abstract

• This article explores an innovative approach for fine-tuning Proportional-Integral (PI) controllers to achieve rapid and energy-efficient responses in linear time-delayed dynamical systems. The method synergistically combines a classical meta-heuristic algorithm with an analytical-geometric stability analysis procedure to minimise a cost function based on quadratic regulator principles. In particular, we employ the D-composition method to characterise the stability map of the closed-loop system, narrowing down the optimisation search space for a genetic algorithm. This holistic strategy not only effectively tackles the complexities introduced by time delays within the optimisation procedure, but also permits us to improve PI controls performance across diverse real-world applications. Furthermore, we include a comprehensive comparative analysis between our results and a PI control that is analytically engineered to elicit maximal exponential decay. The article culminates by showcasing both numerical simulations and experimental control applications, underscoring the practical efficacy of the proposed methodology. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

authors

• Cárdenas Galindo Juan Antonio
• Félix Ávila Liliana Margarita
• González Galván Emilio Jorge
• Méndez Barrios César Fernando Francisco

publication date

• 2024-01-01

keywords

• Controllers; Cost functions; Dynamical systems; Energy efficiency; Genetic algorithms; Heuristic algorithms; Heuristic methods; Time delay; Two term control systems; Energy efficient; Fine tuning; Geometric stability; Innovative approaches; Linear time; Meta-heuristics algorithms; Proportional integral controllers; Proportional-integral control; Time delayed; Time-delayed systems; Closed loop systems

Digital Object Identifier (DOI)

• 10.1007/978-3-031-54763-8_8

PubMed ID

start page

• 77

end page

• 88

volume

• 940 LNNS

issue