Delay Systems with Meromorphic Functions Design

Abstract

The contribution is focused on analysis and synthesis of delay systems in a ring of RQ-meromorphic functions. Controller design is based on solution of Diophantine equations in this ring that leads to Smith predictor like structure. Tuning of the controllers is based on pole-placement method as a desired multiple root of the characteristic closed loop equation. A stable second order transfer function is used as an example to validate the methodology. Furthermore, a biased relay experiment is combined with the proposed control design to bring an autotuning method. Matlab-Simulink examples are given to illustrate the developed approach.

Relay Feedback Autotuning – Implementation and Simulation

“…The formulas for the calculation of estimated parameters (1) are generally known and can be found e.g. [7], [8], [16], [17], various details for relay parameter identification are adopted from [23], [24].…”

“…the ring of stable and proper rational function RPS (e.g. [17], [20]), the ring of stable and proper meromorphic functions RMS, see [8], [19], [21].…”

“…The derived formulas for both estimated systems with or without Pade approximation were published several times, they can be found e.g. [7], [8], [16], [19], [21]. The formulas are incorporated in the program system.…”

“…During the period of three decades, many studies have been reported to extend and improve autotuners principles, see e.g. [5], [6], [8], [9].…”

Classification of Automatic Controllers Diagrams

“…diagrams 1 -4). In order to simplify this problem a special algorithm for automatic definition of numerical values of PID control law tuning parameters (PID autotune) [8] is proposed by manufacturers of PLCs.…”