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< title > Identification of the Stewart Platform using Simscape< / title >
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< h1 class = "title" > Identification of the Stewart Platform using Simscape< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org36eeb29" > 1. Identification< / a >
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< ul >
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< li > < a href = "#orgb4842a1" > 1.1. Simscape Model< / a > < / li >
< li > < a href = "#org4240dd7" > 1.2. Initialize the Stewart Platform< / a > < / li >
< li > < a href = "#org5695094" > 1.3. Identification< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#orge464de2" > 2. States as the motion of the mobile platform< / a >
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< ul >
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< li > < a href = "#org8d12d8c" > 2.1. Initialize the Stewart Platform< / a > < / li >
< li > < a href = "#orgef8d225" > 2.2. Identification< / a > < / li >
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< li > < a href = "#orge68adea" > 2.3. Coordinate transformation< / a > < / li >
< li > < a href = "#org4973ae1" > 2.4. Analysis< / a > < / li >
< li > < a href = "#orge7b97c8" > 2.5. Visualizing the modes< / a > < / li >
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< li > < a href = "#org009b696" > 2.6. Identification< / a > < / li >
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< li > < a href = "#orgf7a52cb" > 2.7. Change of states< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org23d7e7b" > 3. Simple Model without any sensor< / a >
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< ul >
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< li > < a href = "#org2ad9d50" > 3.1. Simscape Model< / a > < / li >
< li > < a href = "#orgbc1f736" > 3.2. Initialize the Stewart Platform< / a > < / li >
< li > < a href = "#org43f8fc6" > 3.3. Identification< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org0502cd2" > 4. Cartesian Plot< / a > < / li >
< li > < a href = "#org32e2eb3" > 5. From a force to force sensor< / a > < / li >
< li > < a href = "#org8ddfd2c" > 6. From a force applied in the leg to the displacement of the leg< / a > < / li >
< li > < a href = "#org5685537" > 7. Transmissibility< / a > < / li >
< li > < a href = "#org3335d1e" > 8. Compliance< / a > < / li >
< li > < a href = "#org5ca7af8" > 9. Inertial< / a > < / li >
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< / ul >
< / div >
< / div >
< p >
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We would like to extract a state space model of the Stewart Platform from the Simscape model.
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< / p >
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< p >
The inputs are:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Symbol< / th >
< th scope = "col" class = "org-left" > Meaning< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > \(\bm{\mathcal{F}}_{d}\)< / td >
< td class = "org-left" > External forces applied in {B}< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{\tau}\)< / td >
< td class = "org-left" > Joint forces< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{\mathcal{F}}\)< / td >
< td class = "org-left" > Cartesian forces applied by the Joints< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{D}_{w}\)< / td >
< td class = "org-left" > Fixed Based translation and rotations around {A}< / td >
< / tr >
< / tbody >
< / table >
< p >
The outputs are:
< / p >
< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Symbol< / th >
< th scope = "col" class = "org-left" > Meaning< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > \(\bm{\mathcal{X}}\)< / td >
< td class = "org-left" > Relative Motion of {B} with respect to {A}< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{\mathcal{L}}\)< / td >
< td class = "org-left" > Joint Displacement< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{F}_{m}\)< / td >
< td class = "org-left" > Force Sensors in each strut< / td >
< / tr >
< tr >
< td class = "org-left" > \(\bm{v}_{m}\)< / td >
< td class = "org-left" > Inertial Sensors located at \(b_i\) measuring in the direction of the strut< / td >
< / tr >
< / tbody >
< / table >
< blockquote >
< p >
An important difference from basic Simulink models is that the states in a physical network are not independent in general, because some states have dependencies on other states through constraints.
