All classes PID & FOPID Metaheuristics Syllabus · Episode 6 of 6

Class PID & FOPID Metaheuristics #6: Robustness Test, Convergence Comparison, and Statistical Analysis

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Tutorial on statistical analysis and robustness test of PID vs FOPID results using Whale Optimization and Harris Hawks Python: Wilcoxon, boxplot, convergence. Episode 6, the closing part of the PID and FOPID metaheuristic optimization series.

Software: Python (NumPy, SciPy, Matplotlib)
Level: Advanced
Duration: ± 8 min
Series total: 52 min · 6 videos
Published: October 25, 2026

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Introduction

Here is the final result, 10 trials for each combination of controller and algorithm, statistical Wilcoxon test, convergence curves, and robustness test when generator parameters change. 4P2OA significantly outperforms and is 3 times more robust to plan changes. Let's start. Hello, welcome to the final episode of the PID and fractional order PID optimization series. Metaheuristics are random, so one trial might just be a lucky case. Scientific journals require several trials and statistical tests. In addition, the actual plan changes due to age and load, so the controller must be robust. Today we will test both.

Step 1: Ten experiments & Wilcoxon test

Create a file named robustness.py There are 4 cases, PID and FOPID, each with WOA and HHO. Each case is run 10 times with different SID. Then we record the final ITAI and its convergence curve. We print the mean, standard deviation, best, and worst values, then perform a Wilcoxon test to check if the differences are statistically significant. Run. PIDWOA is very consistent. Mean 0.0391 with a standard deviation of 0.0001. FOPID-WOA has a mean of 0.0180 and FOPID-HHO 0.0293. The P-Wilcoxon value of FOPID-WOA against PIDWOA is 0.00016 and against FOPID-HHO is 0.00088. Both are far below 0.05. So it is significant.

To Step 2: Robustness test & graphs

Next, the robustness test. We take the best PIDWOA and FOPID-WOA parameters from the previous JSON file, then change the exciter and generator time constant from 50 to 150 percent, and calculate ITAI under each condition without resetting the controller. Run. ITAI-PI increases from 0.039 to 0.1787 at 150 percent, with a range of 0.1397. ITAI-FOPI is at its worst only 0.0651, with a range of 0.0462, three times narrower. Let's look at the graphs. Boxplot shows the FOPID-WOA box much lower than PID, while FOPID-HHO is wider, indicating more inconsistency. The average convergence curve shows FOPID-WOA continuously decreasing until the last iteration. In the robustness test, the PI response changes drastically when the plant slows down, whereas the FOPI curve stabilizes and remains calm in a short time. This is the real advantage of FOPID. Two additional parameters provide flexibility to remain good even when the plant changes.

Done!

Done, and the series is also complete. We have built a complete research on controller tuning, DC motor function and AVR, Ziegler-Nichols, fractional order PID with ustaluk, objective function ETAI, whale optimization and Harris-Hawks from scratch, Optimization of PID and FOPID up to statistical analysis and robustness test. For further research try other algorithms such as Grey Wolf or Marine Predators multi-criteria objective function plan with time delay or implementation on microcontroller. Thank you for following this series. Currently working on a thesis dissertation or research in the field of control systems and optimization? Cerdas Inovasi Digital helps implement control systems from modeling DC motor and AVR generator PI tuning using Ziegler-Nichols fractional order PID up to meta-heuristic optimization such as whale optimization and Harris-Hawks as well as offering Python programming courses for electrical engineering. Want to master the entire series from alias functions up to statistical analysis and robustness test? All six episodes complete with PDF step-by-step guides and source code are available for premium tutorial subscribers. Subscribe starting at Rp69.000 per month save 28% with the 12-month package or one-time payment of Rp999.000 for lifetime access. Want just one class? Buy a single class with lifetime access. Subscribe now on the premium page at cerdasinovasidigital.com. Contact us via WhatsApp or visit cerdasinovasidigital.com. Thank you for watching, see you in the next episode.

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Transcript

0:03Introduction

0:50Step 1: Ten experiments & Wilcoxon test

3:20To Step 2: Robustness test & graphs

5:52Done!

Ask the class material

My notes

Questions & answers

Your instructor

Recommended classes for you

Need more than a video?

Transcript

0:03Introduction

0:50Step 1: Ten experiments & Wilcoxon test

3:20To Step 2: Robustness test & graphs

5:52Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Ten experiments & Wilcoxon test

To Step 2: Robustness test & graphs

Done!

Introduction

Step 1: Ten experiments & Wilcoxon test

To Step 2: Robustness test & graphs

Done!