Stabilization of an Unstable Distillation Column

Dorn, Cornelius; Güttinger, Thomas E.; Wells, Gary J.; Morari, Manfred; Kienle, Achim; Klein, E.; Gilles, E. D.

doi:10.1021/ie9703447

Cited by 30 publications

(36 citation statements)

References 9 publications

(7 reference statements)

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“…There are three steady-state branches: two stable steady-state branches and an unstable branch; this was experimentally verified in an industrial pilot column operated at finite reflux [23,39]. Multiple steady-states can be predicted by analyzing columns with infinite reflux and infinite length [14,38,64].…”

Section: Background Of the Problemmentioning

confidence: 85%

A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations

2016

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Tearing is a long-established decomposition technique, widely adapted across many engineering fields. It reduces the task of solving a large and sparse nonlinear system of equations to that of solving a sequence of low-dimensional ones. The most serious weakness of this approach is well-known: It may suffer from severe numerical instability. The present paper resolves this flaw for the first time. The new approach requires reasonable bound constraints on the variables. The worst-case time complexity of the algorithm is exponential in the size of the largest subproblem of the decomposed system. Although there is no theoretical guarantee that all solutions will be found in the general case, increasing the so-called sample size parameter of the method improves robustness. This is demonstrated on two particularly challenging problems. Our first example is the steady-state simulation a challenging distillation column, belonging to an infamous class of problems where tearing often fails due to numerical instability. This column has three solutions, one of which is missed using tearing, but even with problem-specific methods that are not based on tearing. The other example is the Stewart-Gough platform with 40 real solutions, an extensively studied benchmark in the field of numerical algebraic geometry. For both examples, all solutions are found with a fairly small amount of sampling.

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Section: Background Of the Problemmentioning

confidence: 85%

A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations

2016

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“…In addition, a -20% step change in the boilup results in a stable response with the column settling at a new steady state implying feasibility. These dynamic results serve to highlight that the implementation of feedback control serves to mitigate the non-linear effects of output multiplicity so that an open loop steady transition is prevented (Dorn et al, 1998). Feedback control also ensures feasible operation over a larger disturbance range.…”

Section: Ideal Rd Columnmentioning

confidence: 90%

Reactive Distillation: Control Structure and Process Design for Robustness

Malladi¹,

Kaistha²

2011

Challenges and Paradigms in Applied Robust Control

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“…These multiplicities have been verified experimentally for a ternary homogeneous Ž and a heterogeneous system Muller. and Marquardt, 1997;Dorn et al, 1998 . Ž . Note that the forth type 2b only occurs in reactive distil-Ž .…”

Section: žmentioning

confidence: 99%