Modelling, system identification and control of a fibre optic accelerometer

Cornelius, Justin Calen
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Control of systems are important in most industrial sectors, they nd applications in electronics, machine design and navigation. These control systems often use sensors to work e ectively. One such sensor is an accelerometer, which is used to measure acceleration with one or more degrees of freedom. This research report investigates the modelling, system identi cation and controller design for an accelerometer, a Fibre Optic Accelerometer (FOA). Such a device may be applied in many applications such as anti-skid control, structural failure in buildings and bridges, as well as strategic missile guidance. This report presents a model of a FOA demonstrator which crudely models an industrially developed accelerometer, the demonstrator is made of a jig consisting of a guitar string and electromagnets. Such a model needs to account for a distributed parameter beam combined with a permanent magnet and four electromagnets. The guitar string is modelled using three beam models, namely a spring/damper model, an Assumed Modes Model (ASM) and a Transfer Function Model (TFM). The parameters for these beam models are identi ed using the Nelder-Mead simplex algorithm and the least squares method. The electromagnets within the jig, are modelled using a mathematical model obtained through curve tting of experimental data. The overall FOA sensor is optimised using a lead-lag controller. Five cost functions where investigated, these cost functions are H1, Integral Square Error (ISE), Integral Absolute Error (IAE), Integral Time Square Error (ITSE) and Integral Absolute Time Error (IATE). It was found that the guitar string may be modelled using a single degree of freedom beam model. This is based on a number of reasons, such as the aperture size - through which the tip Light Emitting Diode (LED) projects, the tip mass (permanent magnet) - acting as a natural damper and the fact that Position Sensing Device (PSD) only measures the tip position. It was found that a single degree of freedom model in two orthogonal axes, with a single link beam spring/damper model was the most suitable representation of the guitar string. And the IAE lead-lag controller was found to be the most e ective in controlling a guitar string, this e ectiveness was due to least settling time.
A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial ful lment of the requirements for the degree of Master of Science in Engineering. Johannesburg, 2015
Cornelius, Justin Calen (2015) Modelling, system identification and control of a fibre optic accelerometer, University of the Witwatersrand, Johannesburg, <>