LoRA Fine-Tuned Models for Control Systems Course Q\&A: A Multidimensional Evaluation of Model Scale and Rank Effects

Abstract

Large language models (LLMs) are increasingly used in specialized university courses, but control-systems questions require coordinated terminology, notation, derivations, and stepwise explanations. Direct general-purpose responses may be inconsistently structured and hard to verify. Using exercises and reference solutions from a Linear Control Systems course, we built a supervised fine-tuning dataset of 360 system-user-assistant conversations. We applied LoRA to Qwen2.5-3B-Instruct and Qwen2.5-7B-Instruct. With identical data splits, inference settings, and evaluation protocols, we compared base and fine-tuned models and tested LoRA ranks r=4, 8, and 16. Evaluation used ROUGE, BERTScore, and structured-output features to measure reference-answer similarity and stability of the Solution-Method-Teaching Points format. LoRA improved both similarity and structured-output stability at both sizes. On the current test set, 7B-r16 achieved the highest ROUGE-L (0.4093) and BERTScore-F1 (0.8643), while r=8 offered a better balance between performance and parameter efficiency. Bootstrap resampling showed ROUGE-L gains of 0.0764 [0.0613, 0.0915] for 3B-r16 and 0.0874 [0.0687, 0.1042] for 7B-r16; both intervals exceeded zero, indicating stable textual-similarity improvements on the current test set. These results suggest LoRA can align open-source instruction-tuned models more closely with the language and pedagogical organization of course reference answers. However, the metrics mainly capture textual similarity and formatting consistency, not domain-specific reasoning or mathematical correctness, which require expert assessment and task-specific rubrics.