

CAPTAIN Toolbox website

Transfer Function (TF) modelling subsetThe inputoutput modelling functions allow for robust unbiased estimation of multipleinput transfer function models. Either discretetime models, represented in terms of the backward shift operator, or continuoustime models based on the Laplace Transform operator, are possible. There are numerous algorithms for estimating transfer functions. However, the primary technique employed in the Captain Toolbox is the Instumental Variable approach. In particular, the toolbox provides the recursive and enblock Refined Instrumental Variable (RIV) and Simplified Refined Instrumental Variable (SRIV) algorithms, as well as more conventional least squares approaches. These algorithms are accessed through the functions riv (discrete) and rivc (continuous). IdentificationThe toolbox functions riv/rivc allow for the estimation of transfer functions based on a user specified model structure. However, for a given physical system, an appropriate model structure first needs to be identified, i.e., the most appropriate values for the time delay and the orders of the numerator and denominator polynomials. The toolbox functions rivid/rivcid are employed for this purpose. The two main statistical measures utilised here are the coefficient of determination RT2, based on the response error, which is a simple measure of model fit (where unity indicates perfect fit) and the more sophisticated Young Identification Criterion (YIC), which provides a combined measure of fit and parametric efficiency with large negative values indicating a model which explains the output data well, without overparameterisation. Selected referencesA link to the abstract is provided for some papers.
