A dynamical envelope model for vibratory gyroscopes

In this contribution, a method will be presented to derive an envelope model for vibratory gyroscopes capturing the essential “slow” dynamics (envelope) of the system. The methodology will be exemplarily carried out for a capacitive gyroscope with electrostatic actuators and sensors. The resulting envelope model can be utilized for both transient and steady state simulations with the advantage of a significantly increased simulation speed. Especially for the sensor design and optimization, where usually very complex mathematical models are used, efficient steady state simulations are of certain interest. Another great advantage of this approach is that the steady state solutions in terms of the envelope model are constant. Thus, for the controller design, a linearization of the nonlinear envelope model around the steady state solution yields a linear time-invariant system allowing for the application of the powerful methods known from linear control theory.