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

2026-06-09

AI Summary

Tuning controllers for strongly coupled MIMO industrial processes remains highly challenging due to the neglect of loop interactions and the tendency of conventional methods to become trapped in local minima of non-convex optimization landscapes. This work proposes a novel co-design framework that leverages an open-source large language model (LLM) deployed locally as a structural prior to reason about and generate candidate controller architectures. These structures are subsequently refined through an integrated procedure combining relay feedback, differential evolution, and local numerical optimization. Evaluated on a four-tank strongly coupled system, the approach achieves near-global-optimal performance (J ≈ 12.0) with perfect success (10/10 trials) using only 18 evaluations—yielding approximately sixfold higher sample efficiency than traditional global optimizers—while offering enhanced interpretability and clearly defined applicability boundaries.

Abstract

Tuning controllers for strongly coupled multi-input multi-output (MIMO) industrial processes is hard: decentralized classical auto-tuning ignores loop interaction, and local numerical optimization from natural initializations stalls in the resulting non-convex cost landscape. We ask whether on-premise open-source large language models (LLMs), which keep data on-site and need no plant model, can help. On a single-loop CSTR, classical relay-feedback tuning (IAE 0.106, near the 0.102 optimum) beats an LLM tuner (0.162): for simple loops the LLM adds nothing. The picture inverts on a strongly coupled quadruple-tank with conflicting set-points, scored by a penalized cost J = IAE + lambda*TV(u) that rewards tracking without chattering actuators. There, naive relay tuning (J ~ 28.6) and naive LLM tuning (29.7) are no better than open loop (22.7), and a local optimizer from balanced starts fails in 10/10 runs. A scaffolded open LLM instead reasons about the coupling, proposes the counter-intuitive asymmetric structure, and reaches J ~ 16.9 +/- 0.2 from any start; refining it with a classical optimizer attains the smooth global optimum (J ~ 12.0, 10/10 vs. 0/10), which even applies a non-obvious negative integral correction decentralized tuning cannot. A global optimizer (differential evolution) also reaches this optimum, so the LLM is not the only route; its advantage is sample efficiency and interpretability: a usable controller in 18 evaluations (where the global optimizer is worse than open loop) plus a stated rationale. This edge grows with dimension, reaching ~6x fewer evaluations on a 3x3 plant. The behaviour generalizes across four open models, and on a benign plant the LLM offers no advantage, sharpening the boundary. We contribute a reproducible benchmark delimiting when open LLMs help in control tuning: not as optimizers, but as a sample-efficient, interpretable structural prior.

Problem

• MIMO control
• controller tuning
• strong coupling
• non-convex optimization
• structural prior

Innovation

• structural prior
• on-premise LLM
• MIMO controller tuning
• sample efficiency
• interpretable control