Nonlinear Model Predictive Control for a multi-rotor with heavy slung load

In this paper a novel controller for stable and precise operation of multi-rotors with heavy slung loads is introduced. First, simplified equations of motions for the multi-rotor and slung load are derived. The model is then used to design a Nonlinear Model Predictive Controller (NMPC) that can manage the highly nonlinear dynamics whilst accounting for system constraints. The controller is shown to simultaneously track specified waypoints whilst actively damping large slung load oscillations. A Linear-quadratic regulator (LQR) controller is also derived, and control performance is compared in simulation. Results show the improved performance of the Nonlinear Model Predictive Control (NMPC) controller over a larger flight envelope, including aggressive maneuvers and large slung load displacements. Computational cost remains relatively small, amenable to practical implementation. Such systems for small Unmanned Aerial Vehicles (UAVs) may provide significant benefit to several applications in agriculture, law enforcement and construction.

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.

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.

Microbead dynamics on quartz crystal microbalance at elevated amplitudes

The application of the Quartz Crystal Microbalance (QCM) for biochemical sensing is well known. However, utilizing the nonlinear response of the QCM at elevated amplitudes has received sporadic attention. This study presents results for QCM-analyte interaction that provide insight into the nonlinear dynamics of the QCM with attached analyte. In particular, interactions of the QCM with polystyrene microbeads physisorbed via self-assembled monolayer (SAM) were studied through experiments and modelling. It was found that the response of the QCM coupled to these surface adsorbents is anharmonic even at low oscillation amplitudes and that the nonlinear signals from such interactions are much higher than those for bare quartz. Therefore, these signals can potentially be used as sensitive signatures of adsorbents and their kinetics on the surface. ©2009 IEEE.

The dynamics of industrial emergence

The need to stimulate, identify and nurture new industries is a prominent challenge in advanced economies. While basic science represents a valuable source of new ideas and opportunities, it can often take decades before this science finally finds application in the market. While numerous studies have to date focused on aspects of industrial evolution, (e.g. innovation, internationalisation, new product introduction, technological lifecycles and emerging technologies), far fewer have focused on technology-based industrial emergence. It is clear that if assistance is to be provided to firms and industrial policymakers attempting to navigate industrial emergence then we need an improved understanding of the characteristics and dynamics of this phenomenon. Accordingly, this paper reviews published work from a range of disparate disciplines - evolutionary theory, social construction of technology (SCOT), complexity science, industrial dynamics and technology management - to identify these dynamics. Through this review we conceptualise industrial emergence as a co-evolutionary process in which nonlinear dynamics operate. Industrial emergence is sensitive to the initial availability of resources and the market applications, with growth dependent on the supply-demand coupling, agents' actions to reduce uncertainty and catalytic events. Through synthesizing these key dynamics we go on to propose a conceptual model for industrial emergence. © 2010 IEEE.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

Control of the orientational order and nonlinear optical response of the "push-pull" chromophore RuPZn via specific incorporation into densely packed monolayer ensembles of an amphiphilic four-helix bundle peptide: characterization of the peptide-chromophore complexes.

"Push-pull" chromophores based on extended pi-electron systems have been designed to exhibit exceptionally large molecular hyperpolarizabilities. We have engineered an amphiphilic four-helix bundle peptide to vectorially incorporate such hyperpolarizable chromophores having a metalloporphyrin moiety, with high specificity into the interior core of the bundle. The amphiphilic exterior of the bundle facilitates the formation of densely packed monolayer ensembles of the vectorially oriented peptide-chromophore complexes at the liquid-gas interface. Chemical specificity designed into the ends of the bundle facilitates the subsequent covalent attachment of these monolayer ensembles onto the surface of an inorganic substrate. In this article, we describe the structural characterization of these monolayer ensembles at each stage of their fabrication for one such peptide-chromophore complex designated as AP0-RuPZn. In the accompanying article, we describe the characterization of their macroscopic nonlinear optical properties.

Nonlinear oscillator metamaterial model: numerical and experimental verification.

We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems.

Nonreciprocal scattering by stacked nonlinear magneto-active semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in a self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It is shown that magnetic bias not only renders nonreciprocity of the three-wave mixing process but also significantly enhances the nonlinear interactions in the stacks, especially at the frequencies close to the intrinsic magneto-plasma resonances of the constituent layers. The main mechanisms and properties of the combinatorial frequency generation and emission from the stacks are illustrated by the simulation results, and the effects of the individual layer parameters and the structure arrangement on the stack nonlinear and nonreciprocal response are discussed. © 2014 Elsevier B.V. All rights reserved.

Nonreciprocal nonlinear scattering by stacked magnetoactive semiconductor layers

The combinatorial frequency generation by the periodic stacks of magnetically biased semiconductor layers has been modelled in the self-consistent problem formulation, taking into account the nonlinear dynamics of carriers. It has been shown that the nonlinear response of the magnetoactive semiconductor periodic structure is strongly enhanced by magnetic bias and combinations of the layer physical and geometrical parameters. The effects of the pump wave nonreciprocal reflectance and field displacement on the efficiency of three-wave mixing process is illustrated by the simulation results

Relativistic time effects in financial dynamics

Financial time series have a complex dynamic nature. Many techniques were adopted having in mind standard paradigms of time flow. This paper explores an alternative route involving relativistic effects. It is observed that the measuring perspective influences the results and that we can have different time textures.

Complex dynamics of financial indices

This paper presents a novel method for the analysis of nonlinear financial and economic systems. The modeling approach integrates the classical concepts of state space representation and time series regression. The analytical and numerical scheme leads to a parameter space representation that constitutes a valid alternative to represent the dynamical behavior. The results reveal that business cycles can be clearly revealed, while the noise effects common in financial indices can elegantly be filtered out of the results.