Linear-Time Convexity Test for Low-Order Piecewise Polynomials

2021 ◽  
Vol 31 (1) ◽  
pp. 972-990
Author(s):  
Shambhavi Singh ◽  
Yves Lucet
Keyword(s):  
Linear Time ◽  
Piecewise Polynomials ◽  
Low Order

H 2-Optimal Low Order Transmission Line Models

2019 ◽  
Author(s):  
Bernhard Manhartsgruber
Keyword(s):  
Power Systems ◽  
Transmission Line ◽  
Code Generation ◽  
Transfer Functions ◽  
Linear Time ◽  
State Space Model ◽  
Low Frequency ◽  
Transmission Line Model ◽  
Line Model ◽  
Low Order

Abstract Transmission line modeling has played a crucial role in understanding the dynamics of fluid power systems. A vast body of literature exists from simple lumped parameter approaches to fully coupled three-dimensional fluid structure interaction models. When it comes to computationally efficient, yet physically sound low order models needed for fast computations iteratively called by optimization codes or for the purpose of model based control design, there is still room for improvement. Modal approximations of the input-output behaviour of liquid transmission lines have been around for decades. The basic idea of tuning the parameters of a canonical linear time invariant state space model to fit the transfer functions of a transmission line model in the H2-optimal sense under passivity constraints has been published by the author of the present paper in the past. However, the method so far was barely usable due to numerical difficulties in the underlying optimization process. A new implementation of the method employing quadruple-precision floating point numbers has recently been found to resolve the convergence problems and is reported in the present paper. The new version of the method is based on analytic computation of the cost and constraint functions as well as their gradients in the computer algebra package Maple and automatic code generation for compilation in FORTRAN. Results are very promising because both the entire low frequency behaviour and the first three eigenmodes of a transmission line model can be accurately covered by a model of order eight only.

scholarly journals Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Alejandro Marquez ◽  
Jairo José Espinosa Oviedo ◽  
Darci Odloak
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Linear Model ◽  
Predictive Control ◽  
Linear Time ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Operating Condition ◽  
Order Linear ◽  
Proper Orthogonal ◽  
Low Order

This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.

Low-Order Stabilizer Design for Discrete Linear Time-Varying Internal Model-Based System

2015 ◽  
Vol 20 (6) ◽  
pp. 2666-2677 ◽  
Author(s):  
Xingyong Song ◽  
Pradeep Kumar Gillella ◽  
Zongxuan Sun
Keyword(s):  
Internal Model ◽  
Linear Time ◽  
Time Varying ◽  
Model Based ◽  
Low Order

the effects of resonance with Jupiter in the system of short-period comets

1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák
Keyword(s):  
Structural Effects ◽  
Order Resonance ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Compound Effect ◽  
Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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