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< a accesskey = "h" href = "../index.html" > UP < / a >
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< a accesskey = "H" href = "../index.html" > HOME < / a >
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< h1 class = "title" > Cedrat Actuator< / 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 = "#orgd28b4dd" > 1. Documentation< / a > < / li >
< li > < a href = "#org2594c75" > 2. Parameters< / a > < / li >
< li > < a href = "#org5b8504e" > 3. Identification< / a > < / li >
< li > < a href = "#org919f71c" > 4. Integral Force Feedback< / a > < / li >
< li > < a href = "#org7ec0c4b" > 5. Damped System< / a > < / li >
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< / ul >
< / div >
< / div >
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< h2 id = "orgd28b4dd" > < span class = "section-number-2" > 1< / span > Documentation< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< ul class = "org-ul" >
< li > Blocked force: \(1400\ N\)< / li >
< li > Stiffness: \(10.8\ N/\mu m\)< / li >
< li > Resonance (free-free): \(6450\ Hz\)< / li >
< li > Resonance (blocked-free): \(1750\ Hz\)< / li >
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< li > Height: \(H = 45\ mm\)< / li >
< li > Length: \(L = 80\ mm\)< / li >
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< li > Width: \(22\ mm\)< / li >
< li > Mass: \(160\ g\)< / li >
< / ul >
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< div class = "figure" >
< p > < img src = "figs/cedrat_geometry.png" alt = "cedrat_geometry.png" / >
< / p >
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< / div >
< / div >
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< / div >
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< div id = "outline-container-org2594c75" class = "outline-2" >
< h2 id = "org2594c75" > < span class = "section-number-2" > 2< / span > Parameters< / h2 >
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< div class = "outline-text-2" id = "text-2" >
< div class = "org-src-container" >
< pre class = "src src-matlab" > cedrat.L = < span class = "org-highlight-numbers-number" > 80< / span > ; < span class = "org-comment" > % Total Width of the Actuator[mm]< / span >
cedrat.H = < span class = "org-highlight-numbers-number" > 45< / span > ; < span class = "org-comment" > % Total Height of the Actuator [mm]< / span >
cedrat.L2 = sqrt< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > (< / span > cedrat.L< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > ^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > +< / span > < span class = "org-rainbow-delimiters-depth-2" > (< / span > cedrat.H< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > ^< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % Length of the elipsoidal sections [mm]< / span >
cedrat.alpha = < span class = "org-highlight-numbers-number" > 180< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > *< / span > atan2< span class = "org-rainbow-delimiters-depth-1" > (< / span > cedrat.L< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > , cedrat.H< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % [deg]< / span >
cedrat.mtot = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 160< / span > ; < span class = "org-comment" > % Total mass of the Actuator [kg]< / span >
cedrat.m = cedrat.mtot< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 6< / span > ; < span class = "org-comment" > % Mass of each single element [kg]< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > cedrat.k = < span class = "org-highlight-numbers-number" > 1e9< / span > ; < span class = "org-comment" > % Linear Stiffness of each "blade" [N/m]< / span >
cedrat.c = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > *< / span > sqrt< span class = "org-rainbow-delimiters-depth-1" > (< / span > cedrat.mtot< span class = "org-type" > *< / span > cedrat.k< span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % [N/(m/s)]< / span >
cedrat.ka = < span class = "org-highlight-numbers-number" > 5e7< / span > ; < span class = "org-comment" > % Linear Stiffness of the stack [N/m]< / span >
cedrat.ca = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > *< / span > sqrt< span class = "org-rainbow-delimiters-depth-1" > (< / span > cedrat.mtot< span class = "org-type" > *< / span > cedrat.ka< span class = "org-rainbow-delimiters-depth-1" > )< / span > ; < span class = "org-comment" > % [N/(m/s)]< / span >
cedrat.kr = < span class = "org-highlight-numbers-number" > 10< / span > ; < span class = "org-comment" > % Rotation Stiffness [N*m/(deg)]< / span >
cedrat.cr = < span class = "org-highlight-numbers-number" > 0< / span > .< span class = "org-highlight-numbers-number" > 0001< / span > ; < span class = "org-comment" > % Rotation Damping [N*m/(deg/s)]< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > K_iff = tf< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 0< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > % dummy_mass = < span class = "org-highlight-numbers-number" > 140< / span > ; % [kg]
dummy_mass = < span class = "org-highlight-numbers-number" > 1< / span > ; < span class = "org-comment" > % [kg]< / span >
< / pre >
< / div >
< / div >
< / div >
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< div id = "outline-container-org5b8504e" class = "outline-2" >
< h2 id = "org5b8504e" > < span class = "section-number-2" > 3< / span > Identification< / h2 >
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< div class = "outline-text-2" id = "text-3" >
