Remove badly tangled files
This commit is contained in:
@@ -3383,7 +3383,7 @@ Window used for =pwelch= function.
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* Useful Functions
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** prepareLinearizeIdentification
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:PROPERTIES:
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:header-args:matlab+: :tangle src/prepareLinearizeIdentification.m
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:header-args:matlab+: :tangle ../src/prepareLinearizeIdentification.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:prepareLinearizeIdentification>>
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@@ -3455,7 +3455,7 @@ We do not need to log any signal.
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** prepareTomographyExperiment
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:PROPERTIES:
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:header-args:matlab+: :tangle src/prepareTomographyExperiment.m
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:header-args:matlab+: :tangle ../src/prepareTomographyExperiment.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:prepareTomographyExperiment>>
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@@ -41,249 +41,6 @@
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#+PROPERTY: header-args:latex+ :output-dir figs
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:END:
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* TODO computePsdDispl
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/computePsdDispl.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:computePsdDispl>>
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This Matlab function is accessible [[file:../src/computePsdDispl.m][here]].
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#+begin_src matlab
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function [psd_object] = computePsdDispl(sys_data, t_init, n_av)
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i_init = find(sys_data.time > t_init, 1);
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han_win = hanning(ceil(length(sys_data.Dx(i_init:end, :))/n_av));
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Fs = 1/sys_data.time(2);
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[pdx, f] = pwelch(sys_data.Dx(i_init:end, :), han_win, [], [], Fs);
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[pdy, ~] = pwelch(sys_data.Dy(i_init:end, :), han_win, [], [], Fs);
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[pdz, ~] = pwelch(sys_data.Dz(i_init:end, :), han_win, [], [], Fs);
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[prx, ~] = pwelch(sys_data.Rx(i_init:end, :), han_win, [], [], Fs);
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[pry, ~] = pwelch(sys_data.Ry(i_init:end, :), han_win, [], [], Fs);
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[prz, ~] = pwelch(sys_data.Rz(i_init:end, :), han_win, [], [], Fs);
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psd_object = struct(...
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'f', f, ...
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'dx', pdx, ...
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'dy', pdy, ...
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'dz', pdz, ...
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'rx', prx, ...
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'ry', pry, ...
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'rz', prz);
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end
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#+end_src
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* TODO computeSetpoint
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/computeSetpoint.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:computeSetpoint>>
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This Matlab function is accessible [[file:../src/computeSetpoint.m][here]].
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#+begin_src matlab
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function setpoint = computeSetpoint(ty, ry, rz)
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%%
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setpoint = zeros(6, 1);
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%% Ty
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Ty = [1 0 0 0 ;
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0 1 0 ty ;
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0 0 1 0 ;
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0 0 0 1 ];
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% Tyinv = [1 0 0 0 ;
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% 0 1 0 -ty ;
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% 0 0 1 0 ;
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% 0 0 0 1 ];
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%% Ry
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Ry = [ cos(ry) 0 sin(ry) 0 ;
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0 1 0 0 ;
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-sin(ry) 0 cos(ry) 0 ;
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0 0 0 1 ];
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% TMry = Ty*Ry*Tyinv;
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%% Rz
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Rz = [cos(rz) -sin(rz) 0 0 ;
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sin(rz) cos(rz) 0 0 ;
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0 0 1 0 ;
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0 0 0 1 ];
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% TMrz = Ty*TMry*Rz*TMry'*Tyinv;
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%% All stages
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% TM = TMrz*TMry*Ty;
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TM = Ty*Ry*Rz;
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[thetax, thetay, thetaz] = RM2angle(TM(1:3, 1:3));
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setpoint(1:3) = TM(1:3, 4);
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setpoint(4:6) = [thetax, thetay, thetaz];
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%% Custom Functions
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function [thetax, thetay, thetaz] = RM2angle(R)
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if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
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thetay = -asin(R(3, 1));
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thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
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thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
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else
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thetaz = 0;
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if abs(R(3, 1)+1) < 1e-6 % R31 = -1
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thetay = pi/2;
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thetax = thetaz + atan2(R(1, 2), R(1, 3));
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else
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thetay = -pi/2;
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thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
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end
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end
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end
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end
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#+end_src
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* TODO converErrorBasis
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/converErrorBasis.m
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:header-args:matlab+: :comments none :mkdirp yes :eval no
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:END:
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<<sec:converErrorBasis>>
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This Matlab function is accessible [[file:../src/converErrorBasis.m][here]].
