Structure from Reasoning, Numbers from Search: On-Premise Open LLMs as Structural Priors for Coupled MIMO Controller Tuning

Open-source large language models running on-site can propose effective controller structures for tightly coupled industrial processes where classical tuning methods fail, according to a new study. The work finds that LLMs serve best not as optimizers but as sample-efficient structural priors that guide numerical refinement. The research, posted to arXiv on 9 June 2026, examines whether on-premise open-source LLMs can assist in tuning multi-input multi-output (MIMO) controllers, a task where decentralized classical auto-tuning ignores loop interaction and local numerical optimization frequently stalls in non-convex cost landscapes [1][2]. The authors test the approach on two benchmark systems: a single-loop continuous stirred-tank reactor (CSTR) and a strongly coupled quadruple-tank process with conflicting set-points [1]. On the simple CSTR, classical relay-feedback tuning achieves an integral absolute error (IAE) of 0.106, close to the optimum of 0.102, while the LLM tuner records an IAE of 0.162 [1][2]. The paper states that for single loops the LLM "adds nothing" [2]. The picture reverses on the quadruple-tank system, scored by a penalized cost J that combines tracking error with a penalty on actuator chattering. Naive relay tuning yields a J of approximately 28.6, naive LLM tuning reaches 29.7, and both perform no better than open-loop operation at 22.7 [1][2]. A local optimizer starting from balanced initializations fails in all ten attempts [1]. A scaffolded open LLM, however, reasons about the coupling and proposes a counter-intuitive asymmetric controller structure, reaching a J of roughly 16.9 with a standard deviation of 0.2 from any starting point [1][2]. Refining that structure with a classical optimizer attains the smooth global optimum of approximately 12.0 in ten out of ten runs, a configuration that includes a non-obvious negative integral correction that decentralized tuning cannot produce [1][2]. A global optimizer using differential evolution also reaches this optimum, so the LLM is not the only route [1]. The LLM's advantage lies in sample efficiency and interpretability: it delivers a usable controller in 18 evaluations, at which point the global optimizer remains worse than open loop, and it provides a stated rationale for its proposed structure [1][2]. The efficiency edge grows with problem dimension, reaching roughly six times fewer evaluations on a 3x3 plant [1][2]. The behavior generalizes across four open models, and on a benign plant the LLM offers no advantage, sharpening the boundary of where the technique is useful [1][2]. Large language models are machine learning systems with many parameters trained on vast text corpora for tasks such as language generation [8]. Several open-weight families exist, including DeepSeek, a Chinese company that released its R1 model in January 2025 under permissive licenses [7], and Qwen, developed by Alibaba Cloud and distributed under Apache 2.0 and other licenses [9]. The new study contributes a reproducible benchmark delimiting when open LLMs help in control tuning, characterizing them "not as optimizers, but as a sample-efficient, interpretable structural prior" [1][2].