From ff8df3a9d0abb7d0f573fb48f795bede426a4e01 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 24 Oct 2019 17:45:30 +0200 Subject: [PATCH] Add uniaxial folder with analysis of active damping techniques --- index.html | 653 ++++++------- index.org | 1 + simscape/sim_nano_station_uniaxial.slx | Bin 0 -> 132281 bytes uniaxial/figs | 1 + uniaxial/index.html | 1039 +++++++++++++++++++++ uniaxial/index.org | 1191 ++++++++++++++++++++++++ uniaxial/mat/plants.mat | Bin 0 -> 16092 bytes 7 files changed, 2559 insertions(+), 326 deletions(-) create mode 100644 simscape/sim_nano_station_uniaxial.slx create mode 120000 uniaxial/figs create mode 100644 uniaxial/index.html create mode 100644 uniaxial/index.org create mode 100644 uniaxial/mat/plants.mat diff --git a/index.html b/index.html index e89eeb4..d39275b 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Simscape Model of the Nano-Active-Stabilization-System @@ -258,69 +258,69 @@ for the JavaScript code in this tag.

Table of Contents

@@ -329,6 +329,7 @@ for the JavaScript code in this tag. -
-

1 Simulink project

+
+

1 Simulink project

From the Simulink project mathworks page: @@ -374,8 +375,8 @@ The startup script is defined below and is exported to the project_startup 

freqs = logspace(-1, 3, 1000);
-save_fig = false;
-save('./mat/config.mat', 'freqs', 'save_fig');
+save_fig = false;
+save('./mat/config.mat', 'freqs', 'save_fig');
 
 project = simulinkproject;
 projectRoot = project.RootFolder;
@@ -383,10 +384,10 @@ projectRoot = project.RootFolder;
 myCacheFolder = fullfile(projectRoot, '.SimulinkCache');
 myCodeFolder = fullfile(projectRoot, '.SimulinkCode');
 
-Simulink.fileGenControl('set',...
-    'CacheFolder', myCacheFolder,...
-    'CodeGenFolder', myCodeFolder,...
-    'createDir', true);
+Simulink.fileGenControl('set',...
+    'CacheFolder', myCacheFolder,...
+    'CodeGenFolder', myCodeFolder,...
+    'createDir', true);
@@ -404,8 +405,8 @@ The project also permits to automatically add defined folder to the path when th
-
-

2 Simscape Model

+
+

2 Simscape Model

A simscape model permits to model multi-physics systems. @@ -416,8 +417,8 @@ A simscape model per

-
-

2.1 Solid bodies

+
+

2.1 Solid bodies

Each solid body is represented by a solid block. @@ -426,8 +427,8 @@ The geometry of the solid body can be imported using a step file. T

-
-

2.2 Frames

+
+

2.2 Frames

Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made. @@ -439,8 +440,8 @@ They can be defined from the solid body geometry, or using the -

2.3 Joints

+
+

2.3 Joints

Solid Bodies are connected with joints (between frames of the two solid bodies). @@ -450,7 +451,7 @@ Solid Bodies are connected with joints (between frames of the two solid bodies). There are various types of joints that are all described here.

- +
@@ -583,7 +584,7 @@ Joint blocks are assortments of joint primitives:
  • Constant Velocity: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: CV
    • -
    Table 1: Degrees of freedom associated with each joint
    +
    @@ -875,8 +876,8 @@ Composite Force/Torque sensing: -
    -

    2.4 Measurements

    +
    +

    2.4 Measurements

    A transform sensor block measures the spatial relationship between two frames: the base B and the follower F. @@ -900,8 +901,8 @@ If we want to simulate an inertial sensor, we just have to choose B

    -
    -

    2.5 Excitation

    +
    +

    2.5 Excitation

    We can apply external forces to the model by using an external force and torque block. @@ -914,12 +915,12 @@ Internal force, acting reciprocally between base and following origins is implem

    -
    -

    3 Notes

    +
    +

    3 Notes

    -
    -

    3.1 Simscape files for identification

    +
    +

    3.1 Simscape files for identification

    Table 2: Joint primitives for each joint type
    @@ -988,12 +989,12 @@ Internal force, acting reciprocally between base and following origins is implem -
    -

    3.2 Inputs

    +
    +

    3.2 Inputs

    -
    -

    3.2.1 Perturbations

    +
    +

    3.2.1 Perturbations

    @@ -1041,8 +1042,8 @@ Internal force, acting reciprocally between base and following origins is implem -
    -

    3.2.2 Measurement Noise

    +
    +

    3.2.2 Measurement Noise

    @@ -1076,8 +1077,8 @@ Internal force, acting reciprocally between base and following origins is implem -
    -

    3.2.3 Control Inputs

    +
    +

    3.2.3 Control Inputs

    @@ -1201,8 +1202,8 @@ Internal force, acting reciprocally between base and following origins is implem -
    -

    3.3 Outputs

    +
    +

    3.3 Outputs

    @@ -1320,8 +1321,8 @@ Internal force, acting reciprocally between base and following origins is implem -
    -

    4 Simulink files

    +
    +

    4 Simulink files

    Few different Simulink files are used: @@ -1335,44 +1336,44 @@ Few different Simulink files are used:

    -
    -

    5 Simulink Library

    +
    +

    5 Simulink Library

    A simulink library is developed in order to share elements between the different simulink files.

    -
    -

    5.1 inputs

    +
    +

    5.1 inputs

    -
    -

    5.2 nasslibrary

    +
    +

    5.2 nasslibrary

    -
    -

    5.3 poserrorwrtnassbase

    +
    +

    5.3 poserrorwrtnassbase

    -
    -

    5.4 QuaternionToAngles

    +
    +

    5.4 QuaternionToAngles

    -
    -

    5.5 RotationMatrixToAngle

    +
    +

    5.5 RotationMatrixToAngle

    -
    -

    6 Scripts

    +
    +

    6 Scripts

    -
    -

    6.1 Simulation Initialization

    +
    +

    6.1 Simulation Initialization

    - +

    @@ -1396,15 +1397,15 @@ load( -

    7 Functions

    +
    +

    7 Functions

    -
    -

    7.1 computePsdDispl

    +
    +

    7.1 computePsdDispl

    - +

    @@ -1426,24 +1427,24 @@ This Matlab function is accessible here. [pry, ~] = pwelch(sys_data.Ry(i_init:end, :), han_win, [], [], Fs); [prz, ~] = pwelch(sys_data.Rz(i_init:end, :), han_win, [], [], Fs); - psd_object = struct(... - 'f', f, ... - 'dx', pdx, ... - 'dy', pdy, ... - 'dz', pdz, ... - 'rx', prx, ... - 'ry', pry, ... + psd_object = struct(... + 'f', f, ... + 'dx', pdx, ... + 'dy', pdy, ... + 'dz', pdz, ... + 'rx', prx, ... + 'ry', pry, ... 'rz', prz); end

    -
    -

    7.2 computeSetpoint

    +
    +

    7.2 computeSetpoint

    - +

    @@ -1514,11 +1515,11 @@ setpoint( -

    7.3 converErrorBasis

    +
    +

    7.3 converErrorBasis

    - +

    @@ -1546,11 +1547,11 @@ This Matlab function is accessible here. %% If line vector => column vector if size(pos, 2) == 6 - pos = pos'; + pos = pos'; end if size(setpoint, 2) == 6 - setpoint = setpoint'; + setpoint = setpoint'; end %% Position of the sample in the frame fixed to the Granite @@ -1655,11 +1656,11 @@ error_nass = [dx; dy; dz; th

    -
    -

    7.4 generateDiagPidControl

    + -
    -

    7.5 identifyPlant

    +
    +

    7.5 identifyPlant

    - +

    @@ -1706,7 +1707,7 @@ This Matlab function is accessible here. opts = struct(); %% Populate opts with input parameters - if exist('opts_param','var') + if exist('opts_param','var') for opt = fieldnames(opts_param)' opts.(opt{1}) = opts_param.(opt{1}); end @@ -1720,49 +1721,49 @@ This Matlab function is accessible here. mdl = 'sim_nano_station_id'; %% Input/Output definition - io(1) = linio([mdl, '/Fn'], 1, 'input'); % Cartesian forces applied by NASS - io(2) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion - io(3) = linio([mdl, '/Fs'], 1, 'input'); % External forces on the sample - io(4) = linio([mdl, '/Fnl'], 1, 'input'); % Forces applied on the NASS's legs - io(5) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample - io(6) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs - io(7) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs - io(8) = linio([mdl, '/Es'], 1, 'output'); % Position Error w.r.t. NASS base + io(1) = linio([mdl, '/Fn'], 1, 'input'); % Cartesian forces applied by NASS + io(2) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion + io(3) = linio([mdl, '/Fs'], 1, 'input'); % External forces on the sample + io(4) = linio([mdl, '/Fnl'], 1, 'input'); % Forces applied on the NASS's legs + io(5) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample + io(6) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs + io(7) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs + io(8) = linio([mdl, '/Es'], 1, 'output'); % Position Error w.r.t. NASS base %% Run the linearization G = linearize(mdl, io, 0); - G.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz', ... - 'Dgx', 'Dgy', 'Dgz', ... - 'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz', ... - 'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; - G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', ... - 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6', ... - 'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', ... - 'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'}; + G.InputName = {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz', ... + 'Dgx', 'Dgy', 'Dgz', ... + 'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz', ... + 'F1', 'F2', 'F3', 'F4', 'F5', 'F6'}; + G.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', ... + 'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6', ... + 'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6', ... + 'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'}; %% Create the sub transfer functions % From forces applied in the cartesian frame to displacement of the sample in the cartesian frame - sys.G_cart = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'})); + sys.G_cart = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'})); % From ground motion to Sample displacement - sys.G_gm = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Dgx', 'Dgy', 'Dgz'})); + sys.G_gm = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Dgx', 'Dgy', 'Dgz'})); % From direct forces applied on the sample to displacement of the sample - sys.G_fs = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz'})); + sys.G_fs = minreal(G({'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'}, {'Fsx', 'Fsy', 'Fsz', 'Msx', 'Msy', 'Msz'})); % From forces applied on NASS's legs to force sensor in each leg - sys.G_iff = minreal(G({'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); + sys.G_iff = minreal(G({'Fm1', 'Fm2', 'Fm3', 'Fm4', 'Fm5', 'Fm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); % From forces applied on NASS's legs to displacement of each leg - sys.G_dleg = minreal(G({'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); + sys.G_dleg = minreal(G({'Dm1', 'Dm2', 'Dm3', 'Dm4', 'Dm5', 'Dm6'}, {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'})); % From forces applied on NASS's legs to displacement of each leg - sys.G_plant = minreal(G({'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'})); + sys.G_plant = minreal(G({'Edx', 'Rdy', 'Edz', 'Erx', 'Ery', 'Erz'}, {'Fnx', 'Fny', 'Fnz', 'Mnx', 'Mny', 'Mnz'})); end

