[WIP] Breaking Change - Use Update
Folder name is changed, rework the html templates Change the organisation.
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86
spindle/matlab/spindle_data_processing.m
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86
spindle/matlab/spindle_data_processing.m
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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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%% Add the getAsynchronousError to path
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addpath('./src/');
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% Load Measurement Data
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spindle_1rpm_table = readtable('./mat/10turns_1rpm_icepap.txt');
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spindle_60rpm_table = readtable('./mat/10turns_60rpm_IcepapFIR.txt');
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spindle_1rpm_table(1, :)
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spindle_1rpm = table2array(spindle_1rpm_table);
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spindle_60rpm = table2array(spindle_60rpm_table);
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% Convert Signals from [deg] to [sec]
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speed_1rpm = 360/60; % [deg/sec]
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spindle_1rpm(:, 1) = spindle_1rpm(:, 2)/speed_1rpm; % From position [deg] to time [s]
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speed_60rpm = 360/1; % [deg/sec]
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spindle_60rpm(:, 1) = spindle_60rpm(:, 2)/speed_60rpm; % From position [deg] to time [s]
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% Convert Signals
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% scaling = 1/80000; % 80 mV/um
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scaling = 1e-6; % [um] to [m]
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spindle_1rpm(:, 3:end) = scaling*spindle_1rpm(:, 3:end); % [V] to [m]
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spindle_1rpm(:, 3:end) = spindle_1rpm(:, 3:end)-mean(spindle_1rpm(:, 3:end)); % Remove mean
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spindle_60rpm(:, 3:end) = scaling*spindle_60rpm(:, 3:end); % [V] to [m]
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spindle_60rpm(:, 3:end) = spindle_60rpm(:, 3:end)-mean(spindle_60rpm(:, 3:end)); % Remove mean
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% Ts and Fs for both measurements
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Ts_1rpm = spindle_1rpm(end, 1)/(length(spindle_1rpm(:, 1))-1);
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Fs_1rpm = 1/Ts_1rpm;
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Ts_60rpm = spindle_60rpm(end, 1)/(length(spindle_60rpm(:, 1))-1);
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Fs_60rpm = 1/Ts_60rpm;
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% Find Noise of the ADC [$\frac{m}{\sqrt{Hz}}$]
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data = spindle_1rpm(:, 5);
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dV_1rpm = min(abs(data(1) - data(data ~= data(1))));
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noise_1rpm = dV_1rpm/sqrt(12*Fs_1rpm/2);
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data = spindle_60rpm(:, 5);
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dV_60rpm = min(abs(data(50) - data(data ~= data(50))));
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noise_60rpm = dV_60rpm/sqrt(12*Fs_60rpm/2);
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% Save all the data under spindle struct
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spindle.rpm1.time = spindle_1rpm(:, 1);
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spindle.rpm1.deg = spindle_1rpm(:, 2);
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spindle.rpm1.Ts = Ts_1rpm;
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spindle.rpm1.Fs = 1/Ts_1rpm;
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spindle.rpm1.x = spindle_1rpm(:, 3);
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spindle.rpm1.y = spindle_1rpm(:, 4);
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spindle.rpm1.z = spindle_1rpm(:, 5);
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spindle.rpm1.adcn = noise_1rpm;
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spindle.rpm60.time = spindle_60rpm(:, 1);
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spindle.rpm60.deg = spindle_60rpm(:, 2);
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spindle.rpm60.Ts = Ts_60rpm;
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spindle.rpm60.Fs = 1/Ts_60rpm;
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spindle.rpm60.x = spindle_60rpm(:, 3);
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spindle.rpm60.y = spindle_60rpm(:, 4);
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spindle.rpm60.z = spindle_60rpm(:, 5);
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spindle.rpm60.adcn = noise_60rpm;
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% Compute Asynchronous data
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for direction = {'x', 'y', 'z'}
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spindle.rpm1.([direction{1}, 'async']) = getAsynchronousError(spindle.rpm1.(direction{1}), 10);
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spindle.rpm60.([direction{1}, 'async']) = getAsynchronousError(spindle.rpm60.(direction{1}), 10);
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end
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% Save data
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save('./mat/spindle_data.mat', 'spindle');
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103
spindle/matlab/spindle_model.m
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103
spindle/matlab/spindle_model.m
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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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%% Add the getAsynchronousError to path
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addpath('./src/');
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% Parameters
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mg = 3000; % Mass of granite [kg]
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ms = 50; % Mass of Spindle [kg]
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kg = 1e8; % Stiffness of granite [N/m]
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ks = 5e7; % Stiffness of spindle [N/m]
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% Compute Mass and Stiffness Matrices
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Mm = diag([ms, mg]);
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Km = diag([ks, ks+kg]) - diag(ks, -1) - diag(ks, 1);
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% Compute resonance frequencies
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A = [zeros(size(Mm)) eye(size(Mm)) ; -Mm\Km zeros(size(Mm))];
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eigA = imag(eigs(A))/2/pi;
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eigA = eigA(eigA>0);
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eigA = eigA(1:2);
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% From model_damping compute the Damping Matrix
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modal_damping = 1e-5;
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ab = [0.5*eigA(1) 0.5/eigA(1) ; 0.5*eigA(2) 0.5/eigA(2)]\[modal_damping ; modal_damping];
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Cm = ab(1)*Mm +ab(2)*Km;
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% Define inputs, outputs and state names
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StateName = {...
