http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:679 Continuous-time systems are usually modelled by differential equations arising from physical laws. However, the use of these models in practice requires discretisation. In this thesis we consider sampled-data models for linear and nonlinear systems. We study some of the issues involved in the sampling process, such as the accuracy of the sampled-data models, the artifacts produced by the particular sampling scheme, and the relations to the underlying continuous-time system. We review, extend and present new results, making extensive use of the delta operator which allows a clearer connection between a sampled-data model and the underlying continuous-time system. In the first part of the thesis we consider sampled-data models for linear systems. In this case exact discrete-time representations can be obtained. These models depend, not only on the continuous-time system, but also on the artifacts involved in the sampling process, namely, the sample and hold devices. In particular, these devices play a key role in determining the sampling zeros of the discrete-time model. We consider robustness issues associated with the use of discrete-time models for continuous-time system identification from sampled data. We show that, by using restricted bandwidth frequency domain maximum likelihood estimation, the identification results are robust to (possible) under-modelling due to the sampling process. Sampled-data models provide a powerful tool also for continuous-time optimal control problems, where the presence of constraints can make the explicit solution impossible to find. We show how this solution can be arbitrarily approximated by an associated sampled-data problem using fast sampling rates. We also show that there is a natural convergence of the singular structure of the optimal control problem from discrete- to continuous-time, as the sampling period goes to zero. In Part II we consider sampled-data models for nonlinear systems. In this case we can only obtain approximate sampled-data models. These discrete-time models are simple and accurate in a well defined sense. For deterministic systems, an insightful observation is that the proposed model contains sampling zero dynamics. Moreover, these correspond to the same dynamics associated with the asymptotic sampling zeros in the linear case. The topics and results presented in the thesis are believed to give important insights into the use of sampled-data models to represent linear and nonlinear continuous-time systems. 2011-12-20T22:30:03.785Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:8942 Errors-in-Variables systems have been extensively studied in the literature. We study the impact of sampling on a continuous-time errors-in-variables problem. In particular, we study some approximations of a two dimensional (input-output) continuous-time signal spectrum developed from the sampled-data spectrum. Indeed, some of the paper is tutorial in nature. We also explore the possibility of retrieving the underlying continuous-time system from samples of the input and output signals. 2011-09-14T06:00:13.675Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:661 Models for deterministic continuous-time nonlinear systems typically take the form of ordinary differential equations. To utilize these models in practice invariably requires discretization. In this paper, we show how an approximate sampled-data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order Delta(r+1), where A is the sampling period and r is the system relative degree. The resulting model includes extra zero dynamics which have no counterpart in the underlying continuous-time system. The ideas presented here generalize well-known results for the linear case. We also explore the implications of these results in nonlinear system identification. 2010-04-27T05:39:42.083Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:6042 Most real world systems operate in continuous time. However, to store, analyze or transmit data from such systems the signals must first be sampled. Consequently there has been on-going interest in sampled data models for continuous time systems. The emphasis in the literature to-date has been on three main issues namely the impact of folding, sampled zero dynamics and the associated model error quantification. Existing error analyses have almost exclusively focused on unnormalized performance. However, in many applications relative errors are more important. For example, high performance controllers tend to invert the system dynamics and consequently relative errors underpin closed loop performance issues including robustness and stability. This motivates us to examine the relative errors associated with several common sampled data model types. This analysis reveals that the inclusion of appropriate zero dynamics is essential to ensure that the relative error converges to zero as the sampling period is reduced. 2010-04-27T04:31:49.981Z ]]>