Identify a linear model and visualize the simulated model response with the data from which it was generated.

Load input/output measurements z1, and identify a third-order state-space model sys.

load iddata1 z1;
sys = ssest(z1,3);

sys is a continuous-time identified state-space (idss) model.

Use compare to simulate the sys response and plot it alongside the data z1.

figure
compare(z1,sys)

The plot illustrates the differences between the model response and the original data. The percentage shown in the legend is the NRMSE fitness value. It represents how close the predicted model output is to the data.

To change display options in the plot, right-click the plot to access the context menu. For example:

Identify a linear model and visualize the predicted model response with the data from which it was computed.

Identify a third-order state-space model using the input/output measurements in z1.

load iddata1 z1;
sys = ssest(z1,3);

sys is a continuous-time identified state-space (idss) model.

Now use compare to plot the predicted response. Prediction differs from simulation in that it uses both measured input and measured output when computing the system response. The prediction horizon defines how far in the future to predict, relative to your current measured output point. For this example, set the prediction horizon kstep to 10 steps, and use compare to plot the predicted response against the original measurement data.

kstep = 10;
compare(z1,sys,kstep)

In this plot, each sys data point represents the predicted output associated with output measurement data that was taken at least 10 steps earlier. For instance, the point at t = 15s is based on output measurements taken at or prior to t = 5s. The calculation of this t = 15s sys data point also uses input measurements up to t = 15s, just as a simulation would.

The plot illustrates the differences between the model response and the original data. The percentage shown in the legend is the NRMSE fitness value. It represents how closely the predicted model output matches the data.

To change display and simulation options in the plot, right-click the plot to access the context menu. For example, to plot the error between the predicted output and measured output, select Error Plot from the context menu. To change the prediction horizon value, or to toggle between simulation and prediction, select Prediction Horizon from the context menu.

Identify several model types for the same data, and compare the results to see which best fits the data.

Load the data, which contains iddata object z1 with single input and output.

load iddata1;

From z1, identify a model for each of the following linear forms:

sys_armax = armax(z1,[2 3 1 0]);
sys_ss = ssest(z1,3);
sys_tf = tfest(z1,3);

Using compare, plot the simulated responses for the three models with z1.

compare(z1,sys_armax,sys_ss,sys_tf)

For this set of data, along with the default settings for all the models, the transfer-function form has the best NRMSE fit. However, the fits for all models are within about 1% of each other.

You can interactively control which model responses are displayed in the plot by right-clicking on the plot and hovering over Systems.

Compare the outputs of multiple estimated models of differing types to measured frequency-domain data.

For this example, estimate a process model and an output-error polynomial from frequency response data.

load demofr  % frequency response data
zfr = AMP.*exp(1i*PHA*pi/180);  
Ts = 0.1;
data = idfrd(zfr,W,Ts);  
sys1 = procest(data,'P2UDZ'); 
sys2 = oe(data,[2 2 1]);

sys1, an idproc model, is a continuous-time process model. sys2, an idpoly model, is a discrete-time output-error model.

Compare the frequency response of the estimated models to data.

compare(data,sys1,'g',sys2,'r');

The two models have NRMSE fit values that are nearly equal with respect to the data from which they were calculated.

Modify default behavior when you compare an estimated model to measured data.

Estimate a transfer function for measured data.

load iddata1 z1;
sys = tfest(z1,3);

sys is a continuous-time identified transfer function (idtf) model.

Suppose you want your initial conditions to be zero. The default for compare is to estimate initial conditions from the data.

Create an option set to specify the initial condition handling. To use zero for initial conditions, specify 'z' for the 'InitialCondition' option.

opt = compareOptions('InitialCondition','z');

Compare the estimated transfer function model output to the measured data using the comparison option set.

compare(z1,sys,opt)

Load the data.

load iddata2 z2

Split the data into estimation and validation sets.

z2e = z2(1:200);
z2v = z2(201:400);
plot(z2e,z2v)

Estimate a state-space model and a transfer function model using the estimation data.

sys_ss = ssest(z2e,2);
sys_tf = tfest(z2e,2,1);

Use compare to obtain initial conditions for sys_ss.

[y_ss,fit_ss,ic_ss] = compare(z2e,sys_ss);
ic_ss

ic_ss = 2×1

   -0.0018
    0.0016

ic_ss is a numeric vector of initial states.

[y_tf,fit_tf,ic_tf] = compare(z2e,sys_tf);
ic_tf

ic_tf = 
  initialCondition with properties:

     A: [2x2 double]
    X0: [2x1 double]
     C: [-1.6093 5.1442]
    Ts: 0

ic_tf is an initialCondition object that contains, in state-space form, a model of the free response of sys_tf to the initial conditions. A and C contain the free-response information and X0 contains the initial states.

Now obtain initial conditions for both models at once using the validation data.

[y_sstf,fit_sstf,ic_sstf] = compare(z2v,sys_ss,sys_tf);
ic_sstf

ic_sstf=2×1 cell array
    {2x1 double          }
    {1x1 initialCondition}

ic_sstf is a cell array that contains an initial state vector for sys_ss and an initialCondition object for sys_tf.

compare can provide initial conditions for an existing model with any measurement data set.