    -
    -

    7.6 runSimulation

    +
    +

    7.6 runSimulation

    - +

    @@ -1772,17 +1773,17 @@ This Matlab function is accessible here. 

    function [] = runSimulation(sys_name, sys_mass, ctrl_type, act_damp)
     %% Load the controller and save it for the simulation
-    if strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'none')
+    if strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'none')
       K_obj = load('./mat/K_fb.mat');
       K = K_obj.(sprintf('K_%s_%s', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K');
-    elseif strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'iff')
+      save('./mat/controllers.mat', 'K');
+    elseif strcmp(ctrl_type, 'cl') && strcmp(act_damp, 'iff')
       K_obj = load('./mat/K_fb_iff.mat');
       K = K_obj.(sprintf('K_%s_%s_iff', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K');
+      save('./mat/controllers.mat', 'K');
     elseif strcmp(ctrl_type, 'ol')
       K = tf(zeros(6)); %#ok
-      save('./mat/controllers.mat', 'K');
+      save('./mat/controllers.mat', 'K');
     else
       error('ctrl_type should be cl or ol');
     end
@@ -1791,17 +1792,17 @@ This Matlab function is accessible here.
     if strcmp(act_damp, 'iff')
       K_iff_crit = load('./mat/K_iff_crit.mat');
       K_iff = K_iff_crit.(sprintf('K_iff_%s_%s', sys_mass, sys_name)); %#ok
-      save('./mat/controllers.mat', 'K_iff', '-append');
+      save('./mat/controllers.mat', 'K_iff', '-append');
     elseif strcmp(act_damp, 'none')
       K_iff = tf(zeros(6)); %#ok
-      save('./mat/controllers.mat', 'K_iff', '-append');
+      save('./mat/controllers.mat', 'K_iff', '-append');
     end
 
     %%
     if strcmp(sys_name, 'pz')
-      initializeNanoHexapod(struct('actuator', 'piezo'));
+      initializeNanoHexapod(struct('actuator', 'piezo'));
     elseif strcmp(sys_name, 'vc')
-      initializeNanoHexapod(struct('actuator', 'lorentz'));
+      initializeNanoHexapod(struct('actuator', 'lorentz'));
     else
       error('sys_name should be pz or vc');
     end
@@ -1823,23 +1824,23 @@ This Matlab function is accessible here.
 
     %% Save the result
     filename = sprintf('sim_%s_%s_%s_%s', sys_mass, sys_name, ctrl_type, act_damp);
-    save(sprintf('./mat/%s.mat', filename), ...
-        'time', 'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', 'K');
+    save(sprintf('./mat/%s.mat', filename), ...
+        'time', 'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz', 'K');
 end
    -
    -

    8 Initialize Elements

    +
    +

    8 Initialize Elements

    -
    -

    8.1 Simulation Configuration

    +
    +

    8.1 Simulation Configuration

    - +

    @@ -1849,14 +1850,14 @@ This Matlab function is accessible here. 

    function [] = initializeSimConf(opts_param)
     %% Default values for opts
-    opts = struct('Ts',      1e-4,  ... % Sampling time [s]
-                  'Tsim',    10,    ... % Simulation time [s]
-                  'cl_time', 0,     ... % Close Loop time [s]
-                  'gravity', false  ... % Gravity along the z axis
+    opts = struct('Ts',      1e-4,  ... % Sampling time [s]
+                  'Tsim',    10,    ... % Simulation time [s]
+                  'cl_time', 0,     ... % Close Loop time [s]
+                  'gravity', false  ... % Gravity along the z axis
     );
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -1878,18 +1879,18 @@ This Matlab function is accessible here.
     end
 
     %% Save
-    save('./mat/sim_conf.mat', 'sim_conf');
+    save('./mat/sim_conf.mat', 'sim_conf');
 end
    -
    -

    8.2 Experiment

    +
    +

    8.2 Experiment

    - +

    @@ -1899,21 +1900,21 @@ This Matlab function is accessible here 

    function [] = initializeExperiment(exp_name, sys_mass)
     if strcmp(exp_name, 'tomography')
-        opts_sim = struct(...
-            'Tsim',    5, ...
-            'cl_time', 5  ...
+        opts_sim = struct(...
+            'Tsim',    5, ...
+            'cl_time', 5  ...
         );
         initializeSimConf(opts_sim);
 
         if strcmp(sys_mass, 'light')
-            opts_inputs = struct(...
-                'Dw', true,  ...
-                'Rz', 60     ... % rpm
+            opts_inputs = struct(...
+                'Dw', true,  ...
+                'Rz', 60     ... % rpm
             );
         elseif strcpm(sys_mass, 'heavy')
-            opts_inputs = struct(...
-                'Dw', true,  ...
-                'Rz', 1     ... % rpm
+            opts_inputs = struct(...
+                'Dw', true,  ...
+                'Rz', 1     ... % rpm
             );
         else
             error('sys_mass should be light or heavy');
@@ -1929,11 +1930,11 @@ This Matlab function is accessible here
    -
    -

    8.3 Inputs

    +
    +

    8.3 Inputs

    - +

    @@ -1943,55 +1944,55 @@ This Matlab function is accessible here. 

    function [inputs] = initializeInputs(opts_param)
     %% Default values for opts
-    opts = struct(   ...
-        'Dw', false, ...
-        'Dy', false, ...
-        'Ry', false, ...
-        'Rz', false, ...
-        'Dh', false, ...
-        'Rm', false, ...
-        'Dn', false  ...
+    opts = struct(   ...
+        'Dw', false, ...
+        'Dy', false, ...
+        'Ry', false, ...
+        'Rz', false, ...
+        'Dh', false, ...
+        'Rm', false, ...
+        'Dn', false  ...
     );
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
     end
 
     %% Load Sampling Time and Simulation Time
-    load('./mat/sim_conf.mat', 'sim_conf');
+    load('./mat/sim_conf.mat', 'sim_conf');
 
     %% Define the time vector
     t = 0:sim_conf.Ts:sim_conf.Tsim;
 
     %% Ground motion - Dw
-    if islogical(opts.Dw) && opts.Dw == true
-        load('./mat/perturbations.mat', 'Wxg');
+    if islogical(opts.Dw) && opts.Dw == true
+        load('./mat/perturbations.mat', 'Wxg');
         Dw = 1/sqrt(2)*100*random('norm', 0, 1, length(t), 3);
         Dw(:, 1) = lsim(Wxg, Dw(:, 1), t);
         Dw(:, 2) = lsim(Wxg, Dw(:, 2), t);
         Dw(:, 3) = lsim(Wxg, Dw(:, 3), t);
-    elseif islogical(opts.Dw) && opts.Dw == false
+    elseif islogical(opts.Dw) && opts.Dw == false
         Dw = zeros(length(t), 3);
     else
         Dw = opts.Dw;
     end
 
     %% Translation stage - Dy
-    if islogical(opts.Dy) && opts.Dy == true
+    if islogical(opts.Dy) && opts.Dy == true
         Dy = zeros(length(t), 1);
-    elseif islogical(opts.Dy) && opts.Dy == false
+    elseif islogical(opts.Dy) && opts.Dy == false
         Dy = zeros(length(t), 1);
     else
         Dy = opts.Dy;
     end
 
     %% Tilt Stage - Ry
-    if islogical(opts.Ry) && opts.Ry == true
+    if islogical(opts.Ry) && opts.Ry == true
         Ry = 3*(2*pi/360)*sin(2*pi*0.2*t);
-    elseif islogical(opts.Ry) && opts.Ry == false
+    elseif islogical(opts.Ry) && opts.Ry == false
         Ry = zeros(length(t), 1);
     elseif isnumeric(opts.Ry) && length(opts.Ry) == 1
         Ry = opts.Ry*(2*pi/360)*ones(length(t), 1);
@@ -2000,9 +2001,9 @@ This Matlab function is accessible here.
     end
 
     %% Spindle - Rz
-    if islogical(opts.Rz) && opts.Rz == true
+    if islogical(opts.Rz) && opts.Rz == true
         Rz = 2*pi*0.5*t;
-    elseif islogical(opts.Rz) && opts.Rz == false
+    elseif islogical(opts.Rz) && opts.Rz == false
         Rz = zeros(length(t), 1);
     elseif isnumeric(opts.Rz) && length(opts.Rz) == 1
         Rz = opts.Rz*(2*pi/60)*t;
@@ -2011,9 +2012,9 @@ This Matlab function is accessible here.
     end
 
     %% Micro Hexapod - Dh
-    if islogical(opts.Dh) && opts.Dh == true
+    if islogical(opts.Dh) && opts.Dh == true
         Dh = zeros(length(t), 6);
-    elseif islogical(opts.Dh) && opts.Dh == false
+    elseif islogical(opts.Dh) && opts.Dh == false
         Dh = zeros(length(t), 6);
     else
         Dh = opts.Dh;
@@ -2028,9 +2029,9 @@ This Matlab function is accessible here.
     end
 
     %% Nano Hexapod - Dn
-    if islogical(opts.Dn) && opts.Dn == true
+    if islogical(opts.Dn) && opts.Dn == true
         Dn = zeros(length(t), 6);
-    elseif islogical(opts.Dn) && opts.Dn == false
+    elseif islogical(opts.Dn) && opts.Dn == false
         Dn = zeros(length(t), 6);
     else
         Dn = opts.Dn;
@@ -2038,7 +2039,7 @@ This Matlab function is accessible here.
 
