Application of nonlinear dynamic analysis in the identification and control of nonlinear systems—I. Simple dynamics

Read, Nolan K.; Ray, W. Harmon

doi:10.1016/s0959-1524(97)00021-8

Cited by 20 publications

(23 citation statements)

References 8 publications

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“…The final dimensionless equations are

\begin{matrix} {\overset{x}{true}}_{1} =‐ x_{1} +Da(1‐ x_{1})exp(x_{2}) \\ {\overset{x}{true}}_{2} =‐ x_{1} +BDa(1‐ x_{1})exp(x_{2})‐β(x_{2} ‐u), \end{matrix}

where the dimensionless groups and variables are described above, and u represents a manipulated variable, or a disturbance to the system at steady state. The equilibrium values of x 1s and x 2s are 0.1708 and 1.0508, respectively, at the values of dimensionless groups: Da = 0.072; B = 7.91; β = 0.3 …”

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 96%

“…The plant equations are given with respect to dimensionless groups: Da Damkholer number; B dimensionless hear of reaction; and β dimensionless heat transfer coefficient. The derivation of the two dimensionless equations, and more detailed description of the dimensionless groups and system can be found in classic work by Uppal et al and Read and Ray . The final dimensionless equations are

\begin{matrix} {\overset{x}{true}}_{1} =‐ x_{1} +Da(1‐ x_{1})exp(x_{2}) \\ {\overset{x}{true}}_{2} =‐ x_{1} +BDa(1‐ x_{1})exp(x_{2})‐β(x_{2} ‐u), \end{matrix}

where the dimensionless groups and variables are described above, and u represents a manipulated variable, or a disturbance to the system at steady state.…”

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 99%

“…matches locally that of the plant equations, Eq. , during a series of impulse disturbances described in more detail by Read and Ray . However, on a closer inspection of the normal form equations, Eq.…”

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 99%

“…The algorithm is then validated against several model problems involving systems of chemical reactions that they have been employed before in testing global parameter estimation methods. In addition, the algorithm is applied to a complex multiparameter modeling used to evaluate control strategies in a Nonisothermal CSTR . Finally, the algorithm is applied to the parameter estimation in fitting complex nonlinear rheology models to measurement data.…”

Section: Introductionmentioning

confidence: 99%

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An adaptive parallel tempering method for the dynamic data‐driven parameter estimation of nonlinear models

2016

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An adaptive parallel tempering algorithm is developed in a user‐friendly fashion that efficiently and robustly generates near‐optimum solutions. Using adaptive, implicit, time‐integration methods, the method allows fitting model parameters to dynamic data. The proposed approach is relatively insensitive to the initial guess and requires minimal fine‐tuning: most of the algorithm parameters can be determined adaptively based on the analysis of few model simulations, while default values are proposed for the few remaining ones, the exact values of which do not sensitively affect the solution. The method is extensively validated through its application to a number of algebraic and dynamic global optimization problems from Chemical Engineering literature. We then apply it to a multi‐parameter, highly nonlinear, model of the rheology of a thixotropic system where we show how the present approach can be used to robustly determine model parameters by fitting to dynamic, large amplitude, oscillatory stress vs. shear rate, data. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1937–1958, 2017

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“…The final dimensionless equations are

\begin{matrix} {\overset{x}{true}}_{1} =‐ x_{1} +Da(1‐ x_{1})exp(x_{2}) \\ {\overset{x}{true}}_{2} =‐ x_{1} +BDa(1‐ x_{1})exp(x_{2})‐β(x_{2} ‐u), \end{matrix}

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 96%

\begin{matrix} {\overset{x}{true}}_{1} =‐ x_{1} +Da(1‐ x_{1})exp(x_{2}) \\ {\overset{x}{true}}_{2} =‐ x_{1} +BDa(1‐ x_{1})exp(x_{2})‐β(x_{2} ‐u), \end{matrix}

where the dimensionless groups and variables are described above, and u represents a manipulated variable, or a disturbance to the system at steady state.…”

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 99%

Section: Dynamic Model Parameter Estimation Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An adaptive parallel tempering method for the dynamic data‐driven parameter estimation of nonlinear models

2016

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“…The batch reactor and the distillation column are two examples of uncertain nonlinear systems where the uncertainties are seen as nonlinear or rational parameterized functions, see e.g., [13], [1].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous state and parameter estimation of a class of MIMO nonlinear systems

Ibrir

2015

2015 IEEE 8th GCC Conference &Amp; Exhibition

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An adaptive nonlinear observer is conceived for simultaneous state and parameter estimation of a class of Multiple-Input-Multiple-Output(MIMO) nonlinear systems. Under the persistent excitation condition, it is shown that the overall observer injection gain, that ensures the convergence of the system states and the adaptive parameters, is composed by a sum of a constant and a time-varying gains. It is found that the constantgain output injection is sufficient to make the observer globally convergent under the condition that all the system parameters are known. In addition, if the persistent excitation condition is verified, the time-varying output injection is easily conceived by appropriate selection of a free design parameter. The observer design methodology is stated as the solution of a linear matrix inequality which is numerically tractable. Simulation results are shown to validate the theoretical results.

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Application of nonlinear dynamic analysis in the identification and control of nonlinear systems—I. Simple dynamics

Cited by 20 publications

References 8 publications

An adaptive parallel tempering method for the dynamic data‐driven parameter estimation of nonlinear models

An adaptive parallel tempering method for the dynamic data‐driven parameter estimation of nonlinear models

Simultaneous state and parameter estimation of a class of MIMO nonlinear systems

Fuzzy Reasoning

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