A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction
Cheng, Rendy Po-Ren
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Helicopters can experience high vibration levels, which reduce passenger comfort and cause progressive damage to the aircraft structure and on-board equipment. Because the primary source of excitation is typically the main rotor, special rotor control systems have been proposed to reduce these vibrations at the source. This dissertation addresses one such system, generally known as ``Higher Harmonic Control" (HHC) because it consists of superimposing high frequency rotor inputs to the conventional low frequency ones used to control and maneuver the helicopter. Because both the primary flight control system and the HHC system act on the main rotor, the risk of adverse interactions between the two systems exists. This dissertation focuses on these interactions, which have never been studied before for the lack of suitable mathematical models. The key ingredient is an accurate linearized model of the helicopter, which includes the higher harmonic rotor response, and both the Automatic Flight Control System (AFCS) and the HHC system. Traditional linearization techniques lead to a system with periodic coefficients. Although Floquet theory can be used to study such periodic systems, there are far more control system design theories and software tools that are available for linear time-invariant systems than for periodic systems. Additionally, the theoretical evaluation of the handling qualities of the helicopter requires linear time-invariant systems. This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. On the other hand, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.