Process operating mode monitoring : switching online the right controller

This paper presents a structure which deals with process operating mode monitoring and allows the control law reconfiguration by switching online the right controller. After a short review of the advances in switching based control systems during the last decade, we introduce our approach based on the definition of operating modes of a plant. The control reconfiguration strategy is achieved by online selection of an adequate controller, in a case of active accommodation. The main contribution lies in settling up the design steps of the multicontroller structure and its accurate integration in the operating mode detection and accommodation loop. Simulation results show the effectiveness of the operating mode detection and accommodation (OMDA) structure for which the design steps propose a method to study the asymptotic stability, switching performances improvement, and the tuning of the multimodel based detector

Spatially partitioned embedded Runge-Kutta Methods

We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory

High-order cyclo-difference techniques: An alternative to finite differences

The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy

Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach

Comparison of numerical methods for the calculation of cold atom collisions

Three different numerical techniques for solving a coupled channel Schroedinger equation are compared. This benchmark equation, which describes the collision between two ultracold atoms, consists of two channels, each containing the same diagonal Lennard-Jones potential, one of positive and the other of negative energy. The coupling potential is of an exponential form. The methods are i) a recently developed spectral type integral equation method based on Chebyshev expansions, ii) a finite element expansion, and iii) a combination of an improved Numerov finite difference method and a Gordon method. The computing time and the accuracy of the resulting phase shift is found to be comparable for methods i) and ii), achieving an accuracy of ten significant figures with a double precision calculation. Method iii) achieves seven significant figures. The scattering length and effective range are also obtained.Comment: 22 pages, 3 figures, submitted to J. Comput. Phys. documentstyle [thmsa,sw20aip]{article} in .te