Recent Developments in Stochastic Distribution Control/A Review

Abstract

Figure 1: MWD in chemical control reaction system Mokcumrwe~htd~tributionconuolm polymerisation processesIt is important to control a polymer's molecular weight distribution (MWD) in industrial polymerisation processes because a polymer's end-use properties are strongly dependent on its MWD. Though it is still not an easy control task, extensive studies have been made on how to get a polymer's MWD when the polymerisation kinetic model is available5.6.25. Mostly the MWD is calculated by numerical integration of the polymer material balances or by using the moment generating function. In certain cases, some stochastic models have been proposed for MWD description. For example, for linear chains, Flory's distribution can be used to describe the instantaneous MWD of polyolefin made with single-site-type catalystslI.Industry-scale closed-loop control of MWD is still a challenging subject because the feasibility of on-line measurement of MWD for polymerisation processes remains to be demonstrated. Most research is based on simulated reactors. In order to get a target MWD, especially for batch processes, normally optimal or sub-optimal control trajectories are determined by optimisation design either off-line 6 ,27 or on-line lB . 26 . and then efforts are made to implement these trajectories using control strategies. State observers are often needed to get on-line trajectories lB , while for off-line control trajectories, batch-to-batch modifications to the optimal trajectories may be added so that the target MWD can be achieved after several batches 4 • Figure 1 shows a general MWD system. General research into the control of stochastic systems has been focused on the control of the system output, rather than the probability density function (PDF) of the system output. A number of well-known algorithms have thus been developed such as minimum variance control, linear quadratic Gaussian control, self-tuning control and stochastic control for systems with Markovian jump parameters, etc. In most of the existing approaches, it has been assumed that the random variables in the system are subjected to Gaussian processes. This is based on the fact that most input noises can be characterised as coloured noises, which are generated by a white noise sequence. Although many successful awlications of these developed methods have been reponed, difficulties remain in many cases where this assumption is not valid. As such, a new group of techniques has been developed for the model1ing and control of the probability density functions of the output variables of stochastic systems 3l .The idea of stochastic distribution control is to design the control input so that the PDF of the system output can follow a target PDF. This control purpose is highly demanded in many industrial systems, such as chemical engineering, powder industry, papermaking, and combustion flame distribution processes, etc. Several typical industrial examples are discussed here. Industrial BackgroundA group of new control strategies called stochastic distribution c...

Applying constrained nonlinear generalized PI strategy to PDF tracking control through square root B-spline models

“…This has led to some simulated results for the output PDF control. However, when the linear weight models are tested on a molecular weight distribution control case in Yue and Wang (2003), it has been observed that the closed loop performance cannot be further improved due to the existence of some nonlinearities. As such, to demonstrate the use of the proposed algorithm in this paper, a nonlinear dynamic weight model given by (5) will be used.…”

Fault detection and diagnosis for stochastic systems via output PDFs

“…[7][8][9][10][11][12][13][14][15][16][17] (or observer)-based approaches, the identification-based schemes, and the statistic approaches [6]. However, it is noted that most of the FDD methodologies for stochastic systems only considered Gaussian systems [3] and one of the common features for these methods is performed by using system input and output measures.…”

“…Motivated by such typical examples, studies on stochastic distribution systems (SDSs) and stochastic distribution control have been addressed and studied in (see [5,[9][10][11][12][13][14][15][16][17]). Different from any other previous stochastic control approaches, the stochastic variables are not confined to be Gaussian and the output PDFs of the stochastic system is concerned rather than the mean or variance of the output.…”

Delay-dependent fault detection and diagnosis using B-spline neural networks and nonlinear filters for time-delay stochastic systems

“…Typical examples include the retention of paper making, particle distribution, molecular weight distribution and flame greylevel distribution processing [12]. Motivated by such typical examples, a new group of strategies that control the shape of output probability density functions (PDFs) for stochastic systems have been developed in the past a few yeas (see [5,13]). Different from any other previous stochastic control approaches, the stochastic variables are not confined to be Gaussian and the output PDFs of the stochastic system is concerned rather than the mean or variance of the output.…”