The Research On Time-domain Subspace Identification Based On Continuous-time Models

System identification is a specified field that measurement data are used to build mathematical models for systems. It plays a rather important role in control theo-ry. The mathematical models that are used to describe system dynamics can be either discrete-time models or continuous-time models. Due to the widespread use of com-puters and digital devices, research on discrete-time models identification covers great part of system identification. However, almost all the physical systems can be naturally described by continuous-time models. In addition, continuous-time models identifica-tion has advantages over discrete-time models identification under certain situations. Thus, it makes sense to study continuous-time models identification. Fractional order systems are ubiquitous and their models, which belong to one kind of continuous-time models, are the generalization of traditional integer order models. Studying a class of problems under the fractional order structure can be more general. Subspace method-s are identification methods for multi-input multi-output systems and possess robust numerical properties. Most research on subspace methods was based on discrete-time models. Considering the potential advantages, it is worth studying subspace methods based on continuous-time models. Time domain subspace methods for system identifi-cation based on the structure of continuous-time models is studied in this thesis.Firstly, this thesis seeks to attenuate the effect of output noise by using the opti-mization tool, i.e., nuclear norm minimization. Instrumental variable method exploits the correlation properties between signals, while a noise model is built in this thesis and then included in an optimization problem of nuclear norm minimization. The se-lection of instrumental variable does not need to be considered in nuclear norm method. Instead, the noise information is estimated directly and then removed from the informa-tion contained in the observed data. Nuclear norm method can attenuate the noise effect more efficiently than traditional truncation method. The use of cutting edge optimiza-tion method provides a new aspect for subspace methods based on continuous-time models.Secondly, a recursive version of subspace methods based on continuous-time mod-els is given. Givens rotation and propagator based methods lead to an easy implemen-tation of the algorithms. A new concept of data window is proposed to guarantee a real time efficiency of data so that online estimation can be implemented. In addition, a new kind of instrumental variable based on fractional order derivative is constructed. Two recursive algorithms with or without instrumental variable are given. When appro-priate parameters are chosen, both algorithms show good tracking performance while reducing noise effect.Finally, subspace methods are studied when non-uniform sampling is considered. Note that the study is under the general structure of fractional order systems. The first step is to complement the non-uniform data using fractional Laguerre generating func-tions. The second step is to perform parameter estimation from the complete data using MOESP method. In addition, the derivation of subspace methods based on continuous-time models is given. Time derivatives of signals are handled with Poisson moment functional method and an in-depth analysis on the attenuation of noise effect by Pois-son filter is performed. Simulation examples show that the proposed method works well on different extents of missing data when performing parameter estimation.