Centralized model matching integer/fractional-order controller design for multivariable processes with real-time validation

Abstract

This paper proposes a novel approach to design a centralized model matching integer/fractional-order (FO) controller for multivariable processes. As a first step, for a linear time-delay process, a desired closed-loop reference model is formulated with the inclusion of a linear quadratic regulator with integral controller. The reference model is formulated with the objective of embodying the desired closed-loop specifications. The second step involves equating the closed-loop system with the reference model, leading to a synthesis equation that yields a higher-order controller. In the third step, the lower-order approximant of the controller is obtained by matching a set of approximate generalized time moments/approximate generalized Markov parameters of the higher-order controller to that of its lower-order approximate at a few expansion points in the s-plane. The selection of an optimal set of expansion points is formulated in an optimization problem frame with the aim of minimizing the area between responses of the desired and designed closed-loop systems, keeping the stability of the designed closed-loop system as a constraint. The efficacy of the proposed approach is illustrated by the design of different controllers for time-delay-dominated nonsquare process and FO square process. Comparative analysis is carried out using time-domain performance indices by introducing parameter uncertainty and disturbance signals. To demonstrate the applicability of the proposed method, a real-time investigation is carried out with the design and implementation of a controller for interacting hybrid (conical and spherical) tank process setup.