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Force Panel IDENTIFICATION OF HUMAN TRANSFER FUNCTION

Force Panel IDENTIFICATION OF HUMAN TRANSFER FUNCTION. 2. Human Transfer Function. H( w ). Reference position (to be followed by the finger). Actual finger position. 3. Modelling.

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Force Panel IDENTIFICATION OF HUMAN TRANSFER FUNCTION

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  1. Force Panel IDENTIFICATION OF HUMAN TRANSFER FUNCTION

  2. 2 Human Transfer Function

  3. H(w) Reference position (to be followed by the finger) Actual finger position 3 Modelling

  4. Transfer functions have been used to model how human beings control several types of plants, for example the lane keeping task in automobiles (Kondo-like models) or route keeping in aircraft. A typical transfer function is the following: Where the gain K, the time delay and TN are parameters inherent of the human being (K is also task dependent), TI and TL are adaptive parameters that the subject changes (TL with mental workload) to adapt to the plant dynamics. Plöchl, Edelmann. Driver models in automobile dynamics application, Vehicle System Dynamics, Vol. 45, Nos. 7–8, pp 699–741 , July–August 2007 Simplified: 4 Modelling

  5. Band-Limited Noise fc = 40 Hz Butterworth Lowpass Filter; 1st Order, ft = 0.1 Hz Input and output signals

  6. The transfer function gives the possibility to directly simulate the user behaviour in interacting with any control panel. As an example: - to simulate the appearance of a button to press 100 mm far away from the hand position Noise PSD 100 100 Input: step function Output: simulated trajectory + noise (estimation of final position uncertainty) Model parameters: G = motion gain  = time constant d = delay What if G is less than 1??? Why happens to be like that?? (typically 0.6) 6 button Human Transfer Function - simulating the task of pressing a button

  7. 7 Human Transfer Function - simulating a game interaction

  8. Class work Identification in frequency

  9. 1th work in class: filter outliers due to low finger pressure Main steps – 1 filter outliers

  10. 2th work in class: filter the frequency ratio (that is too noisy to be used as it is) zoom Zoom of the zoom Main steps – 2 filter the FFT ratio

  11. Main steps – 2 filter the FFT ratio

  12. The considered HTF to find are: 1) 2) 3)

  13. 3th work in class: fit the modulus Main steps – 3 fit the modulus of the HTF

  14. 4th work in class: find the phase Main steps – 4 find the HTF delay (t)

  15. % program to complete in class % [to do between square brackets] % so, find '[]' to localize where to write code (or functions) clear all close all; clc; %% Load DATA % [] % [copy the filename to elaborate and its directory] im = strcat('Dati/Segnale_5/fp_acq_03_04_20111004115703.txt'); [header, hh, dd] = readColData(im,8,7,1); tempo = dd(:,1); % time x = dd(:,2); % x finger position red by arduino [ bit ] y = dd(:,3); % y finger position red by arduino [ bit ] f1 = dd(:,4); % first load cell red by arduino [ bit ] f2 = dd(:,5); % second load cell red by arduino [ bit ] f3 = dd(:,6); % third load cell red by arduino [ bit ] x_segnale = dd(:,7); % x reference of the vertical line [ pixel ] x_touch = x * 1.19 - 108.55 ; % x finger position with respect to LCD (calibration) [ pixel ] ID = dd (:, 8 ) ; Class work