< 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 = < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'cedrat_piezo'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/F'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fz'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dw'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dz'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G = linearize< span class = "org-rainbow-delimiters-depth-1" > (< / span > mdl, io, options< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
G.InputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'F'< / span > , < span class = "org-string" > 'Fz'< / span > , < span class = "org-string" > 'Dw'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
G.OutputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Fm'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
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< div id = "org6ebf8c8" class = "figure" >
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< p > < img src = "figs/cedrat_piezo_identified_tf.png" alt = "cedrat_piezo_identified_tf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 2: < / span > Identified Transfer function (< a href = "./figs/cedrat_piezo_identified_tf.png" > png< / a > , < a href = "./figs/cedrat_piezo_identified_tf.pdf" > pdf< / a > )< / p >
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< div id = "outline-container-org919f71c" class = "outline-2" >
< h2 id = "org919f71c" > < span class = "section-number-2" > 4< / span > Integral Force Feedback< / h2 >
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< div class = "outline-text-2" id = "text-4" >
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< div id = "org964c2d0" class = "figure" >
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< p > < img src = "figs/iff_plant_cedrat.png" alt = "iff_plant_cedrat.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > Transfer function from \(F\) to \(F_m\) (< a href = "./figs/iff_plant_cedrat.png" > png< / a > , < a href = "./figs/iff_plant_cedrat.pdf" > pdf< / a > )< / p >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > K_iff = < span class = "org-type" > -< / span > < span class = "org-highlight-numbers-number" > 100000< / span > < span class = "org-type" > /< / span > s< span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > *< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > /< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > +< / span > s< span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-type" > /< / span > < span class = "org-constant" > pi< / span > < span class = "org-type" > /< / span > < span class = "org-highlight-numbers-number" > 100< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< div id = "org090ce7f" class = "figure" >
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< p > < img src = "figs/iff_open_loop_cedrat.png" alt = "iff_open_loop_cedrat.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > Open Loop Gain Transfer Function - Cedrat (< a href = "./figs/iff_open_loop_cedrat.png" > png< / a > , < a href = "./figs/iff_open_loop_cedrat.pdf" > pdf< / a > )< / p >
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< div id = "outline-container-org7ec0c4b" class = "outline-2" >
< h2 id = "org7ec0c4b" > < span class = "section-number-2" > 5< / span > Damped System< / h2 >
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< div class = "outline-text-2" id = "text-5" >
< 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 = < span class = "org-highlight-numbers-number" > 0< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Name of the Simulink File< / span > < / span >
mdl = < span class = "org-string" > 'cedrat_piezo'< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Input/Output definition< / span > < / span >
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/F'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fz'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dw'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'input'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Dz'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
io< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 5< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = linio< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-rainbow-delimiters-depth-2" > [< / span > mdl, < span class = "org-string" > '/Fm'< / span > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-string" > 'output'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-matlab-cellbreak" > < span class = "org-comment" > %% Run the linearization< / span > < / span >
G_iff = linearize< span class = "org-rainbow-delimiters-depth-1" > (< / span > mdl, io, options< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
G_iff.InputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'F'< / span > , < span class = "org-string" > 'Fz'< / span > , < span class = "org-string" > 'Dw'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
G_iff.OutputName = < span class = "org-rainbow-delimiters-depth-1" > {< / span > < span class = "org-string" > 'Dz'< / span > , < span class = "org-string" > 'Fm'< / span > < span class = "org-rainbow-delimiters-depth-1" > }< / span > ;
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< div id = "org2e7eff5" class = "figure" >
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< p > < img src = "figs/cedrat_iff_piezo_identified_tf.png" alt = "cedrat_iff_piezo_identified_tf.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > Identified Transfer function (< a href = "./figs/cedrat_iff_piezo_identified_tf.png" > png< / a > , < a href = "./figs/cedrat_iff_piezo_identified_tf.pdf" > pdf< / a > )< / p >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2019-10-29 mar. 11:06< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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