A Self-Tuning Algorithm for Z-Axis Micro Rate Integrating Gyroscopes

Vibratory micro rate integrating gyroscopes (MRIG) are conventionally modeled using the position and velocity of the gyroscope, as the state space variables. This work describes the dynamic analysis of a z-axis MRIG using an alternate set of dynamic variables, which are the angular momentum, the inner product between position and linear momentum vectors, the Lagrangian and total energy of the system. This alternate description is used to derive the conditions for the ideal gyroscope to operate at the correct precession rate with minimal quadrature. A self-tuning algorithm is presented, which compensates the gyroscope’s damping and sitffness mismatches, while allowing the gyroscope to precess at the correct precession rate with minimal quadrature and reasonable control effort.