System Identification Toolbox

Estimating Parametric Models

Parametric models, such as transfer functions or state-space models, use a small number of parameters to capture system dynamics. The toolbox estimates model parameters and their uncertainties. You can analyze these models, or their linear equivalents, using time- and frequency-response plots such as step, impulse, bode plots, and pole-zero maps.

Estimating and Validating Models 0:50
Estimate multiple parametric models and validate against the validation data set.

Estimating Linear Black-Box Models

You can identify polynomial and state-space models using various estimation routines offered by the toolbox. These routines include autoregressive models (ARX, ARMAX), Box-Jenkins (BJ) models, Output-Error (OE) models, and state-space parameterizations. Estimation techniques include maximum likelihood, predictionerror minimization schemes, and such subspace methods as CVA, MOESP, and N4SID. You can also estimate a model of the noise affecting the observed system.

Specialized Tools for Identifying First-, Second-, and Third-Order Dynamic Models 1:55
Model lower-order, continuous dynamic systems from data using a specialized graphical user interface (GUI) in System Identification Toolbox.

In cases where you only need a low-order continuous-time model, the toolbox provides special capabilities to simplify the estimation process and obtain results quickly. These models are expressed as simple transfer functions involving three or fewer poles, and optionally, a zero, a time-delay, or an integrator.

Estimating Nonlinear Black-Box Models

When linear models are not sufficient to capture system dynamics, you can estimate nonlinear models, such as nonlinear ARX and Hammerstein-Wiener models. Nonlinear ARX models enable you to model nonlinearities using wavelet networks, tree-partitioning, sigmoid networks, and neural networks (with Neural Network Toolbox™, available separately). Using Hammerstein-Wiener models, you can estimate static nonlinear distortions present at the input and/or output of an otherwise linear system. For example, you can estimate the saturation levels affecting the input current into a DC motor, or capture a complex nonlinearity at the output using a piecewise linear nonlinearity.

Estimating Parameters in User-Defined Models

A user-defined (grey-box) model is a set of differential or difference equations with some unknown parameters. The toolbox lets you specify the model structure and estimate its parameters using nonlinear optimization techniques. For linear models you can explicitly specify the structure of state-space matrices and impose constraints on identified parameters. For nonlinear models, you can specify differential equations as MATLAB, C, or Fortran code.