PID tuning for chemical processes commonly relies on identified process models, whereas plant engineers often retune loops iteratively by observing responses, diagnosing deficiencies, adjusting gains, and validating the result. This work formalizes this engineer-like workflow in a language-model-assisted PID tuning framework applicable to both large and small language models (LLMs/SLMs). Hosted LLMs receive closed-loop response features, control-engineering diagnoses, tuning preferences, and internal model control (IMC)-based demonstrations to generate and iteratively correct PID gains under common acceptance criteria. For local deployment, Qwen3-0.6B is adapted through supervised fine-tuning (SFT) with simulation-verified IMC targets and physics-informed group relative policy optimization (PI-GRPO) with non-compensable stability and performance rewards. On 100 first-order plus dead time (FOPDT) and 100 second-order plus dead time (SOPDT) test cases, hosted LLMs (DeepSeek-V4-Flash and Qwen3.7-Plus) achieve final success rates of 75-89% and 77-79%, respectively. As for Qwen3-0.6B, supervised fine-tuning raises first-recommendation success to 86.5%, and PI-GRPO further increases it to 94.0%, primarily improving first-attempt reliability and stability margins.

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