Ranjith M

The flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces - aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.

Lift increment in a pitching and flapping rotor due to stall delay and vortex shedding is investigated. The unsteady aerodynamics and dynamic stall effects on a pitching airfoil section is modeled using Peters-He and Leishman-Beddoes models. Correlation with experimental results, available in literature, is also presented. Effect of frequency and amplitude of pitching and flapping inputs on the performance, specifically, coefficient of thrust is investigated. In addition, the effect of mean angle on lift augmentation is also studied. The correlation brings out clearly the strengths of Peters-He and Leishman-Beddoes model in capturing the aerodynamic environment of rotating blade with a prescribed motion. The unsteady motions imparted onto the blade through pitch and flap prescribed motion shows promise as lift augmentation strategies.

Numerical solutions of flatness-based reformulation of optimal control problems lead to an optimization problem with fewer variables and constraints. However, the expressions for the states and controls in terms of the flat output variables can be highly nonlinear and complicated. Hence, this may lead to expensive function evaluations within the optimization problem, degradation of convexity, and issues with convergence. Thus, a flatness-based reformulation of the optimal control problems may not be a viable alternative for computational guidance and control. Alternatively, a novel flatness-based reduced Hessian sequential quadratic programming algorithm is developed in this paper to solve optimization problems for a six-degree-of-freedom aircraft. An analytical null space basis is derived from the linearized differential constraints, which leads to a reduced-dimensional quadratic program with the discretized flat outputs as decision variables. Unlike flatness-based reformulation of the optimal control problem, the null space/ reduced Hessian method does not introduce additional nonlinearity and preserves the convexity of the optimization problem. A nonlinear model predictive control problem is solved to demonstrate the reduced Hessian algorithm. The algorithm is validated and Monte Carlo trials are performed to assess the effectiveness of the approach. Computational studies show that the current approach is faster than methods that directly exploit sparsity up to a factor of five.

Dynamic soaring is the rationale behind the prolonged flights of a seabird Albatross. It involves utilization of energy from the wind shear present near the earth surface. Small unmanned aerial vehicles (UAVs) can be kept loitering without any external power input by dynamic soaring. In this work, dynamic soaring is used to power UAVs for the surveillance application. A set of 6-DoF point mass equations governing the aircraft motion is used in the optimal control problem formulation. Appropriate constraints considering the material properties of a UAV, and the loiter pattern of dynamic soaring, are imposed on state variables and control parameters. Trajectories are optimized by using GPOPS-II, MATLAB based optimal control software. The problem is optimized for the efficacy of area under surveillance. Variation in the surveillance area is analyzed with the change in the view angle of camera, wind strength, and nature of wind shear profile. Surveillance by dynamic soaring becomes effective with the increase of wind strength and also with the change of wind shear profile towards the logarithmic variation. The minimum requirement of wind strength to perform dynamic soaring has been identified by considering various wind shear profiles. Finally it is concluded that small UAVs (comparable with the size of Albatross) can be constantly kept on surveying using wind energy as the sole power source, as long as free stream wind velocity is greater than the minimum requirement for dynamic soaring.

This paper addresses how dynamic inflow, while improving the correlation with ground-resonance measurements, could make the mode identification of the rotor-body-inflow system demanding. Specifically, the paper demonstrates dynamic inflow effects on the modes of two earlier tested configurations: configuration 1 with a nonmatched stiffness rotor (nonrotating flap and lag stiffnesses are unequal) and configuration 4 with a matched stiffness rotor (these stiffnesses are equal). The experimental model represents a three-bladed hingeless rotor on gimbal support; the blades are rigid, and they have spring-restrained flap-lag hinges; and the gimbal permits roll and pitch motions. The mode identification is based on relative participation of different states in the eigenvector, modal frequency and phase information about these states. For configuration 4, for instance, one of the modes has dominant contributions from multiblade flap cosine and sine states and appreciable contributions from body roll and pitch states and also first harmonic wake states; this mode is identified as the regressive flap mode (RFM), and another mode with fairly comparable characteristics is identified as the inflow mode. The phase differences between these flap states, and between these wake states, are used to distinguish RFM from the inflow mode. The phase information that is exercised herein represents a novelty of this work.