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#+begin_src matlab
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function error_nass = convertErrorBasis(pos, setpoint, ty, ry, rz)
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% convertErrorBasis -
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%
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% Syntax: convertErrorBasis(p_error, ty, ry, rz)
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%
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% Inputs:
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% - p_error - Position error of the sample w.r.t. the granite [m, rad]
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% - ty - Measured translation of the Ty stage [m]
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% - ry - Measured rotation of the Ry stage [rad]
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% - rz - Measured rotation of the Rz stage [rad]
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%
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% Outputs:
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% - P_nass - Position error of the sample w.r.t. the NASS base [m]
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% - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]
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%
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% Example:
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%
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%% If line vector => column vector
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if size(pos, 2) == 6
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pos = pos';
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end
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if size(setpoint, 2) == 6
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setpoint = setpoint';
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end
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%% Position of the sample in the frame fixed to the Granite
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P_granite = [pos(1:3); 1]; % Position [m]
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R_granite = [setpoint(1:3); 1]; % Reference [m]
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%% Transformation matrices of the stages
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% T-y
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TMty = [1 0 0 0 ;
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0 1 0 ty ;
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0 0 1 0 ;
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0 0 0 1 ];
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% R-y
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TMry = [ cos(ry) 0 sin(ry) 0 ;
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0 1 0 0 ;
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-sin(ry) 0 cos(ry) 0 ;
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0 0 0 1 ];
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% R-z
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TMrz = [cos(rz) -sin(rz) 0 0 ;
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sin(rz) cos(rz) 0 0 ;
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0 0 1 0 ;
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0 0 0 1 ];
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%% Compute Point coordinates in the new reference fixed to the NASS base
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% P_nass = TMrz*TMry*TMty*P_granite;
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P_nass = TMrz\TMry\TMty\P_granite;
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R_nass = TMrz\TMry\TMty\R_granite;
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dx = R_nass(1)-P_nass(1);
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dy = R_nass(2)-P_nass(2);
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dz = R_nass(3)-P_nass(3);
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%% Compute new basis vectors linked to the NASS base
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% ux_nass = TMrz*TMry*TMty*[1; 0; 0; 0];
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% ux_nass = ux_nass(1:3);
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% uy_nass = TMrz*TMry*TMty*[0; 1; 0; 0];
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% uy_nass = uy_nass(1:3);
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% uz_nass = TMrz*TMry*TMty*[0; 0; 1; 0];
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% uz_nass = uz_nass(1:3);
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ux_nass = TMrz\TMry\TMty\[1; 0; 0; 0];
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ux_nass = ux_nass(1:3);
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uy_nass = TMrz\TMry\TMty\[0; 1; 0; 0];
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uy_nass = uy_nass(1:3);
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uz_nass = TMrz\TMry\TMty\[0; 0; 1; 0];
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uz_nass = uz_nass(1:3);
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%% Rotations error w.r.t. granite Frame
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% Rotations error w.r.t. granite Frame
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rx_nass = pos(4);
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ry_nass = pos(5);
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rz_nass = pos(6);
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% Rotation matrices of the Sample w.r.t. the Granite
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Mrx_error = [1 0 0 ;
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0 cos(-rx_nass) -sin(-rx_nass) ;
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0 sin(-rx_nass) cos(-rx_nass)];
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Mry_error = [ cos(-ry_nass) 0 sin(-ry_nass) ;
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0 1 0 ;
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-sin(-ry_nass) 0 cos(-ry_nass)];
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Mrz_error = [cos(-rz_nass) -sin(-rz_nass) 0 ;
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sin(-rz_nass) cos(-rz_nass) 0 ;
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0 0 1];
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% Rotation matrix of the Sample w.r.t. the Granite
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Mr_error = Mrz_error*Mry_error*Mrx_error;
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%% Use matrix to solve
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R = Mr_error/[ux_nass, uy_nass, uz_nass]; % Rotation matrix from NASS base to Sample
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[thetax, thetay, thetaz] = RM2angle(R);
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error_nass = [dx; dy; dz; thetax; thetay; thetaz];
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%% Custom Functions
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function [thetax, thetay, thetaz] = RM2angle(R)
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if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
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thetay = -asin(R(3, 1));
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% thetaybis = pi-thetay;
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thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
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% thetaxbis = atan2(R(3, 2)/cos(thetaybis), R(3, 3)/cos(thetaybis));
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thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
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% thetazbis = atan2(R(2, 1)/cos(thetaybis), R(1, 1)/cos(thetaybis));
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else
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thetaz = 0;
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if abs(R(3, 1)+1) < 1e-6 % R31 = -1
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thetay = pi/2;
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thetax = thetaz + atan2(R(1, 2), R(1, 3));
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else
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thetay = -pi/2;
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thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
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end
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end
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end
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end
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#+end_src
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* computeReferencePose
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:PROPERTIES:
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:header-args:matlab+: :tangle ../src/computeReferencePose.m
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@@ -1,398 +0,0 @@
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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% Simscape Model
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% The simulink file for the identification is =sim_micro_station_id.slx=.
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open('identification/matlab/sim_micro_station_id.slx')
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% We load the configuration and we set a small =StopTime=.
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load('mat/conf_simulink.mat');
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set_param(conf_simulink, 'StopTime', '0.5');
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% We initialize all the stages.
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod('actuator', 'piezo');
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initializeSample('mass', 50);
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% Compute the transfer functions
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% We first define some parameters for the identification.
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'sim_micro_station_id';
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%% Micro-Hexapod
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% Input/Output definition
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io(1) = linio([mdl, '/Micro-Station/Fm_ext'],1,'openinput');
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io(2) = linio([mdl, '/Micro-Station/Fg_ext'],1,'openinput');
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io(3) = linio([mdl, '/Micro-Station/Dm_inertial'],1,'output');
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io(4) = linio([mdl, '/Micro-Station/Ty_inertial'],1,'output');
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io(5) = linio([mdl, '/Micro-Station/Ry_inertial'],1,'output');
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io(6) = linio([mdl, '/Micro-Station/Dg_inertial'],1,'output');
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% Run the linearization
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G_ms = linearize(mdl, io, 0);
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% Input/Output names
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G_ms.InputName = {'Fmx', 'Fmy', 'Fmz',...
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'Fgx', 'Fgy', 'Fgz'};
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G_ms.OutputName = {'Dmx', 'Dmy', 'Dmz', ...
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'Tyx', 'Tyy', 'Tyz', ...
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'Ryx', 'Ryy', 'Ryz', ...
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'Dgx', 'Dgy', 'Dgz'};
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%% Save the obtained transfer functions
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save('./mat/id_micro_station.mat', 'G_ms');
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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% Simscape Model
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% The simulink file for the analysis is =sim_micro_station_modal_analysis.slx=.
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open('identification/matlab/sim_micro_station_modal_analysis.slx')
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% We load the configuration and we set a small =StopTime=.
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load('mat/conf_simulink.mat');
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set_param(conf_simulink, 'StopTime', '0.5');
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% We initialize all the stages.
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initializeGround();
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initializeGranite();
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initializeTy();
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initializeRy();
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initializeRz();
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initializeMicroHexapod();
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initializeAxisc();
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initializeMirror();
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initializeNanoHexapod('actuator', 'piezo');
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initializeSample('mass', 50);
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% Identification
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%% Options for Linearized
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options = linearizeOptions;
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options.SampleTime = 0;
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%% Name of the Simulink File
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mdl = 'sim_micro_station_modal_analysis';
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%% Micro-Hexapod
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% Input/Output definition
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io(1) = linio([mdl, '/Micro-Station/F_hammer'],1,'openinput');
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io(2) = linio([mdl, '/Micro-Station/acc9'],1,'output');
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io(3) = linio([mdl, '/Micro-Station/acc10'],1,'output');
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io(4) = linio([mdl, '/Micro-Station/acc11'],1,'output');
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io(5) = linio([mdl, '/Micro-Station/acc12'],1,'output');
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% Run the linearization
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G_ms = linearize(mdl, io, 0);
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% Input/Output names
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G_ms.InputName = {'Fx', 'Fy', 'Fz'};
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G_ms.OutputName = {'x9', 'y9', 'z9', ...
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'x10', 'y10', 'z10', ...
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'x11', 'y11', 'z11', ...
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'x12', 'y12', 'z12'};
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% Plot Results
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figure;
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hold on;
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plot(freqs, abs(squeeze(freqresp(G_ms('x9', 'Fx'), freqs, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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% Compare with measurements
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load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
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dirs = {'x', 'y', 'z'};
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n_acc = 9;
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n_dir = 1; % x, y, z
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n_exc = 1; % x, y, z
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figure;
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hold on;
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plot(freqs, abs(squeeze(FRFs(3*(n_acc-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
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plot(freqs, abs(squeeze(freqresp(G_ms([dirs{n_dir}, num2str(n_acc)], ['F', dirs{n_dir}]), freqs, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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ylabel('Amplitude [m/N]');
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hold off;
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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% Prepare the Simulation
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open('nass_model.slx')
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||||
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% We load the configuration.
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load('mat/conf_simulink.mat');
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% We set a small =StopTime=.
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set_param(conf_simulink, 'StopTime', '0.5');
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% We initialize all the stages.
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initializeGround( 'type', 'rigid');
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initializeGranite( 'type', 'modal-analysis');
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initializeTy( 'type', 'modal-analysis');
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initializeRy( 'type', 'modal-analysis');
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initializeRz( 'type', 'modal-analysis');
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initializeMicroHexapod('type', 'modal-analysis');
|
||||
initializeAxisc( 'type', 'flexible');
|
||||
|
||||
initializeMirror( 'type', 'none');
|
||||
initializeNanoHexapod( 'type', 'none');
|
||||
initializeSample( 'type', 'none');
|
||||
|
||||
initializeController( 'type', 'open-loop');
|
||||
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
|
||||
initializeReferences();
|
||||
initializeDisturbances('enable', false);
|
||||
|
||||
% Estimate the position of the CoM of each solid and compare with the one took for the Measurement Analysis
|
||||
% Thanks to the [[https://fr.mathworks.com/help/physmod/sm/ref/inertiasensor.html][Inertia Sensor]] simscape block, it is possible to estimate the position of the Center of Mass of a solid body with respect to a defined frame.
|
||||
|
||||
|
||||
sim('nass_model')
|
||||
|
||||
% Create a frame at the CoM of each solid body
|
||||
% Now we use one =inertiasensor= block connected on each solid body that measured the center of mass of this solid with respect to the same connected frame.
|
||||
|
||||
% We do that in order to position an accelerometer on the Simscape model at this particular point.
|
||||
|
||||
|
||||
open('identification/matlab/sim_micro_station_com_estimation.slx')
|
||||
|
||||
sim('sim_micro_station_com_estimation')
|
||||
|
||||
|
||||
|
||||
% #+RESULTS:
|
||||
% | | granite bot | granite top | ty | ry | rz | hexa |
|
||||
% |--------+-------------+-------------+-------+--------+-------+-------|
|
||||
% | X [mm] | 0.0 | 51.7 | 0.9 | -0.1 | 0.0 | -0.0 |
|
||||
% | Y [mm] | 0.0 | 753.2 | 0.7 | 5.2 | -0.0 | 0.1 |
|
||||
% | Z [mm] | -250.0 | 22.9 | -17.1 | -146.5 | -23.2 | -47.1 |
|
||||
|
||||
% We now same this for further use:
|
||||
|
||||
granite_bot_com = granite_bot_com.Data(end, :)';
|
||||
granite_top_com = granite_top_com.Data(end, :)';
|
||||
ty_com = ty_com.Data(end, :)';
|
||||
ry_com = ry_com.Data(end, :)';
|
||||
rz_com = rz_com.Data(end, :)';
|
||||
hexa_com = hexa_com.Data(end, :)';
|
||||
|
||||
save('mat/solids_com.mat', 'granite_bot_com', 'granite_top_com', 'ty_com', 'ry_com', 'rz_com', 'hexa_com');
|
||||
|
||||
% Identification of the dynamics of the Simscape Model
|
||||
% We now use a new Simscape Model where 6DoF inertial sensors are located at the Center of Mass of each solid body.
|
||||
|
||||
|
||||
% load('mat/solids_com.mat', 'granite_bot_com', 'granite_top_com', 'ty_com', 'ry_com', 'rz_com', 'hexa_com');
|
||||
|
||||
open('nass_model.slx')
|
||||
|
||||
|
||||
|
||||
% We use the =linearize= function in order to estimate the dynamics from forces applied on the Translation stage at the same position used for the real modal analysis to the inertial sensors.
