Parameter optimization for a high-order band-pass continuous-time sigma-delta modulator MEMS gyroscope using a genetic algorithm approach

Abstract

This paper describes a novel multiobjective parameter optimization method based on a genetic algorithm (GA) for the design of a sixth-order continuous-time, force feedback band-pass sigma-delta modulator (BP-M) interface for the sense mode of a MEMS gyroscope. The design procedure starts by deriving a parameterized Simulink model of the BP-M gyroscope interface. The system parameters are then optimized by the GA. Consequently, the optimized design is tested for robustness by a Monte Carlo analysis to find a solution that is both optimal and robust. System level simulations result in a signal-to-noise ratio (SNR) larger than 90 dB in a bandwidth of 64 Hz with a 200 • s −1 angular rate input signal; the noise floor is about −100 dBV Hz −1/2 . The simulations are compared to measured data from a hardware implementation. For zero input rotation with the gyroscope operating at atmospheric pressure, the spectrum of the output bitstream shows an obvious band-pass noise shaping and a deep notch at the gyroscope resonant frequency. The noise floor of measured power spectral density (PSD) of the output bitstream agrees well with simulation of the optimized system level model. The bias stability, rate sensitivity and nonlinearity of the gyroscope controlled by an optimized BP-M closed-loop interface are 34.15 • h −1 , 22.3 mV •−1 s −1 , 98 ppm, respectively. This compares to a simple open-loop interface for which the corresponding values are 89 • h −1 , 14.3 mV •−1 s −1 , 7600 ppm, and a nonoptimized BP-M closed-loop interface with corresponding values of 60 • h −1 , 17 mV •−1 s −1 , 200 ppm.

Design and Implementation of an Optimized Double Closed-Loop Control System for MEMS Vibratory Gyroscope

“…Furthermore, there is a non-linear term due to the dependence of the feedback force on the proof mass position which has serious implications on stability and performance and cannot predicted with a linear model [29]. Therefore, a genetic algorithm (GA) together with a parameterized system level model is suitable to be used to perform a multi-objective optimization [24,30]. Here, we choose the following parameters as optimization goal functions: i) the proof mass displacement in the sense mode (which should be minimized) in the presence of an input angular rate signal with 200°/s amplitude at 32Hz, ii) the SNR of the output bitstream (which should be maximized), iii) the settling time of the self-oscillation in the drive mode (which should be minimized), iv)  r which should be within the range [-1.5-0.25 to ensure stability of the AGC, as the capacitive pick-off circuit and low pass filter lead to considerable phase shift.…”

“…11); ii) the drive circuit consisting of the AGC control loop to excite the gyroscope to vibrate at its resonant frequency with constant amplitude and iii) the sixth-order continuous-time BP-interface for the sense mode. In order to obtain the final angular rate signal, the output bitstream requires further signal processing, such as phase-sensitive demodulation and low-pass filtering [24]. Fig.…”

“…In order to reduce electro-magnetic interference on the PCB, the ground plane is split into three parts: gyroscope analog readout circuit ground, AGC control circuit ground and digital circuit ground; they are connected together at a single point. Most circuit blocks were partly reused from previous designs [24]. However, the pick-off circuit, compensator circuit, and resonator circuit require special care; their parameters need to be special adjusted according to the results of the system level optimization.…”

“…These linear methodologies neglect all second order effects and nonlinearities in the system, however these can be of importance for AGC and  control loops. In [24] a new approach was used which is based on optimizing the parameters of a band-pass  for the gyroscope sense mode by a Genetic Algorithm (GA), but the drive mode control system was not described.…”

A Straightforward Approach for Synthesizing Electromechanical Sigma-Delta MEMS Accelerometers

“…However due to the unchangeable nature of the MEMS transfer function, there is one degree-of-freedom(DOF) lost in the synthesizing procedure; thus, not all NTFs can be successfully synthesized [12,16]. The traditional approach is relied on for empirical experiments; the synthesis is a "trail-and-error" procedure which costs a lot of simulation time [17,18]. To solve this problem some researchers [12,16,19] proposed an unconstrained topology, where an extra feed-forward path is introduced to provide an extra DOF.…”