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Estimate Transfer Function Models with Unknown Transport Delays

This example shows how to estimate a transfer function model with unknown transport delays and apply an upper bound on the unknown transport delays.

Create a transfer function model with the expected numerator and denominator structure and delay constraints.

For this example, the experiment data consists of two inputs and one output. Both transport delays are unknown and have an identical upper bound. Additionally, the transfer functions from both inputs to the output are identical in structure.

init_sys = idtf(NaN(1,2),[1, NaN(1,3)],'IODelay',NaN);
init_sys.Structure(1).IODelay.Free = true;
init_sys.Structure(1).IODelay.Maximum = 7;

init_sys is an idtf model describing the structure of the transfer function from one input to the output. The transfer function consists of one zero, three poles and a transport delay. NaN indicates unknown coefficients.

init_sys.Structure(1).IODelay.Free = true indicates that the transport delay is not fixed.

init_sys.Structure(1).IODelay.Maximum = 7 sets the upper bound for the transport delay to 7 seconds.

Specify the transfer function from both inputs to the output.

init_sys = [init_sys,init_sys];

Load time-domain system response data and detrend the data.

load co2data;
Ts = 0.5; 
data = iddata(Output_exp1,Input_exp1,Ts);
T = getTrend(data);
T.InputOffset = [170,50];
T.OutputOffset = mean(data.y(1:75));
data = detrend(data, T);

Identify a transfer function model for the measured data using the specified delay constraints.

sys = tfest(data,init_sys);

sys is an idtf model containing the identified transfer function.