Integer and fractional-order model matching controller design algorithm with generalized reference model formulation for nonlinear time delay servo and regulatory problems: A real-time validation

Abstract

This article proposes a frequency domain-based approximate generalized time moment (AGTM)/approximate generalized Markov parameter (AGMP) matching approach to design integer and fractional-order controllers for servo and regulatory problems. Appropriate reference model selection, which is crucial in the model matching controller design method, is overcome by developing a novel generalized reference model formulation procedure that is applicable to servo and regulatory problems. The reference model formulation procedure is based on a linear quadratic regulator with an integral controller with the objective of infusing the desired performance requirements. AGTM/AGMP matching-based controller design approach is a two-stage process capable of handling time delay and saturation nonlinearity. In the first stage, the closed-loop system is equated with the reference model, which results in a synthesis equation for higher-order controller. In the second stage, a lower-order controller is designed based on the approximate matching of the lower-order controller with its higher-order counterpart at a set of real/complex/imaginary numbered expansion points in the s-plane. The competence of the proposed approach is explored by conducting simulations in both open-loop stable and unstable systems taken from the literature. Finally, experimental validation is performed on a real-time conical tank system for water level control and low-frequency oscillation damping in the Heffron–Phillips model, leveraging the Texas Instruments TMDSDOCK28379D experimenter kit to demonstrate the practical applicability of the proposed approach.