Multi-rotor with suspended load: System dynamics and control toolbox

There is an increasing demand for Unmanned Aerial Systems (UAS) to carry suspended loads as this can provide significant benefits to several applications in agriculture, law enforcement and construction. The load impact on the underlying system dynamics should not be neglected as significant feedback forces may be induced on the vehicle during certain flight manoeuvres. The constant variation in operating point induced by the slung load also causes conventional controllers to demand increased control effort. Much research has focused on standard multi-rotor position and attitude control with and without a slung load. However, predictive control schemes, such as Nonlinear Model Predictive Control (NMPC), have not yet been fully explored. To this end, we present a novel controller for safe and precise operation of multi-rotors with heavy slung load in three dimensions. The paper describes a System Dynamics and Control Simulation Toolbox for use with MATLAB/SIMULINK which includes a detailed simulation of the multi-rotor and slung load as well as a predictive controller to manage the nonlinear dynamics whilst accounting for system constraints. It is demonstrated that the controller simultaneously tracks specified waypoints and actively damps large slung load oscillations. A linear-quadratic regulator (LQR) is derived and control performance is compared. Results show the improved performance of the predictive controller for a larger flight envelope, including aggressive manoeuvres and large slung load displacements. The computational cost remains relatively small, amenable to practical implementations.

A highly efficient and consistent method for harvesting large volumes of high-titre lentiviral vectors

Lentiviral vectors pseudotyped with vesicular stomatitis virus glycoprotein (VSV-G) are emerging as the vectors of choice for in vitro and in vivo gene therapy studies. However, the current method for harvesting lentivectors relies upon ultracentrifugation at 50 000 g for 2 h. At this ultra-high speed, rotors currently in use generally have small volume capacity. Therefore, preparations of large volumes of high-titre vectors are time-consuming and laborious to perform. In the present study, viral vector supernatant harvests from vector-producing cells (VPCs) were pre-treated with various amounts of poly-L-lysine (PLL) and concentrated by low speed centrifugation. Optimal conditions were established when 0.005% of PLL (w/v) was added to vector supernatant harvests, followed by incubation for 30 min and centrifugation at 10 000 g for 2 h at 4 degreesC. Direct comparison with ultracentrifugation demonstrated that the new method consistently produced larger volumes (6 ml) of high-titre viral vector at 1 x 10(8) transduction unit (TU)/ml (from about 3000 ml of supernatant) in one round of concentration. Electron microscopic analysis showed that PLL/viral vector formed complexes, which probably facilitated easy precipitation at low-speed concentration (10 000 g), a speed which does not usually precipitate viral particles efficiently. Transfection of several cell lines in vitro and transduction in vivo in the liver with the lentivector/PLL complexes demonstrated efficient gene transfer without any significant signs of toxicity. These results suggest that the new method provides a convenient means for harvesting large volumes of high-titre lentivectors, facilitate gene therapy experiments in large animal or human gene therapy trials, in which large amounts of lentiviral vectors are a prerequisite.

Hingeless-rotor aeromechanical stability in axial and forward flight with wake dynamics

A finite-state wake model is used to investigate aeromechanical stability of hingeless-rotor helicopters in the ground-contact, hover and trimmed-night conditions. The investigation covers three items: (1) the convergence of the damping with increasing number of wake harmonics for the lag regressing, and body pitch and roll modes; (2) a parametric study of the damping over a range of thrust level, advance ratio and number of blades; and (3) correlations, primarily with the damping and frequency measurements of these lag and body modes. The convergence and parametric studies are conducted in the hover and trimmed-flight conditions; they include predictions from the widely used dynamic inflow model. The correlations are conducted in the ground-contact conditions and include predictions from the dynamic inflow and vortex models; recently, this vortex model is proposed for the axial-flight conditions and is used to investigate the coupled free vibrations of rotor flapping and body modes. The convergence and parametric studies show that a finite-state wake model that goes well beyond the dynamic inflow model is required for fairly converged damping, Moreover, the correlations from the finite-state wake, dynamic inflow and vortex models are generally satisfactory.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Helicopter blade flapping with and without small angle assumption in the presence of dynamic stall

The flapping equation for a rotating rigid helicopter blade is typically derived by considering (1)small flap angle, (2) small induced angle of attack and (3) linear aerodynamics. However, the use of nonlinear aerodynamics such as dynamic stall can make the assumptions of small angles suspect as shown in this paper. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived. A semi-empirical dynamic stall aerodynamics model (ONERA model) is used. Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are examined. It is shown that the small flapping assumption, and to a lesser extent, the small induced angle ofattack assumption, can lead to inaccurate predictions of the blade flap response in certain flight conditions for some rotors when nonlinear aerodynamics is considered. (C) 2010 Elsevier Inc. All rights reserved.