     %% Setpoint - Ds
     Ds = zeros(length(t), 6);
-    for i = 1:length(t)
+    for i = 1:length(t)
         Ds(i, :) = computeSetpoint(Dy(i), Ry(i), Rz(i));
     end
 
@@ -2049,22 +2050,22 @@ This Matlab function is accessible here.
     Fs = zeros(length(t), 6);
 
     %% Create the input Structure that will contain all the inputs
-    inputs = struct( ...
-        'Ts', sim_conf.Ts,       ...
-        'Dw', timeseries(Dw, t), ...
-        'Dy', timeseries(Dy, t), ...
-        'Ry', timeseries(Ry, t), ...
-        'Rz', timeseries(Rz, t), ...
-        'Dh', timeseries(Dh, t), ...
-        'Rm', timeseries(Rm, t), ...
-        'Dn', timeseries(Dn, t), ...
-        'Ds', timeseries(Ds, t), ...
-        'Fg', timeseries(Fg, t), ...
-        'Fs', timeseries(Fs, t)  ...
+    inputs = struct( ...
+        'Ts', sim_conf.Ts,       ...
+        'Dw', timeseries(Dw, t), ...
+        'Dy', timeseries(Dy, t), ...
+        'Ry', timeseries(Ry, t), ...
+        'Rz', timeseries(Rz, t), ...
+        'Dh', timeseries(Dh, t), ...
+        'Rm', timeseries(Rm, t), ...
+        'Dn', timeseries(Dn, t), ...
+        'Ds', timeseries(Ds, t), ...
+        'Fg', timeseries(Fg, t), ...
+        'Fs', timeseries(Fs, t)  ...
     );
 
     %% Save
-    save('./mat/inputs.mat', 'inputs');
+    save('./mat/inputs.mat', 'inputs');
 
     %% Custom Functions
     function setpoint = computeSetpoint(ty, ry, rz)
@@ -2121,11 +2122,11 @@ This Matlab function is accessible here.
    -
    -

    8.4 Ground

    +
    +

    8.4 Ground

    - +

    @@ -2142,18 +2143,18 @@ This Matlab function is accessible here. ground.color = [0.5, 0.5, 0.5]; %% Save - save('./mat/stages.mat', 'ground', '-append'); + save('./mat/stages.mat', 'ground', '-append'); end

    -
    -

    8.5 Granite

    +
    +

    8.5 Granite

    - +

    @@ -2186,18 +2187,18 @@ This Matlab function is accessible here. granite.sample_pos = 0.8; % Z-offset for the initial position of the sample [m] %% Save - save('./mat/stages.mat', 'granite', '-append'); + save('./mat/stages.mat', 'granite', '-append'); end

    -
    -

    8.6 Translation Stage

    +
    +

    8.6 Translation Stage

    - +

    @@ -2207,10 +2208,10 @@ This Matlab function is accessible here. 

    function [ty] = initializeTy(opts_param)
     %% Default values for opts
-    opts = struct('rigid', false);
+    opts = struct('rigid', false);
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -2271,18 +2272,18 @@ This Matlab function is accessible here.
     ty.c.rad = 100*(1/5)*sqrt(ty.k.rad/ty.m);
 
     %% Save
-    save('./mat/stages.mat', 'ty', '-append');
+    save('./mat/stages.mat', 'ty', '-append');
 end
    -
    -

    8.7 Tilt Stage

    +
    +

    8.7 Tilt Stage

    - +

    @@ -2292,10 +2293,10 @@ This Matlab function is accessible here. 

    function [ry] = initializeRy(opts_param)
     %% Default values for opts
-    opts = struct('rigid', false);
+    opts = struct('rigid', false);
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -2344,18 +2345,18 @@ This Matlab function is accessible here.
     ry.z_offset = 0.58178; % Z-Offset so that the center of rotation matches the sample center [m]
 
     %% Save
-    save('./mat/stages.mat', 'ry', '-append');
+    save('./mat/stages.mat', 'ry', '-append');
 end
    -
    -

    8.8 Spindle

    +
    +

    8.8 Spindle

    - +

    @@ -2365,10 +2366,10 @@ This Matlab function is accessible here. 

    function [rz] = initializeRz(opts_param)
     %% Default values for opts
-    opts = struct('rigid', false);
+    opts = struct('rigid', false);
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -2413,18 +2414,18 @@ This Matlab function is accessible here.
     rz.c.rot  = 100*sqrt(rz.k.rot/rz.m);
 
     %% Save
-    save('./mat/stages.mat', 'rz', '-append');
+    save('./mat/stages.mat', 'rz', '-append');
 end
    -
    -

    8.9 Micro Hexapod

    +
    +

    8.9 Micro Hexapod

    - +

    @@ -2437,7 +2438,7 @@ This Matlab function is accessible here(); %% Populate opts with input parameters - if exist('opts_param','var') + if exist('opts_param','var') for opt = fieldnames(opts_param)' opts.(opt{1}) = opts_param.(opt{1}); end @@ -2446,7 +2447,7 @@ This Matlab function is accessible here%% Stewart Object micro_hexapod = struct(); micro_hexapod.h = 350; % Total height of the platform [mm] -% micro_hexapod.jacobian = 269.26; % Distance from the top platform to the Jacobian point [mm] +% micro_hexapod.jacobian = 269.26; % Distance from the top platform to the Jacobian point [mm] micro_hexapod.jacobian = 270; % Distance from the top platform to the Jacobian point [mm] %% Bottom Plate - Mechanical Design @@ -2525,12 +2526,12 @@ This Matlab function is accessible here(micro_hexapod); %% Save - save('./mat/stages.mat', 'micro_hexapod', '-append'); + save('./mat/stages.mat', 'micro_hexapod', '-append'); %% function [element] = updateDamping(element) field = fieldnames(element.k); - for i = 1:length(field) + for i = 1:length(field) element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m); end end @@ -2549,7 +2550,7 @@ This Matlab function is accessible here*0.001; % rayon emplacement support base radius_t = stewart.TP.leg.rad*0.001; % top radius in meters - for i = 1:3 + for i = 1:3 % base points angle_m_b = (2*pi/3)* (i-1) - alpha_b; angle_p_b = (2*pi/3)* (i-1) + alpha_b; @@ -2572,24 +2573,24 @@ This Matlab function is accessible here- stewart.pos_base; leg_length = zeros(6, 1); leg_vectors = zeros(6, 3); - for i = 1:6 + for i = 1:6 leg_length(i) = norm(legs(i,:)); leg_vectors(i,:) = legs(i,:) / leg_length(i); end stewart.Leg.lenght = 1000*leg_length(1)/1.5; - stewart.Leg.shape.bot = [0 0; ... - stewart.Leg.rad.bottom 0; ... - stewart.Leg.rad.bottom stewart.Leg.lenght; ... - stewart.Leg.rad.top stewart.Leg.lenght; ... - stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ... + stewart.Leg.shape.bot = [0 0; ... + stewart.Leg.rad.bottom 0; ... + stewart.Leg.rad.bottom stewart.Leg.lenght; ... + stewart.Leg.rad.top stewart.Leg.lenght; ... + stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ... 0 0.2*stewart.Leg.lenght]; %% Calculate revolute and cylindrical axes rev1 = zeros(6, 3); rev2 = zeros(6, 3); cyl1 = zeros(6, 3); - for i = 1:6 + for i = 1:6 rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]); rev1(i,:) = rev1(i,:) / norm(rev1(i,:)); @@ -2604,9 +2605,9 @@ This Matlab function is accessible here('rotation', eye(3)); stewart.upper_leg = struct('rotation', eye(3)); - for i = 1:6 - stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; - stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; + for i = 1:6 + stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; + stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)']; end %% Position Matrix @@ -2614,15 +2615,15 @@ This Matlab function is accessible here%% Compute Jacobian Matrix aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)]; - stewart.J = getJacobianMatrix(leg_vectors', aa'); + stewart.J = getJacobianMatrix(leg_vectors', aa'); end function J = getJacobianMatrix(RM,M_pos_base) % RM: [3x6] unit vector of each leg in the fixed frame % M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame J = zeros(6); - J(:, 1:3) = RM'; - J(:, 4:6) = cross(M_pos_base, RM)'; + J(:, 1:3) = RM'; + J(:, 4:6) = cross(M_pos_base, RM)'; end end @@ -2630,11 +2631,11 @@ This Matlab function is accessible here

    -
    -

    8.10 Center of gravity compensation

    +
    +

    8.10 Center of gravity compensation

    - +

    @@ -2671,17 +2672,17 @@ This Matlab function is accessible here. axisc.c.ax = (1/1)*sqrt(axisc.k.ax/axisc.m); %% Save - save('./mat/stages.mat', 'axisc', '-append'); + save('./mat/stages.mat', 'axisc', '-append'); end

    -
    -

    8.11 Mirror

    +
    +

    8.11 Mirror

    - +

    @@ -2691,13 +2692,13 @@ This Matlab function is accessible here. 

    function [] = initializeMirror(opts_param)
     %% Default values for opts
-    opts = struct(...
-        'shape', 'spherical', ... % spherical or conical
-        'angle', 45 ...
+    opts = struct(...
+        'shape', 'spherical', ... % spherical or conical
+        'angle', 45 ...
     );
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -2718,11 +2719,11 @@ This Matlab function is accessible here.
     mirror.cone_length = mirror.rad*tand(opts.angle)+mirror.h+mirror.jacobian; % Distance from Apex point of the cone to jacobian point
 
     %% Shape
-    mirror.shape = [...
+    mirror.shape = [...
         0 mirror.h-mirror.thickness
-        mirror.hole_rad mirror.h-mirror.thickness; ...
-        mirror.hole_rad 0; ...
-        mirror.rad 0 ...
+        mirror.hole_rad mirror.h-mirror.thickness; ...
+        mirror.hole_rad 0; ...
+        mirror.rad 0 ...
     ];
 
     if strcmp(opts.shape, 'spherical')
@@ -2740,18 +2741,18 @@ This Matlab function is accessible here.
     mirror.shape = [mirror.shape; 0 mirror.h];
 
