Update tangled file
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@ -14,11 +14,11 @@ open('gravimeter.slx')
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% Parameters
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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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@ -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 = 'gravimeterplanarjoints2020a';
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mdl = 'gravimeter';
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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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% -0.000143694057817022 + 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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@ -106,12 +106,12 @@ pole(Gg)
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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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@ -130,29 +130,6 @@ for in_i = 1:3
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end
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% Parameters
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% Control parameters
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g = 1e5;
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g_svd = 1e5;
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% System 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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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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% Bode options.
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P = bodeoptions;
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@ -168,7 +145,6 @@ P.TickLabel.FontSize = 12;
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P.Xlim = [1e-1,1e2];
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P.MagLowerLimMode = 'manual';
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P.MagLowerLim= 1e-3;
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%P.PhaseVisible = 'off';
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@ -176,28 +152,47 @@ P.MagLowerLim= 1e-3;
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w = 2*pi*logspace(-1,2,1000); % [rad/s]
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% generation of the state space model
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% Generation of the State Space Model
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% Mass matrix
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M = [m 0 0
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0 m 0
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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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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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%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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% Jacobian of the bottom sensor
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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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% Jacobian of the actuators
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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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% Stiffness and Damping matrices
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K = k*Jta*Ja;
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C = c*Jta*Ja;
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% State Space Matrices
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E = [1 0 0
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0 1 0
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0 0 1]; %projecting ground motion in the directions of the legs
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@ -208,12 +203,6 @@ AA = [zeros(3) eye(3)
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BB = [zeros(3,6)
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M\Jta M\(k*Jta*E)];
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% BB = [zeros(3,3)
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% M\Jta ];
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%
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% CC = [Ja zeros(3)];
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% DD = zeros(3,3);
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CC = [[Js1;Js2] zeros(4,3);
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zeros(2,6)
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(Js1+Js2)./2 zeros(2,3)
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@ -224,14 +213,15 @@ DD = [zeros(4,6)
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zeros(2,3) eye(2,3)
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zeros(6,6)];
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system_dec = ss(AA,BB,CC,DD);
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% State Space model:
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% - Input = three actuators and three ground motions
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% - Output = the bottom sensor; the top sensor; the ground motion; the half sum; the half difference; the rotation
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system_dec = ss(AA,BB,CC,DD);
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size(system_dec)
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% Comparison with the Simscape Model
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