Comparison of two approaches to on-line parameter and state estimation of nonlinear systems

Abstract

Ind. Eng. Chem. Process Des. Dev. 1986, 25, 809-814 809 mi = function of the acentric factor for the correlation of a N = number of moles p i = Mathias polar parameter P = pressure R = ideal gas constant T = temperature TI = reduced temperature u = molar liquid volume of the mixture vi = molar liquid volume of pure component i xi = mole fraction of component i in the liquid phase 2 = compressibility factor of the mixture 2, = compressibility factor of pure component i Greek Letters ai( TI) = temperature-dependent part of parameter ai y L = activity coefficient of component i in the mixture y i m = infinite-dilution activity coefficient of component i 7 = a/bRT 'pi = fugacity coefficient of component i in the mixture q,* = fugacity coefficient of pure component i Subscripts i, j = component i or j k = either a pure component (k = i ) or a mixture (k = 4) below the critical temperature 0 = property at zero pressure Literature Cited Chang, E.; Calado. J. C. 0.; Street, W. B. J . Chem. Eng. Data 1982, 27, 293. Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-LiquM Equilibrie Using UNIFAC. A Group Conhlbufbn Method; Elsevier: Amsterdam, 1977. Gibbons, R. M.; Laughton. A. P. J . Chem. Soc., Faraday Trans. 2 1984, 80, 1019. Gmehling, J.; Onken, U.; Artl, W. Vapor-Liquid Equilibria Data Collection; DECHEMA Chemistry Data Series I ; Verlag Chemie: Frankfurt/Main, FRO, 1977. Gmehling, J.; Rasmussen. P.; Fredenslund, A. Ind. Eng . Chem. Process Des. D e v . 1982, 27, 118. Hayden, J. G.; O'Connell, J. P. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209. Hlrata. M.; Ohe. S.; Nagahama. K. Computer-Aided Data Book of Vapor-Liquid Equilibria Kodansha: Tokyo, 1975. Knapp, H.; Wing, R.; Plocker, U.; Prausnltz, J. M. Vapor-LiquidEquilibrie forTwo approaches to the on-line identification of parameters and states in systems described by nonlinear ordinary differentlal equations are compared by using an example chemical process. The first approach is based on the Kalman filter approach extended to cover nonlinear systems. The second is based on the application of nonlinear optimization methods to minimize a suitable function of the error in estimation. The Kalman filter approach was found to be sensitive to several factors: the initial guess of the state variables, the statistics of the input and measurement noises, and the nature of the nonlinearity in the describing equations. The second approach, while computationally more intensive, proved to be far superior in terms of the speed of tracking, robustness in the presence of errors in modeling the systems, and noise statistics and in terms of the ability to handle nonlinearity in the system.By use of a critical combination of zeolite catalysts, high space velocity, and high temperature, cracking of some 10 000 volumes of gas oil over 1 volume of catalyst in a single on-stream cycle (Le., without regeneration) has been accomplished. For a supposed single-cycle operation, this would imply a fresh catalyst requirement of 0.3 tons per day for a 20 000 BID cracking operation, without reg...

Análise de técnicas de reconciliação de dados aplicadas a um sistema vaso separador

“…As técnicas selecionadas para a reconciliação de dados foram o filtro de Kalman (Mah et al, 1976), um algoritmo baseado em um preditor-corretor (Bai et al, 2006) e o uso de uma janela móvel (Jang et al, 1986;Liebman et al, 1992).…”

“…O FK na forma que foi proposto inicialmente não apresenta bons resultados em sistemas não lineares. Para emprego em tais sistemas, Jang et al (1986) propuseram o chamado filtro de Kalman estendido (FKE). Ele usa uma formulação iterativa e sequencial do problema de estimação baseada numa descrição linearizada do modelo dinâmico.…”

“…O FKE apresenta desempenho melhor sob perturbação, quando comparado ao FK. Jang et al (1986), e posteriormente Liebman et al (1992), propuseram o uso de uma janela mó-vel no tempo. Essa técnicaé muito eficaz na melhoria do desempenho do controle de um determinado processo.…”

Bayesian estimation via sequential Monte Carlo sampling—Constrained dynamic systems

“…In this section, a popular process engineering problem, an adiabatic CSTR, is studied (Jang, Joseph, & Mukai, 1986;Henson & Seborg, 1997). Governing equations are as follows:…”

Multirate State Estimation Using Moving Horizon Estimation

“…The solution to this optimisation problem is given by the Matrix-Riccati-Equation (Jazwinski, 1970). Due to the increase in computational speed and improvements in software for solving optimisation problems, optimisation based approaches have been developed in the last decades (Jang et al, 1986;Muske et al, 1993). Here, the calculation of the correction part of the EKF is replaced by an optimisation problem.…”