THE INFLUENCE OF CONTROL SYSTEM DESIGN ON THE PERFORMANCE OF VIBRATORY GYROSCOPES

Understanding the influence of the control system on the performance of vibratory gyroscopes is important during the design of such devices. The ability of the control system to reduce the effects of resonator imperfections, on the gyroscope performance, was investigated. The analysis of the control problem presented begins with equations of motion describing the dynamics of a resonator including frequency and damping imperfections. These equations were transformed to slowly varying parameters and averaged. The equations of motion, in this form, provide many insights into the dynamics of the resonator and suggest the control system functions required to effectively operate the resonator as an angular rate sensor. A phase-locked loop-based control system was designed, analyzed and implemented. The control system drives the resonator at resonance to a constant amplitude and nulls the rotation-induced vibrations. It was shown analytically that the first order effects of frequency imperfections can be eliminated by the control system. The effect of damping anisotropy is not reduced by the control system and this is expected to be the major source of error in the closed-loop system. Experimental measurements, of a piezoelectrically actuated and sensed resonator, over a temperature range of 60°C, showed that variation of the zero-rate offset was decreased by an order of magnitude by the force-to-rebalance control. The analytical and experimental results present a convincing argument for the use of force-to-rebalance control in vibratory gyroscopes.