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Introduction <p>Time-Delay Systems (TDS) frequently arise in engineering and biological applications, where inherent delays often impair stability and degrade overall system performance. Conventional Proportional–Integral–Derivative (PID) controllers, although widely adopted, typically struggle to manage nonlinear and delayed dynamics effectively.</p> Purpose <p>This study aimed to develop an enhanced control strategy capable of improving stability, reducing error rates, and optimizing performance in nonlinear TDS. To achieve this, a hybrid Proportional–Integral–Derivative–Acceleration (PIDA) controller framework was introduced.</p> Methods <p>The proposed method combined the Gazelle Optimization Algorithm (GOA) with a Complex-Value Spatio-Temporal Graph Convolutional Neural Network (CVSTGCNN), forming the hybrid GOA-CVSTGCNN approach. In this framework, GOA was used to optimize the gain parameters of the PIDA controller, while CVSTGCNN predicted controller parameters for improved adaptability in nonlinear delayed environments. The algorithm was implemented in MATLAB and benchmarked against established methods, including the Butterfly Optimization Algorithm (BOA), Deep Supply–Demand Optimization Algorithm (SDOA), and the Constrained Genetic Algorithm (CGA).</p> Results <p>The GOA-CVSTGCNN approach achieved a significant reduction in error, recording an error rate of 0.03%, outperforming BOA (0.05%), SDOA (0.07%), and CGA (0.09%). The hybrid strategy efficiently tuned PIDA gains and delivered superior control performance in higher-order nonlinear time-delay systems, with reduced computational complexity and minimized delay effects.</p> Conclusions <p>The proposed GOA-CVSTGCNN hybrid controller demonstrated powerful optimization and prediction capabilities, enabling robust performance enhancement in nonlinear TDS. The method effectively improved stability, reduced error, and addressed limitations found in traditional PID-based control strategies. This structured approach provided a promising pathway for advancing intelligent control design in delayed and nonlinear dynamic systems.</p>

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Optimized Nonlinear Time Delay System using Hybrid GOA-CVSTGCN Approach with Proportional Integral Derivative Controllers

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Arulvadivu. J,
  • S Giriprasad,
  • Manoharan. S,
  • S Gokul

摘要

Introduction

Time-Delay Systems (TDS) frequently arise in engineering and biological applications, where inherent delays often impair stability and degrade overall system performance. Conventional Proportional–Integral–Derivative (PID) controllers, although widely adopted, typically struggle to manage nonlinear and delayed dynamics effectively.

Purpose

This study aimed to develop an enhanced control strategy capable of improving stability, reducing error rates, and optimizing performance in nonlinear TDS. To achieve this, a hybrid Proportional–Integral–Derivative–Acceleration (PIDA) controller framework was introduced.

Methods

The proposed method combined the Gazelle Optimization Algorithm (GOA) with a Complex-Value Spatio-Temporal Graph Convolutional Neural Network (CVSTGCNN), forming the hybrid GOA-CVSTGCNN approach. In this framework, GOA was used to optimize the gain parameters of the PIDA controller, while CVSTGCNN predicted controller parameters for improved adaptability in nonlinear delayed environments. The algorithm was implemented in MATLAB and benchmarked against established methods, including the Butterfly Optimization Algorithm (BOA), Deep Supply–Demand Optimization Algorithm (SDOA), and the Constrained Genetic Algorithm (CGA).

Results

The GOA-CVSTGCNN approach achieved a significant reduction in error, recording an error rate of 0.03%, outperforming BOA (0.05%), SDOA (0.07%), and CGA (0.09%). The hybrid strategy efficiently tuned PIDA gains and delivered superior control performance in higher-order nonlinear time-delay systems, with reduced computational complexity and minimized delay effects.

Conclusions

The proposed GOA-CVSTGCNN hybrid controller demonstrated powerful optimization and prediction capabilities, enabling robust performance enhancement in nonlinear TDS. The method effectively improved stability, reduced error, and addressed limitations found in traditional PID-based control strategies. This structured approach provided a promising pathway for advancing intelligent control design in delayed and nonlinear dynamic systems.