364 IEEE/ASME TRANSACTIONS ONMECHATRONICS, VOL. 10, NO. 4, AUGUST 2005 Control of a Z -Axis MEMS Vibrational Gyroscope Roberto Oboe, Member, IEEE, Riccardo Antonello, Student Member, IEEE, Ernesto Lasalandra, Guido Spinola Durante, and Luciano Prandi Abstract—This paper describes the design of the control loops in a z-axis, MEMS vibrational gyroscope operating in a vacuum en- closure. 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 is briefly 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, pro- portional 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 band-pass 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. Index Terms—AGC design, electromechanical ΔΣ modulator, MEMS gyroscope. I. INTRODUCTION M ICROMACHINED gyroscopes find application in sev- eral fields, including automotive (e.g., in active stability control systems), consumer electronics (e.g., in image stabiliz- ers of camcorders) and inertial navigation [1], [2]. Among the possible solutions for the realization of a MEMS gyroscope, the vibrational gyroscope has the advantage to be obtained by surface micromaching of a silicon substrate. In its simplest im- plementation, shown in Fig. 1, the device is realized by a single mass, suspended over a substrate by silicon springs and free to move along a plane which is parallel to the substrate. Electro- static actuators are used to force the motion of the mass along one direction (drive axis). When the sensor rotates around an axis orthogonal to the die plane (z-axis), the proof mass experi- ences the Coriolis force F, according to the following equation: F(t)= −2mΩ z (t) × ˙ x(t) (1) where m is the proof mass, Ω z is the angular velocity around the z-axis, ˙ x is the proof mass velocity along drive axis, and “×” denotes the vector product. Since drive, sense and rota- tional axes are orthogonal, the Coriolis acceleration is given by a(t)= −2Ω z (t)˙ x(t) and it acts along sense axis. In actual Manuscript received February 20, 2005; revised March 27, 2005. Recom- mended by Guest Editors K.Ohnishi, R. Oboe, and Y. Hori. R. Oboe is with the Department of Mechanical and Structural Engineering, University of Trento, 38050 Trento, Italy (e-mail: roberto.oboe@ing.unitn.it). R. Antonello is with the Department of Information Engineering, Univeristy of Padova, 35131 Padova, Italy (e-mail: richard@dei.unipd.it). E. Lasalandra, G. Spinola Durante, and L. Prandi are with STMicroelec- tronics S.r.l., MEMS Business Unit, 20010 Cornaredo, Italy (e-mail: ernesto. lasalandra@st.com; guido.spinola@st.com; luciano.prandi@st.com). Digital Object Identifier 10.1109/TMECH.2005.852437 Fig. 1. Simplified z -axis vibrational gyroscope. implementations, ˙ x(t) is a fixed frequency sinusoid, then a(t) is a dual sideband (DSB) modulated signal, where Ω z (t) is the information bearing signal and ˙ x(t) is the carrier. Ω z (t) can be retrieved by sensing the Coriolis acceleration and demodulat- ing it with a sinusoidal carrier which is locked in phase with ˙ x(t) (synchronous demodulation). It is worth noticing that the sensitivity of the sensor depends on amplitude of ˙ x. Many researchers have approached the realization of MEMS gyroscopes and a few commercial devices are already available on the market. However, the devices realized are characterized by a limited performance, this mainly due to the limitations in both the mechanical part of the device and on-board compu- tational power. The first generation of vibrational gyroscopes were essentially open loop devices, with an external oscilla- tor driving the oscillating mass. Such devices suffered of a large performance drift, this due essentially to the uncontrolled ampli- tude of the oscillations, which usually varies with temperature. The same problem occurred at the sensing side of the device, since the effect of Coriolis force on displacement is weighted by the ratio between stiffness of suspending springs and suspended mass and the stiffness usually varies with the temperature. To alleviate this problem, some device incorporates a temperature sensor, but the effectiveness of this approach is rather limited. In order to achieve a better performance, some researcher pro- posed the use of control loops at both mass driving and sensing, in addition to other adaptation loop in charge of compensating for fabrication imperfections, obtaining interesting results. In particular, the velocity of the driving mass has to oscillate with controlled amplitude and frequency, so that the scale factor of 1083-4435/$20.00 © 2005 IEEE