Control of a bioprocess using orthonormal basis function fuzzy models

2005 ◽  
Author(s):  
R.J.G.B. Campello ◽  
L.A.C. Meleiro ◽  
W.C. Amaral
Keyword(s):  
Basis Function ◽  
Orthonormal Basis ◽  
Fuzzy Models

Takagi–Sugeno Fuzzy Models in the Framework of Orthonormal Basis Functions

2013 ◽  
Vol 43 (3) ◽  
pp. 858-870 ◽  
Author(s):  
J. B. Machado ◽  
R. J. G. B. Campello ◽  
W. C. Amaral
Keyword(s):  
Orthonormal Basis ◽  
Basis Functions ◽  
Fuzzy Models ◽  
Takagi Sugeno

Investigation of the supercell based orthonormal basis function method for different kinds of fibers

2004 ◽  
Vol 10 (4) ◽  
pp. 296-311 ◽  
Author(s):  
Zhi Wang ◽  
Guobin Ren ◽  
Shuqin Lou ◽  
Weijun Liang
Keyword(s):  
Basis Function ◽  
Function Method ◽  
Orthonormal Basis

scholarly journals Development of FOPDT and SOPDT model from arbitrary process identification data using the properties of orthonormal basis function

2018 ◽  
Vol 7 (2.21) ◽  
pp. 77 ◽  
Author(s):  
Lalu Seban ◽  
Namita Boruah ◽  
Binoy K. Roy
Keyword(s):  
Basis Function ◽  
Delay Time ◽  
Orthonormal Basis ◽  
Control Point ◽  
Second Order ◽  
Step Test ◽  
Step Response ◽  
Order System ◽  
Model Parameters ◽  
First Order

Most of industrial process can be approximately represented as first-order plus delay time (FOPDT) model or second-order plus delay time (FOPDT) model. From a control point of view, it is important to estimate the FOPDT or SOPDT model parameters from arbitrary process input as groomed test like step test is not always feasible. Orthonormal basis function (OBF) are class of model structure having many advantages, and its parameters can be estimated from arbitrary input data. The OBF model filters are functions of poles and hence accuracy of the model depends on the accuracy of the poles. In this paper, a simple and standard particle swarm optimisation technique is first employed to estimate the dominant discrete poles from arbitrary input and corresponding process output. Time constant of first order system or period of oscillation and damping ratio of second order system is calculated from the dominant poles. From the step response of the developed OBF model, time delay and steady state gain are estimated. The parameter accuracy is improved by employing an iterative scheme. Numerical examples are provided to show the accuracy of the proposed method. 

Adaptive Fuzzy Modeling using Orthonormal Basis Functions for Network Traffic Flow Control

2016 ◽  
pp. 270-313
Author(s):  
Flávio Henrique Teles Vieira ◽  
Flávio Geraldo Coelho Rocha ◽  
Álisson Assis Cardoso
Keyword(s):  
Traffic Flow ◽  
Bandwidth Allocation ◽  
Multifractal Analysis ◽  
Orthonormal Basis ◽  
Fuzzy Model ◽  
Basis Functions ◽  
Training Algorithms ◽  
Adaptive Fuzzy ◽  
Fuzzy Models ◽  
Fuzzy Algorithms

In this chapter, we present some Fuzzy training algorithms, such as the Fuzzy LMS (Least Mean Squares) and Fuzzy RLS (Recursive Least Squares) predictors. We use concepts of multifractal analysis to present and validate a Fuzzy LMS predictor based on the autocorrelation function of a multifractal model. We evaluate the efficiency of these algorithms when applied to bandwidth allocation tasks. We also present adaptive predictive OBF (Orthonormal Basis Functions)-Fuzzy models. To this end, we model traffic traces using OBF functions obtained through multifractal analysis. Further, we insert these functions into OBF-Fuzzy models trained with the adaptive training algorithms. Updating the Fuzzy model parameters, we predict future values of real traffic traces. We also present a comparison of prediction performance of different adaptive Fuzzy algorithms including OBF-Fuzzy models. Finally, we verify the performance of the OBF-Fuzzy algorithms in modeling the buffer queueing in a communication network and controlling traffic flow rates.

Minimal partial realization from generalized orthonormal basis function expansions

Automatica ◽  
2002 ◽  
Vol 38 (4) ◽  
pp. 655-669 ◽  
Author(s):  
Thomas J. de Hoog ◽  
Zoltán Szabó ◽  
Peter S.C. Heuberger ◽  
Paul M.J. Van den Hof ◽  
József Bokor
Keyword(s):  
Basis Function ◽  
Orthonormal Basis ◽  
Minimal Partial Realization
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