Modeling and control of capacitive single- and dual-axis MEMS frame gyroscopes

Gyroscopes measure the angular rate with regard to a fixed inertial reference system. Due to their wide fields of application, there exist a vast amount of different gyroscope technologies and designs. Resonant capacitive micro-electromechanical-system (MEMS) frame gyroscopes operate on the basis of two orthogonal vibration modes, which, at the occurrence of an external angular rate, are coupled by means of the Coriolis-effect. Although these sensors have the advantage of small size and low price, their lower accuracy and stability compared to competing sensor technologies have limited their use to low performance applications. However, as extensive research activities have led to a steady increase in performance and reliability in recent years, this sensor technology is getting increasingly attractive even for demanding applications.

To contribute to the ongoing research activities in improving the performance of MEMS gyroscopes, this thesis deals with the modeling and control of capacitive single- and dual-axis MEMS frame gyroscopes. After starting the discussion with the explanation of the build-up and functional principle of two exemplary capacitive MEMS frame gyroscopes, a mathematical concept for the modeling of the generic class of capacitive MEMS frame gyroscopes is presented. Furthermore, a software tool for the automatic generation of the mathematical models in symbolic form is introduced and several mathematical representations with different levels of detail and dynamic ranges are derived for the gyroscopes under consideration. On the basis of so-called envelope models, two variants of a fast and reliable sensor start-up and control procedure with guaranteed maximal start-up time are developed. In addition to that, several different control concepts for the sense oscillators are discussed which allow the compensation of several production induced parasitic effects, result in a better linear sensor behavior, allow for the adaption of the sensor dynamics and increase the sensitivity of the gyroscope. In detail, a decoupled force-feedback and quadrature control concept is presented for the split-mode operation and a combined forcefeedback, quadrature and frequency control concept is discussed which allows for the matched-mode operation of the gyroscope. In order to get an insight into the experimental setup, which was used for the verification of the individual control concepts, a general overview and the most important building blocks of a field programmable gate array implementation are given. It shall be noted that corresponding simulation and measurement results on several prototype gyroscopes are presented throughout the thesis in order to validate the mathematical models, the applied simplifications as well as the proposed control concepts.