     %% Save
-    save('./mat/stages.mat', 'mirror', '-append');
+    save('./mat/stages.mat', 'mirror', '-append');
 end
    -
    -

    8.12 Nano Hexapod

    +
    +

    8.12 Nano Hexapod

    - +

    @@ -2761,10 +2762,10 @@ This Matlab function is accessible here 

    function [nano_hexapod] = initializeNanoHexapod(opts_param)
     %% Default values for opts
-    opts = struct('actuator', 'piezo');
+    opts = struct('actuator', 'piezo');
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             opts.(opt{1}) = opts_param.(opt{1});
         end
@@ -2774,7 +2775,7 @@ This Matlab function is accessible here();
     nano_hexapod.h        = 90;  % Total height of the platform [mm]
     nano_hexapod.jacobian = 175; % Point where the Jacobian is computed => Center of rotation [mm]
-%     nano_hexapod.jacobian = 174.26; % Point where the Jacobian is computed => Center of rotation [mm]
+%     nano_hexapod.jacobian = 174.26; % Point where the Jacobian is computed => Center of rotation [mm]
 
     %% Bottom Plate
     BP = struct();
@@ -2859,12 +2860,12 @@ This Matlab function is accessible here(nano_hexapod);
 
     %% Save
-    save('./mat/stages.mat', 'nano_hexapod', '-append');
+    save('./mat/stages.mat', 'nano_hexapod', '-append');
 
     %%
     function [element] = updateDamping(element)
         field = fieldnames(element.k);
-        for i = 1:length(field)
+        for i = 1:length(field)
             element.c.(field{i}) = 1/element.ksi.(field{i})*sqrt(element.k.(field{i})/element.m);
         end
     end
@@ -2883,7 +2884,7 @@ This Matlab function is accessible here*0.001; % rayon emplacement support base
         radius_t = stewart.TP.leg.rad*0.001; % top radius in meters
 
-        for i = 1:3
+        for i = 1:3
           % base points
           angle_m_b = (2*pi/3)* (i-1) - alpha_b;
           angle_p_b = (2*pi/3)* (i-1) + alpha_b;
@@ -2906,24 +2907,24 @@ This Matlab function is accessible here- stewart.pos_base;
         leg_length = zeros(6, 1);
         leg_vectors = zeros(6, 3);
-        for i = 1:6
+        for i = 1:6
           leg_length(i) = norm(legs(i,:));
           leg_vectors(i,:)  = legs(i,:) / leg_length(i);
         end
 
         stewart.Leg.lenght = 1000*leg_length(1)/1.5;
-        stewart.Leg.shape.bot = [0 0; ...
-                                stewart.Leg.rad.bottom 0; ...
-                                stewart.Leg.rad.bottom stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top stewart.Leg.lenght; ...
-                                stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
+        stewart.Leg.shape.bot = [0 0; ...
+                                stewart.Leg.rad.bottom 0; ...
+                                stewart.Leg.rad.bottom stewart.Leg.lenght; ...
+                                stewart.Leg.rad.top stewart.Leg.lenght; ...
+                                stewart.Leg.rad.top 0.2*stewart.Leg.lenght; ...
                                 0 0.2*stewart.Leg.lenght];
 
         %% Calculate revolute and cylindrical axes
         rev1 = zeros(6, 3);
         rev2 = zeros(6, 3);
         cyl1 = zeros(6, 3);
-        for i = 1:6
+        for i = 1:6
           rev1(i,:) = cross(leg_vectors(i,:), [0 0 1]);
           rev1(i,:) = rev1(i,:) / norm(rev1(i,:));
 
@@ -2938,9 +2939,9 @@ This Matlab function is accessible here('rotation', eye(3));
         stewart.upper_leg = struct('rotation', eye(3));
 
-        for i = 1:6
-          stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
-          stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
+        for i = 1:6
+          stewart.lower_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
+          stewart.upper_leg(i).rotation = [rev1(i,:)', rev2(i,:)', cyl1(i,:)'];
         end
 
         %% Position Matrix
@@ -2948,15 +2949,15 @@ This Matlab function is accessible here%% Compute Jacobian Matrix
         aa = stewart.pos_top_tranform + (stewart.jacobian - stewart.TP.thickness - stewart.SP.height.top)*1e-3*[zeros(6, 2),ones(6, 1)];
-        stewart.J  = getJacobianMatrix(leg_vectors', aa');
+        stewart.J  = getJacobianMatrix(leg_vectors', aa');
     end
 
     function J  = getJacobianMatrix(RM,M_pos_base)
         % RM: [3x6] unit vector of each leg in the fixed frame
         % M_pos_base: [3x6] vector of the leg connection at the top platform location in the fixed frame
         J = zeros(6);
-        J(:, 1:3) = RM';
-        J(:, 4:6) = cross(M_pos_base, RM)';
+        J(:, 1:3) = RM';
+        J(:, 4:6) = cross(M_pos_base, RM)';
     end
 end
    @@ -2964,11 +2965,11 @@ This Matlab function is accessible here
    -
    -

    8.13 Sample

    +
    +

    8.13 Sample

    - +

    @@ -2978,15 +2979,15 @@ This Matlab function is accessible here. 

    function [sample] = initializeSample(opts_param)
     %% Default values for opts
-    sample = struct('radius', 100, ...
-                    'height', 300, ...
-                    'mass',   50,  ...
-                    'offset', 0,   ...
-                    'color',  [0.45, 0.45, 0.45] ...
+    sample = struct('radius', 100, ...
+                    'height', 300, ...
+                    'mass',   50,  ...
+                    'offset', 0,   ...
+                    'color',  [0.45, 0.45, 0.45] ...
     );
 
     %% Populate opts with input parameters
-    if exist('opts_param','var')
+    if exist('opts_param','var')
         for opt = fieldnames(opts_param)'
             sample.(opt{1}) = opts_param.(opt{1});
         end
@@ -3003,7 +3004,7 @@ This Matlab function is accessible here.
     sample.c.z = sqrt(sample.k.y*sample.mass)/10;
 
     %% Save
-    save('./mat/stages.mat', 'sample', '-append');
+    save('./mat/stages.mat', 'sample', '-append');
 end
    @@ -3013,7 +3014,7 @@ This Matlab function is accessible here.

    Author: Dehaeze Thomas

    -

    Created: 2019-10-08 mar. 11:19

    +

    Created: 2019-10-24 jeu. 17:45

    Validate

    diff --git a/index.org b/index.org index 2116bc0..3c4cedd 100644 --- a/index.org +++ b/index.org @@ -42,6 +42,7 @@ :END: - [[file:identification/index.org][Identification of the Micro-Station]] +- [[file:uniaxial/index.org][Uniaxial Model]] - [[file:kinematics/index.org][Kinematics of the station]] - [[file:control/index.org][Control]] - [[file:active_damping/index.org][Active Damping]] diff --git a/simscape/sim_nano_station_uniaxial.slx b/simscape/sim_nano_station_uniaxial.slx new file mode 100644 index 0000000000000000000000000000000000000000..46307f141255bb4c446e7b79810646217ef023b9 GIT binary patch literal 132281 zcmaI7Q;=rS)}@`9mA1`F+qP}nwr$(CZS$?PGb?S|w*ETZ@ke~8JECv)#lG2ljxpAn zD`q@PLHZXcDi9D5B#>g5hCH5bbmcQJ5D+ai5D?10x7xz?b}puNF8V5-4yMk!bRM=g z!)f;R3k--O0I8Jr3dcP#p^7t>)@&9_Y&5+6BbR3SNY$U@D;nzjJZbJGA&L~X3VL6^ zYrk2}yYb{`^V%fxM?tORa{Fe-tb#o?3FYIn^pA_Va26<}7$8%)<1=jGEFBs07wd4M zLKBqxmZ&*j6PjCS){rSKmKJ4=dZPLH^eJF{!N|)kkIy_u>)%-%QMR!zT$#qetx@AP 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z^T`5~TP04jhu5kP$H$v@9va5wg+y&+)C}4jP}SGWiS+PM3`EE6PbeS6%5|^yw4HP5 zy)TR}QZhkTL!B#%UpemE7mm`o?!FvJMD~&DT6)=!4q||w<-Is`Kg-B)6 zh|MP}GRjzft{hV)fS? zu(5^%T-^Z}3OhJjz>%jZ$Wtvhd=CKR02s|5pxc0^zd;C>{~vYXVYhTOfWQP$%zvPC zu>T86#uW$>60oLDlUF6=!c+^e1OVodM{|^bk3iDJ`7caOxHTM#g#YeHqDOCwIMk=_ zGTpgv9+y<6%4T79H59JRj1amxbp7-MF52cz%c#f{U*-y{Db)S7B0VI zeku}MraQ0^C@CROKaO^QIZD4oPV=5X8pB|4Q>c@*Zl?MW>>Bu*cN+)2L{UEIJL{Lp`QJmQK<5r=yAvLpMQ>Vdba6{<|fL4o9~wkKwTI qCzSqSVxlw92l>YgxAhYYv?0H`5*E;&9<`_xAY-5 + + + + + + +Simscape Uniaxial Model + + + + + + + + + + + + + +

    + UP + | + HOME +
    +

    Simscape Uniaxial Model

    + + +

    +The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction. +

    + +

    +This is done in order to more easily study the system and evaluate control techniques. +

    + +
    +

    1 Undamped System

    +
    +
    +
    +

    1.1 Init

    +
    +

    +We initialize all the stages with the default parameters. +The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg. +

    + +
    +
    initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+initializeNanoHexapod(struct('actuator', 'piezo'));
+initializeSample(struct('mass', 50));
+
    +
    + +

    +All the controllers are set to 0. +

    +
    +
    K = tf(0);
+save('./mat/controllers.mat', 'K', '-append');
+K_iff = tf(0);
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_rmc = tf(0);
+save('./mat/controllers.mat', 'K_rmc', '-append');
+K_dvf = tf(0);
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
    +
    +
    +
    + +
    +

