A Novel Fractional‐Order Predictive PI Controller Approach for the Systems With Noninteger Order Delay
Bibliographic record
Abstract
ABSTRACT Time delay (TD) is a common phenomenon in practical systems. Most studies have focused on the classical notion of integer‐order TD. However, it should not be neglected that the delay can also be noninteger. The number of studies on such systems is quite limited due to the complexity of the mathematical analysis. Addressing this gap, this study introduces a novel fractional‐order TD (FOTD) based fractional‐order predictive proportional‐integral (FOPPI) controller, specifically designed for noninteger order delayed systems. Two distinct systems, the first‐order and integrator distributed parameter system (DPS) are considered in the study. The parameters of the proposed FOPPI controller are optimized using the jellyfish search optimization (JSO) algorithm to minimize the time‐weighted integral of absolute error (ITAE) criteria. The performance of the FOPPI controller is compared with optimized PI, fractional‐order PI (FOPI), and integer‐order predictive PI (PPI) controllers. In the study, performance tests such as time domain analysis, limited control signal performance, disturbance rejection at the input and output of the plant under noise, system parameter uncertainty, and frequency response analysis are used to comprehensively investigate the functionality of the controllers. The obtained results show that the time and frequency domain performance of the FOPPI controller is superior to FOPI, PPI, and PI controllers. The findings demonstrate that enhancements in the objective function of up to 62% for the first‐order and up to 80% for the integrator DPS models are attained through the comparative controllers. The FOPPI controller exhibits remarkable robustness and control effort, providing a highly effective choice for uncertain control applications with systems having FOTD.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".