# Fixed-point Based Hierarchical MPC Control Design For a Cryogenic Refrigerator

## TL;DR

This paper introduces a fixed-point based hierarchical model predictive control framework for cryogenic refrigerators, enabling flexible, stable, and smooth control of interconnected thermodynamic cycles without redesigning local controllers.

## Contribution

It presents a novel hierarchical MPC scheme that handles destabilizing interconnections and allows easy behavior modifications by adjusting coordinator parameters.

## Key findings

- Successfully stabilizes cryogenic refrigerator cycles
- Allows behavior changes without local controller modifications
- Enables smooth operator handover

## Abstract

In this paper, a simple and general hierarchical control framework is proposed and validated through the interconnection of the Joule-Thompson and the Brayton cycle stages of a cryogenic refrigerator. The proposed framework enables to handle the case of destabilizing interconnections through state and/or control signals (which is the case of the cryogenic refrigerator example). Moreover, it offers the possibility to simply change the behavior of the overall system (depending on the context) by only changing the coordinator problem's parameters without changing the set of local controllers used by subsystems which is a common industrial requirement regarding industrial control architectures. Finally, the proposed scheme enables a smooth operator handover on a specific subsystem and/or actuator.