Florian Mair

Decoupled Quadrature and Force Feedback Control of Capacitive MEMS Gyroscopes

Abstract This contribution presents the mathematical model of a capacitive MEMS gyroscope containing specific actuators which are capable of compensating mechanical unbalance (quadrature error) as well as the system response to an external angular rate (force feedback). Based on this model a quadrature controller is systematically designed. In order to eliminate the typically weakly damped open-loop dynamics of the gyroscope additionally a combined concept of closed-loop quadrature and force feedback control is introduced. The presented theory is validated by means of both numerical simulations and measurement results utilizing a prototype gyroscope.

Control of Vibratory MEMS Gyroscopes based on Envelope Models

Abstract In this contribution, a systematic method for the design of open- and closed-loop controllers for vibratory MEMS gyroscopes based on so-called envelope models will be presented. The methodology will be carried out for a capacitive gyroscope with electrostatic actuators and sensors. In particular the derivation of an optimized start-up strategy and the design of an unbalance rejection controller will be considered in more detail. The presented theory is validated by numerical simulations as well as by measurement results utilizing a prototype gyroscope.

Hardware implementation of an electrostatic MEMS-actuator linearization

In this paper, an electrostatic actuator linearization will be introduced, which is based on an existing hardware-efficient iterative square root algorithm. The algorithm is solely based on add and shift operations while just needing n/2 iterations for an n bit wide input signal. As a practical example, the nonlinear input transformation will be utilized for the design of the primary mode controller of a capacitive MEMS gyroscope and an implementation of the algorithm in the Verilog hardware description language will be instantiated. Finally, measurement results will validate the feasibility of the presented control concept and its hardware implementation.

Ein Programmpaket zur Modellierung kapazitiver MEMS-Drehratensensoren

Zusammenfassung Dieser Beitrag beschreibt ein Programmpaket zur automatisierten Herleitung des mathematischen Modells in symbolischer Darstellung von kapazitiven MEMS-Drehratensensoren. Im Anschluss an die Beschreibung des Funktionsprinzips eines speziellen einachsigen Drehratensensors mit kapazitivem Antrieb und kapazitiven Auslesestrukturen wird ein mathematisches Konzept zur systematischen Beschreibung einer bestimmten Klasse von Drehratensensoren vorgestellt. Das resultierende System von Differentialgleichungen kann im Computeralgebraprogramm MAPLE zum Reglerentwurf und zur weiteren Analyse verwendet werden und ein automatisierter C-Code-Generator ermöglicht eine nahtlose Einbindung in die Simulationsumgebung von MATLAB/SIMULINK.