Using Non-linear Integral Models in Automatic Control and Measurement Systems for Sensors’ Input Signals’ Recovery

Abstract

The article is devoted to developing methods of dynamic correction of signals registered at the output of a non-linear measuring transducer for the purpose to recover its input signal. Dynamic correction leads to decreased inertia/time response of the measuring transducer and smoothes its non-linearity. Signal recovery problem is resolved based on the non-linear model of measuring transducer as a first kind, second degree polynomial Volterra integral equation. As the problem is ill-posed, the model regularization method is used. The article offers a differential regularization operator transforming the input polynomial integral equation into a polynomial integro-differential equation. For numerical realization of the given models’ type an algorithm based on the difference and quadrature methods is offered. The key problem of limited modelling time when using the kernel, given by the tabular method, is resolved by applying a procedure of restarting of the calculation process with offset of the time interval the integral equation kernel defined on. To resolve the issue of significant short-period errors in calculations after the restart of the calculation process, we offer a method for obtaining solution from two parallel computing processes with tabular kernels offset in time at a half of the time interval they are defined on. A feature of integral models is their resistance to high-frequency interference, which are present in real engineering systems. The obtained results can be used in dynamic correction devices of measuring transducers of automatic control and measurement systems.