Multivariable quantitative feedback theory approach to robust control of vibrational micro-electromechanical systems gyroscope

Abstract

Recent advances in micro-electromechanical systems (MEMS) have led to the creation of small low-cost gyroscopes that have low power consumption levels. This paper presents a novel design methodology for a robust controller that can improve the performance of a vibratory MEMS gyroscopes despite the existence of coupling between vibratory gyroscope modes and inherent model uncertainties. The drive-mode of the gyroscope is able to track a desired sinusoidal trajectory while the sensing mode is bounded against uncertainties. In other words, while the sensing mode of the gyroscope operates under a bounded unknown disturbance and measurement noise, the multivariable robust quantitative feedback theory (QFT)-based controller compensates undesirable mechanical spring coupling between two vibrating directions, regulates both modes, and most significantly compels the output of the sensing mode to be bounded and the output of the drive mode to track a desired sinusoidal reference signal at a given amplitude and frequency. The robust performance of the closed-loop system is verified through a series of frequency-domain analyses. Finally, the effectiveness of the proposed QFT-based controller is demonstrated through simulations.

Keywords

robustness quantitative feedback theory vibratory MEMS gyroscope

Get full access to this article

View all access options for this article.

References

Ljung

P. B.

Micromachined gyroscope with integrated electronics. PhD Thesis, Department of Electrical Engineering, The University of California, Berkeley, 1997.

Clark

W. A.

Micromachined vibratory rate gyroscope. PhD Thesis, Department of Electrical Engineering, The University of California, Berkeley, 1997.

Barbour

Schemidt

Inertial sensor technology trends. IEEE Sen. J., 2001, 1(4), 332–339.

Yazdi

Ayazi

Najafi

Micromachined inertial sensors. Proc. IEEE, 1998, 86(8), 1640–1659.

Clark

W. A.

Howe

R. T.

Horowitz

Surface micromachined Z-axis vibratory rate gyroscope. In Technical Digest of the Solid-state sensor and actuator workshop, Hilton Head Island, June 1996, pp. 283–287.

Shkel

Howe

R. T.

Horowitz

Modeling and simulation of micromachined gyroscopes in the presence of imperfections. In Proceeding of the International Conference on Modeling and simulation of microsystems, San Juan, Puerto Rico, April 1999, pp. 605–608.

Acar

Shkel

A. M.

An approach for increasing dive-mode bandwidth of MEMS vibrational gyroscopes. J. Microelectomech. Syst., 2005, 14(3), 520–528.

Park

Horowitz

Adaptive control for the conventional mode of operation of MEMS gyroscopes. J. Microelectromech. Syst., 2003, 12(1), 101–108.

Park

Horowitz

New adaptive mode of operation for MEMS gyroscopes. Trans. ASME, J. Dyn. Syst. Meas. Control, 2004, 126(4), 800–810.

10.

Zheng

Dong

Gao

Control and rotation rate estimation of vibrational MEMS gyroscopes. In Proceedings of the 16th IEEE International Conference on Control applications, 2007, pp. 118–123 (IEEE Press, Piscataway, New Jersey).

11.

Dong

Zheng

Gao

On control system design for the conventional mode of operation of vibrational gyroscopes. IEEE Sen. J., 2008, 8(11), 1871–1878.

12.

Batur

Sreeramreddy

Khasawneh

Sliding mode control of a simulated MEMS gyroscope. ISA Trans., 2006, 45(1), 99–108.

13.

Fei

Adaptive sliding mode control with application to a MEMS vibratory gyroscope. PhD Thesis, The University of Acron, 2007.

14.

Acar

Shkel

MEMS vibratory gyroscope structural approaches to improve robustness, 2007 (Springer).

15.

Torabi

Vali

Dastgerdi

Robust controller design of MEMS gyroscope using quantitative feedback theory (QFT). The 18th Annual International Conference on Mechanical Engineering, Tehran, Iran, 2010.

16.

Torabi

Vali

Ebrahimi

Bahrami

Robust control of nonlinear MEMS optical switch based on quantitative feedback theory. In Proceedings of the Fifth IEEE International Conference on Nano/micro engineered and molecular systems, 2010 (IEEE Press, Piscataway, New Jersey).

17.

Vali

Modelling and robust control of micro-electro-mechanical systems (MEMS) devices. Master’s Thesis, Mechanical Engineering Department, University of Kashan, Kashan, Iran, 2010 (in Persian).

18.

Yaniv

Quantitative feedback design of linear and non-linear control systems, 1998 (Kluwer, Norwell, Massachusetts).

19.

Horowitz

I. M.

Synthesis of feedback systems, 1963 (Academic Press, New York).

20.

Horowitz

I. M.

Sidi

Synthesis of feedback systems with large plant ignorance for prescribed time domain tolerances. Int. J. Control, 1972, 16, 287–309.

21.

Horowitz

I. M.

Sidi

Optimum synthesis of non-minimum phase feedback system with plant uncertainty. Int. J. Control, 1978, 27, 361–386.

22.

Horowitz

I. M.

Survey of quantitative feedback theory (QFT). Int. J. Control, 1991, 53(2), 255–291.

23.

Horowitz

I. M.

Quantitative feedback design theory (QFT), vol. 1, 1992 (QFT Publications, Boulder, Colorado).

24.

Chait

Yaniv

Multi-input/single-output computer-aided control design using the quantitative feedback theory. Int. J. Robust Nonlinear Control, 1993, 3, 47–54.

25.

Nwokah

O. D. I.

Thompson

D. F.

Algebraic and topological aspects of quantitative feedback theory. Int. J. Control, 1989, 50(4), 1057–1069.