    1.2 Identification

    +
    +
    +
    %% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nano_station_uniaxial';
+
    +
    + +
    +
    %% Input/Output definition
+io(1)  = linio([mdl, '/Dw'],    1, 'input');  % Ground Motion
+io(2)  = linio([mdl, '/Fs'],    1, 'input');  % Force applied on the sample
+io(3)  = linio([mdl, '/Fnl'],   1, 'input');  % Force applied by the NASS
+io(4)  = linio([mdl, '/Fdty'],  1, 'input');  % Parasitic force Ty
+io(5)  = linio([mdl, '/Fdrz'],  1, 'input');  % Parasitic force Rz
+
+io(6)  = linio([mdl, '/Dsm'],  1, 'output'); % Displacement of the sample
+io(7)  = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
+io(8)  = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
+io(9)  = linio([mdl, '/Dgm'],  1, 'output'); % Absolute displacement of the granite
+io(10) = linio([mdl, '/Vlm'],  1, 'output'); % Measured absolute velocity of the top NASS platform
+
    +
    + +
    +
    %% Run the linearization
+G = linearize(mdl, io, options);
+G.InputName  = {'Dw',   ... % Ground Motion [m]
+                'Fs',   ... % Force Applied on Sample [N]
+                'Fn',   ... % Force applied by NASS [N]
+                'Fty',  ... % Parasitic Force Ty [N]
+                'Frz'};     % Parasitic Force Rz [N]
+G.OutputName = {'D',    ... % Measured sample displacement x.r.t. granite [m]
+                'Fnm',  ... % Force Sensor in NASS [N]
+                'Dnm',  ... % Displacement Sensor in NASS [m]
+                'Dgm',  ... % Asbolute displacement of Granite [m]
+                'Vlm'}; ... % Absolute Velocity of NASS [m/s]
+
    +
    +
    +
    + +
    +

    1.3 Sensitivity to Disturbances

    +
    + +
    +

    uniaxial-sensitivity-disturbances.png +

    +

    Figure 1: Sensitivity to disturbances (png, pdf)

    +
    + + + +
    +

    uniaxial-sensitivity-force-dist.png +

    +

    Figure 2: Sensitivity to disturbances (png, pdf)

    +
    +
    +
    + +
    +

    1.4 Plant

    +
    + +
    +

    uniaxial-plant.png +

    +

    Figure 3: Bode plot of the Plant (png, pdf)

    +
    +
    +
    + +
    +

    1.5 Save

    +
    +
    +
    save('./uniaxial/mat/plants.mat', 'G');
+
    +
    +
    +
    +
    + +
    +

    2 Integral Force Feedback

    +
    +

    + +

    +
    +
    +

    2.1 Control Design

    +
    +
    +
    load('./uniaxial/mat/plants.mat', 'G');
+
    +
    + +

    +Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor. +

    + + +
    +

    uniaxial_iff_plant.png +

    +

    Figure 4: Transfer function from forces applied in the legs to force sensor (png, pdf)

    +
    + +

    +The controller for each pair of actuator/sensor is: +

    +
    +
    K_iff = -1000/s;
+
    +
    + + +
    +

    uniaxial_iff_open_loop.png +

    +

    Figure 5: Loop Gain for the Integral Force Feedback (png, pdf)

    +
    +
    +
    + +
    +

    2.2 Identification

    +
    +

    +Let's initialize the system prior to identification. +

    +
    +
    initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+initializeNanoHexapod(struct('actuator', 'piezo'));
+initializeSample(struct('mass', 50));
+
    +
    + +

    +All the controllers are set to 0. +

    +
    +
    K = tf(0);
+save('./mat/controllers.mat', 'K', '-append');
+K_iff = -K_iff;
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_rmc = tf(0);
+save('./mat/controllers.mat', 'K_rmc', '-append');
+K_dvf = tf(0);
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
    +
    + +
    +
    %% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nano_station_uniaxial';
+
    +
    + +
    +
    %% Input/Output definition
+io(1)  = linio([mdl, '/Dw'],    1, 'input');  % Ground Motion
+io(2)  = linio([mdl, '/Fs'],    1, 'input');  % Force applied on the sample
+io(3)  = linio([mdl, '/Fnl'],   1, 'input');  % Force applied by the NASS
+io(4)  = linio([mdl, '/Fdty'],  1, 'input');  % Parasitic force Ty
+io(5)  = linio([mdl, '/Fdrz'],  1, 'input');  % Parasitic force Rz
+
+io(6)  = linio([mdl, '/Dsm'],  1, 'output'); % Displacement of the sample
+io(7)  = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
+io(8)  = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
+io(9)  = linio([mdl, '/Dgm'],  1, 'output'); % Absolute displacement of the granite
+io(10) = linio([mdl, '/Vlm'],  1, 'output'); % Measured absolute velocity of the top NASS platform
+
    +
    + +
    +
    %% Run the linearization
+G_iff = linearize(mdl, io, options);
+G_iff.InputName  = {'Dw',   ... % Ground Motion [m]
+                    'Fs',   ... % Force Applied on Sample [N]
+                    'Fn',   ... % Force applied by NASS [N]
+                    'Fty',  ... % Parasitic Force Ty [N]
+                    'Frz'};     % Parasitic Force Rz [N]
+G_iff.OutputName = {'D',    ... % Measured sample displacement x.r.t. granite [m]
+                    'Fnm',  ... % Force Sensor in NASS [N]
+                    'Dnm',  ... % Displacement Sensor in NASS [m]
+                    'Dgm',  ... % Asbolute displacement of Granite [m]
+                    'Vlm'}; ... % Absolute Velocity of NASS [m/s]
+
    +
    +
    +
    + +
    +

    2.3 Sensitivity to Disturbance

    +
    + +
    +

    uniaxial_sensitivity_dist_iff.png +

    +

    Figure 6: Sensitivity to disturbance once the IFF controller is applied to the system (png, pdf)

    +
    + + +
    +

    uniaxial_sensitivity_dist_stages_iff.png +

    +

    Figure 7: Sensitivity to force disturbances in various stages when IFF is applied (png, pdf)

    +
    +
    +
    + +
    +

    2.4 Damped Plant

    +
    + +
    +

    uniaxial_plant_iff_damped.png +

    +

    Figure 8: Damped Plant after IFF is applied (png, pdf)

    +
    +
    +
    + +
    +

    2.5 Save

    +
    +
    +
    save('./uniaxial/mat/plants.mat', 'G_iff', '-append');
+
    +
    +
    +
    + +
    +

    2.6 Conclusion

    +
    +
    +

    +Integral Force Feedback: +

    + +
    +
    +
    +
    + +
    +

    3 Relative Motion Control

    +
    +

    + +

    +

    +In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input. +

    +
    +
    +

    3.1 Control Design

    +
    +
    +
    load('./uniaxial/mat/plants.mat', 'G');
+
    +
    + +

    +Let's look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor. +

    + + +
    +

    uniaxial_rmc_plant.png +

    +

    Figure 9: Transfer function from forces applied in the legs to leg displacement sensor (png, pdf)

    +
    + +

    +The Relative Motion Controller is defined below. +A Low pass Filter is added to make the controller transfer function proper. +

    +
    +
    K_rmc = s*50000/(1 + s/2/pi/10000);
+
    +
    + + +
    +

    uniaxial_rmc_open_loop.png +

    +

    Figure 10: Loop Gain for the Integral Force Feedback (png, pdf)

    +
    +
    +
    + +
    +

    3.2 Identification

    +
    +

    +Let's initialize the system prior to identification. +

    +
    +
    initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+initializeNanoHexapod(struct('actuator', 'piezo'));
+initializeSample(struct('mass', 50));
+
    +
    + +

    +And initialize the controllers. +

    +
    +
    K = tf(0);
+save('./mat/controllers.mat', 'K', '-append');
+K_iff = tf(0);
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_rmc = -K_rmc;
+save('./mat/controllers.mat', 'K_rmc', '-append');
+K_dvf = tf(0);
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
    +
    + +
    +
    %% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nano_station_uniaxial';
+
    +
    + +
    +
    %% Input/Output definition
+io(1)  = linio([mdl, '/Dw'],    1, 'input');  % Ground Motion
+io(2)  = linio([mdl, '/Fs'],    1, 'input');  % Force applied on the sample
+io(3)  = linio([mdl, '/Fnl'],   1, 'input');  % Force applied by the NASS
+io(4)  = linio([mdl, '/Fdty'],  1, 'input');  % Parasitic force Ty
+io(5)  = linio([mdl, '/Fdrz'],  1, 'input');  % Parasitic force Rz
+
+io(6)  = linio([mdl, '/Dsm'],  1, 'output'); % Displacement of the sample
+io(7)  = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
+io(8)  = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
+io(9)  = linio([mdl, '/Dgm'],  1, 'output'); % Absolute displacement of the granite
+io(10) = linio([mdl, '/Vlm'],  1, 'output'); % Measured absolute velocity of the top NASS platform
+
    +
    + +
    +
    %% Run the linearization
+G_rmc = linearize(mdl, io, options);
+G_rmc.InputName  = {'Dw',   ... % Ground Motion [m]
+                    'Fs',   ... % Force Applied on Sample [N]
+                    'Fn',   ... % Force applied by NASS [N]
+                    'Fty',  ... % Parasitic Force Ty [N]
+                    'Frz'};     % Parasitic Force Rz [N]
+G_rmc.OutputName = {'D',    ... % Measured sample displacement x.r.t. granite [m]
+                    'Fnm',  ... % Force Sensor in NASS [N]
+                    'Dnm',  ... % Displacement Sensor in NASS [m]
+                    'Dgm',  ... % Asbolute displacement of Granite [m]
+                    'Vlm'}; ... % Absolute Velocity of NASS [m/s]
+
    +
    +
    +
    + + +
    +

    3.3 Sensitivity to Disturbance

    +
    + +
    +

    uniaxial_sensitivity_dist_rmc.png +

    +

    Figure 11: Sensitivity to disturbance once the RMC controller is applied to the system (png, pdf)

    +
    + + +
    +

    uniaxial_sensitivity_dist_stages_rmc.png +

    +

    Figure 12: Sensitivity to force disturbances in various stages when RMC is applied (png, pdf)

    +
    +
    +
    + +
    +

    3.4 Damped Plant

    +
    + +
    +

    uniaxial_plant_rmc_damped.png +

    +

    Figure 13: Damped Plant after RMC is applied (png, pdf)

