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.
In this contribution, a method will be introduced 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
transient simulations with the advantage of a significantly increased simulation speed as well as for steady state
simulations. 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.