CDEQ Series: A Provably Stable Control Paradigm for Rotating Detonation Engines Based on Cross-System Topological Isomorphism and Five-Element Thermodynamic Invariance 基于跨系统拓扑同构与五元热力学不变性的旋转爆震发动机可证明稳定控制范式

CDEQ Series: A Provably Stable Control Paradigm for Rotating Detonation Engines

Based on Cross-System Topological Isomorphism and Five-Element Thermodynamic Invariance

中文:基于跨系统拓扑同构与五元热力学不变性的旋转爆震发动机可证明稳定控制范式

Trusted Timestamp: TSA-01-20260309590288827

Jiang Wenjia

Independent Researcher, Shenzhen, China

ORCID: 0009-0000-3850-7286

E-mail: jiangwenjiaszx@outlook.com

Abstract

Rotating Detonation Engines (RDEs) represent the next frontier in hypersonic propulsion, offering superior thermal efficiency through near-isochoric combustion. However, their engineering maturation is hindered by three critical bottlenecks: transient overpressure-induced structural failure, spontaneous detonation mode switching, and severe thermoacoustic coupling. Traditional approaches rely on high-fidelity computational fluid dynamics or model-based control, which cannot guarantee deterministic stability due to excessive model complexity and intrinsic time-scale mismatch.

This paper presents CDEQ Framework, a foundational control paradigm anchored in cross-system topological isomorphism and five-element thermodynamic completeness. By mapping the nonlinear dynamics of RDEs to the century-proven stable control framework of compression-ignition (diesel) engines, the proposed method bypasses detailed flow-field modeling and directly inherits mature control logic. The core innovation lies in the CDEQ Time Charter, which enforces strict time-scale separation under the dual principle of speed-governing-speed and slow-governing-fast.

To meet aerospace-grade safety requirements, a hardware-level heterogeneous sensing array is integrated, including high-frequency pressure sensing, laser non-intrusive detection, electromagnetic ion concentration monitoring, and high-frequency vibration measurement, supported by hardware cross-validation logic. The framework is stabilized by three core theorems: the PCTT-CW Five-Element Clockwise Topology, the CENHE-LEX Nine-Domain Central Equilibrium Constraints, and the GCVT-10 Ten-Step Convergence Criterion.

Implemented entirely in Q14 fixed-point arithmetic, the architecture is designed for field-programmable gate array (FPGA) deployment, enabling microsecond-level closed-loop operation compliant with SIL-4 and DO-178C Level A functional safety standards. This paper focuses on theoretical establishment, architectural design, and engineering verifiability, providing a complete, reproducible, and falsifiable framework for RDE stability control without claiming prototype testing or experimental validation.

Know more CDEQ, V-Function Waiting for you Now!

This framework is mathematically rigorous, formally grounded, and theoretically complete. It is NOT heuristic, empirical, or informal — it is built on solid mathematical foundations for deterministic stability and Lyapunov function construction.

KEY PAPER (Full Theory & Proofs):

A Flower's Smile, V-Functions Arise: Answering Lyapunov's Centennial Question

DOI: 10.5281/zenodo.18927653

A Paradigm Shift in Control Theory
CDEQ V1.2 The Countable Foundation of Stability
DOI: 10.5281/zenodo.18939385

CDEQ V1.3 Mathematical Proof of the PCTT-CW Penta-Cyclic Clockwise Topological Theorem
DOI: 10.5281/zenodo.18988669

CDEQ V1.4: Mathematical Proof of the CENHE-LEX Nonary Central Holding Equilibrium Theorem
DOI: 10.5281/zenodo. 19023440

CDEQ V1.5 GCVT-10 Global Convergence Validation Theorem
DOI: 10.5281/zenodo. 19055969

For the complete mathematical foundation, rigorous derivations, and general solution to Lyapunov's century-old problem — see the key paper above.