400; % Mass [kg]
I = 115; % Inertia [kg m^2]
k = 15e3; % Actuator Stiffness [N/m]
c = 0.03; % Actuator Damping [N/(m/s)]
#+end_src
Bode options.
#+begin_src matlab
P = bodeoptions;
@ -263,10 +248,9 @@ Frequency vector.
0 1 0];
%Jacobian of the actuators
Ja = [1 0 ha/2 %Left horizontal actuator
%1 0 h/2 %Right horizontal actuator
0 1 -la/2 %Left vertical actuator
0 1 la/2]; %Right vertical actuator
Ja = [1 0 ha % Left horizontal actuator
0 1 -la % Left vertical actuator
0 1 la]; % Right vertical actuator
Jta = Ja';
K = k*Jta*Ja;
C = c*Jta*Ja;