On the Inapplicability of the Padé Approximation for Controlling Object Consisting of Delay Link and Integrator

Abstract

The well-known Pade formula is used to approximate the pure delay link. By means of preliminary studies using the modeling method, it was determined that object whose model consists of a series-connected delay link and an integrator is problematic. This paper examines the possibility of using the Pade formula for calculating controllers for objects that are a series connection of an integrator and a delay link. The paper offers the results of research by modeling in the VisSim software. The method of numerical optimization in numerical simulation showed that in this case such an approximation does not effectively solve the problem. Improving the approximation accuracy by increasing the order of the approximating relation does not solve the problem. This paper analyzes the reasons for this discrepancy and proposes an original approximation formula free of these shortcomings. It is shown that the application of the proposed approximation formula makes it possible to effectively and with high accuracy solve the synthesis problem. The results of modeling a system with an exact model and with the proposed model for approximation coincide with high accuracy, which is shown by an example.