# Crosstalk compensation using matrix methods

In almost any force sensor application, forces other than the one(s) being measured will be present. These extraneous forces will invariably cause errors in the measured values through what is called crosstalk. Crosstalk is a phenomenon were the sensor reports an output value for a particular direction when the force that caused the output was in a different direction. Through the use of the mathematical technique described below, this crosstalk error can be all but eliminated.

Force sensors are designed to measure forces and torques along defined axes, typically labeled X, Y and Z. These force sensors can have from one to six measurement channels; three force channels (Fx, Fy and Fz) and three torque or moment channels (Mx, My and Mz). In theory, a load along any one of those measurement axes will not produce an output on any of the other measurement channels.

Unfortunately, this is seldom the case in the real world. For most force sensors, this undesired output, or crosstalk, will be between 1 and 5%. While 1% - 5% crosstalk may not sound like much, if each channel has 1% - 5% crosstalk due to each of the remaining five loads, then the total crosstalk could be as high as 5% - 25%.

There are basically two methods used to reduce this potential source of measurement error. With the first method, the load cell is 'tuned', either mechanically or electrically to reduce the channels output due to off-axis or extraneous loads. While effective, this method is time consuming and is not practical if more than two extraneous loads need to be compensated for.

The other method of crosstalk compensation involves mathematically manipulating the load-cell's output data to correct the crosstalk outputs. It is effective for any number of extraneous loads, and can be characterized as mathematical crosstalk compensation by the application of "cross coupling coefficients", or the inverse matrix method. This is the method that will be discussed here.

When a load is applied to a force sensor, the measurement channel that lines up with that load will respond. However, as described earlier, other measurement channels that are not in line with that applied load will also respond to that load. That's the bad news. The good news is that that response is repeatable for any given load or combination of loads.

This means that by carefully applying these extraneous loads during the calibration process, and recording each channels output response to those loads, an output profile of the sensor can be created. From here, a series of simultaneous equations can be created to describe the crosstalk performance of the force sensor.

By solving this series of equations using any set of simultaneous data from all the channels of the sensor, the true loading condition that produced that unique set of data can be determined. The drawback to this method is that a sensor channel is required for each extraneous load that is present during loading. This usually isn't a problem, since in most instances, a measurement channel is present to monitor all the significant loads present in the application.