Parallel computing concepts and methods for floquet analysis of helicopter trim and stability

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive, Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors, The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated, For illustration, flap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-state three-dimensional wake model are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses, Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Propeller unsteady distortion noise

Turbulence, as naturally occurs in the atmosphere, is known to become highly anisotropic in the presence of the flow induced by a propeller. This turbulent distortion, caused by the streamtube contraction, significantly affects the tonal content of the radiated noise due to turbulence ingestion. We present here an analytic framework in which turbulent distortion may be assessed for any irrotational mean flow which approaches uniform axial flow far upstream. Sound spectra are presented for the case of two rotors in close proximity, for which the distortion is asymmetric. Quantities such as the turbulence spectrum at the rotor face and sound directivity then vary with azimuthal angle φ. © 2010 by Rosalyn A.V. Robison & N. Peake.

Laboratory-scale fluidized bed rig for high-temperature tube wastage studies

As part of a study of the wear of candidate heat exchanger tube materials for use in fluidized bed combustors, two similar laboratory-scale rigs have been built and characterized. Specimens of selected alloys are carried on counter-rotating rotors immersed in a fluidized bed, and are exposed to particle impact velocities of up to approximately 3 ms-1 at temperatures up to 1000°C. The performance of this design of apparatus has been investigated in detail. The effects of several experimental variables have been studied, including angle of particle impact, specimen speed, position of the rotor within the fluidized bed, duration of exposure, bed material particle size, degradation of the bed material, degree of fluidization of the bed, and size of specimen. In many cases the results obtained with steel specimens at elevated temperatures are similar to those observed with polymeric specimens at low temperatures.

A new synoptic survey of Northern Ireland lakes: sampling from the air

Northern Ireland has approximately 1670 lakes, which cover 4.4% of the land surface. However, most of the water area is accounted for by the large lakes such as Lough Neagh (385 km2) and Lower Lough Erne (109.5 km ). The majority of lakes are less than 100 hectares in area. They tend to be distributed towards the south and west of the Province, where extensive drumlin swarms are rich in small waterbodies. In 1988-1991, 610 of the 708 lakes between one and 100 hectares were sampled by the Northern Ireland Lake Survey. The objective was to assess their conservation status based on their aquatic macrophyte flora, but in addition to extensive plant surveys, the water of each lake was analysed for a range of chemical variables. This article reports on a full-scale survey carried out in early March 2002. The survey was taken with help of two helicopters. The authorise summarise the results of the chemical analysis of the survey.

Investigation of boundary layer development in a multistage LP turbine

This paper describes an investigation of the behavior of suction surface boundary layers in a modern multistage Low Pressure turbine. An array of eighteen surface-mounted hot-film anemometers was mounted on a stator blade of the third stage of a 4-stage machine. Data were obtained at Reynolds numbers between 0.9 × 105 and 1.8 × 105 and 1.8 × 105. At the majority of the test conditions, wakes from upstream rotors periodically initiated transition at about 40% surface length. In between these events, laminar separation occurred at about 75% surface length. It is inferred that the effect of the wakes on the performance of the bladerow is limited and that steady flow design methods should provide an adequate assessment of LP turbine performance during design.

Investigation of boundary layer development in a multistage LP turbine

This paper describes an investigation of the behavior of suction surface boundary layers in a modern multistage Low-Pressure turbine. An array of 18 surface-mounted hot-film anemometers was mounted on a stator blade of the third stage of a four-stage machine. Data were obtained at Reynolds numbers between 0.9 × 105 and 1.8 × 105. At the majority of the test conditions, wakes from upstream rotors periodically initiated transition at about 40 percent surface length. In between these events, laminar separation occurred at about 75 percent surface length. Because the wake-affected part of the flow appeared to be only intermittently turbulent, laminar separation also occurred at about 75 percent surface length while this flow was instantaneously laminar. At all but the lowest Reynolds numbers, the time-mean boundary layer appeared to have re-attached by the trailing edge even though it was not fully turbulent. It is inferred that the effect of the wakes on the performance of the blade row is limited and that steady flow design methods should provide an adequate assessment of LP turbine performance during design.

Performance of choked unsteady ejector-nozzles for use in pressure-gain combustors

If the conventional steady flow combustor of a gas turbine is replaced with a device which achieves a pressure gain during the combustion process then the thermal efficiency of the cycle is raised. All such 'Pressure Gain Combustors' (e.g. PDEs, pulse combustors or wave rotors) are inherently unsteady flow devices. For such a device to be practically installed in a gas turbine it is necessary to design a downstream row of turbine vanes which will both accept the combustors unsteady exit flow and deliver a flow which the turbine rotor can accept. The design requirements of such a vane are that its exit flow both retains the maximum time-mean stagnation pressure gain (the pressure gain produced by the combustor is not lost) and minimises the amplitude of unsteadiness (reduces unsteadiness entering the downstream rotor). In this paper the exit of the pressure gain combustor is simulated with a cold unsteady jet. The first stage vane is simulated by a one-dimensional choked ejector nozzle with no turning. The time-mean and rms stagnation pressure at nozzle exit is measured. A number of geometric configurations are investigated and it is shown that the optimal geometry both maximizes time mean stagnation pressure gain (75% of that in the exit of the unsteady jet) and minimizes the amplitude of unsteadiness (1/3 of that in the primary jet). The structure of the unsteady flow within the ejector nozzle is determined computationally. Copyright © 2009 by J Heffer and R Miller.