Nonlinear analysis in process design

Seider, Warren D.; Brengel, David D.; Widagdo, Soemantri

doi:10.1002/aic.690370102

Cited by 58 publications

(31 citation statements)

References 151 publications

(140 reference statements)

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“…The ideas behind this procedure as well as the closely related dynamic programming have been used in the chemical engineering community since before the 1960s; for a detailed treatment see, for example Aris (1961), Roberts (1964), and Lapidus and Luus (1967). It is currently used in fields as diverse as process design (Seider et al, 1991), operation (Tieu et al, 1994), and scheduling and planning (Bhalla and Bower, 1993). Within the processcontrol field, these ideas underly the nonlinear model predictive control (MPC) approach (Li and Biegler, 1988;Garcia et al, 1989;Rawlings et al, 1994), where the optimal control action minimizing an error trajectory to a given time horizon is recalculated and implemented every step.…”

Section: Ocsmentioning

confidence: 99%

Application of a control‐law nonlinearity measure to the chemical reactor analysis

Stack¹,

Doyle²

1997

AIChE Journal

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The optimal control structure has been introduced as a design tool to measure the control-law nonlinearity of a given process design. In this context, control-law nonlinearity is the optimal degree of nonlinear compensation in the controller, a system property distinct from open-loop nonlinearity and determincd by a performance objective and the region of operation as well as the nature of the open-loop system. This approach is extended to the analysis of multivariable systems with output feedback through the application of an extended Kalman filter. Coherence estimation is used as a practical method to measure continuous, open-loop multivariable system nonlinearity. The CSTR with van de Vusse kinetics, a system that features output feedback and a controllaw nonlinearity that changes with operating points, is analyzed. The optimal control structure approach with coherence estimation correctly indicates changes in the controllaw linearity between different operating points and changes as the regions of operation change around a particular operating point. straightforward. Coherence analysis alone (when applied to the open-loop process operator) can lead to inconsistent ranking of nonlinear systems, hence, more complicated methods have been proposed. Abstract-operator-based methods have been proposed by

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Section: Ocsmentioning

confidence: 99%

Application of a control‐law nonlinearity measure to the chemical reactor analysis

Stack¹,

Doyle²

1997

AIChE Journal

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“…These optimal control problems (OCPs) are usually very difficult to solve because of the nonlinear nature of the system dynamics and the existence of constraints on both the control and state variables (Cuthrell and Biegler, 1989; Luus, 1993a,b). Besides, the global optimum is often difficult to achieve due to the insensitivity of the performance index to the control profiles (Seider et al, 1991). Therefore, it is not surprising that most existing methods may fail to solve many of these problems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Dynamic Optimization of Batch and Semicontinuous Bioprocesses

Banga¹,

Alonso²,

Singh³

1997

Biotechnol. Prog.

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The dynamic optimization (optimal control) of batch and semicontinuous bioprocesses, like fed‐batch fermentation and bioproduct batch separation, has received considerable attention in recent years. These constrained dynamic optimization problems are difficult to solve due to their highly nonlinear character and also due to the fact that they usually are multimodal; therefore most proposed methods may fail to find the global optima. Besides, these methods are not always easy to implement and use, mainly because a laborious preparation and/or transformation of the original problem is needed. Here we present a simple yet powerful method that requires no initial preparation stage and that is useful to solve several complex optimal control problems without convergence difficulties. Two fed‐batch bioreactor case studies, taken from the recent literature, and a third case study considering a complex bioproduct dehydration problem are successfully and efficiently solved with our new approach, and its advantages are discussed.

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“…Some recent work in the literature uses strategies that minimize the dependence on the initial guess or approaches that seek all roots of the algebraic system independent of the initial guess. Of these, the following can be cited: multigrid mesh initialization (Sofyan et al, 2003), the homotopy continuation method (Bausa and Marquardt, 2000;McDonald and Floudas, 1995;Seider et al, 1991;Kuno and Seader, 1988;Wayburn and Seader, 1987) and the interval analysis algorithms -applied to flash and phase stability analysis problems (Scurto et al, 2003;Kerfott et al, 1994;Hua et al, 1998a,b;Kerfott and Novoa, 1990).…”

Section: Brazilian Journal Of Chemical Engineeringmentioning

confidence: 99%

A subdivision algorithm for phase equilibrium calculations at high pressures

Corazza

Filho

et al. 2007

Braz. J. Chem. Eng.

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-Phase equilibrium calculations at high pressures have been a continuous challenge for scientists and engineers. Traditionally, this task has been performed by solving a system of nonlinear algebraic equations originating from isofugacity equations. The reliability and accuracy of the solutions are strongly dependent on the initial guess, especially due to the fact that the phase equilibrium problems frequently have multiple roots. This work is focused on the application of a subdivision algorithm for thermodynamic calculations at high pressures. The subdivision algorithm consists in the application of successive subdivisions at a given initial interval (rectangle) of variables and a systematic test to verify the existence of roots in each subinterval. If the interval checked passes in the test, then it is retained; otherwise it is discharged. The algorithm was applied for vapor-liquid, solid-fluid and solid-vapor-liquid equilibrium as well as for phase stability calculations for binary and multicomponent systems. The results show that the proposed algorithm was capable of finding all roots of all high-pressure thermodynamic problems investigated, independent of the initial guess used.

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Nonlinear analysis in process design

Cited by 58 publications

References 151 publications

Application of a control‐law nonlinearity measure to the chemical reactor analysis

Application of a control‐law nonlinearity measure to the chemical reactor analysis

Stochastic Dynamic Optimization of Batch and Semicontinuous Bioprocesses

A subdivision algorithm for phase equilibrium calculations at high pressures

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