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'xs', ... % Displacement of Spindle [m]
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'xg', ... % Displacement of Granite [m]
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'vs', ... % Velocity of Spindle [m]
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'vg', ... % Velocity of Granite [m]
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};
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StateUnit = {'m', 'm', 'm/s', 'm/s'};
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InputName = {...
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'f' ... % Spindle Force [N]
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};
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InputUnit = {'N'};
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OutputName = {...
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'd' ... % Displacement [m]
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};
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OutputUnit = {'m'};
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% Define A, B and C matrices
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% A Matrix
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A = [zeros(size(Mm)) eye(size(Mm)) ; ...
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-Mm\Km -Mm\Cm];
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% B Matrix
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B_low = zeros(length(StateName), length(InputName));
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B_low(strcmp(StateName,'vs'), strcmp(InputName,'f')) = 1;
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B_low(strcmp(StateName,'vg'), strcmp(InputName,'f')) = -1;
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B = blkdiag(zeros(length(StateName)/2), pinv(Mm))*B_low;
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% C Matrix
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C = zeros(length(OutputName), length(StateName));
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C(strcmp(OutputName,'d'), strcmp(StateName,'xs')) = 1;
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C(strcmp(OutputName,'d'), strcmp(StateName,'xg')) = -1;
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% D Matrix
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D = zeros(length(OutputName), length(InputName));
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% Generate the State Space Model
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sys = ss(A, B, C, D);
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sys.StateName = StateName;
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sys.StateUnit = StateUnit;
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sys.InputName = InputName;
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sys.InputUnit = InputUnit;
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sys.OutputName = OutputName;
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sys.OutputUnit = OutputUnit;
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% Bode Plot
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% The transfer function from a disturbance force $f$ to the measured displacement $d$ is shown figure [[fig:spindle_f_to_d]].
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freqs = logspace(-1, 3, 1000);
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figure;
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plot(freqs, abs(squeeze(freqresp(sys('d', 'f'), freqs, 'Hz'))));
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude [m/N]');
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% Save the model
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save('./mat/spindle_model.mat', 'sys');
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144
spindle/matlab/spindle_psd.m
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144
spindle/matlab/spindle_psd.m
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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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% Load the processed data and the model
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load('./mat/spindle_data.mat', 'spindle');
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load('./mat/spindle_model.mat', 'sys');
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% Compute the PSD
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n_av = 4; % Number of average
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[pxx_1rpm, f_1rpm] = pwelch(spindle.rpm1.xasync, hanning(ceil(length(spindle.rpm1.xasync)/n_av)), [], [], spindle.rpm1.Fs);
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[pyy_1rpm, ~] = pwelch(spindle.rpm1.yasync, hanning(ceil(length(spindle.rpm1.yasync)/n_av)), [], [], spindle.rpm1.Fs);
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[pzz_1rpm, ~] = pwelch(spindle.rpm1.zasync, hanning(ceil(length(spindle.rpm1.zasync)/n_av)), [], [], spindle.rpm1.Fs);
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[pxx_60rpm, f_60rpm] = pwelch(spindle.rpm60.xasync, hanning(ceil(length(spindle.rpm60.xasync)/n_av)), [], [], spindle.rpm60.Fs);
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[pyy_60rpm, ~] = pwelch(spindle.rpm60.yasync, hanning(ceil(length(spindle.rpm60.yasync)/n_av)), [], [], spindle.rpm60.Fs);
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[pzz_60rpm, ~] = pwelch(spindle.rpm60.zasync, hanning(ceil(length(spindle.rpm60.zasync)/n_av)), [], [], spindle.rpm60.Fs);
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% Plot the computed PSD
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% The Amplitude Spectral Densities of the displacement of the spindle for the $x$, $y$ and $z$ directions are shown figure [[fig:spindle_psd_xyz_60rpm]]. They correspond to the Asynchronous part shown figure [[fig:spindle_60rpm_sync_async]].