< / p >
< / blockquote >
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< div id = "outline-container-org36eeb29" class = "outline-2" >
< h2 id = "org36eeb29" > < span class = "section-number-2" > 1< / span > Identification< / h2 >
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< div class = "outline-text-2" id = "text-1" >
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< / div >
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< div id = "outline-container-orgb4842a1" class = "outline-3" >
< h3 id = "orgb4842a1" > < span class = "section-number-3" > 1.1< / span > Simscape Model< / h3 >
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< / div >
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< div id = "outline-container-org4240dd7" class = "outline-3" >
< h3 id = "org4240dd7" > < span class = "section-number-3" > 1.2< / span > Initialize the Stewart Platform< / h3 >
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< div class = "outline-text-3" id = "text-1-2" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
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< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org5695094" class = "outline-3" >
< h3 id = "org5695094" > < span class = "section-number-3" > 1.3< / span > Identification< / h3 >
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< div class = "outline-text-3" id = "text-1-3" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_identification'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/tau'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Fext'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/X'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Vm'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Taum'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Lm'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'tau1'< / span > , < span class = "org-string" > 'tau2'< / span > , < span class = "org-string" > 'tau3'< / span > , < span class = "org-string" > 'tau4'< / span > , < span class = "org-string" > 'tau5'< / span > , < span class = "org-string" > 'tau6'< / span > , ...
< span class = "org-string" > 'Fx'< / span > , < span class = "org-string" > 'Fy'< / span > , < span class = "org-string" > 'Fz'< / span > , < span class = "org-string" > 'Mx'< / span > , < span class = "org-string" > 'My'< / span > , < span class = "org-string" > 'Mz'< / span > };
G.OutputName = {< span class = "org-string" > 'Xdx'< / span > , < span class = "org-string" > 'Xdy'< / span > , < span class = "org-string" > 'Xdz'< / span > , < span class = "org-string" > 'Xrx'< / span > , < span class = "org-string" > 'Xry'< / span > , < span class = "org-string" > 'Xrz'< / span > , ...
< span class = "org-string" > 'Vm1'< / span > , < span class = "org-string" > 'Vm2'< / span > , < span class = "org-string" > 'Vm3'< / span > , < span class = "org-string" > 'Vm4'< / span > , < span class = "org-string" > 'Vm5'< / span > , < span class = "org-string" > 'Vm6'< / span > , ...
< span class = "org-string" > 'taum1'< / span > , < span class = "org-string" > 'taum2'< / span > , < span class = "org-string" > 'taum3'< / span > , < span class = "org-string" > 'taum4'< / span > , < span class = "org-string" > 'taum5'< / span > , < span class = "org-string" > 'taum6'< / span > , ...
< span class = "org-string" > 'Lm1'< / span > , < span class = "org-string" > 'Lm2'< / span > , < span class = "org-string" > 'Lm3'< / span > , < span class = "org-string" > 'Lm4'< / span > , < span class = "org-string" > 'Lm5'< / span > , < span class = "org-string" > 'Lm6'< / span > };
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< / pre >
< / div >
< / div >
< / div >
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< / div >
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< div id = "outline-container-orge464de2" class = "outline-2" >
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< h2 id = "orge464de2" > < span class = "section-number-2" > 2< / span > States as the motion of the mobile platform< / h2 >
< div class = "outline-text-2" id = "text-2" >
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< / div >
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< div id = "outline-container-org8d12d8c" class = "outline-3" >
< h3 id = "org8d12d8c" > < span class = "section-number-3" > 2.1< / span > Initialize the Stewart Platform< / h3 >
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< div class = "outline-text-3" id = "text-2-1" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgef8d225" class = "outline-3" >
< h3 id = "orgef8d225" > < span class = "section-number-3" > 2.2< / span > Identification< / h3 >
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< div class = "outline-text-3" id = "text-2-2" >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_identification_simple'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/tau'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/X'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Xdot'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io);
< span class = "org-comment" > % G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};< / span >
< span class = "org-comment" > % G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};< / span >
< / pre >
< / div >
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< p >
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Let’ s check the size of < code > G< / code > :
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > size(G)
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< / pre >
< / div >
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< pre class = "example" >
size(G)
State-space model with 12 outputs, 6 inputs, and 18 states.
'org_babel_eoe'
ans =
'org_babel_eoe'
< / pre >
< p >
We expect to have only 12 states (corresponding to the 6dof of the mobile platform).
