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Estimate Frequency Response Models with Noise Using System Identification Toolbox

Open the Simulink® model, and specify which portion of the model to linearize:

load_system('magball');
io(1) = linio('magball/Desired Height',1);
io(2) = linio('magball/Magnetic Ball Plant',1,'output');

Compute the steady-state operating point, and linearize the model:

op = findop('magball',operspec('magball'),...
                      findopOptions('DisplayReport','off'));
sys = linearize('magball',io,op);

Create a chirp signal, and use it to estimate the frequency response:

in = frest.Chirp('FreqRange',[1 1000],...
                             'Ts',0.001,...
                             'NumSamples',1e4);
[~,simout] = frestimate('magball',io,op,in);

Use System Identification Toolbox™ software to estimate a fifth-order, state-space model. Compare the results of analytical linearization and the state-space model:

input = generateTimeseries(in);
output = simout{1}.Data;
data = iddata(output,input.Data(:),in.Ts);
sys_id = n4sid(detrend(data),5,'cov','none');
bodemag(sys,ss(sys_id('measured')),'r')
legend('Linear model obtained using LINEARIZE',...
       'State-space model using System Identification Toolbox',...
       'Location','SouthWest')