This study extends previous work on analytical linearization of state-space vortex particle methods by incorporating viscous terms. The current framework integrates a panel method for modeling blade surfaces and near-wake, and a viscous vortex particle method (VVPM) to model the far-wake. The code is formulated as a system of ordinary differential equations, resulting in a nonlinear time-periodic (NLTP) system in first-order form. The NLTP dynamics are linearized to yield a linear time-periodic (LTP) representation using two approaches: finite differencing and a novel analytical linearization technique. Harmonic decomposition is then applied to approximate the LTP system as a higher order linear time-invariant model, where the LTP system coefficients become states of the time-invariant dynamics, facilitating time-invariant system analysis techniques. The proposed methodology is implemented in MATLAB (R) and applied to a generic utility helicopter rotor blade, with validation performed against experimental data and CFD. A study was conducted to assess the impact of including viscous effects on the wake structure when modeling ground effect. The accuracy of the linearized models is assessed through comparisons with the nonlinear system in both time and frequency domains. Results indicate that the linearized models effectively capture wake dynamics, particularly for low-mid frequency forcing inputs. Notably, the analytical linearization approach significantly reduces computational cost compared to finite-difference-based methods, achieving an efficiency improvement of O(n2), where n represents the number of system states. This establishes analytical linearization of VVPM as a viable tool for advancing rotorcraft flight dynamics modeling by balancing fidelity with computational efficiency.
This paper discusses the development of a flight dynamics model (or digital twin) of a compact and re-configurable coaxialpropeller-based micro air vehicle (MAY) in hovering, edgewise, and maneuvering flight using a hybrid physics-based plus data-driven approach. The MAY has a mass of 366 g (0.81 lb), and features a 52 mm (2.05 in) diameter cylindrical fuselage, foldable propellers, and a two-axis gimbal thrust-vectoring mechanism for pitch and roll control. The aircraft has been successfully launched from a pneumatic cannon and has achieved stable and controlled flight. A physics-based flight dynamics model of this novel MAY has been developed using the Rotorcraft Comprehensive Analysis System (RCAS). RCAS is able to predict the translational dynamics near hover reasonably well; however, the accuracy decreases for rotational dynamics in edgewise flight, resulting in significant differences between predicted dynamics and flight-test data, known as residual dynamics. The current hybrid model utilizes the residual dynamics via a data-driven approach to correct the physics-based model. Using the measured vehicle states and control inputs, a deep neural network was trained to learn the residual forces and torques. The resulting hybrid model reduced prediction errors by 55% on average compared to the RCAS model based on pure physics.
At present, the vast majority of control design work on winged eVTOLs focuses primarily on a specific flight regime, usually hover or cruise. Transition, however, is an equally critical flight regime that requires a combination of both rotorcraft and airplane control effectors to maintain trim and execute maneuvers. Full flight regime trim strategies are examined for a Lift+Cruise eVTOL aircraft. Control laws are designed for hover, transition, and cruise conditions to satisfy standard flying-qualities requirements based on the characteristic behavior of the vehicle (rotorcraft vs. fixed wing) while ensuring realistic motor limits (peak and continuous) are satisfied. CONDUIT (R) is used to optimize control laws to minimize actuator activity while meeting flying-qualities constraints. Variable-RPM control is shown to be sufficient to satisfy Level 1 flying-qualities requirements in hover and low-speed flight, where control surfaces have inadequate control authority. Time domain simulations are presented to verify controller performance and ensure actuator limits are not violated while following step commands. The aircraft is able to follow commands well in all axes and flight regimes. Successful simulation of transition through the full flight regime (hover-to-cruise and cruise-to-hover) is achieved using a quasi-linear parameter varying stitched model. It was found that elevator sizing and choice of transition speed are strongly linked, and that either a transition speed very near the cruise speed or a large elevator is warranted.
This study integrates extremum-seeking control (ESC) into the primary flight controller of an over-actuated coaxial-compound rotorcraft to reduce fuel consumption during trim and quasi-steady maneuvers. The control architecture includes an inner-loop attitude controller and an outer-loop controller for velocity and altitude. ESC exploits control redundancy by operating in the null space of the control effectiveness matrix along the longitudinal and vertical axes to optimize fuel flow without compromising primary flight objectives. In calm-air simulations, ESC achieved up to 11.6% fuel flow reduction in straight-and-level flight at 100 kt (representative of best endurance airspeed) and up to 4.5% reduction at 180 kt (higher speed trim condition). The controller reached the reduced fuel flow condition within 50 s after activation. Fuel flow reductions were largest for higher gross weights or under increased load factor, as in banked turn maneuvers. Under light-to-moderate turbulence, ESC continued to reduce fuel consumption, with a regularization function ensuring robust convergence and preventing instability due to rapid state fluctuations.
This article focuses on the integration of generalized rotor-on-rotor interactional aerodynamics models in state-variable form within flight dynamics simulations of multi-rotor unmanned aircraft systems, and on their subsequent linearization. The aircraft chosen for this investigation is a resupply coaxial quadcopter. Upon trimming the flight dynamics simulation in hover, linearized models of the dynamics are extracted. Models with and without interference are compared to isolate the role of interactional aerodynamics on this configuration. Model-order reduction methods are used to guide the development of linearized models that are tractable for flight control design while still capturing the effect of rotor-on-rotor interactions on the vehicle flight dynamics. Dynamic inversion based model-following flight control laws based on these reduced-order linearized models are developed and tested on the models with and without the interference. The results indicate that, for the coaxial quadcopter configuration studied, rotor-on-rotor interactions mostly affect trim (steady-state) predictions rather than the overall flight dynamics.
