Abstract
This disclosure presents an integer-based spatial and phase control framework (HVE) designed for embedded systems and actuators. The method replaces conventional floating-point arithmetic and 360-degree metrics with a base resolution of L = 27720. This metric, being the Least Common Multiple (LCM) of integers 1 through 12, guarantees exact integer division for complex mechanical gear ratios and spatial subdivisions.
The framework eliminates progressive floating-point phase drift and provides a computationally lightweight, pure-integer control law suitable for resource-constrained microcontrollers. The mathematical principle is inherently scalable to higher-precision systems (32/64-bit) for cross-disciplinary applications, including Magnetic Resonance Imaging (MRI) spatial encoding, non-invasive neuromodulation (temporal interference), plasma confinement in stellarators, and telecommunications.
The complete C implementation, LUT generators, and documentation are available as open-source prior art at: https://github.com/alexlozovoj1977-cmd/HVE-Phase-Controller. DOI: 10.5281/zenodo.19443378.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Lozovyi, Olexandr, "Harmonic Vector Equilibrium: A Unified Integer-Based Framework for Control, Navigation, and Communication on the Cuboctahedral Matrix", Technical Disclosure Commons, ()
https://www.tdcommons.org/dpubs_series/9736