    +
    +
    +
    + +
    +

    3.5 Save

    +
    +
    +
    save('./uniaxial/mat/plants.mat', 'G_rmc', '-append');
+
    +
    +
    +
    + +
    +

    3.6 Conclusion

    +
    +
    +

    +Relative Motion Control: +

    + +
    +
    +
    +
    + +
    +

    4 Direct Velocity Feedback

    +
    +

    + +

    +

    +In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input. +

    +
    +
    +

    4.1 Control Design

    +
    +
    +
    load('./uniaxial/mat/plants.mat', 'G');
+
    +
    + + +
    +

    uniaxial_dvf_plant.png +

    +

    Figure 14: Transfer function from forces applied in the legs to leg velocity sensor (png, pdf)

    +
    + +
    +
    K_dvf = tf(5e4);
+
    +
    + + +
    +

    uniaxial_dvf_loop_gain.png +

    +

    Figure 15: Transfer function from forces applied in the legs to leg velocity sensor (png, pdf)

    +
    +
    +
    + +
    +

    4.2 Identification

    +
    +

    +Let's initialize the system prior to identification. +

    +
    +
    initializeGround();
+initializeGranite();
+initializeTy();
+initializeRy();
+initializeRz();
+initializeMicroHexapod();
+initializeAxisc();
+initializeMirror();
+initializeNanoHexapod(struct('actuator', 'piezo'));
+initializeSample(struct('mass', 50));
+
    +
    + +

    +And initialize the controllers. +

    +
    +
    K = tf(0);
+save('./mat/controllers.mat', 'K', '-append');
+K_iff = tf(0);
+save('./mat/controllers.mat', 'K_iff', '-append');
+K_rmc = tf(0);
+save('./mat/controllers.mat', 'K_rmc', '-append');
+K_dvf = -K_dvf;
+save('./mat/controllers.mat', 'K_dvf', '-append');
+
    +
    + +
    +
    %% Options for Linearized
+options = linearizeOptions;
+options.SampleTime = 0;
+
+%% Name of the Simulink File
+mdl = 'sim_nano_station_uniaxial';
+
    +
    + +
    +
    %% Input/Output definition
+io(1)  = linio([mdl, '/Dw'],    1, 'input');  % Ground Motion
+io(2)  = linio([mdl, '/Fs'],    1, 'input');  % Force applied on the sample
+io(3)  = linio([mdl, '/Fnl'],   1, 'input');  % Force applied by the NASS
+io(4)  = linio([mdl, '/Fdty'],  1, 'input');  % Parasitic force Ty
+io(5)  = linio([mdl, '/Fdrz'],  1, 'input');  % Parasitic force Rz
+
+io(6)  = linio([mdl, '/Dsm'],  1, 'output'); % Displacement of the sample
+io(7)  = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs
+io(8)  = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs
+io(9)  = linio([mdl, '/Dgm'],  1, 'output'); % Absolute displacement of the granite
+io(10) = linio([mdl, '/Vlm'],  1, 'output'); % Measured absolute velocity of the top NASS platform
+
    +
    + +
    +
    %% Run the linearization
+G_dvf = linearize(mdl, io, options);
+G_dvf.InputName  = {'Dw',   ... % Ground Motion [m]
+                    'Fs',   ... % Force Applied on Sample [N]
+                    'Fn',   ... % Force applied by NASS [N]
+                    'Fty',  ... % Parasitic Force Ty [N]
+                    'Frz'};     % Parasitic Force Rz [N]
+G_dvf.OutputName = {'D',    ... % Measured sample displacement x.r.t. granite [m]
+                    'Fnm',  ... % Force Sensor in NASS [N]
+                    'Dnm',  ... % Displacement Sensor in NASS [m]
+                    'Dgm',  ... % Asbolute displacement of Granite [m]
+                    'Vlm'}; ... % Absolute Velocity of NASS [m/s]
+
    +
    +
    +
    + +
    +

    4.3 Sensitivity to Disturbance

    +
    + +
    +

    uniaxial_sensitivity_dist_dvf.png +

    +

    Figure 16: Sensitivity to disturbance once the DVF controller is applied to the system (png, pdf)

    +
    + + +
    +

    uniaxial_sensitivity_dist_stages_dvf.png +

    +

    Figure 17: Sensitivity to force disturbances in various stages when DVF is applied (png, pdf)

    +
    +
    +
    + +
    +

    4.4 Damped Plant

    +
    + +
    +

    uniaxial_plant_dvf_damped.png +

    +

    Figure 18: Damped Plant after DVF is applied (png, pdf)

    +
    +
    +
    + +
    +

    4.5 Save

    +
    +
    +
    save('./uniaxial/mat/plants.mat', 'G_dvf', '-append');
+
    +
    +
    +
    + +
    +

    4.6 Conclusion

    +
    +
    +

    +Direct Velocity Feedback: +

    + +
    +
    +
    +
    +
    +

    5 Comparison of Active Damping Techniques

    +
    +

    + +

    +
    +
    +

    5.1 Load the plants

    +
    +
    +
    load('./uniaxial/mat/plants.mat', 'G', 'G_iff', 'G_rmc', 'G_dvf');
+
    +
    +
    +
    + +
    +

    5.2 Sensitivity to Disturbance

    +
    + +
    +

    uniaxial_sensitivity_dist_comp.png +

    +

    Figure 19: Sensitivity to disturbance - Comparison (png, pdf)

    +
    + + +
    +

    uniaxial_sensitivity_dist_stages_comp.png +

    +

    Figure 20: Sensitivity to force disturbances - Comparison (png, pdf)

    +
    +
    +
    + +
    +

    5.3 Damped Plant

    +
    + +
    +

    uniaxial_plant_damped_comp.png +

    +

    Figure 21: Damped Plant - Comparison (png, pdf)

