PWM Closed-Loop Accelerometer Control for Negative Spring Stability
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Solution Overview
Problem
Capacitive accelerometers suffer from a 'negative spring rate' issue, where the attractive electrostatic force increases with displacement, leading to instability and bias shifts, especially outside a specific frequency range, limiting their open loop gain and sensitivity.
Innovation Solution
A closed-loop control system using pulse width modulation (PWM) drive signals with an adjustable mark/space ratio and differential voltage servo to maintain a constant electrostatic force, balancing mechanical inertial forces with electrostatic forces, thereby keeping the proof mass at the null position regardless of displacement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional capacitive accelerometers are operated in closed loop, then the proof mass can be restored to the null position, but the negative spring rate causes instability and bias shifts especially outside a specific frequency range
Solution Approach 1:
The patent changes the electrical parameters (voltage and charge distribution) applied to the electrodes to counteract the negative spring rate effect. By dynamically adjusting the electrical forces in response to proof mass position, the system maintains stability across a wider frequency range while reducing bias shifts and improving measurement precision.
2Reliability
If PWM drive signals with high frequency are used to restore the proof mass, then the null position can be maintained, but the open loop gain is limited and bias shifts occur outside a particular frequency range
Solution Approach 1:
The patent implements a feedback mechanism where the system continuously monitors the proof mass position and adjusts the PWM drive signals accordingly. This closed-loop feedback allows the system to maintain the proof mass at the null position while dynamically compensating for frequency-dependent bias shifts, thereby extending the useful frequency range and improving measurement precision.
3Force
If the attractive electrostatic force increases with displacement, then the electrostatic force can restore the proof mass, but the negative spring rate creates instability
Solution Approach 1:
The patent makes the electrostatic force dynamic by continuously adjusting the voltage and charge distribution on the electrodes based on the proof mass position. This dynamic adjustment transforms the static negative spring rate into a controllable variable, allowing the system to maintain stability while still utilizing electrostatic forces for proof mass restoration.
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
This approach reduces or eliminates the negative spring rate effect, allowing the use of lower resonant frequency MEMS devices with higher open loop gain, improving sensitivity and reducing bias errors, while maintaining a wide acceleration measurement range.
Implementation Method 1
the attractive electrostatic force between the proof mass and an electrode increases as the displacement of the proof mass increases
Implementation Method 2
This happens by virtue of Coulomb's law—as the proof mass is displaced from the null position, the attractive force between it and the electrode that is closer to the proof mass as a result of the displacement is increased
Implementation Method 3
The resonant frequency of the MEMS device is defined by the mass of the proof mass and the positive spring constant of the compliant support legs
Implementation Method 4
a gaseous medium trapped inside the device provides damping for the proof mass when it moves in a sensing direction in response to an acceleration being applied
Data Source
AI summary
An accelerometer closed loop control system comprising: a capacitive accelerometer comprising a proof mass moveable relative to first and second fixed capacitor electrodes; a PWM generator to generate in-phase and anti-phase PWM drive signals with an adjustable mark/space ratio, wherein said drive signals are applied to the first and second electrodes such that they are charged alternately; an output signal detector to detect a pick-off signal from the accelerometer representing a displacement of the proof mass from a null position to provide an error signal, wherein the null position is the position of the proof mass relative to the fixed electrodes when no acceleration is applied; a PWM servo operating in closed loop to vary the mark/space ratio of said PWM drive signals in response to the error signal so that mechanical inertial forces are balanced by electrostatic forces.