|
||||
|
||||
%% Options for Linearized
|
||||
options = linearizeOptions;
|
||||
options.SampleTime = 0;
|
||||
|
||||
%% Name of the Simulink File
|
||||
mdl = 'nass_model';
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Translation Stage/Modal Analysis/F_hammer'], 1, 'openinput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Granite/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Translation Stage/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Tilt Stage/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Spindle/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
io(io_i) = linio([mdl, '/Micro-Station/Micro Hexapod/Modal Analysis/accelerometer'], 1, 'openoutput'); io_i = io_i + 1;
|
||||
|
||||
% Run the linearization
|
||||
G_ms = linearize(mdl, io, 0);
|
||||
|
||||
%% Input/Output definition
|
||||
clear io; io_i = 1;
|
||||
G_ms.InputName = {'Fx', 'Fy', 'Fz'};
|
||||
G_ms.OutputName = {'gtop_x', 'gtop_y', 'gtop_z', 'gtop_rx', 'gtop_ry', 'gtop_rz', ...
|
||||
'ty_x', 'ty_y', 'ty_z', 'ty_rx', 'ty_ry', 'ty_rz', ...
|
||||
'ry_x', 'ry_y', 'ry_z', 'ry_rx', 'ry_ry', 'ry_rz', ...
|
||||
'rz_x', 'rz_y', 'rz_z', 'rz_rx', 'rz_ry', 'rz_rz', ...
|
||||
'hexa_x', 'hexa_y', 'hexa_z', 'hexa_rx', 'hexa_ry', 'hexa_rz'};
|
||||
|
||||
|
||||
|
||||
% The output of =G_ms= is the acceleration of each solid body.
|
||||
% In order to obtain a displacement, we divide the obtained transfer function by $1/s^{2}$;
|
||||
|
||||
G_ms = G_ms/s^2;
|
||||
|
||||
% Compare with measurements
|
||||
% We now load the Frequency Response Functions measurements during the Modal Analysis (accessible [[file:../../meas/modal-analysis/index.org][here]]).
|
||||
|
||||
|
||||
load('../meas/modal-analysis/mat/frf_coh_matrices.mat', 'freqs');
|
||||
load('../meas/modal-analysis/mat/frf_com.mat', 'FRFs_CoM');
|
||||
|
||||
|
||||
|
||||
% We then compare the measurements with the identified transfer functions using the Simscape Model.
|
||||
|
||||
|
||||
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
|
||||
stages = {'gbot', 'gtop', 'ty', 'ry', 'rz', 'hexa'}
|
||||
|
||||
n_stg = 3;
|
||||
n_dir = 6; % x, y, z, Rx, Ry, Rz
|
||||
n_exc = 2; % x, y, z
|
||||
|
||||
f = logspace(0, 3, 1000);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg-1) + n_dir, n_exc, :)))./((2*pi*freqs).^2)');
|
||||
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_exc}]), f, 'Hz'))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]');
|
||||
hold off;
|
||||
xlim([1, 200]);
|
||||
|
||||
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
|
||||
stages = {'gtop', 'ty', 'ry', 'rz', 'hexa'}
|
||||
|
||||
f = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
for n_stg = 1:2
|
||||
for n_dir = 1:3
|
||||
subplot(3, 2, (n_dir-1)*2 + n_stg);
|
||||
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
|
||||
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]');
|
||||
if n_dir == 3
|
||||
xlabel('Frequency [Hz]');
|
||||
end
|
||||
hold off;
|
||||
xlim([10, 1000]);
|
||||
ylim([1e-12, 1e-6]);
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:identification_comp_bot_stages
|
||||
% #+CAPTION: caption ([[./figs/identification_comp_bot_stages.png][png]], [[./figs/identification_comp_bot_stages.pdf][pdf]])
|
||||
% [[file:figs/identification_comp_bot_stages.png]]
|
||||
|
||||
|
||||
|
||||
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
|
||||
stages = {'ry', 'rz', 'hexa'}
|
||||
|
||||
f = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
for n_stg = 1:2
|
||||
for n_dir = 1:3
|
||||
subplot(3, 2, (n_dir-1)*2 + n_stg);
|
||||
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+2) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
|
||||
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]');
|
||||
if n_dir == 3
|
||||
xlabel('Frequency [Hz]');
|
||||
end
|
||||
hold off;
|
||||
xlim([10, 1000]);
|
||||
ylim([1e-12, 1e-6]);
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:identification_comp_mid_stages
|
||||
% #+CAPTION: caption ([[./figs/identification_comp_mid_stages.png][png]], [[./figs/identification_comp_mid_stages.pdf][pdf]])
|
||||
% [[file:figs/identification_comp_mid_stages.png]]
|
||||
|
||||
|
||||
|
||||
dirs = {'x', 'y', 'z', 'rx', 'ry', 'rz'};
|
||||
stages = {'hexa'}
|
||||
|
||||
f = logspace(1, 3, 1000);
|
||||
|
||||
figure;
|
||||
for n_stg = 1
|
||||
for n_dir = 1:3
|
||||
subplot(3, 1, (n_dir-1) + n_stg);
|
||||
title(['F ', dirs{n_dir}, ' to ', stages{n_stg}, ' ', dirs{n_dir}]);
|
||||
hold on;
|
||||
plot(freqs, abs(squeeze(FRFs_CoM(6*(n_stg+4) + n_dir, n_dir, :)))./((2*pi*freqs).^2)');
|
||||
plot(f, abs(squeeze(freqresp(G_ms([stages{n_stg}, '_', dirs{n_dir}], ['F', dirs{n_dir}]), f, 'Hz'))));
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
ylabel('Amplitude [m/N]');
|
||||
if n_dir == 3
|
||||
xlabel('Frequency [Hz]');
|
||||
end
|
||||
hold off;
|
||||
xlim([10, 1000]);
|
||||
ylim([1e-12, 1e-6]);
|
||||
end
|
||||
end
|
||||
@@ -1,407 +0,0 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
% Simscape Model
|
||||
% <<sec:simscape_model>>
|
||||
|
||||
|
||||
open('nass_model.slx');
|
||||
|
||||
|
||||
|
||||
% We load the shared simulink configuration and we set the =StopTime=.