    +
    +
    +
    +
    +

    5.4 Conclusion

    +
    +
    +
    +
    +

    Author: Dehaeze Thomas

    +

    Created: 2019-10-24 jeu. 17:44

    +

    Validate

    +
    + + diff --git a/uniaxial/index.org b/uniaxial/index.org new file mode 100644 index 0000000..874e239 --- /dev/null +++ b/uniaxial/index.org @@ -0,0 +1,1191 @@ +#+TITLE: Simscape Uniaxial Model +:DRAWER: +#+STARTUP: overview + +#+LANGUAGE: en +#+EMAIL: dehaeze.thomas@gmail.com +#+AUTHOR: Dehaeze Thomas + +#+HTML_LINK_HOME: ../index.html +#+HTML_LINK_UP: ../index.html + +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: +#+HTML_HEAD: + +#+HTML_MATHJAX: align: center tagside: right font: TeX + +#+PROPERTY: header-args:matlab :session *MATLAB* +#+PROPERTY: header-args:matlab+ :comments org +#+PROPERTY: header-args:matlab+ :results none +#+PROPERTY: header-args:matlab+ :exports both +#+PROPERTY: header-args:matlab+ :eval no-export +#+PROPERTY: header-args:matlab+ :output-dir figs +#+PROPERTY: header-args:matlab+ :tangle matlab/modal_frf_coh.m +#+PROPERTY: header-args:matlab+ :mkdirp yes + +#+PROPERTY: header-args:shell :eval no-export + +#+PROPERTY: header-args:latex :headers '("\\usepackage{tikz}" "\\usepackage{import}" "\\import{$HOME/Cloud/thesis/latex/}{config.tex}") +#+PROPERTY: header-args:latex+ :imagemagick t :fit yes +#+PROPERTY: header-args:latex+ :iminoptions -scale 100% -density 150 +#+PROPERTY: header-args:latex+ :imoutoptions -quality 100 +#+PROPERTY: header-args:latex+ :results raw replace :buffer no +#+PROPERTY: header-args:latex+ :eval no-export +#+PROPERTY: header-args:latex+ :exports both +#+PROPERTY: header-args:latex+ :mkdirp yes +#+PROPERTY: header-args:latex+ :output-dir figs +:END: + +* Introduction :ignore: +The idea is to use the same model as the full Simscape Model but to restrict the motion only in the vertical direction. + +This is done in order to more easily study the system and evaluate control techniques. + +* Undamped System +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); +#+end_src + +#+begin_src matlab + open 'simscape/sim_nano_station_uniaxial.slx' +#+end_src + +** Init +We initialize all the stages with the default parameters. +The nano-hexapod is a piezoelectric hexapod and the sample has a mass of 50kg. + +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); + initializeNanoHexapod(struct('actuator', 'piezo')); + initializeSample(struct('mass', 50)); +#+end_src + +All the controllers are set to 0. +#+begin_src matlab + K = tf(0); + save('./mat/controllers.mat', 'K', '-append'); + K_iff = tf(0); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_rmc = tf(0); + save('./mat/controllers.mat', 'K_rmc', '-append'); + K_dvf = tf(0); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +** Identification +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nano_station_uniaxial'; +#+end_src + +#+begin_src matlab + %% Input/Output definition + io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion + io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample + io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS + io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty + io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz + + io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample + io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs + io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs + io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite + io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform +#+end_src + +#+begin_src matlab + %% Run the linearization + G = linearize(mdl, io, options); + G.InputName = {'Dw', ... % Ground Motion [m] + 'Fs', ... % Force Applied on Sample [N] + 'Fn', ... % Force applied by NASS [N] + 'Fty', ... % Parasitic Force Ty [N] + 'Frz'}; % Parasitic Force Rz [N] + G.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m] + 'Fnm', ... % Force Sensor in NASS [N] + 'Dnm', ... % Displacement Sensor in NASS [m] + 'Dgm', ... % Asbolute displacement of Granite [m] + 'Vlm'}; ... % Absolute Velocity of NASS [m/s] +#+end_src + +** Sensitivity to Disturbances +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$D_w$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-'); + % plot(freqs, abs(squeeze(freqresp(G('Dgm', 'Dw'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + + subplot(2, 1, 2); + title('$F_s$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial-sensitivity-disturbances.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial-sensitivity-disturbances +#+CAPTION: Sensitivity to disturbances ([[./figs/uniaxial-sensitivity-disturbances.png][png]], [[./figs/uniaxial-sensitivity-disturbances.pdf][pdf]]) +[[file:figs/uniaxial-sensitivity-disturbances.png]] + + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$F_{ty}$ to $D$'); + plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + + subplot(2, 1, 2); + title('$F_{rz}$ to $D$'); + plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial-sensitivity-force-dist.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial-sensitivity-force-dist +#+CAPTION: Sensitivity to disturbances ([[./figs/uniaxial-sensitivity-force-dist.png][png]], [[./figs/uniaxial-sensitivity-force-dist.pdf][pdf]]) +[[file:figs/uniaxial-sensitivity-force-dist.png]] + +** Plant +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial-plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial-plant +#+CAPTION: Bode plot of the Plant ([[./figs/uniaxial-plant.png][png]], [[./figs/uniaxial-plant.pdf][pdf]]) +[[file:figs/uniaxial-plant.png]] + +** Save +#+begin_src matlab + save('./uniaxial/mat/plants.mat', 'G'); +#+end_src + +* Integral Force Feedback +<> +** Introduction :ignore: +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); +#+end_src + +#+begin_src matlab + open 'simscape/sim_nano_station_uniaxial.slx' +#+end_src + +** Control Design +#+begin_src matlab + load('./uniaxial/mat/plants.mat', 'G'); +#+end_src + +Let's look at the transfer function from actuator forces in the nano-hexapod to the force sensor in the nano-hexapod legs for all 6 pairs of actuator/sensor. + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_iff_plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_iff_plant +#+CAPTION: Transfer function from forces applied in the legs to force sensor ([[./figs/uniaxial_iff_plant.png][png]], [[./figs/uniaxial_iff_plant.pdf][pdf]]) +[[file:figs/uniaxial_iff_plant.png]] + +The controller for each pair of actuator/sensor is: +#+begin_src matlab + K_iff = -1000/s; +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(K_iff*G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [N/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(K_iff*G('Fnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_iff_open_loop.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_iff_open_loop +#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/uniaxial_iff_open_loop.png][png]], [[./figs/uniaxial_iff_open_loop.pdf][pdf]]) +[[file:figs/uniaxial_iff_open_loop.png]] + +** Identification +Let's initialize the system prior to identification. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); + initializeNanoHexapod(struct('actuator', 'piezo')); + initializeSample(struct('mass', 50)); +#+end_src + +All the controllers are set to 0. +#+begin_src matlab + K = tf(0); + save('./mat/controllers.mat', 'K', '-append'); + K_iff = -K_iff; + save('./mat/controllers.mat', 'K_iff', '-append'); + K_rmc = tf(0); + save('./mat/controllers.mat', 'K_rmc', '-append'); + K_dvf = tf(0); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nano_station_uniaxial'; +#+end_src + +#+begin_src matlab + %% Input/Output definition + io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion + io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample + io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS + io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty + io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz + + io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample + io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs + io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs + io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite + io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform +#+end_src + +#+begin_src matlab + %% Run the linearization + G_iff = linearize(mdl, io, options); + G_iff.InputName = {'Dw', ... % Ground Motion [m] + 'Fs', ... % Force Applied on Sample [N] + 'Fn', ... % Force applied by NASS [N] + 'Fty', ... % Parasitic Force Ty [N] + 'Frz'}; % Parasitic Force Rz [N] + G_iff.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m] + 'Fnm', ... % Force Sensor in NASS [N] + 'Dnm', ... % Displacement Sensor in NASS [m] + 'Dgm', ... % Asbolute displacement of Granite [m] + 'Vlm'}; ... % Absolute Velocity of NASS [m/s] +#+end_src + +** Sensitivity to Disturbance +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$D_w$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Dw'), freqs, 'Hz'))), 'k--', 'DisplayName', 'IFF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_s$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fs'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_iff.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_iff +#+CAPTION: Sensitivity to disturbance once the IFF controller is applied to the system ([[./figs/uniaxial_sensitivity_dist_iff.png][png]], [[./figs/uniaxial_sensitivity_dist_iff.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_iff.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$F_{ty}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fty'), freqs, 'Hz'))), 'k--', 'DisplayName', 'IFF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_{rz}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_stages_iff.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_stages_iff +#+CAPTION: Sensitivity to force disturbances in various stages when IFF is applied ([[./figs/uniaxial_sensitivity_dist_stages_iff.png][png]], [[./figs/uniaxial_sensitivity_dist_stages_iff.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_stages_iff.png]] + +** Damped Plant +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fn'), freqs, 'Hz'))), 'k--', 'DisplayName', 'IFF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + legend('location', 'northeast'); + + ax2 = subplot(2, 1, 2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff('D', 'Fn'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_plant_iff_damped.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_plant_iff_damped +#+CAPTION: Damped Plant after IFF is applied ([[./figs/uniaxial_plant_iff_damped.png][png]], [[./figs/uniaxial_plant_iff_damped.pdf][pdf]]) +[[file:figs/uniaxial_plant_iff_damped.png]] + +** Save +#+begin_src matlab + save('./uniaxial/mat/plants.mat', 'G_iff', '-append'); +#+end_src + +** Conclusion +#+begin_important +Integral Force Feedback: +#+end_important + +* Relative Motion Control +<> +** Introduction :ignore: +In the Relative Motion Control (RMC), a derivative feedback is applied between the measured actuator displacement to the actuator force input. + +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); +#+end_src + +#+begin_src matlab + open 'simscape/sim_nano_station_uniaxial.slx' +#+end_src + +** Control Design +#+begin_src matlab + load('./uniaxial/mat/plants.mat', 'G'); +#+end_src + +Let's look at the transfer function from actuator forces in the nano-hexapod to the measured displacement of the actuator for all 6 pairs of actuator/sensor. + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(G('Dnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(G('Dnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_rmc_plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_rmc_plant +#+CAPTION: Transfer function from forces applied in the legs to leg displacement sensor ([[./figs/uniaxial_rmc_plant.png][png]], [[./figs/uniaxial_rmc_plant.pdf][pdf]]) +[[file:figs/uniaxial_rmc_plant.png]] + +The Relative Motion Controller is defined below. +A Low pass Filter is added to make the controller transfer function proper. +#+begin_src matlab + K_rmc = s*50000/(1 + s/2/pi/10000); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(K_rmc*G('Dnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(K_rmc*G('Dnm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_rmc_open_loop.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_rmc_open_loop +#+CAPTION: Loop Gain for the Integral Force Feedback ([[./figs/uniaxial_rmc_open_loop.png][png]], [[./figs/uniaxial_rmc_open_loop.pdf][pdf]]) +[[file:figs/uniaxial_rmc_open_loop.png]] + +** Identification +Let's initialize the system prior to identification. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); + initializeNanoHexapod(struct('actuator', 'piezo')); + initializeSample(struct('mass', 50)); +#+end_src + +And initialize the controllers. +#+begin_src matlab + K = tf(0); + save('./mat/controllers.mat', 'K', '-append'); + K_iff = tf(0); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_rmc = -K_rmc; + save('./mat/controllers.mat', 'K_rmc', '-append'); + K_dvf = tf(0); + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nano_station_uniaxial'; +#+end_src + +#+begin_src matlab + %% Input/Output definition + io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion + io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample + io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS + io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty + io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz + + io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample + io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs + io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs + io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite + io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform +#+end_src + +#+begin_src matlab + %% Run the linearization + G_rmc = linearize(mdl, io, options); + G_rmc.InputName = {'Dw', ... % Ground Motion [m] + 'Fs', ... % Force Applied on Sample [N] + 'Fn', ... % Force applied by NASS [N] + 'Fty', ... % Parasitic Force Ty [N] + 'Frz'}; % Parasitic Force Rz [N] + G_rmc.