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gm = minreal(G);
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< / pre >
< / div >
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< pre class = "example" >
Gm = minreal(G);
6 states removed.
< / pre >
< p >
And indeed, we obtain 12 states.
< / p >
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< / div >
< / div >
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< div id = "outline-container-orge68adea" class = "outline-3" >
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< h3 id = "orge68adea" > < span class = "section-number-3" > 2.3< / span > Coordinate transformation< / h3 >
< div class = "outline-text-3" id = "text-2-3" >
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< p >
We can perform the following transformation using the < code > ss2ss< / code > command.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gt = ss2ss(Gm, Gm.C);
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< / pre >
< / div >
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< p >
Then, the < code > C< / code > matrix of < code > Gt< / code > is the unity matrix which means that the states of the state space model are equal to the measurements \(\bm{Y}\).
< / p >
< p >
The measurements are the 6 displacement and 6 velocities of mobile platform with respect to \(\{B\}\).
< / p >
< p >
We could perform the transformation by hand:
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > At = Gm.C< span class = "org-type" > *< / span > Gm.A< span class = "org-type" > *< / span > pinv(Gm.C);
Bt = Gm.C< span class = "org-type" > *< / span > Gm.B;
Ct = eye(12);
Dt = zeros(12, 6);
Gt = ss(At, Bt, Ct, Dt);
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org4973ae1" class = "outline-3" >
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< h3 id = "org4973ae1" > < span class = "section-number-3" > 2.4< / span > Analysis< / h3 >
< div class = "outline-text-3" id = "text-2-4" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > [V,D] = eig(Gt.A);
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< / pre >
< / div >
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< table border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
< colgroup >
< col class = "org-right" / >
< col class = "org-right" / >
< col class = "org-right" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-right" > Mode Number< / th >
< th scope = "col" class = "org-right" > Resonance Frequency [Hz]< / th >
< th scope = "col" class = "org-right" > Damping Ratio [%]< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-right" > 1.0< / td >
< td class = "org-right" > 174.5< / td >
< td class = "org-right" > 0.9< / td >
< / tr >
< tr >
< td class = "org-right" > 2.0< / td >
< td class = "org-right" > 174.5< / td >
< td class = "org-right" > 0.7< / td >
< / tr >
< tr >
< td class = "org-right" > 3.0< / td >
< td class = "org-right" > 202.1< / td >
< td class = "org-right" > 0.7< / td >
< / tr >
< tr >
< td class = "org-right" > 4.0< / td >
< td class = "org-right" > 237.3< / td >
< td class = "org-right" > 0.6< / td >
< / tr >
< tr >
< td class = "org-right" > 5.0< / td >
< td class = "org-right" > 237.3< / td >
< td class = "org-right" > 0.5< / td >
< / tr >
< tr >
< td class = "org-right" > 6.0< / td >
< td class = "org-right" > 283.8< / td >
< td class = "org-right" > 0.5< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
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< div id = "outline-container-orge7b97c8" class = "outline-3" >
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< h3 id = "orge7b97c8" > < span class = "section-number-3" > 2.5< / span > Visualizing the modes< / h3 >
< div class = "outline-text-3" id = "text-2-5" >
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< p >
To visualize the i’ th mode, we may excite the system using the inputs \(U_i\) such that \(B U_i\) is co-linear to \(\xi_i\) (the mode we want to excite).
