Date of Award


Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy


Electrical & Electronic Engineering

First Advisor

Dr. Tom O' Mahony


Over the past ten years, hybrid systems, and piecewise affine (PWA) systems in particular have been viewed as viable option for modelling nonlinear systems. Many methods have been developed to cater for the identification of a PWA model from input/output data. This thesis focuses on the clustering based identification approach. This method uses a Least Squares (LS) identification algorithm which, in this thesis, is shown to perform poorly in practice. The clustering based algorithm is also limited by the number of initialisation parameters that need to be chosen. These parameters have a significant influence on the resulting PWA model accuracy, yet the guidelines for their selection are not adequately addressed in the literature. The user is left with no recourse but to experiment, which is often a frustrating and time-expensive solution.

The primary objective of this research is then to develop an algorithm that performs better in practice and is easier to initialise. Specifically, the main contribution is the development of a Piecewise Affine Output Error (PWA-OE) algorithm. The proposed PWA-OE algorithm is shown to outperform the original algorithm on simulation and real experimental Radio-Frequency MicroElectroMechanical Systems (RF-MEMS) data. Based on this data, the average performance improvement is impressive - the integral of absolute modelling error was reduced by 51.5%. The proposed algorithm is also shown to be less sensitive to the initial tuning parameters and initialisation recommendations were developed. The net result is a more straightforward and appealing identification method.

The second major contribution of this research is a detailed modelling study of a Radio Frequency MicroElectroMechanical Systems (RF-MEMS) switch. To the author’s knowledge, this is the first application of PWA models to MEMS systems. To realise the model, experimental data was obtained from a capacitive MEMS switch and the proposed PWA-OE algorithm was applied. The resulting model is highly accurate and incorporates both the opening and closing dynamics. In comparison to existing MEMS switch models, the PWA model offers the combined advantages of accuracy and simplicity. Furthermore, the PWA format is tailored for controller design e.g. the design of soft landing voltage profiles and this is a further benefit of the approach.

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