|
||||
|
||||
load('mat/conf_simulink.mat');
|
||||
set_param(conf_simulink, 'StopTime', '5');
|
||||
|
||||
|
||||
|
||||
% We first initialize all the stages.
|
||||
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
initializeNanoHexapod('actuator', 'piezo');
|
||||
initializeSample('mass', 1);
|
||||
|
||||
|
||||
|
||||
% We initialize the reference path for all the stages.
|
||||
% All stage is set to its zero position except the Spindle which is rotating at 60rpm.
|
||||
|
||||
initializeReferences('Rz_type', 'rotating', 'Rz_period', 1);
|
||||
|
||||
% Simulation Setup
|
||||
% And we initialize the disturbances to be equal to zero.
|
||||
|
||||
initializeDisturbances(...
|
||||
'Dwx', false, ... % Ground Motion - X direction
|
||||
'Dwy', false, ... % Ground Motion - Y direction
|
||||
'Dwz', false, ... % Ground Motion - Z direction
|
||||
'Fty_x', false, ... % Translation Stage - X direction
|
||||
'Fty_z', false, ... % Translation Stage - Z direction
|
||||
'Frz_z', false ... % Spindle - Z direction
|
||||
);
|
||||
|
||||
|
||||
|
||||
% We simulate the model.
|
||||
|
||||
sim('nass_model');
|
||||
|
||||
|
||||
|
||||
% And we save the obtained data.
|
||||
|
||||
tomo_align_no_dist = struct('t', t, 'MTr', MTr);
|
||||
save('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist', '-append');
|
||||
|
||||
% Analysis
|
||||
|
||||
load('experiment_tomography/mat/experiment.mat', 'tomo_align_no_dist');
|
||||
t = tomo_align_no_dist.t;
|
||||
MTr = tomo_align_no_dist.MTr;
|
||||
|
||||
Edx = squeeze(MTr(1, 4, :));
|
||||
Edy = squeeze(MTr(2, 4, :));
|
||||
Edz = squeeze(MTr(3, 4, :));
|
||||
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
|
||||
Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
|
||||
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
|
||||
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
|
||||
ylabel('Displacement [m]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:exp_tomo_without_dist_trans
|
||||
% #+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_without_dist_trans.png][png]], [[./figs/exp_tomo_without_dist_trans.pdf][pdf]])
|
||||
% [[file:figs/exp_tomo_without_dist_trans.png]]
|
||||
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
|
||||
ylabel('Rotation [rad]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
% Simulation Setup
|
||||
% We now activate the disturbances.
|
||||
|
||||
initializeDisturbances(...
|
||||
'Dwx', true, ... % Ground Motion - X direction
|
||||
'Dwy', true, ... % Ground Motion - Y direction
|
||||
'Dwz', true, ... % Ground Motion - Z direction
|
||||
'Fty_x', true, ... % Translation Stage - X direction
|
||||
'Fty_z', true, ... % Translation Stage - Z direction
|
||||
'Frz_z', true ... % Spindle - Z direction
|
||||
);
|
||||
|
||||
|
||||
|
||||
% We simulate the model.
|
||||
|
||||
sim('nass_model');
|
||||
|
||||
|
||||
|
||||
% And we save the obtained data.
|
||||
|
||||
tomo_align_dist = struct('t', t, 'MTr', MTr);
|
||||
save('experiment_tomography/mat/experiment.mat', 'tomo_align_dist', '-append');
|
||||
|
||||
% Analysis
|
||||
|
||||
load('experiment_tomography/mat/experiment.mat', 'tomo_align_dist');
|
||||
t = tomo_align_dist.t;
|
||||
MTr = tomo_align_dist.MTr;
|
||||
|
||||
Edx = squeeze(MTr(1, 4, :));
|
||||
Edy = squeeze(MTr(2, 4, :));
|
||||
Edz = squeeze(MTr(3, 4, :));
|
||||
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
|
||||
Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
|
||||
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
|
||||
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
|
||||
ylabel('Displacement [m]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:exp_tomo_dist_trans
|
||||
% #+CAPTION: X-Y-Z translation of the sample w.r.t. the granite when performing tomography experiment with disturbances ([[./figs/exp_tomo_dist_trans.png][png]], [[./figs/exp_tomo_dist_trans.pdf][pdf]])
|
||||
% [[file:figs/exp_tomo_dist_trans.png]]
|
||||
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
|
||||
ylabel('Rotation [rad]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
% Simulation Setup
|
||||
% We first set the wanted translation of the Micro Hexapod.
|
||||
|
||||
P_micro_hexapod = [0.01; 0; 0]; % [m]
|
||||
|
||||
|
||||
|
||||
% We initialize the reference path.
|
||||
|
||||
initializeReferences('Dh_pos', [P_micro_hexapod; 0; 0; 0], 'Rz_type', 'rotating', 'Rz_period', 1);
|
||||
|
||||
|
||||
|
||||
% We initialize the stages.