< / p >
< p >
\[ U(t) = e^{\alpha t} ( ) \]
< / p >
< p >
Let’ s first sort the modes and just take the modes corresponding to a eigenvalue with a positive imaginary part.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > ws = imag(diag(D));
[ws,I] = sort(ws)
ws = ws(7< span class = "org-type" > :< / span > end); I = I(7< span class = "org-type" > :< / span > end);
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< / pre >
< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > 1:length(ws)< / span >
< / pre >
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< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > i_mode = I(< span class = "org-constant" > i< / span > ); < span class = "org-comment" > % the argument is the i'th mode< / span >
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > lambda_i = D(i_mode, i_mode);
xi_i = V(< span class = "org-type" > :< / span > ,i_mode);
a_i = real(lambda_i);
b_i = imag(lambda_i);
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< / pre >
< / div >
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< p >
Let do 10 periods of the mode.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > t = linspace(0, 10< span class = "org-type" > /< / span > (imag(lambda_i)< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > ), 1000);
U_i = pinv(Gt.B) < span class = "org-type" > *< / span > real(xi_i < span class = "org-type" > *< / span > lambda_i < span class = "org-type" > *< / span > (cos(b_i < span class = "org-type" > *< / span > t) < span class = "org-type" > +< / span > 1< span class = "org-constant" > i< / span > < span class = "org-type" > *< / span > sin(b_i < span class = "org-type" > *< / span > t)));
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< / pre >
< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > U = timeseries(U_i, t);
< / pre >
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< / div >
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< p >
Simulation:
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > load(< span class = "org-string" > 'mat/conf_simscape.mat'< / span > );
< span class = "org-matlab-simulink-keyword" > set_param< / span > (< span class = "org-variable-name" > conf_simscape< / span > , < span class = "org-string" > 'StopTime'< / span > , num2str(t(< span class = "org-variable-name" > end< / span > )));
< span class = "org-matlab-simulink-keyword" > sim< / span > (mdl);
< / pre >
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< / div >
< p >
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Save the movie of the mode shape.
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< / p >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > smwritevideo(mdl, sprintf(< span class = "org-string" > 'figs/mode%i'< / span > , < span class = "org-constant" > i< / span > ), ...
< span class = "org-string" > 'PlaybackSpeedRatio'< / span > , 1< span class = "org-type" > /< / span > (b_i< span class = "org-type" > /< / span > 2< span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > ), ...
< span class = "org-string" > 'FrameRate'< / span > , 30, ...
< span class = "org-string" > 'FrameSize'< / span > , [800, 400]);
< / pre >
< / div >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-keyword" > end< / span >
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< / pre >
< / div >
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< div id = "orgb15855a" class = "figure" >
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< p > < img src = "figs/mode1.gif" alt = "mode1.gif" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Identified mode - 1< / p >
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< / div >
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< div id = "org1816e59" class = "figure" >
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< p > < img src = "figs/mode3.gif" alt = "mode3.gif" / >
< / p >
< p > < span class = "figure-number" > Figure 2: < / span > Identified mode - 3< / p >
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< / div >
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< div id = "org01c8dca" class = "figure" >
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< p > < img src = "figs/mode5.gif" alt = "mode5.gif" / >
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< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Identified mode - 5< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org009b696" class = "outline-3" >
< h3 id = "org009b696" > < span class = "section-number-3" > 2.6< / span > Identification< / h3 >
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< div class = "outline-text-3" id = "text-2-6" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_identification'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/tau'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Lm'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
< span class = "org-comment" > % G.InputName = {'tau1', 'tau2', 'tau3', 'tau4', 'tau5', 'tau6'};< / span >
< span class = "org-comment" > % G.OutputName = {'Xdx', 'Xdy', 'Xdz', 'Xrx', 'Xry', 'Xrz', 'Vdx', 'Vdy', 'Vdz', 'Vrx', 'Vry', 'Vrz'};< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > size(G)
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< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgf7a52cb" class = "outline-3" >
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< h3 id = "orgf7a52cb" > < span class = "section-number-3" > 2.7< / span > Change of states< / h3 >
< div class = "outline-text-3" id = "text-2-7" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > At = G.C< span class = "org-type" > *< / span > G.A< span class = "org-type" > *< / span > pinv(G.C);
