A General Theory for Piloted and UAS Handling Qualities and Control

Abstract:
The Pilot-selected Group Delay Ratio (P-GDR) heuristic is proposed, where the pilot enforces an optimal group delay ratio between the open and closed loop phase slopes at the closed loop dominant frequency. Capturing the slope of the phase at the most critical frequency (the dominant mode frequency), GDR-based control allows the pilot-in-loop system with a damping of 0.2 to mimic the stability and signal latency of an optimally damped second order system. UAS design could also benefit from the simplicity and efficiency of GDR control. A Unified Normative HQR (UN-HQR) methodology is proposed, which computes two components of HQRs: 1) HQRα, reflecting the cost of oscillation through decay rate, and 2) HQRe, reflecting the cost arising from tracking error. This paper demonstrates that ADS-33’s phase delay and bandwidth serve as proxies for the mathematical inverses of closed-loop stability (decay rate) and task performance. While legacy criteria track these symptoms, the pilot’s internal regulation targets the end-state goals of stability and energy. By mapping handling quality requirements directly to decay rate and RMS error, the UN-HQR framework aligns with the pilot's linear sensing of these parameters. The resulting linear relationships between HQRα and decay rate, and between HQRe and RMS error, allow the UN-HQR methodology to replace complex, task-specific geometries with simple, universal orthogonal boundaries. By extension, the Disturbance Rejection Bandwidth (DRB) used in UAS criteria is shown to be a frequency-domain proxy for the system's inherent decay rate and its ability to minimize error energy. The UN-HQR framework replaces this proxy with direct axes of decay rate and normalized RMS error, providing a universal, linear standard for UAS mission success that remains invariant to vehicle scale or disturbance intensity. Integrating P-GDR with a pilot model produced closed-loop frequency response predictions that aligned well with preliminary pilot-in-loop tracking data. Notably, P-GDR control is shown to naturally satisfy the Crossover Model without requiring explicit slope constraints, suggesting that the classic -20 dB/decade slope is an outcome of the pilot's GDR-based stability regulation. Together, P-GDR and UN-HQR predicted PIORs and HQRs that closely matched pilot ratings for a flight study and a VMS simulation study. A general procedure for applying P-GDR and UN-HQR to piloted and UAS handling qualities specification is presented.

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