The Application of Parametric Excitation in MEMS Gyroscopes

Abstract

Parametric excitation, via electrostatic stiffness modulation, can be exploited in resonant MEMS gyroscopes. In the case of the Rate gyroscope, which is by far the most common type of MEMS gyro, parametric excitation may be used to amplify either the primary mode of the gyro or the response to the angular rate. Both approaches will be discussed. In the more complex mode of operation, known as “Rate Integrating” the output of the gyro is angle directly as opposed to angular velocity in the case of Rate gyro. In this rate integrating mode of operation parametric excitation does offer an effective energy control used to initiate, sustain the vibration and minimise damping perturbations. Parametric amplification of the primary mode of the rate gyroscope is presented and supported with experimental results. In this implementation parametric excitation is combined with external harmonic forcing of the primary mode in order to reduce electrical feedthrough of the driving signal to the sense electrodes. A practical parametric excitation scheme implemented using Digital Signal Processing has been developed to enable either amplification of the primary mode of the gyroscope or amplification of the response to the applied angular velocity. Parametric amplification of the primary mode of the gyroscope is achieved by frequency tracking and regulation of the amplitudes of the harmonic forcing and parametric excitation to maintain a desired parametric gain by closed loop PID control. Stable parametric amplification of the primary mode by a factor of 20 is demonstrated experimentally. This has important benefits regarding the minimisation of electrical feedthrough of the drive signal to the sense electrodes of the secondary mode. By taking advantage of the phase dependence of parametric amplification and the orthogonality of the Coriolis force and quadrature forcing, the response to the applied angular velocity may be parametrically amplified by applying excitation of a particular phase directly to the sensing mode. The major advantage of parametric amplification applied to MEMs gyroscopes is that it can mechanically amplify the Coriolis response before being picked off electrically. This is particularly advantageous for sensors where electronic noise is the major noise contributor. In this case parametric amplification can significantly improve the signal to noise ratio of the secondary mode by an amount approximately equal to the parametric amplification. Preliminary rate table tests performed in open loop demonstrate a magnification of the signal to noise ratio of the secondary mode by a factor of 9.5.

Nonlinear Dynamics of a Microscale Rate Integrating Gyroscope with a Disk Resonator under Parametric Excitation

“…The development of algorithms for generation and control of oscillations of such systems is an active reseach area [20,[28][29][30][31][32][33][34][35]. The papers [36][37][38] address the issues of parametric excitation and maintenance of MEMS resonator oscillations taking into account nonlinear factors.…”