  16. % extract time tempo = tempo - tempo(1) ; Tc = tempo(end) / length(tempo) ; tempo = 0 : (length(tempo) - 1) ; tempo = tempo * Tc ; % filter repeated data on the ARDUINO ID IIf = find( [ 1; diff(ID)] ) ; data_finger = x_touch( IIf ) ; % x finger position filtered data_input = x_segnale( IIf ) ; % x reference filtered tempo = tempo( IIf ) ; % time filtered tempo = tempo - tempo(1) ; figure, plot( tempo/1000, data_finger, 'b', tempo/1000, data_input, 'r' ) title('Reference and finger position'), grid on %% 1. Filtering outliers % [filtrare i salti dovuti a scarsa pressione del dito] meanF = mean (f1(IIf) + f2(IIf) + f3(IIf)) ; % mean of the load figure, plot( tempo/1000, data_finger, 'b', tempo/1000, (f1(IIf) + f2(IIf) + f3(IIf) - meanF) *10 + 300, 'r' ) title('Finger position and applied force'), grid on % [] soglia_Dx = 100 ; data_finger = FiltraOutliers_CELLE(data_finger, data_input, soglia_Dx) ; Class work

  17. %% 2. Trasfer Function estimation data_input = data_input - mean(data_input) ; data_finger = data_finger - mean(data_finger) ; % FFT computation F_Iinput = fft(data_input) / length(data_input) ; F_Ooutput = fft(data_finger) / length(data_finger) ; % plot of the transform ratio Hs = F_Ooutput ./ F_Iinput ; Hs(1) = 1 ; % (to recover the fact that the mean values were just eliminated) ffTF = 1000 * ( 0:(length(data_input)-1) ) / tempo(end) ; % Frequency vector [Hz] figure, plot(ffTF, abs(F_Iinput), 'r'), hold on plot(ffTF, abs(F_Ooutput)) plot(ffTF, abs(Hs), 'c') legend('Input','Output','Hs') xlabel ('Frequency [Hz]') % [] % [to filter the experimental transfer function 'Hs' just obtained by FFT ratio] plotta = 1 ; Hs = Filtro_Hs( Hs, F_Iinput, F_Ooutput, ffTF, plotta ) ; Class work

  18. %% just rename the variables: Iinput = data_input ; Ooutput = data_finger ; %% 3. FITTING modulus with lsqnonlin % [] % write a function 'FittingFrequenza' % par_ini = [0 2*pi*0.2 2*pi*0.1 2*pi*2] % solo primo ordine, 4 par par_ini = [0 2*pi*0.2 2*pi*0.1 0.7 2*pi*2] % anche secondo ordine, 5 par if length(par_ini) == 4 % 1th order par_ott = lsqnonlin(@(par) FittingFrequenza(par, Hs, ffTF, 0), par_ini, ... [0 0 0 0], [100 100 100 100]) ; elseif length(par_ini) == 5 % 2nd order par_ott = lsqnonlin(@(par) FittingFrequenza(par, Hs, ffTF, 0), par_ini, ... [0 0 0 0 0], [100 100 100 100 100]) ; % con [0 100 90 0 0] si fa 2d ordine end Class work

  19. %__________________________________ % % 4. estimate the parameter delay %__________________________________ % [] % write a function simulink 'CompDinamica' that simulates the model without delay % use the function 'corr' to estimate the delay % 0. neglect the mean values Iinput = Iinput - mean(Iinput) ; Ooutput = Ooutput - mean(Ooutput) ; % 1. dynamical simulation without delay par = par_ott ; if length(par) == 4 % solo primi ordini sim('CompDinamica_1ord') elseif length(par) == 5 % secondo ordine sottosmorzato sim('CompDinamica_2ord') end Comp_Iinput = interp1(time, Comp_Iinput, tempo/1000)' ; Class work

  20. % 2. correlation of the output with the simulated output (without delay) % [] % [use the function 'corr'] tau = 0 ; par_ott(1) = tau ; % plot results FittingFrequenza(par_ott, Hs, ffTF, 1) ; % !!!!!!!!!!!!!!!!!!!!!!!!! ModelloHTF(par_ott, ffTF, 1) ; %% SIMULATION OF A STEP INPUT WITH THE HTF par = par_ott ; if length(par) == 4 % 1th order sim('simulazione_1ord') elseif length(par) == 5 % 2nd order sim('simulazione_2ord') end figure, plot(time, step, time, step_out), title('Step input simulation') Class work

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