Elyazar, Edrico Septian (2026) Optimasi Dinamis dan Analisis Ekonomi Produksi Bioetanol dari Nira Aren (Arenga Pinnata) dengan Fermentasi Fed-Batch menggunakan Prinsip Maksimum Pontryagin. Other thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Nira Aren (Arenga pinnata) merupakan bahan baku bioetanol berproduktivitas tinggi. Namun, karakteristik High Gravity dari nira segar (> 150 g/L) memicu inhibisi substrat pada ragi Saccharomyces cerevisiae, sehingga menurunkan efisiensi metode batch konvensional. Penelitian ini mengusulkan strategi fed-batch menggunakan Prinsip Maksimum Pontryagin (PMP) guna menentukan laju suplai substrat optimal (u∗(t)).
Tujuannya adalah memaksimalkan profit aktual dari perolehan massa bioetanol sekaligus meminimalkan biaya pengadaan nira aren. Model matematika dibangun berbasis neraca massa reaktor volume variabel dengan kinetika inhibisi Haldane-Levenspiel, lalu diselesaikan secara numerik menggunakan Forward-Backward Sweep Method (FBSM). Hasil simulasi membuktikan PMP menghasilkan hukum kontrol dinamis yang sangat adaptif. Perbandingan ekonomi dilakukan terhadap dua skenario batch: volume awal 18 L dan iso-volume 60 L. Pada harga bahan baku kompetitif (w2 = 10, tf = 32 jam), PMP meningkatkan profit aktual hingga 626,95% dibandingkan Batch 18 L dan 118,08% dibandingkan Batch 60 L. Pada harga nira yang ekstrem (w2 = 800), PMP secara adaptif menekan laju suplai namun tetap unggul hingga 313,20% di atas Batch 18 L. Akan tetapi, pada durasi panjang (tf ≥ 24 jam), kinerja PMP tersaturasi oleh batas volume reaktor (Vmax) dan inhibisi produk. Selain itu, selektivitas produk (SP/Z) terbukti konstan pada 11,26. Hal ini menegaskan bahwa PMP bekerja mengoptimalkan kuantitas pemrosesan makroskopis tanpa mengubah efisiensi metabolisme mikroskopis ragi.
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Sugar palm (Arenga pinnata) sap is a high-productivity bioethanol feedstock. However, the High Gravity characteristic of fresh sap (>150 g/L) induces substrate inhibition in the yeast Saccharomyces cerevisiae, thereby reducing the efficiency of conventional batch fermentation. This study proposes a fed-batch operational strategy using Pontryagin’s Maximum Principle (PMP) to determine the optimal substrate feeding rate (u ∗ (t)). The objective is to maximize actual profit from total bioethanol mass yield while minimizing the cost of sugar palm sap procurement. The mathematical model is constructed based on the mass balance of a variable-volume bioreactor with Haldane–Levenspiel inhibition kinetics, then solved numerically using the ForwardBackward Sweep Method (FBSM). Simulation results confirm that PMP produces a highly adaptive dynamic control law. Economic comparison was conducted against two batch scenarios: initial volume of 18 L and iso-volume of 60 L. At competitive feedstock prices (w2 = 10, tf = 32 hours), PMP increases actual profit by 626.95% over Batch 18 L and 118.08% over Batch 60 L. At extreme sap prices (w2 = 800), PMP adaptively suppresses the feed rate yet still outperforms Batch 18 L by 313.20%. However, for long durations (tf ≥ 24 hours), PMP performance is saturated by the reactor volume limit (Vmax) and product inhibition. Furthermore, the product selectivity (SP/Z) remains constant at 11.26 across all scenarios. This confirms that PMP optimizes macroscopic processing quantity without altering the yeast’s microscopic metabolic efficiency.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | Bioetanol, Fermentasi Fed-Batch, Inhibisi Substrat, Nira Aren, Prinsip Maksimum Pontryagin, Bioethanol, Fed-batch Fermentation, Substrate Inhibition, Sugar Palm Sap, Pontryagin’s Maximum Principle. |
| Subjects: | Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Edrico Septian Elyazar |
| Date Deposited: | 24 Jul 2026 03:32 |
| Last Modified: | 24 Jul 2026 03:42 |
| URI: | http://repository.its.ac.id/id/eprint/136720 |
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