The principal architect of the toolbox is Professor Lennart Ljung, a recognized leader in the field of system identification.
System Identification Toolbox lets you create models from measured input-output data. You can:
When preparing data for identifying models, you need to specify information such as input-output channel names, sampling time, and intersample behavior. The toolbox lets you attach this information to the data, which facilitates visualization of data, domain conversion, and various preprocessing tasks.
Measured data often has offsets, slow drifts, outliers, missing values, and other anomalies. The toolbox removes such anomalies by performing operations such as detrending, filtering, resampling, and reconstruction of missing data. The toolbox can analyze the suitability of data for identification and provide diagnostics on the persistence of excitation, existence of feedback loops, and presence of nonlinearities.
The toolbox estimates the impulse and frequency responses of the system directly from measured data. Using these responses, you can analyze system characteristics, such as dominant time constants, input delays, and resonant frequencies. You can also use these characteristics to configure the parametric models during estimation.
Parametric models, such as transfer functions or state-space models, use a small number of parameters to capture system dynamics. System Identification Toolbox estimates model parameters and their uncertainties from time-response and frequency-response data. You can analyze these models using time-response and frequency-response plots, such as step, impulse, Bode plots, and pole-zero maps.
System Identification Toolbox helps validate the accuracy of identified models using independent sets of measured data from a real system. For a given set of input data, the toolbox computes the output of the identified model and lets you compare that output with the measured output from a real system. You can also view the prediction error and produce time-response and frequency-response plots with confidence bounds to visualize the effect of parameter uncertainties on model responses.
System Identification Toolbox lets you estimate multi-input multi-output continuous or discrete-time transfer functions with a specified number of poles and zeros. You can specify the transport delay or let the toolbox determine it automatically. In cases where you need a low-order continuous-time model in pole-zero form, the toolbox lets you estimate process models, which are simple transfer functions involving three or fewer poles, and optionally, a zero, a time-delay, and an integrator.
You can identify polynomial and state-space models using estimation routines provided in the toolbox. These routines include autoregressive models (ARX, ARMAX), Box-Jenkins models, Output-Error models, and state-space parameterizations. Estimation techniques include maximum likelihood, prediction-error minimization schemes, and subspace methods based on N4SID, CVA, and MOESP algorithms. You can also estimate a model of the noise affecting the observed system. For all estimations, you can designate fixed model parameters and specify bounds for free parameters.
You can use identified linear models directly with Control System Toolbox functions for analysis and compensator design without converting the models.
You can also identify process models from measured input-output data in the PID Tuner app in Control System Toolbox. You can interactively adjust system parameters such as gain and pole locations to match model response to measured output. System Identification Toolbox can then use these parameter values as initial guesses to automatically find parameter values that provide the best fit between the model and the measured data. Once the process model is created, the PID Tuner app uses it for automatically tuning PID Controller gains.
You can also use System Identification Toolbox with Simulink Control Design™, when tuning gains of PID Controller block. If the Simulink model linearizes to zero, System Identification Toolbox lets you estimate the process models from simulation input-output data in the PID Tuner Once the process model is created, PID Tuner uses it to tune the PID Controller block gains.
When linear models are not sufficient for capturing system dynamics, you can use System Identification Toolbox to estimate nonlinear models, such as nonlinear ARX and Hammerstein-Wiener.
Nonlinear ARX models enable you to model nonlinearities using wavelet networks, tree-partitioning, sigmoid networks, and neural networks (with Deep Learning Toolbox™). Using Hammerstein-Wiener models, you can estimate static nonlinear distortions present at the input and output of an otherwise linear system. For example, you can estimate the saturation levels affecting the input current running a DC motor, or capture a complex nonlinearity at the output using a piecewise linear nonlinearity.
A user-defined (grey-box) model is a set of differential or difference equations with some unknown parameters. If you understand the physics of your system and can represent the system as a grey-box model, System Identification 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. You can specify differential equations as MATLAB, C, or Fortran code.
System Identification Toolbox provides Simulink blocks for online parameter estimation. Applications for online parameter estimation include fault monitoring and adaptive control.
System Identification Toolbox lets you perform two types of online parameter estimation: recursive polynomial model estimation and recursive least squares estimation.
The Recursive Polynomial Model Estimator block estimates discrete-time, polynomial models of ARX or ARMAX structure from input and output data that are provided as inputs to the block. The toolbox lets you specify the order of the model and select the estimation method to use.
The Recursive Least Squares Estimator block estimates parameters of a model that maps model inputs (regressors) to a model output. The model has to be a linear combination of the regressors, but it can be used to describe nonlinear systems.
You can use online parameter estimation blocks for simulation and implementation. Using these blocks in simulation lets you validate the algorithms and choose the best model structure for your application.
A time series is one or more measured output channels with no measured input. System Identification Toolbox lets you create time-series data models to forecast future signal values based on previous ones. You can estimate time-series models using both time-domain and frequency-domain data.
You can estimate time-series spectra that describe time-series variations using cyclic components at different frequencies. You can also estimate parametric autoregressive (AR), autoregressive and moving average (ARMA), autoregressive integrated moving average (ARIMA), and state-space time-series models.