Analysis of high-fidelity reduced-order linearized time-invariant helicopter models for integrated flight and on-blade control applications

Abstract

Linearized time-periodic models are extracted from a high fidelity comprehensive nonlinear helicopter model at a low-speed descending flight as well as a cruise condition. A Fourier expansion based model reduction method is used to generate linearized time-invariant models from the time-periodic system. The linearized models, intended for studies examining the interaction between on-blade control and the primary flight control system, are very large in size with a few thousand states each. Therefore, a truncation method based on Hankel singular values is used to reduce the size of the LTI models. The reduced-order LTI models are then verified against the nonlinear model by comparing the hub load responses to an open-loop flap deflection. However, on-blade control is usually implemented in closed-loop mode, therefore, the reduced-order LTI models are verified for closed-loop performance fidelity. The higher harmonic controller is used with the 2/rev-5/rev harmonic components of the flap deflection as the control input and vibratory hub loads are the output. Closed-loop performance of the full-order LTI model, reduced-order LTI model, and the nonlinear model is compared at both the low-speed descending flight and the cruise flight conditions. The flap deflection histories and the vibratory loads predicted using the full-order and the reduced-order LTI models agree very well at both flight conditions when the flap deflection is limited to be less than 20. The results show that the reduced-order LTI models capture all the relevant dynamics and are suitable for studying closed-loop on-blade vibration control and its interactions with the primary flight control system, as long as the dynamic stall effects are not significant.