Sliding Mode Control-Based Autopilots for Leaderless Consensus of Unmanned Aerial Vehicles

In this brief, decentralized sliding mode controllers that enable a connected and leaderless swarm of unmanned aerial vehicles (UAVs) to reach a consensus in altitude and heading angle are presented. In addition, sliding mode control-based autopilot designs to control those states for which consensus is not required are also presented. By equipping each UAV with this combination of controllers, it can autonomously decide on being a member of the swarm or fly independently. The controllers are designed using a coupled nonlinear dynamic model, derived for the YF-22 aircraft, where the aerodynamic forces and moments are linear functions of the states and inputs.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Experiments and Lagrangian simulations on the formation of droplets in continuous mode

Experimental and computational studies on the dynamics of millimeter-scale cylindrical liquid jets are presented. The influences of the modulation amplitude and the nozzle geometry on jet behavior have been considered. Laser Doppler anemometry (LDA) was used in order to extract the velocity field of a jet along its length, and to determine the velocity modulation amplitude. Jet shapes and breakup dynamics were observed via shadowgraph imaging. Aqueous solutions of glycerol were used for these experiments. Results were compared with Lagrangian finite-element simulations with good quantitative agreement. © 2011 The American Physical Society.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Experiments and Lagrangian simulations on the formation of droplets in drop-on-demand mode

The creation and evolution of millimeter-sized droplets of a Newtonian liquid generated on demand by the action of pressure pulses were studied experimentally and simulated numerically. The velocity response within a model, large-scale printhead was recorded by laser Doppler anemometry, and the waveform was used in Lagrangian finite-element simulations as an input. Droplet shapes and positions were observed by shadowgraphy and compared with their numerically obtained analogues. © 2011 American Physical Society.

Concentrated-Mass Cantilever Enhances Multiple Harmonics In Tapping-Mode Atomic Force Microscopy

The natural frequencies of a cantilever probe can be tuned with an attached concentrated mass to coincide with the higher harmonics generated in a tapping-mode atomic force microscopy by the nonlinear tip-sample interaction force. We provide a comprehensive map to guide the choice of the mass and the position of the attached particle in order to significantly enhance the higher harmonic signals containing information on the material properties. The first three eigenmodes can be simultaneously excited with only one carefully positioned particle of specific mass to enhance multiple harmonics. Accessing the interaction force qualitatively based on the high-sensitive harmonic signals combines the real-time material characterization with the imaging capability. (C) 2008 American Institute of Physics.

Crack propagation in the power-law nonlinear viscoelastic material

An analysis on crack creep propagation problem of power-law nonlinear viscoelastic materials is presented. The creep incompressilility assumption is used. To simulate fracture behavior of craze region, it is assumed that in the fracture process zone near the crack tip, the cohesive stress sigma(f) acts upon the crack surfaces and resists crack opening. Through a perturbation method, i. e., by superposing the Mode-I applied force onto a referential uniform stress state, which has a trivial solution and gives no effect on the solution of the original problem, the nonlinear viscoelastic problem is reduced to linear problem. For weak nonlinear materials, for which the power-law index n similar or equal to 1, the expressions of stress and crack surface displacement are derived. Then, the fracture process zone local energy criterion is proposed and based on which the formulas of cracking incubation time t

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Resonant mode analysis in toroidal cavities with elliptic cross-sections

Resonant cavity modes in a torus with elliptical cross section are studied by means of a direct variational method. The nonlinear effects of toroidicity and ellipticity on the frequency of the basic mode are analyzed simply and systematically without the restriction of linear theory. It is shown that the toroidicity effect on the m = 0 transverse magnetic mode is less-than-or-equal-to 11%. The frequency of the mode shifts approximately 11-29% when the elongation of the cross section changes from 1 to 2. The effects of toroidicity and ellipticity differ for each resonant mode.

High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

Sliding Mode Control Strategy for Wind Turbine Power Maximization

The efficiency of the wind power conversions systems can be greatly improved using an appropriate control algorithm. In this work, a sliding mode control for variable speed wind turbine that incorporates a doubly fed induction generator is described. The electrical system incorporates a wound rotor induction machine with back-to-back three phase power converter bridges between its rotor and the grid. In the presented design the so-called vector control theory is applied, in order to simplify the electrical equations. The proposed control scheme uses stator flux-oriented vector control for the rotor side converter bridge control and grid voltage vector control for the grid side converter bridge control. The stability analysis of the proposed sliding mode controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. Finally simulated results show, on the one hand, that the proposed controller provides high-performance dynamic characteristics, and on the other hand, that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

Sliding mode position control for real-time control of induction motors

A sliding mode position control for high-performance real-time applications of induction motors in developed in this work. The design also incorporates a simple flux estimator in order to avoid the flux sensors. Then, the proposed control scheme presents a low computational cost and therefore can be implemented easily in a real-time applications using a low cost DSP-processor. The stability analysis of the controller under parameter uncertainties and load disturbances in provided using Lyapunov stability theory. Finally, simulated and experimental results show that the proposed controller with the proposed observer provides a good trajectory tracking and that this scheme is robust with respect to plant parameter variations and external load disturbances.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.