One of the recent developments in physical reservoir computing, which uses the complex dynamics of a physical system as a computational resource, is the use of a pneumatic pipeline system as a computational resource. This uses the dynamics of air for computation, and because it is lightweight and power-saving, it is used for gait-assist control using a soft exoskeleton with pneumatic rubber artificial muscles. In this study, we verified that by feeding back the estimated information to a pneumatic pipeline system, the pneumatic physical reservoir computing can generate periodic pressure changes as a stable limit cycle, such as those seen in walking. A pneumatic reservoir with feedback loops was modeled to generate limit cycles in the simulation, and it was confirmed that the system could generate limit cycles with high accuracy even from initial positions far from the target limit cycle. This system is expected to be applied to assist walking movements with a soft exoskeleton with a lightweight computational device.