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m] + 'Fnm', ... % Force Sensor in NASS [N] + 'Dnm', ... % Displacement Sensor in NASS [m] + 'Dgm', ... % Asbolute displacement of Granite [m] + 'Vlm'}; ... % Absolute Velocity of NASS [m/s] +#+end_src + + +** Sensitivity to Disturbance +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$D_w$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Dw'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_s$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fs'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_rmc.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_rmc +#+CAPTION: Sensitivity to disturbance once the RMC controller is applied to the system ([[./figs/uniaxial_sensitivity_dist_rmc.png][png]], [[./figs/uniaxial_sensitivity_dist_rmc.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_rmc.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$F_{ty}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fty'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_{rz}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Frz'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_stages_rmc.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_stages_rmc +#+CAPTION: Sensitivity to force disturbances in various stages when RMC is applied ([[./figs/uniaxial_sensitivity_dist_stages_rmc.png][png]], [[./figs/uniaxial_sensitivity_dist_stages_rmc.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_stages_rmc.png]] + +** Damped Plant +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fn'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + legend('location', 'northeast'); + + ax2 = subplot(2, 1, 2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc('D', 'Fn'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_plant_rmc_damped.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_plant_rmc_damped +#+CAPTION: Damped Plant after RMC is applied ([[./figs/uniaxial_plant_rmc_damped.png][png]], [[./figs/uniaxial_plant_rmc_damped.pdf][pdf]]) +[[file:figs/uniaxial_plant_rmc_damped.png]] + +** Save +#+begin_src matlab + save('./uniaxial/mat/plants.mat', 'G_rmc', '-append'); +#+end_src + +** Conclusion +#+begin_important +Relative Motion Control: +#+end_important + +* Direct Velocity Feedback +<> +** Introduction :ignore: +In the Relative Motion Control (RMC), a feedback is applied between the measured velocity of the platform to the actuator force input. + +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); +#+end_src + +#+begin_src matlab + open 'simscape/sim_nano_station_uniaxial.slx' +#+end_src + +** Control Design +#+begin_src matlab + load('./uniaxial/mat/plants.mat', 'G'); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(G('Vlm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(G('Vlm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_dvf_plant.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_dvf_plant +#+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/uniaxial_dvf_plant.png][png]], [[./figs/uniaxial_dvf_plant.pdf][pdf]]) +[[file:figs/uniaxial_dvf_plant.png]] + +#+begin_src matlab + K_dvf = tf(5e4); +#+end_src + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + plot(freqs, abs(squeeze(freqresp(K_dvf*G('Vlm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + + ax2 = subplot(2, 1, 2); + plot(freqs, 180/pi*angle(squeeze(freqresp(K_dvf*G('Vlm', 'Fn'), freqs, 'Hz'))), 'k-'); + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_dvf_loop_gain.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_dvf_loop_gain +#+CAPTION: Transfer function from forces applied in the legs to leg velocity sensor ([[./figs/uniaxial_dvf_loop_gain.png][png]], [[./figs/uniaxial_dvf_loop_gain.pdf][pdf]]) +[[file:figs/uniaxial_dvf_loop_gain.png]] + +** Identification +Let's initialize the system prior to identification. +#+begin_src matlab + initializeGround(); + initializeGranite(); + initializeTy(); + initializeRy(); + initializeRz(); + initializeMicroHexapod(); + initializeAxisc(); + initializeMirror(); + initializeNanoHexapod(struct('actuator', 'piezo')); + initializeSample(struct('mass', 50)); +#+end_src + +And initialize the controllers. +#+begin_src matlab + K = tf(0); + save('./mat/controllers.mat', 'K', '-append'); + K_iff = tf(0); + save('./mat/controllers.mat', 'K_iff', '-append'); + K_rmc = tf(0); + save('./mat/controllers.mat', 'K_rmc', '-append'); + K_dvf = -K_dvf; + save('./mat/controllers.mat', 'K_dvf', '-append'); +#+end_src + +#+begin_src matlab + %% Options for Linearized + options = linearizeOptions; + options.SampleTime = 0; + + %% Name of the Simulink File + mdl = 'sim_nano_station_uniaxial'; +#+end_src + +#+begin_src matlab + %% Input/Output definition + io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion + io(2) = linio([mdl, '/Fs'], 1, 'input'); % Force applied on the sample + io(3) = linio([mdl, '/Fnl'], 1, 'input'); % Force applied by the NASS + io(4) = linio([mdl, '/Fdty'], 1, 'input'); % Parasitic force Ty + io(5) = linio([mdl, '/Fdrz'], 1, 'input'); % Parasitic force Rz + + io(6) = linio([mdl, '/Dsm'], 1, 'output'); % Displacement of the sample + io(7) = linio([mdl, '/Fnlm'], 1, 'output'); % Force sensor in NASS's legs + io(8) = linio([mdl, '/Dnlm'], 1, 'output'); % Displacement of NASS's legs + io(9) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute displacement of the granite + io(10) = linio([mdl, '/Vlm'], 1, 'output'); % Measured absolute velocity of the top NASS platform +#+end_src + +#+begin_src matlab + %% Run the linearization + G_dvf = linearize(mdl, io, options); + G_dvf.InputName = {'Dw', ... % Ground Motion [m] + 'Fs', ... % Force Applied on Sample [N] + 'Fn', ... % Force applied by NASS [N] + 'Fty', ... % Parasitic Force Ty [N] + 'Frz'}; % Parasitic Force Rz [N] + G_dvf.OutputName = {'D', ... % Measured sample displacement x.r.t. granite [m] + 'Fnm', ... % Force Sensor in NASS [N] + 'Dnm', ... % Displacement Sensor in NASS [m] + 'Dgm', ... % Asbolute displacement of Granite [m] + 'Vlm'}; ... % Absolute Velocity of NASS [m/s] +#+end_src + +** Sensitivity to Disturbance +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$D_w$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Dw'), freqs, 'Hz'))), 'k--', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_s$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fs'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_dvf.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_dvf +#+CAPTION: Sensitivity to disturbance once the DVF controller is applied to the system ([[./figs/uniaxial_sensitivity_dist_dvf.png][png]], [[./figs/uniaxial_sensitivity_dist_dvf.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_dvf.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$F_{ty}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fty'), freqs, 'Hz'))), 'k--', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_{rz}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Frz'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_stages_dvf.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_stages_dvf +#+CAPTION: Sensitivity to force disturbances in various stages when DVF is applied ([[./figs/uniaxial_sensitivity_dist_stages_dvf.png][png]], [[./figs/uniaxial_sensitivity_dist_stages_dvf.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_stages_dvf.png]] + +** Damped Plant +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fn'), freqs, 'Hz'))), 'k--', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + legend('location', 'northeast'); + + ax2 = subplot(2, 1, 2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf('D', 'Fn'), freqs, 'Hz'))), 'k--'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_plant_dvf_damped.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_plant_dvf_damped +#+CAPTION: Damped Plant after DVF is applied ([[./figs/uniaxial_plant_dvf_damped.png][png]], [[./figs/uniaxial_plant_dvf_damped.pdf][pdf]]) +[[file:figs/uniaxial_plant_dvf_damped.png]] + +** Save +#+begin_src matlab + save('./uniaxial/mat/plants.mat', 'G_dvf', '-append'); +#+end_src + +** Conclusion +#+begin_important +Direct Velocity Feedback: +#+end_important +* Comparison of Active Damping Techniques +<> +** Matlab Init :noexport:ignore: +#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name) + <> +#+end_src + +#+begin_src matlab :exports none :results silent :noweb yes + <> +#+end_src + +#+begin_src matlab :tangle no + simulinkproject('../'); +#+end_src + +#+begin_src matlab + open 'simscape/sim_nano_station_uniaxial.slx' +#+end_src + +** Load the plants +#+begin_src matlab + load('./uniaxial/mat/plants.mat', 'G', 'G_iff', 'G_rmc', 'G_dvf'); +#+end_src + +** Sensitivity to Disturbance +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$D_w$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Dw'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Dw'), freqs, 'Hz'))), 'k:', 'DisplayName', 'IFF'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Dw'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Dw'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/m]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_s$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fs'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fs'), freqs, 'Hz'))), 'k:'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fs'), freqs, 'Hz'))), 'k--'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fs'), freqs, 'Hz'))), 'k-.'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_comp +#+CAPTION: Sensitivity to disturbance - Comparison ([[./figs/uniaxial_sensitivity_dist_comp.png][png]], [[./figs/uniaxial_sensitivity_dist_comp.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_comp.png]] + +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + subplot(2, 1, 1); + title('$F_{ty}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fty'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fty'), freqs, 'Hz'))), 'k:', 'DisplayName', 'IFF'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fty'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fty'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); + legend('location', 'northeast'); + + subplot(2, 1, 2); + title('$F_{rz}$ to $D$'); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Frz'), freqs, 'Hz'))), 'k-'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Frz'), freqs, 'Hz'))), 'k'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Frz'), freqs, 'Hz'))), 'k--'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Frz'), freqs, 'Hz'))), 'k-.'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); xlabel('Frequency [Hz]'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_sensitivity_dist_stages_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_sensitivity_dist_stages_comp +#+CAPTION: Sensitivity to force disturbances - Comparison ([[./figs/uniaxial_sensitivity_dist_stages_comp.png][png]], [[./figs/uniaxial_sensitivity_dist_stages_comp.pdf][pdf]]) +[[file:figs/uniaxial_sensitivity_dist_stages_comp.png]] + +** Damped Plant +#+begin_src matlab :exports none + freqs = logspace(0, 3, 1000); + + figure; + + ax1 = subplot(2, 1, 1); + hold on; + plot(freqs, abs(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-', 'DisplayName', 'OL'); + plot(freqs, abs(squeeze(freqresp(G_iff('D', 'Fn'), freqs, 'Hz'))), 'k:', 'DisplayName', 'IFF'); + plot(freqs, abs(squeeze(freqresp(G_rmc('D', 'Fn'), freqs, 'Hz'))), 'k--', 'DisplayName', 'RMC'); + plot(freqs, abs(squeeze(freqresp(G_dvf('D', 'Fn'), freqs, 'Hz'))), 'k-.', 'DisplayName', 'DVF'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log'); + ylabel('Amplitude [m/N]'); set(gca, 'XTickLabel',[]); + legend('location', 'northeast'); + + ax2 = subplot(2, 1, 2); + hold on; + plot(freqs, 180/pi*angle(squeeze(freqresp(G('D', 'Fn'), freqs, 'Hz'))), 'k-'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_iff('D', 'Fn'), freqs, 'Hz'))), 'k:'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_rmc('D', 'Fn'), freqs, 'Hz'))), 'k--'); + plot(freqs, 180/pi*angle(squeeze(freqresp(G_dvf('D', 'Fn'), freqs, 'Hz'))), 'k-.'); + hold off; + set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); + ylabel('Phase [deg]'); xlabel('Frequency [Hz]'); + ylim([-180, 180]); + yticks([-180, -90, 0, 90, 180]); + + linkaxes([ax1,ax2],'x'); +#+end_src + +#+HEADER: :tangle no :exports results :results none :noweb yes +#+begin_src matlab :var filepath="figs/uniaxial_plant_damped_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") + <> +#+end_src + +#+NAME: fig:uniaxial_plant_damped_comp +#+CAPTION: Damped Plant - Comparison ([[./figs/uniaxial_plant_damped_comp.png][png]], [[./figs/uniaxial_plant_damped_comp.pdf][pdf]]) +[[file:figs/uniaxial_plant_damped_comp.png]] +** Conclusion diff --git a/uniaxial/mat/plants.mat b/uniaxial/mat/plants.mat new file mode 100644 index 0000000000000000000000000000000000000000..1e3496555c9c721c5629af606eb46268313a7049 GIT binary patch literal 16092 zcmbWebx<5Z+xCmQ22XGaB)Gc=cS!=lg9d_y;Ig;}NP^o!(BKJ9fW?Bt;tq?uFR(1E zoILOQe&?M3zVDo_nXc}hsq3Da>Z)H~_w?u~o9Zg7u!;)^vFa(C@;iO_=*Y)v_|fjO zljkRQ8CDHleKTbVF+Nt+PmXq<9UWLbJ!Du-U3^&$>_4-Lh_MPw$_NR`2urYv2nkEG z{vVblOpO07m|A+||5}>=&Vc+Kdt2K|jQ0|(`xx()@d#{jRQ!b|`ZiBaS;mKZ1`I97 zdwTGxp-RSJ;@4oJy~c=JB_Zr|K}@?1N0o2bc22B#7`A6P+5gcq{J-^F{@;4<->~|n 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