Компенсация температурных погрешностей в кориолисовых вибрационных гироскопах

Вивчається вплив змін температури на вихідні сигнали коріолісових вібраційних гіроскопів через перехресне демпфірування. Розроблено математичну модель температурних впливів, параметри якої було ідентифіковано з використанням експериментальних даних. Запропоновано низькорівневу систему компенсації температурних похибок, роботу якої було перевірено за допомогою реалістичного чисельного моделювання.The effect of temperature variations on the output of Coriolis vibratory gyroscope (CVG) in general and with cylindrical sensitive element in particular via cross-damping is studied in this paper. Zero rate output of CVG is observed when temperature of the sensor varies. It is believed that temperature variations cause this bias through the temperature dependent cross-damping. In this case excited primary oscillations of the sensitive element will induce secondary (output) oscillations even without external rotation being applied to the sensor. In order to develop mathematical model for this phenomenon it is first analysed how cross-damping affects dynamics of the CVG sensitive element. By means of using amplitude-phase variables demodulated model of the CVG sensitive element is developed. As a result, transfer functions connecting temperature as an input and temperature induced angular rate as an output were derived. Obtained transfer function allows efficient analysis of errors due to the cross-damping, which not only is present in the system, but can vary due to the different reasons. Assuming that the cross-damping coefficient is a function of the temperature shift from the calibration temperature, it can be approximated using polynomial. Temperature related coefficients of this model can be determined experimentally when ambient temperature is known (measured) and angular rate is absent. However, in most of the cases we observe angular rate as the gyro output. In order to relate angular rate to the input cross damping, steady state of the transfer function is used. Thus parameters of the cross-damping model could now be identified from the experimental data. In order to validate cross-damping model, obtained temperature related angular rate can be subtracted from the gyroscope output, producing compensated output. It has been demonstrated the identified model successfully compensates bias for the steady temperature, while performs only fair during temperature transitions. In order to deal successfully with transient processes in CVG dynamics due to the temperature, temperature compensation system using cross-coupling compensation has been developed. This system significantly improved undesired influence of the temperature dependent cross-damping. However, proposed system still requires temperature sensor being used in the system. In our future research we plan to use model of cross-damping errors to develop stochastic system of temperature errors compensation that will not require temperature measurements.В данной работе изучается влияние изменений температуры на выходных сигналы кориолисовых вибрационных гиросокопов через перекрестное демпфирование. Разработана математическая модель температурных воздействий, параметры которой были идентифицированы с использованием экспериментальных данных. Предложена низкоуровневая система компенсации температурных погрешностей, работа которой была проверена путем реалистичного численного моделирования

Coriolis vibratory gyroscopes: theory and design

This book provides the latest theoretical analysis and design methodologies of different types of Coriolis vibratory gyroscopes (CVG). Together, the chapters analyze different types of sensitive element designs and their kinematics, derivation of motion equations, analysis of sensitive elements dynamics in modulated and demodulated signals, calculation and optimization of main performance characteristics, and signal processing and control. Essential aspects of numerical simulation of CVG using Simulink® are also covered. This is an ideal book for graduate students, researchers, and engineers working in fields that require gyroscope application, including but not limited to: inertial sensors and systems, automotive and consumer electronics, small unmanned aircraft control systems, personal mobile navigation systems and related software development, and augmented and virtual reality systems

КОМПЕНСАЦІЯ ТЕМПЕРАТУРНИХ ПОХИБОК У КОРІОЛІСОВИХ ВІБРАЦІЙНИХ ГІРОСКОПАХ

The effect of temperature variations on the output of Coriolis vibratory gyroscope (CVG) in general and with cylindrical sensitive element in particular via cross-damping is studied in this paper. Zero rate output of CVG is observed when temperature of the sensor varies. It is believed that temperature variations cause this bias through the temperature dependent cross-damping. In this case excited primary oscillations of the sensitive element will induce secondary (output) oscillations even without external rotation being applied to the sensor.In order to develop mathematical model for this phenomenon it is first analysed how cross-damping affects dynamics of the CVG sensitive element. By means of using amplitude-phase variables demodulated model of the CVG sensitive element is developed. As a result, transfer functions connecting temperature as an input and temperature induced angular rate as an output were derived. Obtained transfer function allows efficient analysis of errors due to the cross-damping, which not only is present in the system, but can vary due to the different reasons.Assuming that the cross-damping coefficient is a function of the temperature shift from the calibration temperature, it can be approximated using polynomial. Temperature related coefficients of this model can be determined experimentally when ambient temperature is known (measured) and angular rate is absent. However, in most of the cases we observe angular rate as the gyro output. In order to relate angular rate to the input cross damping, steady state of the transfer function is used. Thus parameters of the cross-damping model could now be identified from the experimental data.In order to validate cross-damping model, obtained temperature related angular rate can be subtracted from the gyroscope output, producing compensated output. It has been demonstrated the identified model successfully compensates bias for the steady temperature, while performs only fair during temperature transitions.In order to deal successfully with transient processes in CVG dynamics due to the temperature, temperature compensation system using cross-coupling compensation has been developed. This system significantly improved undesired influence of the temperature dependent cross-damping. However, proposed system still requires temperature sensor being used in the system. In our future research we plan to use model of cross-damping errors to develop stochastic system of temperature errors compensation that will not require temperature measurements.В данной работе изучается влияние изменений температуры на выходных сигналы кориолисовых вибрационных гиросокопв через перекрестное демпфирование. Разработана математическая модель температурных воздействий, параметры которой были идентифицированы с использованием экспериментальных данных. Предложена низкоуровневая система компенсации температурных погрешностей, работа которой была проверену путем реалистичного численного моделирования.Вивчається вплив змін температури на вихідні сигнали коріолісових вібраційних гіроскопів через перехресне демпфірування. Розроблено математичну модель температурних впливів, параметри якої було ідентифіковано з використанням експериментальних даних. Запропоновано низькорівневу систему компенсації температурних похибок, роботу якої було перевірено за допомогою реалістичного чисельного моделювання.

Синтез компенсаційних коріолісових вібраційних гіроскопів

 Synthesis of the Coriolis vibratory gyroscopes compensation with the help of the Wiener-Kolmogorov procedure led to the proper transfer function of the optimal feedback controller is proposed in this paper. CVG as the object of compensation is considered as sensitive element transfer function, which was obtained after analysis of it’s dynamics in terms of the amplitude-phase variables. Efficiency of the obtained transfer function of the optimal feedback controller is demonstrated by means of numerical simulation. Описан синтез передаточной функции оптимального регулятора обратной связи с использованием подхода Винера–Колмогорова. Кориолисов вибрационный гироскоп как объект компенсации рассмотрен в качестве передаточной функции его чувствительного элемента, полученной после анализа его динамики в выражениях амплитудно-фазовых переменных. Эффективность полученной передаточной функции оптимального регулятора обратной связи продемонстрировано посредством численного моделирования. Описано синтез передавальної функції оптимального регулятора зворотного зв’язку за допомогою підходу Вінера–Колмогорова. Коріолісів вібраційний гіроскоп як об’єкт компенсації розглянуто як передавальну функцію його чутливого елемента, яка була отримана після аналізу його динаміки у вираженнях амплітудно-фазових змінних. Ефективність отриманої передавальної функції оптимального регулятора зворотного зв’язку продемонстровано за допомогою числового моделювання