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This article upgrades the RC linear model presented for piezoresistive force sensors. Amplitude nonlinearity is found in sensor conductance, and a characteristic equation is formulated for modeling its response under DC-driving voltages below 1 V. The feasibility of such equation is tested on four FlexiForce model A201-100 piezoresistive sensors by varying the sourcing voltage and the applied forces. Since the characteristic equation proves to be valid, a method is presented for obtaining a specific sensitivity in sensor response by calculating the appropriate sourcing voltage and feedback resistor in the driving circuit; this provides plug-and-play capabilities to the device and reduces the start-up time of new applications where piezoresistive devices are to be used. Finally, a method for bypassing the amplitude nonlinearity is presented with the aim of reading sensor capacitance.

Piezoresistive force sensors have demonstrated to be a good solution for applications demanding non-invasive force readings [

On the other hand, load cells have demonstrated to be reliable force-measurement devices in many different systems [

In certain research fields, such as biomechanics, biomedical engineering and haptics, it is necessary to perform non-invasive force readings. Such readings cannot be carried out using bulky load cells. Whether it is necessary to measure contact force on a knee joint [

Previous work [

In [

The A201-100 piezoresistive sensor was chosen for this study because the manufacturer has developed many specific sensors for research [

Most research articles regarding the A201-100 sensor present performance comparisons among different piezoresistive devices [_{s2}_{s2}_{s}_{s}

Parameter _{g}_{o}_{o}

Then _{o}

Finally, combining

Besides the already-identified frequency nonlinearity [

If the DC source, _{s1}_{o}

In order to study such behavior, the input voltage, _{s1}_{o}^{2}, smaller than the sensor’s sensing area of 71.3 mm^{2}, this ensures that every sensor is evenly loaded in each trial and avoids the pressure falling outside the sensing area of the sensor. _{s1}_{o}_{o}

The minus sign in _{o}_{s1}^{2}^{2}^{2}

Parameters

In order to get a comprehensive view of sensor behavior, a relationship between _{s}

_{s}_{g}

We should clarify that _{g}_{s1}

With the aim of demonstrating that

Note that the

Nevertheless, _{s1}

_{g}_{s}

The effect of the feedback resistor can be deduced from the fact that _{g}_{g}

Henceforth _{s1}_{ref}_{g}/R_{ref}_{g}

However, it must be noted from

Since a general-sensor model was deduced in _{s1}_{g}_{ref}_{s1}_{g}

Note that the _{g}_{s1}_{g}

With the aim of proposing a method for obtaining a specific PFS sensitivity, it is necessary to fit the general-sensor model in _{g}

Note that _{o}_{s1}

In practice, the experimental data were gathered in the same way as described in Section 3.1. Nevertheless, the fit here described embraces all variables and coefficients at once (_{o}_{s1}

^{2}^{2}^{2}^{2}

Once the fit is done, it is possible to assemble the general-sensor equation by substituting into _{ref}_{g}_{s1}_{g}_{t}_{s1}

However, _{s1}

If the PFS is sourced with voltages above 1V, the fitting curve in _{s1}

Despite the fact that the coefficient of determination remained high for all sensors under study (exhibiting an average value of ^{2}

It has been demonstrated that sensor conductance is not constant if there are changes in the input voltage. By relating _{s2}

Under AC sourcing, the nonlinear term,

Specifically, the frequency analyses carried out in [_{s}_{s1}_{s1}

In contrast, the tests carried out in [_{s}_{o}

Neither procedure is addressed in this paper, because a method is proposed in Section 5 for bypassing the amplitude nonlinearity under AC operation, regardless of whether the input voltage is lower or higher than 1 V.

Hyperbolic-tangent nonlinearity was hard to detect in our previous work [_{s2}

A close look at _{o}_{o}

Factors _{s}

Multiplying _{o}

Considering that the composition of two odd functions is an odd function, the first term of

The harmonics come from the decomposition of the

Note that

The above expression is useful for reading sensor capacitance, because the other factors in _{o}V_{x}]_{s}

_{o}/A_{s}_{s}

We would like to stress that different methods for measuring capacitance were evaluated [_{s}_{s}_{s}_{g}A_{s}_{x}

With the aim of demonstrating the statements presented herein, we carried out a series of capacitance and conductance measurements on four PFSs under different sourcing and force conditions. The tests are classified below according to sourcing type.

Forces were applied within the range of 0 N to 250 N under seven sourcing conditions, starting at 0.4 V, with increments of 0.1 V, up to 1 V. For every supply voltage, the sensor sensitivity,

Sensors were then characterized in terms of

With the aim of demonstrating the typical error resulting from the assumption of linear-sensor response, the values of

Two facts may be drawn from

Second, the average error for all sensors resulting from the estimation of the y-intercept coefficient, _{o}

Input amplitudes are not restricted to be under 1 V for the AC sourcing experiments, because the intention is to subject the feasibility of the measuring scheme in _{s}_{s}

Considering:

That the black data points in

That the feasibility of the measuring scheme in

_{s1}

_{s}

_{s1}

_{s1}

An attempt was made to fit a linear trendline to the black data points in _{s}_{s}_{o}

On the other hand, the red data points in ^{2}^{2}^{2}

From

In other words, we have theoretically and experimentally demonstrated that the black data points from _{s1}_{s}_{s}

For sourcing voltages below 1 V, a comprehensive model for the FlexiForce model A201-100 piezoresistive device has been developed and tested. A nonlinear response has been identified in sensor conductance corresponding to a hyperbolic tangent function.

A general method for obtaining a specific sensitivity,

The authors have theoretically and experimentally demonstrated that sensor capacitance is constant regardless of changes in the input voltage whenever the driving voltage is held below 1 V. The feasibility of a measuring scheme for bypassing conductance nonlinearity has also been presented and tested.

Conversely, the experimental results support the hypothesis of constant capacitance for input voltages above 1 V. Nonetheless, it is necessary to develop a theoretical model for sensor conductance for sourcing voltages above 1V before declaring that sensor capacitance remains unchangeable at such sourcing voltages. Future work will mainly focus on adding the puck area as a variable in the general-sensor model. This would allow the final user to assess how the sensor sensitivity is affected when the puck area is changed.

This work has been partially funded by the Spanish Ministry for Innovation and Science through grant DPI2010-18702 which has funded personnel costs and by AECID through grant PCI-iberoamerica D/030531/10 which has funded equipment and consumable costs.

Piezoresistive sensor under study.

Typical variation of resistance and conductance for an A201-100 FlexiForce sensor (image taken from [

_{s1} vs. V_{o}

Graph representing the variation of sensor parameters

Surface resulting from the three dimensional fit of the PFS-general model to the experimental data points shown as empty circles in the plot.

Graph of the

Graph representing the relation of _{s1} vs. V_{o}

General diagram for measuring _{s}_{o}V_{x}]

Sensor Sensitivity,

Sensor capacitance, _{s}

Comparison table of the average errors resulting from the estimation of

Average error (%) in |
2.79 | 1.07 | 2.67 | 1.62 | 2.04 |

Average error (%) in |
10.3 | 10.3 | 10.8 | 14 | 11.35 |

Average error (%) in |
9.46 | 12.5 | 10.9 | 8.2 | 10.27 |

Average error (%) in |
13.5 | 20.3 | 13.3 | 10.9 | 14.5 |