# Benchmarking and Reasoning Distillation of Large Language Models for Feedback Controller Design in Complex Dynamical Systems

arXiv: https://arxiv.org/abs/2608.07004 · HTML: https://mlsanity.com/paper/2608.07004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 7 of 7)

- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra](https://mlsanity.com/paper/2404.03647/) (2024)
- [ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise](https://mlsanity.com/paper/2410.19811/) (2024)
- [Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs](https://mlsanity.com/paper/2509.16204/) (2025)
- [LLM-Agent-Controller: A Universal Multi-Agent Large Language Model System as a Control Engineer](https://mlsanity.com/paper/2505.19567/) (2025)
- [AgenticControl: An Automated Control Design Framework Using Large Language Models](https://mlsanity.com/paper/2506.19160/) (2025)
- [Cloud to Edge: Benchmarking LLM Inference On Hardware-Accelerated Single-Board Computers](https://mlsanity.com/paper/2604.24785/) (2026)

## Abstract (arXiv)

Although remarkable capabilities have been demonstrated by Large Language Models (LLMs) across scientific domains, feedback controller design remains underexplored. Existing benchmarks focus mainly on linear single-Degree-of-Freedom (DoF) systems and large API-hosted models, leaving performance on complex controller-design tasks and feasibility for edge deployment unclear. To address these limitations, we introduce the Complex Dynamics-to-Control Benchmark for Large Language Models (CoDyControlBench), comprising 132 system configurations across five evaluation dimensions: number of DoF, system type, coupling level, damping regime, and controller type. Six state-of-the-art LLMs were evaluated over three independent runs, including three commercial models (GPT, Gemini, and Claude) and three open-source models (GLM, DeepSeek, and Qwen). GPT achieved the highest design success rate at 94.8%, whereas Qwen showed the lowest rate at 50.0%. Across the benchmark dimensions, DoF and controller type exhibited the largest model-averaged variations in design success, with success-rate ranges of 36.3% and 17.6%, respectively, exceeding those associated with system type, coupling level, and damping regime. Comparison of GPT and Qwen showed that their performance gap arose mainly from the control-design knowledge, particularly gain selection and the use of transient-limiting mechanisms. For edge deployment, a specialized 1.5B-parameter model was developed through reasoning distillation. The reasoning-distilled model outperformed the answer-distilled and base model on CoDyControlBench, maintained stable performance across 1-6 DoFs, and achieved successful traget tracking in all three physical trials on a pneumatic-artificial-muscle-driven robotic arm. These results establish a benchmark baseline and highlight the potential of lightweight, edge-deployable controller-design models.