This paper introduces a novel approach to integrating large language model (LLM) agents into automated production systems, aimed at enhancing task automation and flexibility. We organize production operations within a hierarchical framework based on the automation pyramid. Atomic operation functionalities are modeled as microservices, which are executed through interface invocation within a dedicated digital twin system. This allows for a scalable and flexible foundation for orchestrating production processes. In this digital twin system, low-level, hardware-specific data is semantically enriched and made interpretable for LLMs for production planning and control tasks. Large language model agents are systematically prompted to interpret these production-specific data and knowledge. Upon receiving a user request or identifying a triggering event, the LLM agents generate a process plan. This plan is then decomposed into a series of atomic operations, executed as microservices within the real-world automation system. We implement this overall approach on an automated modular production facility at our laboratory, demonstrating how the LLMs can handle production planning and control tasks through a concrete case study. This results in an intuitive production facility with higher levels of task automation and flexibility. Finally, we reveal the several limitations in realizing the full potential of the large language models in autonomous systems and point out promising benefits. Demos of this series of ongoing research series can be accessed at: https://github.com/YuchenXia/GPT4IndustrialAutomation