Extracting Numerical Model Data

You can extract the following numerical data from linear model objects:

• Coefficients and uncertainty

  For example, extract state-space matrices (A, B, C, D and K) for state-space models, and polynomials (a, b, c, d and f) for polynomial models.

  If you estimated model uncertainty data, this information is stored in the model in the form of the parameter covariance matrix. You can fetch the covariance matrix (in its raw or factored form) using the getcov command. The covariance matrix represents uncertainties in parameter estimates and is used to compute:

  • Confidence bounds on model output plots, Bode plots, residual plots, and pole-zero plots

  • Standard deviation in individual parameter values. For example, one standard deviation in the estimated value of the A polynomial in an ARX model, returned by the polydata command and displayed by the present command.

• Dynamic and noise models

  For linear models, the general symbolic model description is given by:

  

  G is an operator that takes the measured inputs u to the outputs and captures the system dynamics, also called the measured model. H is an operator that describes the properties of the additive output disturbance and takes the hypothetical (unmeasured) noise source inputs e to the outputs, also called the noise model. When you estimate a noise model, the toolbox includes one noise channel e for each output in your system.

The following table summarizes the commands for extracting model coefficients and uncertainty.

Commands for Extracting Model Coefficients and Uncertainty Data

[H,w,CovH] = freqresp(m)

[A,B,C,D,F,dA,dB,dC,dD,dF] = ...
       polydata(m)

[A,B,C,D,K,X0,...
 dA,dB,dC,dD,dK,dX0] = ...
       idssdata(Model)

[Num,Den,Ts,dNum,dDen] = ...
     tfdata(Model)

[Z,P,K,Ts,covZ,covP,covK] = ...
     zpkdata(m)

You can also extract numerical model data by using dot notation to access model properties. For example, m.A displays the A polynomial coefficients from model m. Alternatively, you can use the get command, as follows: get(m,'A').

Tip   To view a list of model properties, type get(model).

You can operate on extracted model data as you would on any other MATLAB vectors, matrices and cell arrays. You can also pass these numerical values to Control System Toolbox commands, for example, or Simulink blocks.

Refining Linear Parametric Models

Transforming Between Discrete-Time and Continuous-Time Representations

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