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figure;
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hold on;
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plot(f_1rpm, (pxx_1rpm).^.5, 'DisplayName', '$P_{xx}$ - 1rpm');
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plot(f_1rpm, (pyy_1rpm).^.5, 'DisplayName', '$P_{yy}$ - 1rpm');
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plot(f_1rpm, (pzz_1rpm).^.5, 'DisplayName', '$P_{zz}$ - 1rpm');
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% plot(f_1rpm, spindle.rpm1.adcn*ones(size(f_1rpm)), '--k', 'DisplayName', 'ADC - 1rpm');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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legend('Location', 'northeast');
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xlim([f_1rpm(2), f_1rpm(end)]);
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% #+NAME: fig:spindle_psd_xyz_1rpm
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% #+CAPTION: Power spectral density of the Asynchronous displacement - 1rpm
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% #+RESULTS: fig:spindle_psd_xyz_1rpm
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% [[file:figs/spindle_psd_xyz_1rpm.png]]
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figure;
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hold on;
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plot(f_60rpm, (pxx_60rpm).^.5, 'DisplayName', '$P_{xx}$ - 60rpm');
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plot(f_60rpm, (pyy_60rpm).^.5, 'DisplayName', '$P_{yy}$ - 60rpm');
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plot(f_60rpm, (pzz_60rpm).^.5, 'DisplayName', '$P_{zz}$ - 60rpm');
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% plot(f_60rpm, spindle.rpm60.adcn*ones(size(f_60rpm)), '--k', 'DisplayName', 'ADC - 60rpm');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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legend('Location', 'northeast');
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xlim([f_60rpm(2), f_60rpm(end)]);
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% Compute the response of the model
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Tfd = abs(squeeze(freqresp(sys('d', 'f'), f_60rpm, 'Hz')));
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% Plot the PSD of the Force using the model
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figure;
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plot(f_60rpm, (pxx_60rpm.^.5)./Tfd, 'DisplayName', '$P_{xx}$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$N/\sqrt{Hz}$]');
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xlim([f_60rpm(2), f_60rpm(end)]);
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% Estimated Shape of the PSD of the force
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s = tf('s');
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Wd_simple = 1e-8/(1+s/2/pi/0.5)/(1+s/2/pi/100);
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Wf_simple = Wd_simple/tf(sys('d', 'f'));
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TWf_simple = abs(squeeze(freqresp(Wf_simple, f_60rpm, 'Hz')));
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% Wf = 0.48902*(s+327.9)*(s^2 + 109.6*s + 1.687e04)/((s^2 + 30.59*s + 8541)*(s^2 + 29.11*s + 3.268e04));
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% Wf = 0.15788*(s+418.6)*(s+1697)^2*(s^2 + 124.3*s + 2.529e04)*(s^2 + 681.3*s + 9.018e05)/((s^2 + 23.03*s + 8916)*(s^2 + 33.85*s + 6.559e04)*(s^2 + 71.43*s + 4.283e05)*(s^2 + 40.64*s + 1.789e06));
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Wf = (s+1697)^2*(s^2 + 114.5*s + 2.278e04)*(s^2 + 205.1*s + 1.627e05)*(s^2 + 285.8*s + 8.624e05)*(s+100)/((s+0.5)*3012*(s^2 + 23.03*s + 8916)*(s^2 + 17.07*s + 4.798e04)*(s^2 + 41.17*s + 4.347e05)*(s^2 + 78.99*s + 1.789e06));
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TWf = abs(squeeze(freqresp(Wf, f_60rpm, 'Hz')));
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% PSD in [N]
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% Above $200Hz$, the Amplitude Spectral Density seems dominated by noise coming from the electronics (charge amplifier, ADC, ...). So we don't know what is the frequency content of the force above that frequency. However, we assume that $P_{xx}$ is decreasing with $1/f$ as it seems so be the case below $100Hz$ (figure [[fig:spindle_psd_xyz_60rpm]]).
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% We then fit the PSD of the displacement with a transfer function (figure [[fig:spindle_psd_d_comp_60rpm]]).
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figure;
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hold on;
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plot(f_60rpm, (pxx_60rpm.^.5)./Tfd, 'DisplayName', '$\sqrt{P_{xx}}/|T_{d/f}|$');
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plot(f_60rpm, TWf, 'DisplayName', 'Wf');
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plot(f_60rpm, TWf_simple, '-k', 'DisplayName', 'Wfs');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$N/\sqrt{Hz}$]');
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xlim([f_60rpm(2), f_60rpm(end)]);
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legend('Location', 'northeast');
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% PSD in [m]
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% To obtain the PSD of the force $f$ that induce such displacement, we use the following formula:
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% \[ \sqrt{PSD(d)} = |T_{d/f}| \sqrt{PSD(f)} \]
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% And so we have:
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% \[ \sqrt{PSD(f)} = |T_{d/f}|^{-1} \sqrt{PSD(d)} \]
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% The obtain Power Spectral Density of the force is displayed figure [[fig:spindle_psd_f_comp_60rpm]].
