Structure Discrimination and Identification of Nonlinear Systems

System identification is the science of obtaining mathematical models of dynamic systems from measured data. System identification collaborates with other branches of science from the measurement of the physical quantities to statistics and applied mathematics, and even pure mathematics. The models of dynamic systems are linear or nonlinear. Linear models can be represented in different ways, such as transfer function, ARMAX, state space, frequency response functions, and impulse response functions. The two latter are non-parametric models while those of former are parametric models. Many different model structures exist that can capture nonlinear dynamics. The ones covered in this work are block-oriented models, and nonlinear state space models. For block-oriented model identification it is important to have informative data. In the first part of the thesis, the mean (DC) and standard deviation std) values of a multisine signal are designed such that the estimated best linear approximation (BLA) has minimum total distortion (= nonlinear + noise distortion). These high-quality linear approximations allow for detection of the structure of the block-oriented model. Next, it is shown that a nonlinear state space model with polynomial nonlinear terms can capture hysteretic behaviour. The so called polynomial nonlinear state space (PNLSS) model is a flexible model, but this flexibility comes at the price of a large number of parameters. In the thesis, a decoupling method is applied that reduces the number of parameters, while the output error of the decoupled model is similar to that of the full PNLSS model. The structure of block-oriented models is not always unique. The same input/output behaviour can be obtained with a different structure. To obtain uniqueness, extra prior knowledge should be exploited. In this part of the thesis, a nonlinear feedback structure with a Wiener-Hammerstein (WH) branch is studied. This structure can be realized with the WH branch in the feedback or the feedforward branch. The uniqueness of the structure is studied provided that the individual blocks in the model are causal and stable. It is shown that this extra prior knowledge is not always suffcient.

Jaar van publicatie:2018

Trefwoorden:Identification

Toegankelijkheid:Closed