Optimization of multiple‐fraction batch distillation with recycled waste cuts

Diehl, Moritz; Schäfer, Andreas; Bock, Hans Georg; Schlöder, Johannes P.; Leineweber, Daniel B.

doi:10.1002/aic.690481214

Cited by 14 publications

(8 citation statements)

References 16 publications

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“…In this paper for the discussion of spectral intervals, we restrict ourselves to regular DAEs, i. e., we require that (1) (or (3) locally) has a unique solution for sufficiently smooth E, A, f (F ) and appropriately chosen (consistent) initial conditions, see [50] for a discussion of existence and uniqueness of solution of more general nonregular DAEs. DAEs like (1) and (3) arise in constrained multibody dynamics [36], electrical circuit simulation [38,39], chemical engineering [32,33] and many other applications, in particular when the dynamics of a system is constrained or when different physical models are coupled together in automatically generated models [64]. While DAEs provide a very convenient modeling concept, many numerical difficulties arise due to the fact that the dynamics is constrained to a manifold, which often is only given implicitly, see [9,41,67] or the recent textbook [50].…”

Section: Introductionmentioning

confidence: 44%

Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations

Linh

Mehrmann

2009

J Dyn Diff Equat

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Lyapunov and exponential dichotomy spectral theory is extended from ordinary differential equations (ODEs) to nonautonomous differential-algebraic equations (DAEs). By using orthogonal changes of variables, the original DAE system is transformed into appropriate condensed forms, for which concepts such as Lyapunov exponents, Bohl exponents, exponential dichotomy and spectral intervals of various kinds can be analyzed via the resulting underlying ODE. Some essential differences between the spectral theory for ODEs and that for DAEs are pointed out. It is also discussed how numerical methods for computing the spectral intervals associated with Lyapunov and Sacker-Sell (exponential dichotomy) can be extended from those methods proposed for ODEs. Some numerical examples are presented to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 44%

Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations

Linh

Mehrmann

2009

J Dyn Diff Equat

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“…DAEs arise in constrained multibody dynamics [27], electrical circuit simulation [32,33], chemical engineering [25,26] and many other applications, in particular when the dynamics of a system is constrained or when different physical models are coupled together in automatically generated models [42]. While DAEs provide a very convenient modeling concept, many numerical difficulties arise due to the fact that the dynamics is constrained to a manifold, which often is only given implicitly, see [36].…”

Section: Introductionsupporting

confidence: 39%

QR methods and error analysis for computing Lyapunov and Sacker–Sell spectral intervals for linear differential-algebraic equations

Linh¹,

Mehrmann

Vleck

2010

Adv Comput Math

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In this paper, we propose and investigate numerical methods based on QR factorization for computing all or some Lyapunov or Sacker-Sell spectral intervals for linear differential-algebraic equations. Furthermore, a perturbation and error analysis for these methods is presented. We investigate how errors in the data and in the numerical integration affect the accuracy of the approximate spectral intervals. Although we need to integrate numerically some differential-algebraic systems on usually very long time-intervals, under certain assumptions, it is shown that the error of the computed spectral intervals can be controlled by the local error of numerical integration and the error in solving the algebraic constraint. Some numerical examples are presented to illustrate the theoretical results.Communicated by Rafael Bru.

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“…The number of time grid points used in this paper was 40 per half stride, similar to comparable studies (Posa et al, 2014; Posa and Tedrake, 2013). The MS results were obtained via an established MS framework (MUSCOD (Diehl et al, 2001). The number of shooting intervals was also 40.…”

Section: Methodsmentioning

confidence: 99%

Selecting gaits for economical locomotion of legged robots

Yesilevskiy

Remy

2015

The International Journal of Robotics Research

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This paper explores the benefits of using multiple gaits in a single robot. Inspired by nature, where humans and animals use different gaits to increase their energetic economy, we analyzed how increasing speed affects the choice of gait, and how the choice of gait influences optimal speed. To this end, we used optimal control as a tool to identify motions that minimize the cost of transport of two detailed models: a planar biped and a planar quadruped. Both of these models are actuated with high compliance series elastic actuators that enable a rich set of natural dynamics. These models have damping in their springs, feet with mass, and realistic limitations on actuator torques and velocities. They therefore serve as an intermediary between past simpler models and hardware. We discovered optimal motions with an established multiple shooting implementation that relies on pre-defined contact sequences, and with a direct collocation implementation in which the footfall pattern was an outcome of the optimization. Both algorithms confirmed findings from biology. For both models, changing gaits as speed varies leads to greatly increased energetic economy. For bipeds, the optimal gaits were walking at low speeds, grounded running at intermediate speeds, and running at high speeds. For quadrupeds, the optimal gaits were four-beat walking at low speeds and trotting at intermediate speeds. At high speeds, galloping and trotting were the best gaits, with nearly equal performance. We found that the transition between gaits was primarily driven by damping losses and negative actuator work, with collisions playing a relatively small role.

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Optimization of multiple‐fraction batch distillation with recycled waste cuts

Cited by 14 publications

References 16 publications

Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations

Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations

QR methods and error analysis for computing Lyapunov and Sacker–Sell spectral intervals for linear differential-algebraic equations

Selecting gaits for economical locomotion of legged robots

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