A new formulation of the lag theorem from the course of operational calculus

Abstract

Aim. The classical lag theorem from the course of operational calculus has shown unsatisfactory results on a variety of specific examples made up of elementary functions. The article presents a new formula for the delay theorem, which gives correct results.

Methodology. The method consists in determining the images of functions with a delay by direct calculation from the Laplace integral, or using a linear combination of tabular images. The solutions obtained are compared with the images obtained using the classical delay theorem. The comparison of the results obtained by the two methods turned out to be unsatisfactory for all the examples.

Results. A new, correct delay theorem is formulated and the corresponding formula is presented. The results of applying the new formula gave correct results. An error has been identified that occurred during the derivation of the classical delay formula. It consists in the fact that in the process of deducing the formula, one integral term was unlawfully deleted.

Research implications. Operational calculus is used in automatic control theory and in electrical circuit calculations. The corrected delay theorem allows one to obtain correct results in the named systems, where signals with delay are present.