diff --git a/docs/Comparison.docx b/docs/Comparison.docx new file mode 100644 index 0000000..18f6207 Binary files /dev/null and b/docs/Comparison.docx differ diff --git a/docs/Modal decomposition for control of MIMO system.pptx b/docs/Modal decomposition for control of MIMO system.pptx new file mode 100644 index 0000000..7f2aa9e Binary files /dev/null and b/docs/Modal decomposition for control of MIMO system.pptx differ diff --git a/docs/modal_control_gravimeter_numerical.m b/docs/modal_control_gravimeter_numerical.m new file mode 100644 index 0000000..677fbb1 --- /dev/null +++ b/docs/modal_control_gravimeter_numerical.m @@ -0,0 +1,103 @@ +clc +clear all +close all + +%% System properties +g = 100000; +w0 = 2*pi*.5; % MinusK BM1 tablle +l = 0.5; %[m] +la = 1; %[m] +h = 1.7; %[m] +ha = 1.7;% %[m] +m = 400; %[kg] +k = 15e3;%[N/m] +kv = k; +kh = 15e3; +I = 115;%[kg m^2] +dampv = 0.03; +damph = 0.03; +s = tf('s'); + +%% State-space model +M = [m 0 0 + 0 m 0 + 0 0 I]; + +la = l; +ha = h; +kv = k; +kh = k; + +%Jacobian of the bottom sensor +Js1 = [1 0 h/2 + 0 1 -l/2]; + +%Jacobian of the top sensor +Js2 = [1 0 -h/2 + 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 +Jah = [1 0 ha/2]; +Jav = [0 1 -la/2 %Left vertical actuator + 0 1 la/2]; %Right vertical actuator +Jta = Ja'; +Jtah = Jah'; +Jtav = Jav'; +K = kv*Jtav*Jav + kh*Jtah*Jah; +C = dampv*kv*Jtav*Jav+damph*kh*Jtah*Jah; + +E = [1 0 0 + 0 1 0 + 0 0 1]; %projecting ground motion in the directions of the legs + +AA = [zeros(3) eye(3) + -M\K -M\C]; + +BB = [zeros(3,3) + M\Jta ]; + +% CC = [[Js1;Js2] zeros(4,3)]; +CC = [[Jah;Jav] zeros(3,3)]; + +% DD = zeros(4,3); +DD = zeros(3); + +G = ss(AA,BB,CC,DD); +%% Modal coordinates +[V,D] = eig(M\K); +Mm = V'*M*V; % Modal mass matrix +Dm = V'*C*V; % Modal damping matrix +Km = V'*K*V; % Modal stiffness matrix + +Bm = inv(Mm)*V'*Jta; +% Cm = [Js1;Js2]*V; +Cm = [Jah;Jav]*V; + + +omega = real(sqrt(inv(Mm)*Km)); +zeta = real(0.5*inv(Mm)*Dm*inv(omega)); + +Gm = [1/(s^2+2*zeta(1,1)*omega(1,1)*s+omega(1,1)^2),0,0; + 0,1/(s^2+2*zeta(2,2)*omega(2,2)*s+omega(2,2)^2),0; + 0,0,1/(s^2+2*zeta(3,3)*omega(3,3)*s+omega(3,3)^2)]; +figure(1) +bode(G,Cm*Gm*Bm) +figure(2) +bode(G,Gm) + +%% Controller +s = tf('s'); +w0 = 2*pi*0.1; +Kc = 100/(1+s/w0); +Knet = inv(Bm)*Kc*inv(Cm); +Gc = -lft(G,Knet); +isstable(Gc) + + + + + diff --git a/docs/svd.pptx b/docs/svd.pptx new file mode 100644 index 0000000..307a955 Binary files /dev/null and b/docs/svd.pptx differ diff --git a/figs/coupled_plant_bode.pdf b/figs/coupled_plant_bode.pdf new file mode 100644 index 0000000..0326900 --- /dev/null +++ b/figs/coupled_plant_bode.pdf @@ -0,0 +1,5026 @@ +%PDF-1.4 +% +1 0 obj +<< +/Producer (Apache FOP Version 2.4.0-SNAPSHOT: PDFDocumentGraphics2D) +/CreationDate (D:20210305112642+01'00') +>> +endobj +2 0 obj +<< +/Type /ExtGState +/CA 0.2509804 +>> +endobj +3 0 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