Improving the performance of piezoresistive force sensors by modeling sensor capacitance

Abstract

Piezoresistive force sensors exhibit considerable lower accuracy compared with load cells and force measuring systems based in strain gauges, however a new method for measuring forces using piezoresistive sensors is described in this paper, leading to a considerable increase in the repeatability of force readings. The new method consists of reading sensor's conductance and capacitance by applying DC and sinusoidal waveforms, thereby allow us to determine a multivariable estimation of force, instead of using the traditional, purely resistive model that has been used up to now. A study of sensor nonlinearities is also described which will allow us to determine the optimal setup to perform capacitance readings under sinusoidal excitation.

Detailed Study of Amplitude Nonlinearity in Piezoresistive Force Sensors

“…Hyperbolic-tangent nonlinearity was hard to detect in our previous work [20,21], because it produces neither saturation nor exponential growth in the output voltage. An additional circumstance prevents the detection of amplitude nonlinearity; to show this, V s2 was replaced in Equation (20) with a sine function, and Equation (12) was used to state Equation (20) in terms of q as shown below: $V_o=-\left[\frac{1}{q}\text{atanh}\hspace{0.17em}\left(\frac{A_s}{k}\hspace{0.17em}\text{sin}\hspace{0.17em}(2\pi \hspace{0.17em}\mathit{ft})\right)+2\pi \hspace{0.17em}{\mathrm{italicfC}}_s{R}_g{A}_s \text{cos}(2\pi \mathit{ft})\right]$…”

“…Unfortunately, we are unable to estimate the underlying error stemming from the capacitance readings reported in [20,21], whether the input sine wave has an amplitude of 0.5 V or 3 V. Where the input sine wave has an amplitude of 0.5 V, Equation (20) must be solved analytically in terms of θ and A o , which is a challenging task beyond the scope of this article; and where the input sine wave is 3 V, a comprehensive model of the amplitude nonlinearity must be developed for input voltages above 1V, and then such model must be included in the differential Equation (1).…”

“…The method detailed in [20,21] consists in reading sensor conductance and capacitance by applying DC and sine waveforms; thereby it is possible to perform a multivariable estimation of force that dramatically reduces force-estimation errors.…”

“…Previous work [ 20 , 21 ] has demonstrated that the repeatability of piezoresistive force sensors may be increased by performing capacitance readings under AC sourcing. The method detailed in [ 20 , 21 ] consists in reading sensor conductance and capacitance by applying DC and sine waveforms; thereby it is possible to perform a multivariable estimation of force that dramatically reduces force-estimation errors.…”

“…In [ 20 , 21 ] an RC-parallel-electrical model was identified for the FlexiForce A201-100 piezoresistive force sensor (PFS); in addition, a frequency nonlinearity in sensor response when the frequency of the driving signal exceeded a certain value was found and appropriately named “the divergent frequency”. However, we have recently found that the PFS exhibits additional nonlinearities related with the amplitude of the driving signal, and thus the RC model and the corresponding equations must be modified to account for this newly found amplitude nonlinearity.…”