The rotary-wing analogue of fixed-wing soaring is illustrated in this work. Periodic energy-neutral trajectories for a rotorcraft where energy is harvested from a spatially varying (de-terministic) wind field is computed as solution to an optimal control problem. The extracted energy aids in countering the losses due to drag on the rotor and fuselage. We illustrate that an updraft component in the wind field is necessary for enabling periodic motion. For this reason, thermal columns provide an ideal setting for such manoeuvres, while the wind field typically considered for fixed-wing dynamic soaring is inadequate. A non-spinning frame formulation, inspired by a six-degrees-of-freedom (6DoF) boomerang model is adopted for developing the equations of motion of the rotorcraft. Optimal periodic trajectories within a Gaussian thermal model are obtained by considering collective, cyclic and linear twist inputs for the rotor blades.

A good understanding of rotor noise mechanisms, such as blade-vortex, rotor-turbulence and rotor-wake interactions, is essential in order to devise strategies to control them and help in complying with noise regulations. In this paper, the effects of aerodynamic interactions between rotors on acoustics will be investigated. A quick but relatively accurate computation of main rotor-tail rotor as well as coaxial rotors interactions and the resulting unsteady loads that lead to strong acoustic emissions would be useful in developing optimum designs for rotor blades with low noise generating characteristics. The strategy is to utilize finite state wake models to capture the effects of unsteady aerodynamics that are computationally less intensive compared to CFD or free wake methods. The flow-fields above and below the rotor are computed using an extended form of Peters-Morillo model. The Ffowcs Williams-Hawkings equation is used to determine the acoustic field. Acoustic predictions for a coaxial rotor system and for a main rotortail rotor configuration with the incorporation of rotor-wake interaction effects are presented. These results are compared with the acoustic signatures obtained for the case of non-interacting rotors. The total noise for the aerodynamically interacting coaxial rotor system is found to be higher by 2-3 dB compared to the aerodynamically non-interacting coaxial rotor system. A similar analysis is done for noise levels of tail rotor which also predicts an increase in SPL by about 2 dB with the inclusion of interaction effects.

The development, validation, and applications of an object-oriented free-wake solver for multi-rotor and fixed-wing systems are outlined here. Advantages of utilizing the object-oriented philosophy for modeling the multi-rotor/wing free-wake problem are described. To explore the feasibility of utilizing conventional desktop workstations, the vortex lattice methodology's time complexity is examined as an evolving n-body problem and the advantage gained from employing wake roll up models is demonstrated. Modifications in typical formulae to leverage features of multi-core systems and improvements in computational performance obtained from these modifications are illustrated using a roofline analysis. The free-wake solver incorporating these optimizations is then employed—after extensive validation—to simulate a distributed propulsion aircraft and a multi-rotor urban mobility vehicle. The paper also proposes a novel lattice skew parameter for monitoring instabilities in wake solutions commonly observed in rotorcraft free-wake analysis.

Dynamic inflow effects on stability and modes of a coupled rotor-fuselage system are investigated. Dynamic inflow effects are incorporated using Peters-He model. Characteristics of different modes associated with a coupled rotor-fuselage system are investigated. In addition to the magnitude of the states in the eigenvector (periodic eigenvector in general), phases of the states are also used to characterize the modes. From this approach, the effect of wake on different modes is demonstrated for two earlier tested configurations under ground-contact conditions. The ambiguity in naming a mode (due to participation of different states) is resolved from the relative phases of the relevant states.

A well-known phenomenon in rotorcraft, the ground effect, occurs when a rotor is at close proximity to the ground creating an obstruction to the trailing wake from the rotor. This results in an increase in thrust and a decreased inflow through the rotor disk, in turn affecting handling qualities. Until recently, analytical modelling of ground effect involved using empirical factors or method of images to account for the variation in thrust as a function of the elevation. The Morillo-Peters dynamic inflow model has now been known to satisfactorily predict the variations in rotor thrust for a rotor in ground effect. Although the variation in thrust seem to agree with empirical formulations, the model needs to be evaluated with experimental or computational simulations by comparing the variation of inflow over the rotor disk. An investigation on how closely the model predicts the inflow distribution is beneficial to future developments, considering the possibility of extending the model to other dynamic environments involving ground effect. This paper draws a comparison between the inflow models of Morillo, Ke Yu and Peters, Nowak and He, and a CFD package, RotCFD, for a hovering rotor in ground effect.