A design of LQG controller for high performance MEMS accelerometer

This paper presents a novel design structure of a closed-loop Sigma-Delta modulator using a Linear-Quadratic-Gaussian (LQG) controller, which can reduce the influence of possible dispersions of the sensing element and offset the effect of the external disturbance. Specifically, a Kalman state estimator is employed to estimate the system state of Sigma-Delta modulator, and the LQG controller is designed based on the theory of linear quadratic optimal control with the estimated state. The LQG controller with the Kalman state estimator can maintain the proof mass near its position of equilibrium, which makes it possible to enhance the performance of the MEMS accelerometers. Experimental results from the proposed architecture shows an increase of more than 5X improved in signal quantization noise ratio compared to the pure closed-loop Sigma-Delta modulator, and also the proposed Sigma-Delta modulator with the LQG controller improves the performance of disturbance attenuation and system robustness.