Bt = G.C< span class = "org-type" > *< / span > G.B;
Ct = eye(12);
Dt = zeros(12, 6);
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > Gt = ss(At, Bt, Ct, Dt);
< / pre >
< / div >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > size(Gt)
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< / pre >
< / div >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org23d7e7b" class = "outline-2" >
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< h2 id = "org23d7e7b" > < span class = "section-number-2" > 3< / span > Simple Model without any sensor< / h2 >
< div class = "outline-text-2" id = "text-3" >
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< / div >
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< div id = "outline-container-org2ad9d50" class = "outline-3" >
< h3 id = "org2ad9d50" > < span class = "section-number-3" > 3.1< / span > Simscape Model< / h3 >
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< div class = "outline-text-3" id = "text-3-1" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > open < span class = "org-string" > 'stewart_identification_simple.slx'< / span >
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< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orgbc1f736" class = "outline-3" >
< h3 id = "orgbc1f736" > < span class = "section-number-3" > 3.2< / span > Initialize the Stewart Platform< / h3 >
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< div class = "outline-text-3" id = "text-3-2" >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart);
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stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
< / pre >
< / div >
< / div >
< / div >
2020-02-11 18:04:45 +01:00
< div id = "outline-container-org43f8fc6" class = "outline-3" >
< h3 id = "org43f8fc6" > < span class = "section-number-3" > 3.3< / span > Identification< / h3 >
2020-02-11 15:50:52 +01:00
< div class = "outline-text-3" id = "text-3-3" >
2020-01-29 17:52:04 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > stateorder = {...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_1_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_2_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_3_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_4_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_5_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple/Solver Configuration/EVAL_KEY/INPUT_6_1_1'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.p'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Rz.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.cylindrical_joint.Pz.v'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_2.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_3.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_4.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_5.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_6.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_F.S.w'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.Q'< / span > ,...
< span class = "org-string" > 'stewart_platform_identification_simple.Stewart_Platform.Strut_1.Subsystem.spherical_joint_M.S.w'< / span > };
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Options for Linearized< / span > < / span >
options = linearizeOptions;
options.SampleTime = 0;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'stewart_platform_identification_simple'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
clear io; io_i = 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/tau'< / span > ], 1, < span class = "org-string" > 'openinput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/X'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
io(io_i) = linio([mdl, < span class = "org-string" > '/Xdot'< / span > ], 1, < span class = "org-string" > 'openoutput'< / span > ); io_i = io_i < span class = "org-type" > +< / span > 1;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize(mdl, io, options);
G.InputName = {< span class = "org-string" > 'tau1'< / span > , < span class = "org-string" > 'tau2'< / span > , < span class = "org-string" > 'tau3'< / span > , < span class = "org-string" > 'tau4'< / span > , < span class = "org-string" > 'tau5'< / span > , < span class = "org-string" > 'tau6'< / span > };
G.OutputName = {< span class = "org-string" > 'Xdx'< / span > , < span class = "org-string" > 'Xdy'< / span > , < span class = "org-string" > 'Xdz'< / span > , < span class = "org-string" > 'Xrx'< / span > , < span class = "org-string" > 'Xry'< / span > , < span class = "org-string" > 'Xrz'< / span > , < span class = "org-string" > 'Vdx'< / span > , < span class = "org-string" > 'Vdy'< / span > , < span class = "org-string" > 'Vdz'< / span > , < span class = "org-string" > 'Vrx'< / span > , < span class = "org-string" > 'Vry'< / span > , < span class = "org-string" > 'Vrz'< / span > };
2019-03-22 12:03:59 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-01-29 17:52:04 +01:00
< pre class = "src src-matlab" > size(G)
< / pre >
< / div >
2019-08-26 11:58:44 +02:00
2020-01-29 17:52:04 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > G.StateName
2019-03-22 12:03:59 +01:00
< / pre >
< / div >
2020-01-29 17:52:04 +01:00
< / div >
< / div >
< / div >
2019-03-22 12:03:59 +01:00
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org0502cd2" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org0502cd2" > < span class = "section-number-2" > 4< / span > Cartesian Plot< / h2 >
< div class = "outline-text-2" id = "text-4" >
2019-03-22 12:03:59 +01:00
< p >
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From a force applied in the Cartesian frame to a displacement in the Cartesian frame.
