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Introduction to Mechanical Microsensors
Published in Robert B. Northrop, Introduction to Instrumentation and Measurements, 2018
When a pair of masses is driven to oscillate with equal amplitude, but in opposite directions (180° out of phase), in the same plane, rotation about the input (Z) axis generates Coriolis moments that act orthogonally at the vibrating mass attachment point (see Figure 12.6). Equations for these Coriolis moments were developed in Section 7.2.2.3. The same principle of vibrating masses has been used by Systron Donner Inertial Division, Concord, CA, to make a family of angular rate gyros using MEM technology. The vibrating masses are the vibrating arms of a dual, quartz MEM TF. For example, Systron Donner Inertial Division’s GyroChip™ II, QRS14 MEM angular rate sensor has a ±100°/s full-scale range, a ≤50 Hz signal bandwidth, a threshold of <0.004°/s, and an output noise of <0.05°/s/√Hz. The sensor linearity is given at <0.05% of full range (QRS 2012). The readout system for the Systron Donner Inertial’s QRS14 rate gyro is shown in Figure 12.7, adapted from Figure 4 in QRS (2012). The excitation system has been omitted from Figure 12.7 for simplicity. Note that the Coriolis moments induced in the top quartz TF MEM structure by ϕ˙ are coupled to and excite oscillations in the bottom (readout) TF. A PSD, followed by an LPF, is used to extract an output (DC) signal, Vo, proportional to the angular input rate, ϕ˙. Systron Donner Inertial also offers the QRS116 Single-Axis Tactical Grade Analog Gyroscope (±100°/s) and the QRS28 Dual-Axis Gyroscope.
Roll angle estimator based on angular rate measurements for bicycles
Published in Vehicle System Dynamics, 2019
Emilio Sanjurjo, Miguel A. Naya, Javier Cuadrado, Arend L. Schwab
For big roll angles, a new approach for measuring the roll angle was developed in this work. The method is based on the existent relationship between the angular rates measured by the angular rate sensor if a null pitch rate is considered. This approximation relies on the fact that the long term mean of the pitch rate is null during riding. Introducing the null pitch rate assumption, Equation (6b) becomes: and the roll angle estimation can be calculated as where is the sign of the z angular rate. Both versions of this equation are mathematically equivalent, but the second one is more convenient in practice, when noisy measurements taken from real sensors are used, thus avoiding the division by zero.