Model-based control concepts for vibratory MEMS gyroscopes

In this contribution, a systematic method for the design of openand closedloop controllers for vibratory MEMS gyroscopes based on so-called envelope models will be presented. The methodology will be exemplarily carried out for a gyroscope with electrostatic actuation and read-out elements. The specifically designed capacitive actuators of the gyroscope are capable of compensating the system’s inherent mechanical unbalance (quadrature compensation) as well as the system’s response to an external angular rate (force feedback). The utilized envelope model solely captures the relevant system dynamics of the gyroscope while at the same time describing the actuation and read-out mechanisms simplified to a suitable level of detail thus providing the basis for an efficient and systematic control design. In order to demonstrate the proposed methodology, an optimized start-up strategy for the control of the primary oscillation is designed. Furthermore, the approach is utilized for the deviation of a basic quadrature controller for the secondary oscillation. In order to account for the typically weakly damped open-loop dynamics of the gyroscope and the transient coupling between the quadrature and the angular rate signal a more sophisticated combined concept of closed-loop quadrature and force feedback control is introduced. Both simulation and measurement results obtained for a prototype gyroscope validate the mathematical models and prove the feasibility of the proposed concepts.