Luciano Prandi

Control of a Z-axis MEMS vibrational gyroscope

The paper describes the design of the control loops in a Z-axis, MEMS vibrational gyroscope. In this device, a silicon mass is driven through electrostatic actuator so that it has a sinusoidal linear motion, with a controlled speed. The design of a suitable controller, capable of maintaining the required speed and with prescribed restoring capabilities after shocks has been derived and described in the paper. Attached to the driving mass, a second mass, free to move in the direction orthogonal to the motion of the first mass, is subjected to a Coriolis force, proportional to the product of the first mass speed by Z-axis rotational speed. The sensing of the Coriolis force and, in turn, of the Z-axis rotational speed, is performed in closed loop fashion, with a 1-bit quantized actuation. The restoring force that brings the motion of the second mass to zero is equivalent to the output bit stream of a sigma-delta converter and contains the information of the Coriolis force. The design of this second control loop and a detailed analysis on the signal-to-noise ratio achievable with the proposed design is reported.

Automatic Mode Matching in MEMS Vibrating Gyroscopes Using Extremum-Seeking Control

In order to enhance the sensitivity and to reduce the readout circuit complexity of any angular velocity microsensor (vibrating gyroscope), it is crucial to reduce the frequency mismatch of its resonant modes of vibration. Achieving a good matching accuracy during fabrication is rather difficult because of tolerances and process variations that detrimentally affect the manufacturing precision. Moreover, even assuming to achieve a good frequency matching through fabrication or postfabrication calibration, it is very likely that parametric variations induced by the external environment during the normal operation of the device disrupt any initial tuning. For these reasons, in this paper, an alternative way to accomplish the frequency-matching condition is suggested, which exploits a real-time adjusting mechanism based on an automatic mode-matching control loop. In particular, this paper describes the details of an adaptive controller capable of automatically matching the resonant frequencies of the two main modes of vibration of a single-axis vibrating microgyroscope, under the provision that there is an underlying mechanism through which the frequency mismatch can be controlled by adjusting a suitable tunable parameter. The controller is designed by considering the requirement of reducing its complexity, so that it can be easily implemented on cheap sensors. Owing to a key observation that allows the recast of the frequency-matching problem as a maximization problem, the proposed mode-matching controller is actually designed as a standard perturbation-based extremum-seeking controller, which can be implemented by using few analog electronic components. The proposed solution has been tested on the LISY300AL yaw-rate microelectromechanical system gyroscope manufactured by STMicroelectronics, showing that a mode matching of nearly 1 Hz or less can be easily attained.

A low-power 3-axis digital-output MEMS gyroscope with single drive and multiplexed angular rate readout

Motivated by the increasing demand of integrated inertial-sensing solutions for motion processing and dead-reckoning navigation in handheld devices and low-cost GPS navigators, this paper reports the details of a 3-axis silicon MEMS vibratory gyroscope that fulfills the pressing market requirements for low power consumption, small size and low cost. Thanks to a compact mechanical design that combines a triple tuning-fork structure within a single vibrating element, our solution achieves satisfactory performance in terms of thermal stability, cross-axis error, and acoustic noise immunity by using a small die size. Furthermore, the presence of a single primary vibration mode for the excitation of the 3 tuning-forks, together with the possibility of sensing the pickoff modes in a multiplexing fashion, allows to design a small-area, low-power ASIC.

Open loop compensation of the quadrature error in MEMS vibrating gyroscopes

This paper presents a simple, yet effective approach for rejecting the quadrature error in MEMS vibratory gyroscopes. The proposed solution consists of an open loop compensation that is performed on the proof-mass displacement readout signal provided by a standard capacitive sensing interface based on parallel-plate capacitors. The compensating signal is generated and calibrated according to the nominal quadrature error to reject, and is injected into the system by means of a compensation circuit based on a dynamically reconfigurable capacitor bank. The compensation scheme described in the paper has been implemented on ASIC and experimentally tested on a real MEMS vibratory gyroscope. Experimental results show that the proposed solution assures good rejection capabilities, even for very large quadrature errors that unavoidably saturates the sensor readout interface.

Design of a Delta-Sigma Bandpass Demodulator for a Z-Axis MEMS Vibrational Gyroscope

This paper describes the design of a ∆Σ bandpass demodulator for a Z-axis MEMS vibrational gyroscope. In this MEMS device, a silicon mass is driven through electrostatic actuator so that it has a sinusoidal linear motion, with a controlled speed. Attached to such driving mass, a second mass, free to move in the direction orthogonal to the motion of the first mass, is subjected to a Coriolis force, proportional to the product of the first mass speed by Z-axis rotational speed. The sensing of the Coriolis force and, in turn, of the Z-axis rotational speed, is performed in closed loop fashion, by measuring the restoring force needed for keeping the sensing mass at the equilibrium position. The restoring force is applied to the sensing mass through a quantized actuation signal, which is obtained from the output bit stream of a band- pass Delta-Sigma converter, containing the information of the Coriolis force. The design of the sensing control loop and simulation results regarding the signal-to-noise ratio achievable with the proposed design is reported. Finally, the issue of the realization of the proposed solution with switched capacitor (SC) technology is also addressed. I. INTRODUCTION

A Demodulation Technique for the Sensing Circuit of a MEMS Gyroscope

This paper deals with the design of a digital sensing interface for a MEMS gyroscope. In such devices, the information regarding the angular rate Omegaz(t) experienced by the sensor is contained in a suppressed carrier-dual side band (SC-DSB) signal, which has Omegaz (t) as modulating component. Hence, a demodulation must be carried out in order to retrieve a measurement of the angular rate. The demodulation process presented in the paper consists of a quantization stage of the SC-DSB signal, which is performed with a three-level band-pass DeltaSigma converter, followed by a digital demodulation of the DeltaSigma bit-stream with a given digital sequence. Several simulation results are reported to evaluate system performances

Low Cost Silicon Coriolis’ Gyroscope Paves the Way to Consumer IMU

During the last two years MEMS linear accelerometers have reinvented the way of playing a game, protecting your sensitive data on HDD, using your mobile devices smartly or making your washing machine less power hungry. Consumer and Industrial Markets have taken advantage from “The MEMS Consumerization Wave”, driven by STMicroelectronics, which introduced a wide portfolio of two and three-axis motion sensors meeting customer requirements in terms of size, performances, quality and price.