We explore the usage of large language models (LLM) in human-in-the-loop human-in-the-plant cyber-physical systems (CPS) to translate a high-level prompt into a personalized plan of actions, and subsequently convert that plan into a grounded inference of sequential decision-making automated by a real-world CPS controller to achieve a control goal. We show that it is relatively straightforward to contextualize an LLM so it can generate domain-specific plans. However, these plans may be infeasible for the physical system to execute or the plan may be unsafe for human users. To address this, we propose CPS-LLM, an LLM retrained using an instruction tuning framework, which ensures that generated plans not only align with the physical system dynamics of the CPS but are also safe for human users. The CPS-LLM consists of two innovative components: a) a liquid time constant neural network-based physical dynamics coefficient estimator that can derive coefficients of dynamical models with some unmeasured state variables; b) the model coefficients are then used to train an LLM with prompts embodied with traces from the dynamical system and the corresponding model coefficients. We show that when the CPS-LLM is integrated with a contextualized chatbot such as BARD it can generate feasible and safe plans to manage external events such as meals for automated insulin delivery systems used by Type 1 Diabetes subjects.