43,932 research outputs found
Nonparametric nonlinear model predictive control
Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC
Nonlinear Model of non-Debye Relaxation
We present a simple nonlinear relaxation equation which contains the Debye
equation as a particular case. The suggested relaxation equation results in
power-law decay of fluctuations. This equation contains a parameter defining
the frequency dependence of the dielectric permittivity similarly to the
well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole
and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric
permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper
behaviour at large frequency; (iii) its imaginary part, conductivity, shows a
power-law frequency dependence \sigma ~ \omega^n where n<1 corresponds to
empirical Jonscher's universal relaxation law while n>1 is also observed in
several experiments. The nonlinear equation proposed may be useful in various
fields of relaxation theory
A discrete nonlinear model with substrate feedback
We consider a prototypical model in which a nonlinear field (continuum or
discrete) evolves on a flexible substrate which feeds back to the evolution of
the main field. We identify the underlying physics and potential applications
of such a model and examine its simplest one-dimensional Hamiltonian form,
which turns out to be a modified Frenkel-Kontorova model coupled to an extra
linear equation. We find static kink solutions and study their stability, and
then examine moving kinks (the continuum limit of the model is studied too). We
observe how the substrate effectively renormalizes properties of the kinks. In
particular, a nontrivial finding is that branches of stable and unstable kink
solutions may be extended beyond a critical point at which an effective
intersite coupling vanishes; passing this critical point does not destabilize
the kink. Kink-antikink collisions are also studied, demonstrating alternation
between merger and transmission cases.Comment: a revtex text file and 6 ps files with figures. Physical Review E, in
pres
Nonlinear model predictive control for hydrogen production in an ethanol steam reformer with membrane separation
© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper presents a new Nonlinear Model Predictive Control (NMPC) design for an Ethanol Steam Reformer with Pd-Ag membrane separation stage. The reformer is used to produce pure hydrogen able to feed a Proton Exchange Membrane Fuel Cell. Mass and energy balances are used to obtain the nonlinear dynamic model of both the reforming and the separation stages. Constraints, system nonlinearities and flexible cost function are the main reasons to select an NMPC controller, which is tested against the ordinary differential equations as simulation model, and has an internal model based on the sample data technique.Accepted versio
The Schauder estimate in kinetic theory with application to a toy nonlinear model
This article is concerned with the Schauder estimate for linear kinetic
Fokker-Planck equations with H\"older continuous coefficients. This equation
has an hypoelliptic structure. As an application of this Schauder estimate, we
prove the global well-posedness of a toy nonlinear model in kinetic theory.
This nonlinear model consists in a non-linear kinetic Fokker-Planck equation
whose steady states are Maxwellian and whose diffusion in the velocity variable
is proportional to the mass of the solution
Nonlinear model order reduction via Dynamic Mode Decomposition
We propose a new technique for obtaining reduced order models for nonlinear
dynamical systems. Specifically, we advocate the use of the recently developed
Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the
nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix
that correlates spatial features while simultaneously associating the activity
with periodic temporal behavior. With this decomposition, one can obtain a
fully reduced dimensional surrogate model and avoid the evaluation of the
nonlinear term in the online stage. This allows for an impressive speed up of
the computational cost, and, at the same time, accurate approximations of the
problem. We present a suite of numerical tests to illustrate our approach and
to show the effectiveness of the method in comparison to existing approaches
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