A pressure regulating system that is suited to regulate the pressure of a gas includes a regulating device suited to regulate the pressure of a first gas stream, provided with an inlet for the gas at a supply pressure and with an outlet for the gas at a regulated pressure that is lower than the supply pressure; a vortex tube suited to receive a gas stream through an inlet, separate it into a hot portion and a cold portion and deliver the hot and cold portions through corresponding outlets; a heat exchanger coupled with the vortex tube in order to heat the first gas stream before it flows into the regulating device; a recovery duct suited to collect a first portion of the first gas stream at a collection point located downstream of the heat exchanger and to convey it to the inlet of the vortex tube.