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. 2022 Jun 24;12:10769. doi: 10.1038/s41598-022-15087-9

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Depiction of the four phases of the pressure regulating process. During Phase 1, the air passage is fully closed, while we supply air from a constant high pressure source. In Phase 2, the user turns the control knob to displace the top cantilevers. As the top cantilever restoring force (F_T) increases, the air passage between the chambers remains closed. In Phase 3, when F_T surpasses a threshold value, the air passage opens. Finally, in Phase 4, the pressure in the low-pressure air chamber reaches the desired level set by the position of control knob and the passage will close. Once the pressure is set by the user, the device cycles between Phase 3 and Phase 4 to maintain the desired output pressure.