A method to compensate periodic errors by gain tuning in instrumentation

The method described uses multiprobes without individual probes accuracy calibrations. By simple gain (or sensitivity) tuning, perfect compensation of any arbitrary frequency component of an error is achieved. Online calculations or estimations of the periodic error are not required, and significant improvements are achieved just by initial tuning of the gains of separate probes. In Sections II and III, we first derive a mathematical model of the periodic error and then propose a new method to compensate it. In. Section IV, we derive the minimum number of probes needed to compensate a given number of frequency components of the periodic error, and present two algorithms to calculate the gains for separate probes. In Section V, we show two simulated and one experimental example of periodic error compensation. One of the simulated examples is applied to a rotary type of a sensor and the other to a linear type of a sensor. Minimum number of probes needed to compensate multiple frequency components is also derived. The method is successfully demonstrated on two simulated and one experimental example, where one and two frequency components of a periodic error are perfectly compensated. The method is applicable both to rotary and to linear types of sensors