Update gravimeter parameters
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figs/gravimeter_model.png
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@ -14,11 +14,11 @@ open('gravimeter.slx')
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% Parameters
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l = 0.5; % Length of the mass [m]
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la = 0.5; % Position of Act. [m]
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l = 0.5/2; % Length of the mass [m]
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la = 0.5/2; % Position of Act. [m]
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h = 1.7; % Height of the mass [m]
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ha = 1.7; % Position of Act. [m]
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h = 1.7/2; % Height of the mass [m]
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ha = 1.7/2; % Position of Act. [m]
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m = 400; % Mass [kg]
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I = 115; % Inertia [kg m^2]
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@ -33,7 +33,7 @@ g = 0; % Gravity [m/s2]
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% System Identification - Without Gravity
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%% Name of the Simulink File
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mdl = 'gravimeter';
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mdl = 'gravimeterplanarjoints2020a';
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%% Input/Output definition
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clear io; io_i = 1;
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@ -57,12 +57,12 @@ pole(G)
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% #+begin_example
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% pole(G)
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% ans =
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% -0.000473481142385801 + 21.7596190728632i
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% -0.000473481142385801 - 21.7596190728632i
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% -7.49842879459177e-05 + 8.6593576906982i
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% -7.49842879459177e-05 - 8.6593576906982i
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% -5.15386867925747e-06 + 2.27025295182755i
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% -5.15386867925747e-06 - 2.27025295182755i
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% -0.000143694057817022 + 11.9872485389527i
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% -0.000143694057817022 - 11.9872485389527i
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% -7.49842879371933e-05 + 8.65931816830372i
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% -7.49842879371933e-05 - 8.65931816830372i
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% -4.25202990156283e-06 + 2.06202312114216i
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% -4.25202990156283e-06 - 2.06202312114216i
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% #+end_example
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% The plant as 6 states as expected (2 translations + 1 rotation)
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@ -104,14 +104,14 @@ pole(Gg)
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% #+RESULTS:
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% #+begin_example
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% pole(G)
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% pole(Gg)
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% ans =
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% -10.9848275341276 + 0i
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% 10.9838836405193 + 0i
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% -7.49855396089326e-05 + 8.65962885769976i
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% -7.49855396089326e-05 - 8.65962885769976i
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% -6.68819341967921e-06 + 0.83296042226902i
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% -6.68819341967921e-06 - 0.83296042226902i
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% -7.49842906813125e-05 + 8.6594885739673i
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% -7.49842906813125e-05 - 8.6594885739673i
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% 7.08960832564352 + 0i
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% -7.08989438800737 + 0i
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% 1.70627135943515 + 0i
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% -1.70628118924799 + 0i
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% #+end_example
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index.html
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72
index.org
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index.org
@ -47,7 +47,13 @@
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:PROPERTIES:
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:header-args:matlab+: :tangle gravimeter/script.m
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:END:
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** Matlab Init :noexport:ignore:
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** Introduction
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#+name: fig:gravimeter_model
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#+caption: Model of the gravimeter
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[[file:figs/gravimeter_model.png]]
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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@ -67,11 +73,11 @@
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Parameters
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#+begin_src matlab
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l = 0.5/2; % Length of the mass [m]
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la = 0.5/2; % Position of Act. [m]
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l = 1.0; % Length of the mass [m]
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la = 0.5; % Position of Act. [m]
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h = 1.7/2; % Height of the mass [m]
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ha = 1.7/2; % Position of Act. [m]
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h = 3.4; % Height of the mass [m]
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ha = 1.7; % Position of Act. [m]
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m = 400; % Mass [kg]
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I = 115; % Inertia [kg m^2]
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@ -112,12 +118,12 @@ Parameters
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#+begin_example
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pole(G)
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ans =
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-0.000143694057817022 + 11.9872485389527i
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-0.000143694057817022 - 11.9872485389527i
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-7.49842879371933e-05 + 8.65931816830372i
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-7.49842879371933e-05 - 8.65931816830372i
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-4.25202990156283e-06 + 2.06202312114216i
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-4.25202990156283e-06 - 2.06202312114216i
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-0.000473481142385795 + 21.7596190728632i
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-0.000473481142385795 - 21.7596190728632i
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-7.49842879459172e-05 + 8.6593576906982i
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-7.49842879459172e-05 - 8.6593576906982i
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-5.1538686792578e-06 + 2.27025295182756i
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-5.1538686792578e-06 - 2.27025295182756i
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#+end_example
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The plant as 6 states as expected (2 translations + 1 rotation)
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@ -170,12 +176,12 @@ We can now see that the system is unstable due to gravity.
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#+begin_example
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pole(Gg)
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ans =
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-7.49842906813125e-05 + 8.6594885739673i
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-7.49842906813125e-05 - 8.6594885739673i
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7.08960832564352 + 0i
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-7.08989438800737 + 0i
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1.70627135943515 + 0i
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-1.70628118924799 + 0i
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-10.9848275341252 + 0i
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10.9838836405201 + 0i
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-7.49855379478109e-05 + 8.65962885770051i
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-7.49855379478109e-05 - 8.65962885770051i
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-6.68819548733559e-06 + 0.832960422243848i
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-6.68819548733559e-06 - 0.832960422243848i
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#+end_example
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#+begin_src matlab :exports none
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@ -205,27 +211,6 @@ ans =
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** Analytical Model
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*** Parameters
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Control parameters
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#+begin_src matlab
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g = 1e5;
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g_svd = 1e5;
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#+end_src
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System parameters
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#+begin_src matlab
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l = 0.5; % Length of the mass [m]
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la = 0.5; % Position of Act. [m]
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h = 1.7; % Height of the mass [m]
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ha = 1.7; % Position of Act. [m]
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m = 400; % Mass [kg]
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I = 115; % Inertia [kg m^2]
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k = 15e3; % Actuator Stiffness [N/m]
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c = 0.03; % Actuator Damping [N/(m/s)]
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#+end_src
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Bode options.
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#+begin_src matlab
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P = bodeoptions;
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@ -256,17 +241,16 @@ Frequency vector.
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0 0 I];
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%Jacobian of the bottom sensor
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Js1 = [1 0 h/2
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Js1 = [1 0 h/2
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0 1 -l/2];
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%Jacobian of the top sensor
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Js2 = [1 0 -h/2
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0 1 0];
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0 1 0];
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%Jacobian of the actuators
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Ja = [1 0 ha/2 %Left horizontal actuator
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%1 0 h/2 %Right horizontal actuator
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0 1 -la/2 %Left vertical actuator
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0 1 la/2]; %Right vertical actuator
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Ja = [1 0 ha % Left horizontal actuator
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0 1 -la % Left vertical actuator
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0 1 la]; % Right vertical actuator
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Jta = Ja';
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K = k*Jta*Ja;
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C = c*Jta*Ja;
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