Respiratory pressure treatment apparatus include automated methodologies for controlling modulation of pressure during an inspiratory phase or an expiratory phase of patient respiration. The changes in pressure result in various pressure waveforms that may be suitable for treating patients suffering from respiratory insufficiency such as Chronic Obstructive Pulmonary Disease. In example embodiments, a pressure rise or pressure increase may be controlled during a period of patient expiration by implementation of linear, cubic and/or quartic functions that serve as control parameters in a processor that controls a flow generator. One or more of the functions may optionally serve as a control parameter to control the pressure increase during an expiration period and a following decrease during the period of expiration. In some embodiments, such functions may further control a decrease in pressure during a period of patient inspiration, such as a decrease prior to mid-inspiration.