2019-03-22 12:03:59 +01:00
< / p >
< div class = "org-src-container" >
2020-01-29 17:52:04 +01:00
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_cart(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_cart(2, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_cart(3, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
bode(G.G_cart, freqs);
< / pre >
< / div >
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org32e2eb3" class = "outline-2" >
2020-02-11 15:50:52 +01:00
< h2 id = "org32e2eb3" > < span class = "section-number-2" > 5< / span > From a force to force sensor< / h2 >
< div class = "outline-text-2" id = "text-5" >
2020-01-29 17:52:04 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$F_{m_i}/F_{i}$'< / span > );
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [N/N]'< / span > );
legend(< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'southeast'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_forc(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$F_{m_i}/F_{i}$'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_forc(2, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$F_{m_j}/F_{i}$'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_forc(3, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_forc(4, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_forc(5, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_forc(6, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [N/N]'< / span > );
legend(< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'southeast'< / span > );
< / pre >
< / div >
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org8ddfd2c" class = "outline-2" >
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< h2 id = "org8ddfd2c" > < span class = "section-number-2" > 6< / span > From a force applied in the leg to the displacement of the leg< / h2 >
< div class = "outline-text-2" id = "text-6" >
2020-01-29 17:52:04 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$D_{i}/F_{i}$'< / span > );
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/N]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_legs(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k-'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$D_{i}/F_{i}$'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_legs(2, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'DisplayName'< / span > , < span class = "org-string" > '$D_{j}/F_{i}$'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_legs(3, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_legs(4, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_legs(5, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
plot(freqs, abs(squeeze(freqresp(G.G_legs(6, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))), < span class = "org-string" > 'k--'< / span > , < span class = "org-string" > 'HandleVisibility'< / span > , < span class = "org-string" > 'off'< / span > );
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/N]'< / span > );
legend(< span class = "org-string" > 'location'< / span > , < span class = "org-string" > 'northeast'< / span > );
< / pre >
< / div >
< / div >
< / div >
2020-02-11 15:27:39 +01:00
< div id = "outline-container-org5685537" class = "outline-2" >
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< h2 id = "org5685537" > < span class = "section-number-2" > 7< / span > Transmissibility< / h2 >
< div class = "outline-text-2" id = "text-7" >
2020-01-29 17:52:04 +01:00
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(2, 2), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(3, 3), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/m]'< / span > );
2019-03-22 12:03:59 +01:00
< / pre >
< / div >
< div class = "org-src-container" >
2020-01-29 17:52:04 +01:00
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_tran(4, 4), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(5, 5), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(6, 6), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [$\frac{rad/s}{rad/s}$]'< / span > );
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 2), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_tran(1, 3), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/m]'< / span > );
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< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org3335d1e" class = "outline-2" >
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< h2 id = "org3335d1e" > < span class = "section-number-2" > 8< / span > Compliance< / h2 >
< div class = "outline-text-2" id = "text-8" >
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< p >
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From a force applied in the Cartesian frame to a relative displacement of the mobile platform with respect to the base.
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< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_comp(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_comp(2, 2), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_comp(3, 3), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/N]'< / span > );
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< / pre >
< / div >
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< / div >
< / div >
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< div id = "outline-container-org5ca7af8" class = "outline-2" >
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< h2 id = "org5ca7af8" > < span class = "section-number-2" > 9< / span > Inertial< / h2 >
< div class = "outline-text-2" id = "text-9" >
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< p >
From a force applied on the Cartesian frame to the absolute displacement of the mobile platform.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
hold on;
plot(freqs, abs(squeeze(freqresp(G.G_iner(1, 1), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_iner(2, 2), freqs, < span class = "org-string" > 'Hz'< / span > ))));
plot(freqs, abs(squeeze(freqresp(G.G_iner(3, 3), freqs, < span class = "org-string" > 'Hz'< / span > ))));
hold off;
< span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale'< / span > , < span class = "org-string" > 'log'< / span > ); < span class = "org-type" > set< / span > (< span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'YScale'< / span > , < span class = "org-string" > 'log'< / span > );
xlabel(< span class = "org-string" > 'Frequency [Hz]'< / span > ); ylabel(< span class = "org-string" > 'Amplitude [m/N]'< / span > );
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< / pre >
< / div >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2020-02-11 mar. 17:51< / p >
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< / div >
< / body >
< / html >
