From 05e6ed4473691708ab694122314b80ba3b5dcd1f Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 21 Sep 2020 13:08:36 +0200 Subject: [PATCH] Export figures --- figs/open_loop_tf.pdf | 3126 ++++++++++++++++-------- figs/open_loop_tf.png | Bin 200564 -> 231505 bytes figs/stewart_platform_legs.pdf | Bin 0 -> 227919 bytes figs/stewart_platform_legs.png | Bin 0 -> 109113 bytes figs/stewart_platform_rotations.pdf | Bin 0 -> 78128 bytes figs/stewart_platform_rotations.png | Bin 0 -> 135542 bytes figs/stewart_platform_translations.pdf | Bin 0 -> 76027 bytes figs/stewart_platform_translations.png | Bin 0 -> 129948 bytes index.html | 239 ++ stewart_platform/drone_platform.slx | Bin 51036 -> 51199 bytes 10 files changed, 2310 insertions(+), 1055 deletions(-) create mode 100644 figs/stewart_platform_legs.pdf create mode 100644 figs/stewart_platform_legs.png create mode 100644 figs/stewart_platform_rotations.pdf create mode 100644 figs/stewart_platform_rotations.png create mode 100644 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+

SVD Control

+ + +
+

1 Simscape Model - Gravimeter

+
+
+
+

1.1 Simulink

+
+
+
open('gravimeter.slx')
+
+
+ +
+
%% Name of the Simulink File
+mdl = 'gravimeter';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/F1'], 1, 'openinput');  io_i = io_i + 1;
+io(io_i) = linio([mdl, '/F2'], 1, 'openinput');  io_i = io_i + 1;
+io(io_i) = linio([mdl, '/F3'], 1, 'openinput');  io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Acc_side'], 1, 'openoutput'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Acc_side'], 2, 'openoutput'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Acc_top'], 1, 'openoutput'); io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Acc_top'], 2, 'openoutput'); io_i = io_i + 1;
+
+G = linearize(mdl, io);
+G.InputName  = {'F1', 'F2', 'F3'};
+G.OutputName = {'Ax1', 'Az1', 'Ax2', 'Az2'};
+
+
+ +

+The plant as 6 states as expected (2 translations + 1 rotation) +

+ +
+
size(G)
+
+
+ +
+State-space model with 4 outputs, 3 inputs, and 6 states.
+
+ + + +
+

open_loop_tf.png +

+

Figure 1: Open Loop Transfer Function from 3 Actuators to 4 Accelerometers

+
+
+
+
+ +
+

2 Simscape Model - Stewart Platform

+
+
+
+

2.1 Jacobian

+
+

+First, the position of the “joints” (points of force application) are estimated and the Jacobian computed. +

+ +
+
open('stewart_platform/drone_platform_jacobian.slx');
+
+
+ +
+
sim('drone_platform_jacobian');
+
+
+ +
+
Aa = [a1.Data(1,:);
+      a2.Data(1,:);
+      a3.Data(1,:);
+      a4.Data(1,:);
+      a5.Data(1,:);
+      a6.Data(1,:)]';
+
+Ab = [b1.Data(1,:);
+      b2.Data(1,:);
+      b3.Data(1,:);
+      b4.Data(1,:);
+      b5.Data(1,:);
+      b6.Data(1,:)]';
+
+As = (Ab - Aa)./vecnorm(Ab - Aa);
+
+l = vecnorm(Ab - Aa)';
+
+J = [As' , cross(Ab, As)'];
+
+save('./jacobian.mat', 'Aa', 'Ab', 'As', 'l', 'J');
+
+
+
+
+ +
+

2.2 Simulink

+
+
+
open('stewart_platform/drone_platform.slx');
+
+
+ +

+Definition of spring parameters +

+
+
kx = 50; % [N/m]
+ky = 50;
+kz = 50;
+
+cx = 0.025; % [Nm/rad]
+cy = 0.025;
+cz = 0.025;
+
+
+ +

