Vibrating Inertial Sensor Calibration for Stiffness Coupling Errors
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Solution Overview
Problem
Existing MEMS inertial sensors suffer from manufacturing imperfections that lead to errors in angular velocity and orientation measurements due to non-identity of the stiffness matrix and mechanical coupling between vibration axes, which cannot be effectively compensated by existing calibration methods.
Innovation Solution
A calibration method that determines the inverse excitation and detection matrices by applying sinusoidal disturbances through trim commands, directly modifying the stiffness matrix to correct for these imperfections, allowing for precise angular velocity and orientation measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If manufacturing techniques are used to create MEMS sensors, then production cost is reduced, but manufacturing precision deteriorates due to imperfections in stiffness matrix and mechanical coupling
Solution Approach 1:
The calibration method performs preliminary characterization of the stiffness matrix and coupling coefficients before actual measurement operations. By determining these parameters in advance through systematic excitation and detection, the system compensates for manufacturing imperfections and achieves high precision without requiring perfect manufacturing.
2Device complexity
If existing calibration methods are used, then device complexity is maintained, but measurement precision deteriorates due to inability to compensate for manufacturing imperfections
Solution Approach 1:
The calibration method implements feedback by using detection transducers to measure the actual response of the resonator to known excitation forces. These measurements feed back into the calculation of stiffness matrix elements and coupling coefficients, which are then used to correct subsequent measurements, creating a closed-loop system that continuously compensates for manufacturing variations.
Solution Approach 2:
The system performs self-calibration by using its own excitation and detection capabilities to characterize its imperfections. The sensor uses its built-in transducers to apply forces, measure responses, and automatically compute correction parameters without requiring external calibration equipment or complex additional components.
3Measurement precision
If trim commands are applied to modify stiffness matrix, then measurement precision is improved, but device complexity increases due to additional calibration procedures
Solution Approach 1:
The method changes the parameters of the resonator system by applying trim commands that modify the stiffness matrix elements and coupling coefficients. By systematically varying these parameters through controlled excitation and measuring the responses, the calibration process identifies the actual parameters and uses this information to correct measurements, transforming a complex physical adjustment problem into a calculable parameter optimization task.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method significantly reduces excitation and detection errors, improving the accuracy and reliability of MEMS inertial sensors by pre-compensating excitation forces and correcting detected motion values.
Implementation Method 1
a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y
Implementation Method 2
The detection method involves applying a bias voltage between the fixed and moving combs and observing the resulting charge variations due to capacitance differences between the fixed and moving combs caused by variations in the spacing between their teeth
Implementation Method 3
When the gyroscope rotates around the z-axis, perpendicular to the xy-plane (called the sensitive axis), the combination of the forced vibration with the angular rotation vector generates, through the Coriolis effect, forces that set the moving masses into natural vibration perpendicular to the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotation speed
Implementation Method 4
They are suspended from fixed anchor points A on the plate by orthotropic suspension springs RS
Data Source
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AI summary
Method (100) for calibrating an inertial angular sensor (10) comprising the steps of: A for at least two electrical angles (θj) of the vibration wave: A1 applying, via each of the three trim commands CTi, a sinusoidal stiffness disturbance PSi having a disturbance frequency fi, and for each disturbance applied: A11 determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi, from the excitation commands determined by the drives, B determining from the three estimated excitation forces Fei i=1,2,3 stored in step A11, three matrices 2x2 M'i, a matrix M'i being representative of the gyrometer response to the disturbance PSi, C determining and storing an estimated inverse excitation matrix (formula (A)) and an estimated inverse detection matrix (formula B) from the three matrices M'i determined in step B, an excitation matrix E and a detection matrix D each being representative of the effects of the excitation chain and the effect of the detection chain of the sensor, respectively.