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figure;
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hold on;
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plot(f_60rpm, pxx_60rpm.^.5, 'DisplayName', '$\sqrt{P_{xx}}$');
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plot(f_60rpm, TWf.*Tfd, 'DisplayName', '$|W_f|*|T_{d/f}|$');
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD [$m/\sqrt{Hz}$]');
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xlim([f_60rpm(2), f_60rpm(end)]);
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legend('Location', 'northeast');
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% Compute the resulting RMS value [m]
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figure;
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hold on;
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plot(f_60rpm, 1e9*cumtrapz(f_60rpm, (pxx_60rpm)).^.5, '--', 'DisplayName', 'Exp. Data');
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plot(f_60rpm, 1e9*cumtrapz(f_60rpm, ((TWf.*Tfd).^2)).^.5, '--', 'DisplayName', 'Estimated');
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hold off;
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set(gca, 'XScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('CPS [$nm$ rms]');
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xlim([f_60rpm(2), f_60rpm(end)]);
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legend('Location', 'southeast');
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% Compute the resulting RMS value [m]
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figure;
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hold on;
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plot(f_1rpm, 1e9*cumtrapz(f_1rpm, (pxx_1rpm)), '--', 'DisplayName', 'Exp. Data');
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plot(f_1rpm, 1e9*(f_1rpm(end)-f_1rpm(1))/(length(f_1rpm)-1)*cumsum(pxx_1rpm), '--', 'DisplayName', 'Exp. Data');
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hold off;
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set(gca, 'XScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('CPS [$nm$ rms]');
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xlim([f_1rpm(2), f_1rpm(end)]);
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legend('Location', 'southeast');
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75
spindle/matlab/spindle_time_domain.m
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75
spindle/matlab/spindle_time_domain.m
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@@ -0,0 +1,75 @@
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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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% Load the processed data
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load('./mat/spindle_data.mat', 'spindle');
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% Plot X-Y-Z position with respect to Time - 1rpm
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figure;
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hold on;
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plot(spindle.rpm1.time, spindle.rpm1.x);
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||||
plot(spindle.rpm1.time, spindle.rpm1.y);
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||||
plot(spindle.rpm1.time, spindle.rpm1.z);
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hold off;
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xlabel('Time [s]'); ylabel('Amplitude [m]');
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legend({'tx - 1rpm', 'ty - 1rpm', 'tz - 1rpm'});
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% Plot X-Y-Z position with respect to Time - 60rpm
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% The measurements for the spindle turning at 60rpm are shown figure [[fig:spindle_xyz_60rpm]].
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||||
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figure;
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hold on;
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plot(spindle.rpm60.time, spindle.rpm60.x);
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plot(spindle.rpm60.time, spindle.rpm60.y);
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||||
plot(spindle.rpm60.time, spindle.rpm60.z);
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hold off;
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xlabel('Time [s]'); ylabel('Amplitude [m]');
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legend({'tx - 60rpm', 'ty - 60rpm', 'tz - 60rpm'});
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||||
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% Plot Synchronous and Asynchronous - 1rpm
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figure;
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hold on;
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plot(spindle.rpm1.time, spindle.rpm1.x);
|
||||
plot(spindle.rpm1.time, spindle.rpm1.xasync);
|
||||
hold off;
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||||
xlabel('Time [s]'); ylabel('Amplitude [m]');
|
||||
legend({'tx - 1rpm - Sync', 'tx - 1rpm - Async'});
|
||||
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% Plot Synchronous and Asynchronous - 60rpm
|
||||
% The data is split into its Synchronous and Asynchronous part (figure [[fig:spindle_60rpm_sync_async]]). We then use the Asynchronous part for the analysis in the following sections as we suppose that we can deal with the synchronous part with feedforward control.
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(spindle.rpm60.time, spindle.rpm60.x);
|
||||
plot(spindle.rpm60.time, spindle.rpm60.xasync);
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Amplitude [m]');
|
||||
legend({'tx - 60rpm - Sync', 'tx - 60rpm - Async'});
|
||||
|
||||
% Plot X against Y
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(spindle.rpm1.x, spindle.rpm1.y);
|
||||
plot(spindle.rpm60.x, spindle.rpm60.y);
|
||||
hold off;
|
||||
xlabel('X Amplitude [m]'); ylabel('Y Amplitude [m]');
|
||||
legend({'1rpm', '60rpm'});
|
||||
|
||||
% Plot X against Y - Asynchronous
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(spindle.rpm1.xasync, spindle.rpm1.yasync);
|
||||
plot(spindle.rpm60.xasync, spindle.rpm60.yasync);
|
||||
hold off;
|
||||
xlabel('X Amplitude [m]'); ylabel('Y Amplitude [m]');
|
||||
legend({'1rpm', '60rpm'});
|
||||
Reference in New Issue
Block a user