|
||||
|
||||
initializeMicroHexapod('AP', P_micro_hexapod);
|
||||
|
||||
|
||||
|
||||
% And we initialize the disturbances to zero.
|
||||
|
||||
initializeDisturbances(...
|
||||
'Dwx', false, ... % Ground Motion - X direction
|
||||
'Dwy', false, ... % Ground Motion - Y direction
|
||||
'Dwz', false, ... % Ground Motion - Z direction
|
||||
'Fty_x', false, ... % Translation Stage - X direction
|
||||
'Fty_z', false, ... % Translation Stage - Z direction
|
||||
'Frz_z', false ... % Spindle - Z direction
|
||||
);
|
||||
|
||||
|
||||
|
||||
% We simulate the model.
|
||||
|
||||
sim('nass_model');
|
||||
|
||||
|
||||
|
||||
% And we save the obtained data.
|
||||
|
||||
tomo_not_align = struct('t', t, 'MTr', MTr);
|
||||
save('experiment_tomography/mat/experiment.mat', 'tomo_not_align', '-append');
|
||||
|
||||
% Analysis
|
||||
|
||||
load('experiment_tomography/mat/experiment.mat', 'tomo_not_align');
|
||||
t = tomo_not_align.t;
|
||||
MTr = tomo_not_align.MTr;
|
||||
|
||||
Edx = squeeze(MTr(1, 4, :));
|
||||
Edy = squeeze(MTr(2, 4, :));
|
||||
Edz = squeeze(MTr(3, 4, :));
|
||||
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
|
||||
Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
|
||||
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
|
||||
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
|
||||
ylabel('Displacement [m]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:exp_tomo_offset_trans
|
||||
% #+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_tomo_offset_trans.png][png]], [[./figs/exp_tomo_offset_trans.pdf][pdf]])
|
||||
% [[file:figs/exp_tomo_offset_trans.png]]
|
||||
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
|
||||
ylabel('Rotation [rad]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
% Simulation Setup
|
||||
% We set the reference path.
|
||||
|
||||
initializeReferences('Dy_type', 'triangular', 'Dy_amplitude', 10e-3, 'Dy_period', 1);
|
||||
|
||||
|
||||
|
||||
% We initialize the stages.
|
||||
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
initializeNanoHexapod('actuator', 'piezo');
|
||||
initializeSample('mass', 1);
|
||||
|
||||
|
||||
|
||||
% And we initialize the disturbances to zero.
|
||||
|
||||
initializeDisturbances(...
|
||||
'Dwx', false, ... % Ground Motion - X direction
|
||||
'Dwy', false, ... % Ground Motion - Y direction
|
||||
'Dwz', false, ... % Ground Motion - Z direction
|
||||
'Fty_x', false, ... % Translation Stage - X direction
|
||||
'Fty_z', false, ... % Translation Stage - Z direction
|
||||
'Frz_z', false ... % Spindle - Z direction
|
||||
);
|
||||
|
||||
|
||||
|
||||
% We simulate the model.
|
||||
|
||||
sim('nass_model');
|
||||
|
||||
|
||||
|
||||
% And we save the obtained data.
|
||||
|
||||
ty_scan = struct('t', t, 'MTr', MTr);
|
||||
save('experiment_tomography/mat/experiment.mat', 'ty_scan', '-append');
|
||||
|
||||
% Analysis
|
||||
|
||||
load('experiment_tomography/mat/experiment.mat', 'ty_scan');
|
||||
t = ty_scan.t;
|
||||
MTr = ty_scan.MTr;
|
||||
|
||||
Edx = squeeze(MTr(1, 4, :));
|
||||
Edy = squeeze(MTr(2, 4, :));
|
||||
Edz = squeeze(MTr(3, 4, :));
|
||||
% The angles obtained are u-v-w Euler angles (rotations in the moving frame)
|
||||
Ery = atan2( squeeze(MTr(1, 3, :)), squeeze(sqrt(MTr(1, 1, :).^2 + MTr(1, 2, :).^2)));
|
||||
Erx = atan2(-squeeze(MTr(2, 3, :))./cos(Ery), squeeze(MTr(3, 3, :))./cos(Ery));
|
||||
Erz = atan2(-squeeze(MTr(1, 2, :))./cos(Ery), squeeze(MTr(1, 1, :))./cos(Ery));
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Edx, 'DisplayName', '$\epsilon_{x}$')
|
||||
ylabel('Displacement [m]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Edy, 'DisplayName', '$\epsilon_{y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Edz, 'DisplayName', '$\epsilon_{z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:exp_ty_scan_trans
|
||||
% #+CAPTION: X-Y-Z translation of the sample w.r.t. granite when performing tomography experiment with no disturbances ([[./figs/exp_ty_scan_trans.png][png]], [[./figs/exp_ty_scan_trans.pdf][pdf]])
|
||||
% [[file:figs/exp_ty_scan_trans.png]]
|
||||
|
||||
|
||||
figure;
|
||||
ax1 = subplot(1, 3, 1);
|
||||
plot(t, Erx, 'DisplayName', '$\epsilon_{\theta x}$')
