Estimate Transfer Function Models in the System Identification App

This topic shows how to estimate transfer function models in the System Identification app.

Prerequisites

In the System Identification app, select Estimate > Transfer Function Models
The Transfer Functions dialog box opens.
Tip
For more information on the options in the dialog box, click Help.
In the Number of poles and Number of zeros fields, specify the number of poles and zeros of the transfer function as nonnegative integers.
Multi-Input, Multi-Output Models
For systems that are multiple input, multiple output, or both:
- To use the same number of poles or zeros for all the input/output pairs, specify a scalar.
- To use a different number of poles and zeros for the input/output pairs, specify an ny-by-nu matrix. ny is the number of outputs and nu is the number of inputs.
  Alternatively, click .
  The Model Orders dialog box opens where you specify the number of poles and zeros for each input/output pair. Use the Output list to select an output.
Select Continuous-time or Discrete-time to specify whether the model is a continuous- or discrete-time transfer function.
For discrete-time models, the number of poles and zeros refers to the roots of the numerator and denominator polynomials expressed in terms of the lag variable q^-1.
(For discrete-time models only) Specify whether to estimate the model feedthrough. Select the Feedthrough check box.
A discrete-time model with 2 poles and 3 zeros takes the following form:
$H (z^{- 1}) = \frac{b 0 + b 1 z^{- 1} + b 2 z^{- 2} + b 3 z^{- 3}}{1 + a 1 z^{- 1} + a 2 z^{- 2}}$
When the model has direct feedthrough, b0 is a free parameter whose value is estimated along with the rest of the model parameters b1, b2, b3, a1, a2. When the model has no feedthrough, b0 is fixed to zero.
Multi-Input, Multi-Output Models
For models that are multi input, multi output or both, click Feedthrough.
The Model Orders dialog box opens, where you specify to estimate the feedthrough for each input/output pair separately. Use the Output list to select an output.
Expand the I/O Delay section to specify nominal values and constraints for transport delays for different input/output pairs.
Use the Output list to select an output. Select the Fixed check box to specify a transport delay as a fixed value. Specify its nominal value in the Delay field.
Expand the Estimation Options section to specify estimation options.
- Set the range slider to the desired passband to specify the frequency range over which the transfer function model must fit the data. By default the entire frequency range (0 to Nyquist frequency) is covered.
- Select Display progress to view the progress of the optimization.
- Select Estimate covariance to estimate the covariance of the transfer function parameters.
- (For frequency-domain data only) Specify whether to allow the estimation process to use parameter values that may lead to unstable models. Select the Allow unstable models option.
  Setting this option is same as setting the estimation option Focus to 'prediction' at the command line. An unstable model is delivered only if it produces a better fit to the data than other stable models computed during the estimation process.
- Specify how to treat the initial conditions in the Initial condition list. For more information, see Specifying Initial Conditions for Iterative Estimation of Transfer Functions.
- Specify the algorithm used to initialize the values of the numerator and denominator coefficients in the Initialization method list.
  - IV — Instrument Variable approach.
  - SVF — State Variable Filters approach.
  - N4SID — Generalized Poisson Moment Functions approach.
  - GPMF — Subspace state-space estimation approach.
  - All — Combination of all of the above approaches. The software tries all the above methods and selects the method that yields the smallest value of prediction error norm.
Click Regularization to obtain regularized estimates of model parameters. Specify the regularization constants in the Regularization Options dialog box. To learn more, see Regularized Estimates of Model Parameters.
Click Iterations Options to specify options for controlling the iterations. The Options for Iterative Minimization dialog box opens.
Iteration Options
In the Options for Iterative Minimization dialog box, you can specify the following iteration options:
- Search Method — Method used by the iterative search algorithm. Search method is auto by default. The descent direction is calculated using gn (Gauss-Newton), gna (Adaptive Gauss-Newton), lm (Levenberg-Marquardt), lsqnonlin (Trust-Region Reflective Newton), and grad (Gradient Search) successively at each iteration until a sufficient reduction in error is achieved.
- Output weighting — Weighting applied to the loss function to be minimized. Use this option for multi-output estimations only. Specify as 'noise' or a positive semidefinite matrix of size equal the number of outputs.
- Maximum number of iterations — Maximum number of iterations to use during search.
- Termination tolerance — Tolerance value when the iterations should terminate.
- Error threshold for outlier penalty — Robustification of the quadratic criterion of fit.
Click Estimate to estimate the model. A new model gets added to the System Identification app.

Next Steps

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Estimate Transfer Function Models in the System Identification App

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