Discrete-time realization of fractional-order proportional integral controller for a class of fractional-order system

Abstract

The approximation of the fractional-order controller (FOC) has already been recognized as a distinguished field of research in the literature of system and control. In this paper, a two-step design approach is presented to realize a fractional-order proportional integral controller (FOPI) for a class of fractional-order plant model. The design goals are based on some frequency domain specifications. The first stage of the work is focused on developing the pure continuous-time FOC, while the second stage actually realizes the FOPI controller in discrete-time representation. The presented approach is fundamentally dissimilar with respect to the conventional approaches of z -domain. In the process of realizing the FOC, the delta operator has been involved as a generating function due to its exclusive competency to unify the discrete-time system and its continuous-time counterpart at low sampling time limit. The well-known continued fraction expansion (CFE) method has been employed to approximate the FOPI controller in delta-domain. Simulation outcomes exhibit that the discrete-time FOPI controller merges to its continuous-time counterpart at the low sampling time limit. The robustness of the overall system is also investigated in delta-domain.

The Generalized Discrete Proportional Derivative and Its Applications

“…This exploration encompasses scenarios where the right-hand side incorporates a Caratheodory-type multivalued nonlinearity, extending the analysis to infinite intervals. Furthermore, [26] introduces a comprehensive two-step design approach aimed at implementing a fractional-order proportional integral controller tailored for a specific class of fractional-order plant models. Motivated by the preceding discussions and incentives, the principal objective of this paper is to delve into the concept of the GDPD.…”

Simulating two-dimensional optimal control problem of fractional partial differential equations

“…[16] presented an numerical method for solving a category of the integer order two-dimensional optimal control problems by using the Ritz method and the hybrid Legendre Block-Pulse functions. The study of the fractional-order system has attracted significant attention among the researchers and engineers [40,34,38,41,19]. So it makes a sense to study fractional type of two-dimensional optimal control problems.…”