Design and performance test of digital rebalance loop for MEMS gyroscope

In this paper, a digital rebalance loop for MEMS gyroscope is designed and its performance test is performed. First, the system model of MEMS gyroscope is established by dynamic analysis. Then, the digital rebalance loop is designed using modern control technique. The performance of the digital rebalance loop is compared with that of conventional PID rebalance loop. Through frequency response analysis using MATLAB and experiments using a real MEMS gyroscope and digital controller, which is realized using digital signal processor (DSP), it is confirmed that the controller improves the performance of the gyroscope. Introduction A gyroscope is a basic inertial sensor, which can measure an external angular rate. The MEMS gyroscope is an inertial angular rate sensor fabricated using MEMS technology. When an external angular rate is applied to the MEMS gyroscope, the proof mass vibrating at resonant frequency is forced to vibrate in orthogonal direction due to the Coriolis force. The angular rate can be estimated by measuring the amplitude of the orthogonal oscillation. However, such operation, with open loop operation, has small bandwidth and narrow dynamic range. Furthermore, the system nonlinearity becomes larger as the amplitude of the orthogonal oscillation does. To overcome these disadvantages, a closed loop controller named rebalance loop can be used. The rebalance loop is a kind of feedback controller that keeps the orthogonal oscillation small. The magnitude of the feedback signal is proportional to the Coriolis force. Therefore, the control input is used for the estimation of external angular rate inputs. Furthermore, the bandwidth of the gyroscope can be made large by using suitable compensator [1, 3]. The rebalance loops are classified into two categories according to their torquing method. One is an analog rebalance loop that uses an analog torquing method, and the other is a digital rebalance loop that uses a digital torquing method. The former is simple in controller structure and relatively easy to achieve wide bandwidth. However, it is composed of analog circuits, which makes it difficult to realize complex control system designed using modern multivariable control theory such as H∞ controller. On the contrary, the latter is somewhat complex in its controller structure, but it can easily accommodate complex multivariable controller by just computer programming. Furthermore, an additional A/D converter that digitalizes the gyroscope output is not necessary since the gyroscope output is modulated in PWM (Pulse Width Modulation) form [4]. In the following, the principle of operation of the MEMS gyroscope is introduced, and the model of the gyroscope is explained. Next, the multivariable H∞ controller is designed and analyzed. Finally, designed controller is implemented using electronic components and DSP. Key Engineering Materials Vols. 326-328 (2006) pp 249-252 online at http://www.scientific.net © (2006) Trans Tech Publications, Switzerland Online available since 2006/Dec/01 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-14/04/08,12:19:35) Principle of Operation An operation of micro gyroscope is based on the motion of vibrating oscillation. The proof mass is driven along the driving axis (x-axis) at the resonant frequency of the driving mode as shown in Fig. 1. When an angular rate input along z-axis is applied to the sensor, the oscillation of the mass along the sensing axis (y-axis) is induced due to the Coriolis force, which is modulated by the oscillation along the driving axis. The angular rate can be estimated by measuring the amplitude of the orthogonal oscillation. Fig. 1 Simple model of MEMS vibrating gyroscope Model Equations of System The governing equations of the vibratory gyroscope can be expressed as follows. The equation of the micro gyroscope can be simply expressed as a second order mass-spring-damper system. The dynamic model equation of sensing axis is given as Eq. 1: