Micromachined vibratory gyroscopes controlled by a high order band-pass sigma delta modulator.

Abstract—This work reports on the design of novel closed-loop control systems for the sense mode of a vibratory-rate gyroscope based on a high-order sigma-delta modulator (SDM). A low-pass and two distinctive bandpass topologies are derived, and their advantages discussed. So far, most closed-loop force-feedback control systems for these sensors were based on low-pass SDM’s. Usually, the sensing element of a vibratory gyroscope is designed with a high quality factor to increase the sensitivity and, hence, can be treated as a mechanical resonator. Furthermore, the output characteristic of vibratory rate gyroscopes is narrowband amplitude- modulated signal. Therefore, a bandpass M is a more appropriate control strategy for a vibratory gyroscope than a low-pass SDM. Using a high-order bandpass SDM, the control system can adopt a much lower sampling frequency compared with a low-pass SDM while achieving a similar noise floor for a given oversampling ratio (OSR). In addition, a control system based on a high-order bandpass SDM is superior as it not only greatly shapes the quantization noise, but also alleviates tonal behavior, as is often seen in low-order SDM control systems, and has good immunities to fabrication tolerances and parameter mismatch. These properties are investigated in this study at system level

A closed-loop digitally controlled MEMS gyroscope with unconstrained Sigma-Delta force-feedback

In this paper, we describe the system architecture and prototype measurements of a MEMS gyroscope system with a resolution of 0.025 degrees/s/root Hz. The architecture makes extensive use of control loops, which are mostly in the digital domain. For the primary mode both the amplitude and the resonance frequency are tracked and controlled. The secondary mode readout is based on unconstrained Sigma Delta force-feedback, which does not require a compensation filter in the loop and thus allows more beneficial quantization noise shaping than prior designs of the same order. Due to the force-feedback, the gyroscope has ample dynamic range to correct the quadrature error in the digital domain. The largely digital setup also gives a lot of flexibility in characterization and testing, where system identification techniques have been used to characterize the sensors. This way, a parasitic direct electrical coupling between actuation and readout of the mass-spring systems was estimated and corrected in the digital domain. Special care is also given to the capacitive readout circuit, which operates in continuous time

Readout Method And Electronic Bandwidth Control For A Silicon In-plane Tuning Fork Gyroscope

Disclosed are methods and a sensor architecture that utilizes the residual quadrature error in a gyroscope to achieve and maintain perfect mode-matching, i.e., ~0 Hz split between the drive and sense mode frequencies, and to electronically control sensor bandwidth. In a reduced-to-practice embodiment, a 6 mW, 3V CMOS ASIC and control algorithm are interfaced to a mode-matched MEMS tuning fork gyroscope to implement an angular rate sensor with bias drift as low as 0.15°/hr and angle random walk of 0.003°/√hr, which is the lowest recorded to date for a silicon MEMS gyroscope. The system bandwidth can be configured between 0.1 Hz and 1 kHz.Georgia Tech Research Coporatio

1-Bit processing based model predictive control for fractionated satellite missions

In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller. As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work. Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components. Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission. The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers

1-Bit processing based model predictive control for fractionated satellite missions

In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller. As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work. Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components. Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission. The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers

Small-size MEMS accelerometer encapsulated in vacuum using Sigma-Delta modulation

A vacuum encapsulated MEMS accelerometer using Sigma-Delta modulation is here presented. Three different modulation orders (second, third, and fourth) were implemented in a field-programable gate array (FPGA), enabling flexibility for tuning the loop parameters in real-time. Three devices were measured, and the results are in good agreement with simulations performed in Simulink. A noise figure of 123 μg/√Hz for a bandwidth of 400 Hz and a range of at least ±1 g was experimentally measured. A figure of merit considering device size and bandwidth is proposed, highlighting the relevance of the results for the current state of the art.FCT - Fundação para a Ciência e a Tecnologia (PDE/BDE/114563/2016

