AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA025080034
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RESEARCH ARTICLE

Proportional integral derivative plus control for nonlinear discrete-time state-dependent parameter: Industrial applications

E. M. Shaban1,2*
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1 Department of Mechanical Engineering Technology, College of Applied Industrial Technology, Jazan University, Jazan, Saudi Arabia
2 On leave from Faculty of Engineering (Mataria), Helwan University, Cairo, Egypt
IJOCTA, 025080034 https://doi.org/10.36922/IJOCTA025080034
Received: 21 February 2025 | Revised: 20 March 2025 | Accepted: 11 April 2025 | Published online: 16 July 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

In modern industrial automation, control of nonlinear systems with complex dynamics poses significant challenges, especially when dealing with discrete time models that incorporate state-dependent parameters. Addressing this need, this paper explores the Proportional-integral-derivative-plus (PID+) control approach applied to nonlinear systems characterized by state-dependent parameter (SDP) discrete-time models. Two industrial applications are demonstrated as follows: a bitumen tank system and a reeling/packing machine used in a bitumen membrane sheet production line. Both systems are modeled using discrete-time transfer functions with SDP structures. The present work extends the novel SDP-PID+ approach by formulating its control algorithms and integrating additional proportional and input compensators. This enhancement enables effective and intuitive handling of processes characterized by discrete-time transfer functions with any order and sampling time delay. The approach enables a straightforward implementation of the SDP-PID+ algorithm across two distinct industrial applications, considering their varying response times. The approach reduces the time required to design the SDP-PID+ method for the selected applications while also demonstrating enhanced robustness and performance. It effectively mitigates disturbances and accommodates nonlinearities, higher-order dynamics, and delays.

Keywords
Proportional-integral-derivative control
State-dependent parameter models
Non-minimal state space
State variable feedback
Funding
None.
Conflict of interest
The author has no relevant financial or nonfinancial interests to disclose.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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