+We load the Jacobian. +

+
+
load('./jacobian.mat', 'Aa', 'Ab', 'As', 'l', 'J');
+
+
+ + +

+The dynamics is identified from forces applied by each legs to the measured acceleration of the top platform. +

+
+
%% Name of the Simulink File
+mdl = 'drone_platform';
+
+%% Input/Output definition
+clear io; io_i = 1;
+io(io_i) = linio([mdl, '/u'],               1, 'openinput');  io_i = io_i + 1;
+io(io_i) = linio([mdl, '/Inertial Sensor'], 1, 'openoutput'); io_i = io_i + 1;
+
+G = linearize(mdl, io);
+G.InputName  = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
+G.OutputName = {'Ax', 'Ay', 'Az', 'Arx', 'Ary', 'Arz'};
+
+
+ +

+Thanks to the Jacobian, we compute the transfer functions in the frame of the legs and in an inertial frame. +

+
+
Gx = -G*inv(J');
+Gx.InputName  = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
+
+Gl = -J*G;
+Gl.OutputName  = {'A1', 'A2', 'A3', 'A4', 'A5', 'A6'};
+
+
+ + +
+

stewart_platform_translations.png +

+

Figure 2: Stewart Platform Plant from forces applied by the legs to the acceleration of the platform

+
+ + +
+

stewart_platform_rotations.png +

+

Figure 3: Stewart Platform Plant from torques applied by the legs to the angular acceleration of the platform

+
+ + +
+

stewart_platform_legs.png +

+

Figure 4: Stewart Platform Plant from forces applied by the legs to displacement of the legs

+
+
+
+
+
+
+

Author: Dehaeze Thomas

+

Created: 2020-09-21 lun. 13:07

+
+ + diff --git a/stewart_platform/drone_platform.slx b/stewart_platform/drone_platform.slx index f4ef85431544d78a28489d7643d6a07fe52de163..d4d91345e9a100e28f3243bbf28773f3b0d0c82f 100644 GIT binary patch delta 29461 zcmZ6yLy#s+7c|XyU4=TalO&LLizD{Y`cx5#uVsE26UGR8@*Xs>T5DUq}dTf40sA2YQrSYjY?uw;50I2@%;0?TWA~ zUAY2q!AuP1)FgNPQk$6%Z!PRl#9pIWR<0~DjvU9Sp*-AOZjRTqAqO?{pOmH=PTg?; zDF<17BZHAh_=K%7DZAV=w+auMGZ4=d`iZOWvnz^*=PL-z{Ah6N%dpGCS%yaWJC~`| z^|DCI3SP7g4WoJlKV46O7Jn^$frs-md4>Ve&I^((+7mp9oC!g$0a`;J_TA-6#e{hU zR(nbUG=I1t6y4I7PXtX34iDkq&{?RNX5ks$ig4E*ax<6^6uBr%o2Zwuc9#BHe%|fb zZ62CRuRo8p^;!&^@qTmfEG8{kO|0MGo0OC@%n(_~cBKY<-XB-D_}PFHf&?-#4K4sU z5K!;uDa4TH0AYYDn(JK27FNuYP{~;V;>%6DDvz&(bXbSQydl_D>Ai zzPcnK!wr1B{14Bzo^)~p?tj&I>X(UMlec(eK`R=OJaVe8GEP{Tn_F6XB<-ITRGLH= zN`mZ_H^C+mKK7d35ksI6lQlJE60k+q>pZH9Q>5ABrbLMIv6;JEy$#mijK`3 zWdzRN))ilcjeJrM6)`^y{gS(F9SB585(F^sWo`ZYA+O*j`rF$(TTZ-FlP3XDA-5)- zHhLvJzPJj_2r`_}O1%}&)t3oLs=8#3Nc>PU!_Vt*)eP0=VC7AOVt=SVxBpdy+3>_f 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