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.

Nonlinear Model Predictive Spread Acceleration Guidance with Impact Angle Constraint for Stationary Targets

A new technique named as model predictive spread acceleration guidance (MPSAG) is proposed in this paper. It combines nonlinear model predictive control and spread acceleration guidance philosophies. This technique is then used to design a nonlinear suboptimal guidance law for a constant speed missile against stationary target with impact angle constraint. MPSAG technique can be applied to a class of nonlinear problems, which leads to a closed form solution of the lateral acceleration (latax) history update. Guidance command assumed is the lateral acceleration (latax), applied normal to the velocity vector. The new guidance law is validated by considering the nonlinear kinematics with both lag-free as well as first order autopilot delay. The simulation results show that the proposed technique is quite promising to come up with a nonlinear guidance law that leads to both very small miss distance as well as the desired impact angle.

Nonlinear Model Predictive Spread Acceleration Guidance with Impact Angle Constraint for Slow-moving Targets

A new technique named as model predictive spread acceleration guidance (MPSAG) is proposed in this paper. It combines nonlinear model predictive control and spread acceleration guidance philosophies. This technique is then used to design a nonlinear suboptimal guidance law for a constant speed missile against stationary target with impact angle constraint. MPSAG technique can be applied to a class of nonlinear problems, which leads to a closed form solution of the lateral acceleration (latax) history update. Guidance command assumed is the lateral acceleration (latax), applied normal to the velocity vector. The new guidance law is validated by considering the nonlinear kinematics with both lag-free as well as first order autopilot delay. The simulation results show that the proposed technique is quite promising to come up with a nonlinear guidance law that leads to both very small miss distance as well as the desired impact angle.

Linear and nonlinear model large-eddy simulations of a plane jet

The nonlinear Kosovic, and mixed Leray and α subgrid scale models are contrasted with linear Smagorinsky and Yoshizawa Large Eddy Simulations for a Re = 4000 plane jet simulation. Comparisons are made with Direct Numerical Simulation data and measurements. Global properties of the jet such as the spreading and centreline velocity decay rates are investigated. The mean-flow and turbulence parameters in the self-similar region are also studied. All models generally give encouraging agreement with the Direct Numerical Simulation data and reliable measurements. Solution differences for the models are relatively minor, none giving clear improvements for all data comparisons.

A nonlinear model for assessing multiple probabilistic risks: A case study in South five-island of Changdao National Nature Reserve in China

Several methods for estimating the potential impacts caused by multiple probabilistic risks have been suggested. These existing methods mostly rely on the weight sum algorithm to address the need for integrated risk assessment. This paper develops a nonlinear model to perform such an assessment. The joint probability algorithm has been applied to the model development. An application of the developed model in South five-island of Changdao National Nature Reserve, China, combining remote sensing data and a GIS technique, provides a reasonable risk assessment. Based on the case study, we discuss the feasibility of the model. We propose that the model has the potential for use in identifying the regional primary stressor, investigating the most vulnerable habitat, and assessing the integrated impact of multiple stressors. (C) 2006 Elsevier Ltd. All rights reserved.

A Fast Nonlinear Model Identification Method

The identification of nonlinear dynamic systems using linear-in-the-parameters models is studied. A fast recursive algorithm (FRA) is proposed to select both the model structure and to estimate the model parameters. Unlike orthogonal least squares (OLS) method, FRA solves the least-squares problem recursively over the model order without requiring matrix decomposition. The computational complexity of both algorithms is analyzed, along with their numerical stability. The new method is shown to require much less computational effort and is also numerically more stable than OLS.

Fast automatic two-stage nonlinear model identification based on the extreme learning machine

It is convenient and effective to solve nonlinear problems with a model that has a linear-in-the-parameters (LITP) structure. However, the nonlinear parameters (e.g. the width of Gaussian function) of each model term needs to be pre-determined either from expert experience or through exhaustive search. An alternative approach is to optimize them by a gradient-based technique (e.g. Newton’s method). Unfortunately, all of these methods still need a lot of computations. Recently, the extreme learning machine (ELM) has shown its advantages in terms of fast learning from data, but the sparsity of the constructed model cannot be guaranteed. This paper proposes a novel algorithm for automatic construction of a nonlinear system model based on the extreme learning machine. This is achieved by effectively integrating the ELM and leave-one-out (LOO) cross validation with our two-stage stepwise construction procedure [1]. The main objective is to improve the compactness and generalization capability of the model constructed by the ELM method. Numerical analysis shows that the proposed algorithm only involves about half of the computation of orthogonal least squares (OLS) based method. Simulation examples are included to confirm the efficacy and superiority of the proposed technique.

On Infinite Time Performance of Nonlinear Model Predictive Controllers

This paper addresses the problem of infinite time performance of model predictive controllers applied to constrained nonlinear systems. The total performance is compared with a finite horizon optimal cost to reveal performance limits of closed-loop model predictive control systems. Based on the Principle of Optimality, an upper and a lower bound of the ratio between the total performance and the finite horizon optimal cost are obtained explicitly expressed by the optimization horizon. The results also illustrate, from viewpoint of performance, how model predictive controllers approaches to infinite optimal controllers as the optimization horizon increases.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.