|
||||
ylabel('Rotation [rad]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax2 = subplot(1, 3, 2);
|
||||
plot(t, Ery, 'DisplayName', '$\epsilon_{\theta y}$')
|
||||
xlabel('Time [s]');
|
||||
legend('location', 'northeast');
|
||||
|
||||
ax3 = subplot(1, 3, 3);
|
||||
plot(t, Erz, 'DisplayName', '$\epsilon_{\theta z}$')
|
||||
legend('location', 'northeast');
|
||||
|
||||
linkaxes([ax1,ax2,ax3],'x');
|
||||
xlim([2, inf]);
|
||||
@@ -1,27 +0,0 @@
|
||||
function [] = prepareLinearizeIdentification(args)
|
||||
|
||||
arguments
|
||||
args.nass_actuator char {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo'
|
||||
args.sample_mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
|
||||
end
|
||||
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
|
||||
initializeNanoHexapod('actuator', args.nass_actuator);
|
||||
initializeSample('mass', args.sample_mass);
|
||||
|
||||
initializeReferences();
|
||||
initializeDisturbances('enable', false);
|
||||
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
initializeSimscapeConfiguration('gravity', true);
|
||||
|
||||
initializeLoggingConfiguration('log', 'none');
|
||||
@@ -1,29 +0,0 @@
|
||||
function [] = prepareTomographyExperiment(args)
|
||||
|
||||
arguments
|
||||
args.nass_actuator char {mustBeMember(args.nass_actuator,{'piezo', 'lorentz'})} = 'piezo'
|
||||
args.sample_mass (1,1) double {mustBeNumeric, mustBePositive} = 50 % [kg]
|
||||
args.Rz_period (1,1) double {mustBeNumeric, mustBePositive} = 1 % [s]
|
||||
end
|
||||
|
||||
initializeGround();
|
||||
initializeGranite();
|
||||
initializeTy();
|
||||
initializeRy();
|
||||
initializeRz();
|
||||
initializeMicroHexapod();
|
||||
initializeAxisc();
|
||||
initializeMirror();
|
||||
|
||||
initializeNanoHexapod('actuator', args.nass_actuator);
|
||||
initializeSample('mass', args.sample_mass);
|
||||
|
||||
initializeReferences('Rz_type', 'rotating', 'Rz_period', args.Rz_period);
|
||||
|
||||
initializeDisturbances();
|
||||
|
||||
initializeController('type', 'open-loop');
|
||||
|
||||
initializeSimscapeConfiguration('gravity', true);
|
||||
|
||||
initializeLoggingConfiguration('log', 'all');
|
||||
@@ -1,23 +0,0 @@
|
||||
function [psd_object] = computePsdDispl(sys_data, t_init, n_av)
|
||||
i_init = find(sys_data.time > t_init, 1);
|
||||
|
||||
han_win = hanning(ceil(length(sys_data.Dx(i_init:end, :))/n_av));
|
||||
Fs = 1/sys_data.time(2);
|
||||
|
||||
[pdx, f] = pwelch(sys_data.Dx(i_init:end, :), han_win, [], [], Fs);
|
||||
[pdy, ~] = pwelch(sys_data.Dy(i_init:end, :), han_win, [], [], Fs);
|
||||
[pdz, ~] = pwelch(sys_data.Dz(i_init:end, :), han_win, [], [], Fs);
|
||||
|
||||
[prx, ~] = pwelch(sys_data.Rx(i_init:end, :), han_win, [], [], Fs);
|
||||
[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, ...
|
||||
'rz', prz);
|
||||
end
|
||||
@@ -1,59 +0,0 @@
|
||||
function setpoint = computeSetpoint(ty, ry, rz)
|
||||
%%
|
||||
setpoint = zeros(6, 1);
|
||||
|
||||
%% Ty
|
||||
Ty = [1 0 0 0 ;
|
||||
0 1 0 ty ;
|
||||
0 0 1 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
% Tyinv = [1 0 0 0 ;
|
||||
% 0 1 0 -ty ;
|
||||
% 0 0 1 0 ;
|
||||
% 0 0 0 1 ];
|
||||
|
||||
%% Ry
|
||||
Ry = [ cos(ry) 0 sin(ry) 0 ;
|
||||
0 1 0 0 ;
|
||||
-sin(ry) 0 cos(ry) 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
% TMry = Ty*Ry*Tyinv;
|
||||
|
||||
%% Rz
|
||||
Rz = [cos(rz) -sin(rz) 0 0 ;
|
||||
sin(rz) cos(rz) 0 0 ;
|
||||
0 0 1 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
% TMrz = Ty*TMry*Rz*TMry'*Tyinv;
|
||||
|
||||
%% All stages
|
||||
% TM = TMrz*TMry*Ty;
|
||||
|
||||
TM = Ty*Ry*Rz;
|
||||
|
||||
[thetax, thetay, thetaz] = RM2angle(TM(1:3, 1:3));
|
||||
|
||||
setpoint(1:3) = TM(1:3, 4);
|
||||
setpoint(4:6) = [thetax, thetay, thetaz];
|
||||
|
||||
%% Custom Functions
|
||||
function [thetax, thetay, thetaz] = RM2angle(R)
|
||||
if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
|
||||
thetay = -asin(R(3, 1));
|
||||
thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
|
||||
thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
|
||||
else
|
||||
thetaz = 0;
|
||||
if abs(R(3, 1)+1) < 1e-6 % R31 = -1
|
||||
thetay = pi/2;
|
||||
thetax = thetaz + atan2(R(1, 2), R(1, 3));
