System identification in alternative shift operators with applications and some other topics

Sammanfattning: This thesis mainly concentrates on two issues of system identification, namely identification for controller design and identification with orthonormal basis functions. In identification for controller design one seeks to obtain sufficient knowledge about the plant to design a high-performance controller. The frequency domain method proposed in this thesis is applicable to plants that are typical to process industry. While designing a high-performance controller it is desirable to keep the amount of identification experiments small. This has been achieved by choosing the next experimental conditions in an adaptive manner, i.e. the current experimental conditions depend on past data. The remaining parts of the thesis are concerned with identification by means of orthonormal basis functions, especially the Laguerre and Kautz functions. These particular functions have been chosen due to their simple mathematical structure and due to the fact that their dynamics are similar to the nature of a wide range of industrial processes. Linear, time-invariant, multi-input multi-output systems are considered. In system identification one usually uses the entire measurement data in order to find an appropriate plant model. In this thesis, the data is projected onto the Laguerre and Kautz functions, respectively, and only the projection coefficients, also called expansion coefficients or Laguerre/Kautz coefficients, are used for identification. As the considered orthonormal basis functions provide the user with some additional degrees of freedom in the time constants of the functions, noise and unmodelled dynamics can be attenuated through a judicious choice of these time constants. Furthermore, the projection leads to a considerable data reduction. After the projection of the measurement data, classical identification methods as subspace identification or the least squares method can be used to identify a model which, after a certain mapping, can for example be used for controller design. The suggested method has been derived for the identification of continuous and discrete models and has been successfully employed for the estimation of a coal injection process, a vibration process, subprocesses of a sugar mill, a paper machine headbox and time delay estimation. For the case of time delay estimation, error bounds on the estimation error have been derived. Results from applications show that the presented method in many cases outperforms classical linear methods and provides good linear approximations of non-linear processes. Furthermore, the excitation characteristics and numerical properties of the expansion coefficients have been studied and compared to the properties of the measurement data sets.