The method of measurand reconstruction based on the simplified model

Abstract

The value of measurand reconstruction based on the result of observation of the output of the measurement path belongs to the so-called ill-conditioned operation. It is so even for the well-known dynamic of the track type linear differential equation. This task is sensitive to any distortion and measuring errors by which generally requires the use of complex mathematical operations. If the measuring circuit has a linear dynamics specified by impulse responses and step responses, then using a simplified model of dynamics, obtained by expanding in Taylor series a convolution of the integrand function, you can easily restore the state of the input by observing the output state. The error of the model depends on the second derivative of the signal being played and it is negligibly small for a short time horizon. The paper proposes to use a model whose parameters can be selected in such a way that the error of the simplified model was dependent only on the fourth or higher derivatives of the input signal. This method gives good results for a smooth input signal with negligible values of derivatives higher than the third order. Complicated dependencies of the parameters of the model on the type of dynamic measurement channel and its parameters, can be reduced to a simple, universal form. This was possible thanks to the pre subjecting the output signal operation of multiple integrations, it is easy to make and accurate.