Modeling Lead-Lag Dynamics for Rotorcraft-Pilot-Couplings Investigation

Rotorcraft-pilot couplings (RPCs) involve vehicle destabilization due to active participation of the pilot in the control loop. RPCs, also known as 'pilot induced/assisted oscillations' (PIO/PAO), have been always a problem of concern for aircraft safety. Paradoxically, recent experiences learned that the RPCs on modern helicopters are much more difficult to predict and suppress than in the past. The problem is that the RPCs of modern rotorcraft are often associated with the higher frequency spectrum of rotor aeroelastic modes. The goal of the present paper is to develop an analytical helicopter body-flap-lag mathematical model and obtain insight into the response of the poorly damped lead-lag mode to cyclic control input excitations. It is known that such controls may result in pilot-induced body roll and pitch vibrations. It will be demonstrated that, for a hovering helicopter, both, the attitude and rate feedback controllers, destabilize primarily the regressing flap mode. While high gains in attitude feedback controller reduce the damping of regressing flap mode, high gains in rate feedback controller move the frequency of regressing flap mode closer to the frequency of the regressing lag mode and drive unstable the air resonance mode, i.e. a low frequency mode characterizing the coupling between the regressing lag and body roll/pitch motion. Soft-inplane rotors are the most susceptible to air resonance instabilities as their lag mode is weakly damped. The paper will demonstrate that the body roll mode tends to couple primarily with the flapping motion which in turn couples with the lag motion and can contribute to the destabilizing flap-roll coupling in an RPC event. For a hovering helicopter, the paper derives stability criteria and boundaries for the roll attitude feedback/roll rate feedback gains. These criteria can be used by the FCS and rotor designer to avoid RPCs.