Simscape Uniaxial Model
+Table of Contents
+ ++The goal here is to extract the Power Spectral Density of the sources of perturbation. +
+ ++The sources of perturbations are: +
+-
+
- Ground Motion +
- Parasitic forces applied in the system when scanning with the Translation Stage and the Spindle. +These forces can be due to imperfect guiding for instance. +
+Because we cannot measure directly the perturbation forces, we have the measure the effect of those perturbations on the system (in terms of velocity for instance using geophones) and then, using a model, compute the forces that induced such velocity. +
+ +-
+
- Section 1: transfer functions from the disturbance forces to the relative velocity of the hexapod with respect to the granite are computed using the Simscape Model representing the experimental setup +
1 Identification
+%% Options for Linearized +options = linearizeOptions; +options.SampleTime = 0; + +%% Name of the Simulink File +mdl = 'sim_micro_station_disturbances'; ++
%% Micro-Hexapod +% Input/Output definition +io(1) = linio([mdl, '/Dw'], 1, 'input'); % Ground Motion +io(2) = linio([mdl, '/Fty'], 1, 'input'); % Parasitic force Ty +io(3) = linio([mdl, '/Frz'], 1, 'input'); % Parasitic force Rz +io(4) = linio([mdl, '/Dgm'], 1, 'output'); % Absolute motion - Granite +io(5) = linio([mdl, '/Dhm'], 1, 'output'); % Absolute Motion - Hexapod +io(6) = linio([mdl, '/Vm'], 1, 'output'); % Relative Velocity hexapod/granite ++
% Run the linearization +G = linearize(mdl, io, 0); + +% Input/Output names +G.InputName = {'Dw', 'Fty', 'Frz'}; +G.OutputName = {'Dgm', 'Dhm', 'Vm'}; ++
2 Sensitivity to Disturbances
+ +
+
+
+3 Power Spectral Density of the effect of the disturbances
++ +The PSD of the relative velocity between the hexapod and the marble in \([(m/s)^2/Hz]\) are loaded for the following sources of disturbance: +
+-
+
- Slip Ring Rotation +
- Scan of the translation stage (effect in the vertical direction and in the horizontal direction) +
+Also, the Ground Motion is measured. +
+ +gm = load('./disturbances/mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv'); +rz = load('./disturbances/mat/pxsp_r.mat', 'f', 'pxsp_r'); +tyz = load('./disturbances/mat/pxz_ty_r.mat', 'f', 'pxz_ty_r'); +tyx = load('./disturbances/mat/pxe_ty_r.mat', 'f', 'pxe_ty_r'); ++
+We now compute the relative velocity between the hexapod and the granite due to ground motion. +
+gm.psd_rv = gm.psd_gm.*abs(squeeze(freqresp(G('Vm', 'Dw'), gm.f, 'Hz'))).^2; ++
+The Power Spectral Density of the relative motion/velocity of the hexapod with respect to the granite are shown in figures 4 and 5. +
+ ++The Cumulative Amplitude Spectrum of the relative motion is shown in figure 6. +
+ + +
+
Figure 4: Amplitude Spectral Density of the relative velocity of the hexapod with respect to the granite due to different sources of perturbation (png, pdf)
+
+
+4 Compute the Power Spectral Density of the disturbance force
++Now, from the extracted transfer functions from the disturbance force to the relative motion of the hexapod with respect to the granite (section 2) and from the measured PSD of the relative motion (section 3), we can compute the PSD of the disturbance force. +
+ +rz.psd_f = rz.pxsp_r./abs(squeeze(freqresp(G('Vm', 'Frz'), rz.f, 'Hz'))).^2; +tyz.psd_f = tyz.pxz_ty_r./abs(squeeze(freqresp(G('Vm', 'Fty'), tyz.f, 'Hz'))).^2; ++
+5 Noise Budget
++Now, from the compute spectral density of the disturbance sources, we can compute the resulting relative motion of the Hexapod with respect to the granite using the model. +We should verify that this is coherent with the measurements. +
+ + + + + + + +
+
+
6 Save
++The PSD of the disturbance force are now saved for further noise budgeting when control is applied. +
+ +dist_f = struct(); +dist_f.f = gm.f; % Frequency Vector [Hz] +dist_f.psd_gm = gm.psd_gm; % Power Spectral Density of the Ground Motion [m^2/Hz] +dist_f.psd_ty = tyz.psd_f; % Power Spectral Density of the force induced by the Ty stage in the Z direction [N^2/Hz] +dist_f.psd_rz = rz.psd_f; % Power Spectral Density of the force induced by the Rz stage in the Z direction [N^2/Hz] + +save('./disturbances/mat/disturbance-forces.mat', 'dist_f'); ++