- Title
- Theoretical analysis and practical applications of continuous-time system identification
- Creator
- Pan, Siqi
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2021
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Continuous-time system identification is concerned with the construction of continuous-time models of dynamical systems using measured input and output data. This thesis considers the theoretical analysis and practical applications of estimators that are classified as the direct approach in this field, which identifies a continuous-time model directly from measured data. This is contrary to the indirect approach, which requires an intermediate discrete-time model to be estimated. Due to the prevalence of digital computers, estimation of continuous-time systems nowadays is conducted in a completely digital manner, i.e. only sampled data are available as measurements and all prefilters in the estimators are implemented digitally. This then requires a mechanism for discretisation, and therefore the specification of the intersample behaviour of the signals, to be incorporated into the direct continuous-time estimators. The contributions of this thesis are divided into two parts. The first part of this thesis studies the theoretical properties of some of the prevalent estimators in direct continuous-time system identification, and the second part is concerned with the practical applications and extensions of these estimators. Incorporating a mechanism for discretisation of the continuous-time prefilters complicates the analysis of direct continuous-time estimators. For this reason, the theoretical analyses of these estimators in the existing literature have, to some extent, ignored the discretisation mechanism and hence are not considered to be satisfactory. In Part I of this thesis, we provide a comprehensive analysis on the asymptotic properties of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) as well as two other direct continuous-time estimators that are closely related to it. First, the generic consistency of the SRIVC estimator is analysed by explicitly incorporating the intersample behaviour of the measured input and output. The conditions under which the estimator is generically consistent are given, with the consequences of misspecifying the intersample behaviours of the measured signals on consistency examined separately. Next, the asymptotic efficiency of the SRIVC estimator is studied. The asymptotic Cramer-Rao lower bound is derived for systems parameterised under the output error model structure and compared to the derived asymptotic covariance of the SRIVC estimator. It is concluded that the SRIVC estimator is asymptotically efficient under the output error model structure. The intersample behaviour assumptions of the measured signals under which the asymptotic efficiency can be lost are also discussed. In addition, the consistency of the Instrumental-Variable-based State Variable Filter (IVSVF) estimator, which can be considered as a non-iterative version of the SRIVC estimator, is also examined. A bias elimination procedure is then proposed to remove the asymptotic bias of the IVSVF estimator. Based on the knowledge and insights gained through the theoretical analyses, we provide guidelines for the correct implementations of the estimators and discuss the implications of using them in a practical situation. This then leads to Part II of the thesis, which demonstrates the use of the direct continuous-time estimators through several practical applications. The SRIVC estimator is employed in a biological application for modeling the membrane properties of Type II vestibular hair cells of mice to estimate the membrane capacitance and resistance at different membrane potentials. The recursive form of the IVSVF estimator is then used to identify the change in the membrane properties during in vitro experiments to detect neurotransmitter release from hair cells upon the reception of a chemical called acetylcholine. The second application involves the identification of a cantilever beam, which is modeled as a lightly damped resonant system that can be difficult to identify in practice. We show that the SRIVC estimator can be used to estimate the parameters of the cantilever beam system with satisfactory results obtained. Having applied the direct continuous-time estimators in practice, it is noted that the existing methods are only able to identify linear systems that are time-invariant or slowly time-varying. Hence, a novel adaptive direct continuous-time estimator is proposed to track linear systems with slowly time-varying parameters subject to abrupt changes. The performance of the proposed estimator is then compared with the recursive IVSVF estimator through simulation studies.
- Subject
- system identification; continuous-time system identification; instrumental variable; consistency; statistical efficiency
- Identifier
- http://hdl.handle.net/1959.13/1440270
- Identifier
- uon:41111
- Rights
- Copyright 2021 Siqi Pan
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
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| View Details Download | ATTACHMENT01 | Thesis | 9 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 938 KB | Adobe Acrobat PDF | View Details Download |