Optimization of simulated moving bed chromatography with fractionation and feedback: Part II. Fractionation of both outlets

A new improvement based on outlet fractionation and feedback has been developed for simulated moving bed (SMB) chromatography. In this contribution, this fractionation and feedback SMB (FF-SMB) concept is extended to the general scenario which integrates a simultaneous fractionation of both outlet streams. A model-based optimization approach, previously adopted to investigate single fractionation, is extended to consider this flexible fractionation policy. Quantitative optimization studies based on a specific separation problem reveal that the double fractionation is the most efficient operating scheme in terms of maximum feed throughput, while the two existing single fractionation modes discussed in our previous study are also significantly superior to the conventional SMB operation. The advantages of the double fractionation extension are further demonstrated in terms of several more detailed performance criteria. In order to evaluate the applicability of the fractionation and feedback modification, the effect of product purity, adsorption selectivity, column efficiency and column number on the relative potential of FF-SMB over SMB is examined.     

Chaos control of fractional order Rabinovich–Fabrikant system and synchronization between chaotic and chaos controlled fractional order Rabinovich–Fabrikant system

In this article the local stability of the Rabinovich–Fabrikant (R–F) chaotic system with fractional order time derivative is analyzed using fractional Routh–Hurwitz stability criterion. Feedback control method is used to control chaos in the considered fractional order system and after controlling the chaos the authors have introduced the synchronization between fractional order non-chaotic R–F system and the chaotic R–F system at various equilibrium points. The fractional derivative is described in the Caputo sense. Numerical simulation results which are carried out using Adams–Boshforth–Moulton method show that the method is effective and reliable for synchronizing the systems.     

Relaxation in nonconvex optimal control problems described by fractional differential equations

We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously.     

Achievement of chaotic synchronization trajectories of master-slave manipulators with feedback control strategy

This paper addresses a master-slave synchronization strategy for complex dynamic systems based on feedback control.This strategy is applied to 3-DOF planar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors.A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors.The dynamical equations of master-slave mani...     

A production system with two job classes,changeover times and revisitation

This paper, motivated by the need to predict performance of production systems with random arrivals, setup times and revisitation, presents an imbedded Markov chain analysis of the underlyingM/G/1 queue with two customer classes, changeover times and instantaneous Bernoulli feedback. It is assumed that jobs are scheduled according to the exhaustive alternative priority queue discipline. Expressions for the mean waiting time and the nonsaturation condition are derived under two different priority assignments to the repeat customers. Sojourn times under these priority assignments are shown to possess a convex ordering. Results of the study are also applicable to data communication networks that operate under cyclic switching mechanisms. Research supported in part by Natural Sciences and Engineering Research Council of Canada.     

On open-loop and feedback attainability of a closed set for nonlinear control systems

In this note, we investigate the existence of controls which allow to reach a given closed set K through trajectories of a nonlinear control system. In the case where the set is sufficiently regular we give a condition allowing to find a feedback control law which ensures the existence of trajectories to reach the set. We also consider the case where all the trajectories reach K. When K is not necessarily attainable but only viable, we build a set-valued feedback for which the set is invariant. Our approach concerns continuous dynamics, possibly not C¹, so our methods do not come from geometric control theory. Furthermore, we do not require any regularity of the set K in order to obtain our results, except when we want to establish the existence of a feedback control law to achieve our goals.     

Forcing matchings on square grids

Let G be a graph that admits a perfect matching. The forcing number of a perfect matching M of G is defined as the smallest number of edges in a subset S M, such that S is in no other perfect matching. We show that for the 2n × 2n square grid, the forcing number of any perfect matching is bounded below by n and above by n². Both bounds are sharp. We also establish a connection between the forcing problem and the minimum feedback set problem. Finally, we present some conjectures about forcing numbers in other graphs.     

Fluorescence feedback control of a diode pumped solid state laser

We implement active feedback control in a Q-switched diode-pumped Nd:YVO₄ laser by monitoring the fluorescence intensity from the laser crystal. When the initial inversion level indicated by the detected fluorescence has reached a predetermined value, Q-switching is initiated. The Q-switched pulse energy is stabler with our feedback scheme based on the fluorescence intensity than that with the conventional Q-switching when pumping source is not stable.     

粘性解框架下的完全耦合正倒向随机系统最优控制问题的验证定理

研究了完全耦合正倒向随机控制系统的最优控制问题.得到了粘性解框架下的,控制变量同时出现在正倒向随机系统的漂移项和扩散项中的最优控制问题的验证定理.还讨论了验证定理在构造随机最优反馈控制中的应用.     

Synchronization of a growing chaotic network model

Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon, which is helpful for the understanding of working mechanisms in neuronal networks, social network, etc. In this paper, we will investigate the synchronization phenomenon in a network model. A feedback control scheme is proposed for the synchronization of the given complex networks. The obtained result indicates that synchronization can be achieved for growing chaotic network model. Method enhance the synchronizability of the given model are given at the same time. Finally, numerical simulations are given to show the effectiveness of obtained results.