What does this research mean for the field?

The Proportional-Integral-Retarded (PIR) controller significantly improves response speed and reduces integral square error in heat diffusion systems compared to traditional PID and fuzzy-PID controllers. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Develop, analyze, and evaluate the stability and dynamic performance of a derivative-free proportional-integral-retarded (PIR) controller designed for heat diffusion systems.

August 23, 2026AlgorithmsOpen Access

Stability Analysis and Assessment of a Proportional-Integral-Retarded Controller Designed for the Heat Diffusion System

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Authors

YSYamama A. ShafeekUniversity of Technology - Iraq AHAmjad J. HumaidiUniversity of Technology - Iraq

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Implication

Control system analysis demonstrates enhanced stability and faster response with proportional-integral-retarded control in heat diffusion systems, indicating superior thermal regulation.

Key Points

Develop, analyze, and evaluate the stability and dynamic performance of a derivative-free proportional-integral-retarded (PIR) controller designed for heat diffusion systems.
Designed a PIR controller utilizing an intentional retarded term to avoid derivative noise amplification and provide oscillation damping in time-delay systems.
Mapped parameter stability regions using stability boundary loci analysis.
Evaluated dynamic performance against traditional PID and fuzzy-PID controllers under a +18 °C step input and external disturbance.
PIR control reduced settling time by 77.082% compared to standard PID and by 74.992% compared to fuzzy-PID controllers during a +18 °C step input.
Integral square error was reduced by 54.15% with the PIR controller relative to the conventional PID system.
Peak response deviation under an +18 °C disturbance was 0.167 °C lower in the PIR system than in the PID control system.

Cite This Study

Shafeek et al. (2026) studied this question.

synapsesocial.com/papers/6a8aae5c7677a341144476a5 https://doi.org/10.3390/a19080701

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Implication

Control system analysis demonstrates enhanced stability and faster response with proportional-integral-retarded control in heat diffusion systems, indicating superior thermal regulation.

Stability Analysis and Assessment of a Proportional-Integral-Retarded Controller Designed for the Heat Diffusion System

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Key Points

Cite This Study

Stability Analysis and Assessment of a Proportional-Integral-Retarded Controller Designed for the Heat Diffusion System

Discussion

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Implication

Key Points

Cite This Study

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