|
||||
else
|
||||
thetay = -pi/2;
|
||||
thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
@@ -1,125 +0,0 @@
|
||||
function error_nass = convertErrorBasis(pos, setpoint, ty, ry, rz)
|
||||
% convertErrorBasis -
|
||||
%
|
||||
% Syntax: convertErrorBasis(p_error, ty, ry, rz)
|
||||
%
|
||||
% Inputs:
|
||||
% - p_error - Position error of the sample w.r.t. the granite [m, rad]
|
||||
% - ty - Measured translation of the Ty stage [m]
|
||||
% - ry - Measured rotation of the Ry stage [rad]
|
||||
% - rz - Measured rotation of the Rz stage [rad]
|
||||
%
|
||||
% Outputs:
|
||||
% - P_nass - Position error of the sample w.r.t. the NASS base [m]
|
||||
% - R_nass - Rotation error of the sample w.r.t. the NASS base [rad]
|
||||
%
|
||||
% Example:
|
||||
%
|
||||
|
||||
%% If line vector => column vector
|
||||
if size(pos, 2) == 6
|
||||
pos = pos';
|
||||
end
|
||||
|
||||
if size(setpoint, 2) == 6
|
||||
setpoint = setpoint';
|
||||
end
|
||||
|
||||
%% Position of the sample in the frame fixed to the Granite
|
||||
P_granite = [pos(1:3); 1]; % Position [m]
|
||||
R_granite = [setpoint(1:3); 1]; % Reference [m]
|
||||
|
||||
%% Transformation matrices of the stages
|
||||
% T-y
|
||||
TMty = [1 0 0 0 ;
|
||||
0 1 0 ty ;
|
||||
0 0 1 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
% R-y
|
||||
TMry = [ cos(ry) 0 sin(ry) 0 ;
|
||||
0 1 0 0 ;
|
||||
-sin(ry) 0 cos(ry) 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
% R-z
|
||||
TMrz = [cos(rz) -sin(rz) 0 0 ;
|
||||
sin(rz) cos(rz) 0 0 ;
|
||||
0 0 1 0 ;
|
||||
0 0 0 1 ];
|
||||
|
||||
%% Compute Point coordinates in the new reference fixed to the NASS base
|
||||
% P_nass = TMrz*TMry*TMty*P_granite;
|
||||
P_nass = TMrz\TMry\TMty\P_granite;
|
||||
R_nass = TMrz\TMry\TMty\R_granite;
|
||||
|
||||
dx = R_nass(1)-P_nass(1);
|
||||
dy = R_nass(2)-P_nass(2);
|
||||
dz = R_nass(3)-P_nass(3);
|
||||
|
||||
%% Compute new basis vectors linked to the NASS base
|
||||
% ux_nass = TMrz*TMry*TMty*[1; 0; 0; 0];
|
||||
% ux_nass = ux_nass(1:3);
|
||||
% uy_nass = TMrz*TMry*TMty*[0; 1; 0; 0];
|
||||
% uy_nass = uy_nass(1:3);
|
||||
% uz_nass = TMrz*TMry*TMty*[0; 0; 1; 0];
|
||||
% uz_nass = uz_nass(1:3);
|
||||
|
||||
ux_nass = TMrz\TMry\TMty\[1; 0; 0; 0];
|
||||
ux_nass = ux_nass(1:3);
|
||||
uy_nass = TMrz\TMry\TMty\[0; 1; 0; 0];
|
||||
uy_nass = uy_nass(1:3);
|
||||
uz_nass = TMrz\TMry\TMty\[0; 0; 1; 0];
|
||||
uz_nass = uz_nass(1:3);
|
||||
|
||||
%% Rotations error w.r.t. granite Frame
|
||||
% Rotations error w.r.t. granite Frame
|
||||
rx_nass = pos(4);
|
||||
ry_nass = pos(5);
|
||||
rz_nass = pos(6);
|
||||
|
||||
% Rotation matrices of the Sample w.r.t. the Granite
|
||||
Mrx_error = [1 0 0 ;
|
||||
0 cos(-rx_nass) -sin(-rx_nass) ;
|
||||
0 sin(-rx_nass) cos(-rx_nass)];
|
||||
|
||||
Mry_error = [ cos(-ry_nass) 0 sin(-ry_nass) ;
|
||||
0 1 0 ;
|
||||
-sin(-ry_nass) 0 cos(-ry_nass)];
|
||||
|
||||
Mrz_error = [cos(-rz_nass) -sin(-rz_nass) 0 ;
|
||||
sin(-rz_nass) cos(-rz_nass) 0 ;
|
||||
0 0 1];
|
||||
|
||||
% Rotation matrix of the Sample w.r.t. the Granite
|
||||
Mr_error = Mrz_error*Mry_error*Mrx_error;
|
||||
|
||||
%% Use matrix to solve
|
||||
R = Mr_error/[ux_nass, uy_nass, uz_nass]; % Rotation matrix from NASS base to Sample
|
||||
|
||||
[thetax, thetay, thetaz] = RM2angle(R);
|
||||
|
||||
error_nass = [dx; dy; dz; thetax; thetay; thetaz];
|
||||
|
||||
%% Custom Functions
|
||||
function [thetax, thetay, thetaz] = RM2angle(R)
|
||||
if abs(abs(R(3, 1)) - 1) > 1e-6 % R31 != 1 and R31 != -1
|
||||
thetay = -asin(R(3, 1));
|
||||
% thetaybis = pi-thetay;
|
||||
thetax = atan2(R(3, 2)/cos(thetay), R(3, 3)/cos(thetay));
|
||||
% thetaxbis = atan2(R(3, 2)/cos(thetaybis), R(3, 3)/cos(thetaybis));
|
||||
thetaz = atan2(R(2, 1)/cos(thetay), R(1, 1)/cos(thetay));
|
||||
% thetazbis = atan2(R(2, 1)/cos(thetaybis), R(1, 1)/cos(thetaybis));
|
||||
else
|
||||
thetaz = 0;
|
||||
if abs(R(3, 1)+1) < 1e-6 % R31 = -1
|
||||
thetay = pi/2;
|
||||
thetax = thetaz + atan2(R(1, 2), R(1, 3));
|
||||
else
|
||||
thetay = -pi/2;
|
||||
thetax = -thetaz + atan2(-R(1, 2), -R(1, 3));
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
end
|
||||
Reference in New Issue
Block a user