Linear Time Invariant Approximations of Linear Time Periodic Systems for Integrated Flight and Vibration Control
Lopez, Mark Joseph Santos
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Recent developments in active rotor control have shown significant coupling between flight and vibration control systems which are traditionally designed independently. This coupling results in performance degradation of the vibration controller particularly during maneuvering flight. Thus, an integrated flight and rotor control design is desired to address coupling and improve performance. Due to the strong periodic nature of rotorcraft at higher forward speeds, accurate models for rotorcraft must take the form of linear time periodic (LTP) models which are inconvenient for control design and handling qualities evaluations. Instead, linear time invariant (LTI) model approximations are desired, as they provide a convenient and well understood framework for analysis, control design, and handling qualities assessments. While LTI approximations for LTP systems have been recently developed to include states to represent the vibrations of the rotor harmonics, the fidelity of such LTI systems has not been well validated. Furthermore, the current formulation of a full LTI state space approximation relies on an LTP system which is in second order form; this presents difficulties for degrees of freedom not explicitly in second order form such as body and inflow degrees of freedom. This work develops methodologies for assessing the fidelity of LTI approximations of LTP systems. Having a complete fidelity assessment, these LTI approximations are then used in the development and evaluation of a full flight envelope integrated flight and vibration reduction controller. This full flight envelope integrated controller is evaluated in a nonlinear simulation using realistic piloted maneuvers. Specifically, this work accomplishes the following: 1) Development of a generalized LTI approximation of first order LTP models. 2) Verification of the LTI approximation against the original nonlinear model. 3) Evaluation of the fidelity of LTI system dynamics compared to LTP system dynamics using modal participation. 4) Formulation of reduced order models based on modal participation. 5) Evaluation of input-output fidelity of reduced order models using additive uncertainty, nu-gap metric, and generalized stability margin techniques. 6) Design and analysis of a single fixed point vibration controller, integrated with a stabilized flight control system, that is assessed using realistic maneuvers. 7) Robustness evaluations of the fixed point controller, and 8) Further improvements using controller scheduling to create a full flight envelope controller. An example is given for each step using a UH-60A rotorcraft model in the context of development of an integrated flight and vibration controller.