From 311b120cf4b1812873db4dc90ad314790a7bce47 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Fri, 5 Mar 2021 11:48:02 +0100 Subject: [PATCH] Compare SVD/Jacobian/Modal decoupling --- docs/Comparison.docx | Bin 0 -> 14205 bytes ...omposition for control of MIMO system.pptx | Bin 0 -> 1025787 bytes docs/modal_control_gravimeter_numerical.m | 103 + docs/svd.pptx | Bin 0 -> 472530 bytes figs/coupled_plant_bode.pdf | 5026 +++++++++++++++++ figs/coupled_plant_bode.png | Bin 0 -> 220077 bytes figs/decoupling_modal.pdf | Bin 0 -> 40432 bytes figs/decoupling_modal.png | Bin 0 -> 10252 bytes figs/decoupling_svd.pdf | Bin 0 -> 41231 bytes figs/decoupling_svd.png | Bin 0 -> 9746 bytes figs/gravimeter_block_com.pdf | Bin 42618 -> 11266 bytes figs/gravimeter_block_decentralized.pdf | Bin 14371 -> 14371 bytes figs/jacobian_decoupling_arch.pdf | Bin 0 -> 42854 bytes figs/jacobian_decoupling_arch.png | Bin 0 -> 12143 bytes figs/jacobian_plant.pdf | Bin 0 -> 60946 bytes figs/jacobian_plant.png | Bin 0 -> 86127 bytes figs/modal_plant.pdf | Bin 0 -> 61239 bytes figs/modal_plant.png | Bin 0 -> 79480 bytes figs/model_test_decoupling.pdf | Bin 0 -> 16468 bytes figs/model_test_decoupling.png | Bin 0 -> 23490 bytes figs/model_test_decoupling_spurious_res.pdf | Bin 0 -> 16803 bytes figs/model_test_decoupling_spurious_res.png | Bin 0 -> 24879 bytes figs/plant_frame_L.pdf | Bin 91944 -> 91944 bytes figs/svd_plant.pdf | Bin 0 -> 59424 bytes figs/svd_plant.png | Bin 0 -> 80944 bytes svd-control.html | 1617 ++++-- svd-control.org | 639 +++ svd-control.pdf | Bin 3863375 -> 4240409 bytes 28 files changed, 7013 insertions(+), 372 deletions(-) create mode 100644 docs/Comparison.docx create mode 100644 docs/Modal decomposition for control of MIMO system.pptx create mode 100644 docs/modal_control_gravimeter_numerical.m create mode 100644 docs/svd.pptx create mode 100644 figs/coupled_plant_bode.pdf create mode 100644 figs/coupled_plant_bode.png create mode 100644 figs/decoupling_modal.pdf create mode 100644 figs/decoupling_modal.png create mode 100644 figs/decoupling_svd.pdf create mode 100644 figs/decoupling_svd.png create mode 100644 figs/jacobian_decoupling_arch.pdf create mode 100644 figs/jacobian_decoupling_arch.png create mode 100644 figs/jacobian_plant.pdf create mode 100644 figs/jacobian_plant.png create mode 100644 figs/modal_plant.pdf create mode 100644 figs/modal_plant.png create mode 100644 figs/model_test_decoupling.pdf create mode 100644 figs/model_test_decoupling.png create mode 100644 figs/model_test_decoupling_spurious_res.pdf create mode 100644 figs/model_test_decoupling_spurious_res.png create mode 100644 figs/svd_plant.pdf create mode 100644 figs/svd_plant.png diff --git a/docs/Comparison.docx b/docs/Comparison.docx new file mode 100644 index 0000000000000000000000000000000000000000..18f6207113c34c42a5ad176ad845b446e7b537d4 GIT binary patch literal 14205 zcmeHu19v6J*7k|fv2EMv*tTukwmY^vcE?G_?%3?u=-5feUuN!|J2QP}eShG+wa(e= 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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 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