CMOS systems and circuits for sub-degree per hour MEMS gyroscopes

The objective of our research is to develop system architectures and CMOS circuits that interface with high-Q silicon microgyroscopes to implement navigation-grade angular rate sensors. The MEMS sensor used in this work is an in-plane bulk-micromachined mode-matched tuning fork gyroscope (M² – TFG ), fabricated on silicon-on-insulator substrate. The use of CMOS transimpedance amplifiers (TIA) as front-ends in high-Q MEMS resonant sensors is explored. A T-network TIA is proposed as the front-end for resonant capacitive detection. The T-TIA provides on-chip transimpedance gains of 25MΩ, has a measured capacitive resolution of 0.02aF /√Hz at 15kHz, a dynamic range of 104dB in a bandwidth of 10Hz and consumes 400μW of power. A second contribution is the development of an automated scheme to adaptively bias the mechanical structure, such that the sensor is operated in the mode-matched condition. Mode-matching leverages the inherently high quality factors of the microgyroscope, resulting in significant improvement in the Brownian noise floor, electronic noise, sensitivity and bias drift of the microsensor. We developed a novel architecture that utilizes the often ignored residual quadrature error in a gyroscope to achieve and maintain perfect mode-matching (i.e.0Hz split between the drive and sense mode frequencies), as well as electronically control the sensor bandwidth. A CMOS implementation is developed that allows mode-matching of the drive and sense frequencies of a gyroscope at a fraction of the time taken by current state of-the-art techniques. Further, this mode-matching technique allows for maintaining a controlled separation between the drive and sense resonant frequencies, providing a means of increasing sensor bandwidth and dynamic range. The mode-matching CMOS IC, implemented in a 0.5μm 2P3M process, and control algorithm have been interfaced with a 60μm thick M2−TFG to implement an angular rate sensor with bias drift as low as 0.1°/hr ℃ the lowest recorded to date for a silicon MEMS gyro.Ph.D.Committee Chair: Farrokh Ayazi; Committee Member: Jennifer Michaels; Committee Member: Levent Degertekin; Committee Member: Paul Hasler; Committee Member: W. Marshall Leac

Readout Method And Electronic Bandwidth Control For A Silicon In-plane Tuning Fork Gyroscope

Disclosed are methods and a sensor architecture that utilizes the residual quadrature error in a gyroscope to achieve and maintain perfect mode-matching, i.e., ~0 Hz split between the drive and sense mode frequencies, and to electronically control sensor bandwidth. In a reduced-to-practice embodiment, a 6 mW, 3V CMOS ASIC and control algorithm are interfaced to a mode-matched MEMS tuning fork gyroscope to implement an angular rate sensor with bias drift as low as 0.15°/hr and angle random walk of 0.003°/√hr, which is the lowest recorded to date for a silicon MEMS gyroscope. The system bandwidth can be configured between 0.1 Hz and 1 kHz.Georgia Tech Research Corporatio

Actuation Techniques For Frequency Modulated MEMS Gyroscopes

This thesis focuses on the design and implementation of an analog actuation circuit for a novel frequency-modulated MEMS gyroscope. The gyroscope detects angular rotations as the difference between the natural frequencies of two closely spaced drive and sense modes rather than the magnitude of displacement in the sense direction. Furthermore, the actuation system features a resonant drive (RLC) circuit that amplifies the gyroscope actuation signal. The input to the circuit is an amplitude-modulated (AM) signal composed of a carrier signal modulated with a base signal that excites the gyroscope drive mode. The carrier frequency corresponds to the electrical resonance frequency of the drive circuit. This research develops techniques for the stabilization of the circuit output through close loop feedback. First, we attempt to increase the signal-to-noise ratio of the modulating signal by implementing feedback and feedforward control loops (AGC). The feedback controller closes the loop on the entire conditioning circuit for the modulating signal while the feedforward controller acts on the input signal to the conditioning circuit. The feedforward and the feedback controllers derive an error signal representing the signal noise by comparing the input and output signal, respectively, with a reference signal. However, we find that the breadboard circuit implementations of our control strategies performed similar to a baseline uncontrolled function generator due to the additional noise input from the breadboard and the additional components used to implement the controller, such as the amplifiers. Next, we develop a single-harmonic amplitude-stabilized actuation scheme for the gyroscope to minimize multi-frequency excitations and reduce amplitude fluctuations to improve the gyroscope precision. A low pass filter is applied to the AM signal to obtain a single sideband full carrier (SSB-FC) signal. Since the capacitance of RLC circuit changes due to the vibration of the gyroscope, this variation in capacitance causes a shift in the frequency response of the RLC circuit, resulting in variation in the circuit gain. Three feedback control topologies are implemented to stabilize the signal by first detecting the change in signal level, and then amplifying or attenuating the signal level in order to maintain a constant gyroscope actuation level. The control strategy with the best performance involves feeding back the RMS of the output signal to control the amplitude of the carrier signal and feeding back the average of the output signal’s envelope to control the bias level of the modulating signal. Using control this strategy, the peak magnitude at the carrier frequency dropped approximately 2% as the capacitance is varied from 15 pF to 16 pF, awhile the other two control strategies changed 9% and 6%