Obtaining a transfer function from tfestimate

So i have some data read in from an excel file (attachment) and i want to make a transfer function from this data. So i've used tfestimate to calculate the phase and amplitude to plot this in a bode.

with the bode I've calculated the parameters for my potential PID. Allthough i would like to test this before I'm actually going to set the PID. So i want to simulate this. Rltool does not work because it does not have real coefficients.

Does anyone know how to make a transfer function out of my data or how to simulate this data with and without PID?

Thanks in advance!

if true
  data = xlsread('RapportLijn1Waswater1.xlsx','blad1','B2000:D5000');
  Ts = 1; % In seconden
  Fs = 1/Ts; % Een beeld per 9 seconden
  Input = data(:,2); % Setpoint
  Output =data(:,1); % Processvalue
  LMN = data(:,3); % Aanstuurwaarde klep in %
  Fmax = Fs/2; % Max waarde tot waar bode nuttig is

    %%Analyse mbv tfestimate

    [TF_tfe, F_tfe]=tfestimate(LMN,Output,[],[],[],1/Ts);
    A_tfe=abs(TF_tfe);
    Ph_tfe=unwrap(angle(TF_tfe));

    W_tfe=2*pi*F_tfe;
    A_tfe_dB=20*log10(A_tfe);
    Ph_tfe_deg=180/pi*Ph_tfe;

    %%Afbeelden

    figure('units','normalized','outerposition',[0 0 1 1]);
    subplot(2,1,1) % Rij, Kolom, Figuurnummer
    set(semilogx(W_tfe,A_tfe_dB,'k'),'linewidth',1.5);
    line([Fs/2 Fs/2],[-100 100]) % Tot Fs/2 is bruikbare gedeelte
    grid on
    subplot(2,1,2) % Rij, Kolom, Figuurnummer
    set(semilogx(W_tfe, Ph_tfe_deg, 'k'),'linewidth',1.5);
    line([Fmax Fmax],[-500 500]) % Tot Fs/2 is bruikbare gedeelte
    set(gca, 'YTick',[-180 -90 0 90  180])
    grid on

    %%Berekenen PID

    Wpm = 0.02454;
    PM = 100;
    Apm = 38.19;
    Wz = Wpm/2;
    Kp = (10^(-Apm/20))/1.25
    Td = 1/(2*Wz)
    Ti = 4*Td
end

Answer 1

[Arkadiy Turevskiy]

Hi,

If you have access to System Identification Toolbox, you could use it to estimate a transfer function that you can use for simulation. For example, you could use tfest function. This function basically returns a Linear Time-Invariant system. You can use it with Control System Toolbox or in Simulink.

For example, you could do something like this:

% create iddata object by specifying output signal, input signal, and sampling time
data=iddata(output,input,sample_time);
% estimate a transfer function with 2 poles and 1 zero
sys=tfest(data,2,1);
% tune a PID Controller for the estimated transfer function
C=pidtune(sys,'pid');
% compute a closed-loop transfer function
CL=feedback(C*sys,1);
% plot closed-loop step response
step(CL);