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SUMMARYPossible propagation mechanisms in propene polymerization using heterogeneous catalysts are described by combinations of Bernoulli and first-or even second-order Markov models. Both NMR-measured pentad fractions and GPC a)-measured molecular weight distributions are directly taken into account to fit an appropriate propagation model for a specific catalyst. The analytical data so obtained have been used for an examination of the applicability of multi-site propagation models and for estimation of the main parameters in each model. The propagation and termination probabilities are estimated, as are "mix" parameters giving the fraction of the polymer population stemming from each kind of propagation mechanism. In this way the subpopulation produced by each site is characterized in terms of tacticity and molecular weight distribution. A three-site model is required to explain the measured data properly.

Controllers for processes which frequently return to a number of modes of operation should be adapted through mode recognition.

Abstract. Many processes operate only around a limitednumber of operation points.In order to have adequatecontrol around each operation point, an adaptive controller couldbe used.Then,if the operationpoint changesoften, a largenumberof parameters wouldhaveto be adapted overand over again. This prohibits application of conventional adaptive control, which is more suited for processes with slowly changing parameters. Furthermore, continuous adaptation is not always needed or desired. An extensionof adaptive controlis presented, in whichforeachoperation point the process behaviourcan be storedin a memory, retrieved fromit andevaluated. These functions are coordinatedby a "supervisor". This conceptis referred to as supervisory control. It leadsto an adaptive control structure which, after a learningphase, quickly adjusts the controller parameters based on retrievalof old information, withouttheneedto fully relearneachtime. Thisapproach has been tested on an experimental set-upof a flexiblebeam, but it is directly applicable to processes in e.g, the (petro)chemical industryas well.Keywords. Adaptivecontrol;Automatic tuning; Learning systems; Mode-switch processes; Timevaryingsystems; Supervisory control. 1.INTRODUCTIONMany processes cannotbe controlled adequately by a fixed controller, Then forappropriate control, anadaptivecontroller or evena variable controller structure is needed.Whentheprocess operates ina limited number of operating points, a limited number of controllers suffices. In practical situations a controller will not onlyyieldsatisfactory control performance intheoperation point, but also in the neighbourhood of this operatingpoint. Theset of operating conditions where one controller performs well, is called a mode. Processes which frequently return toan earlierseen mode will be referred to as mode-switch processes (Hilhorst et al., 1991a). In practice there are several processes which exhibit this behaviour and operatein a limited numberof modes only. Suchprocesses arecommon in e.g, the process industry and in robotics. For instance, thismode-SWitch behaviour is encountered ina chemicalreactorin which theyield andquality of theproduct has to be optimized to meet market demands, or in a robot whichhas to transport a limited number of payloads withdifferent masses.In orderto meetthe control demands in each operatingpoint,the useof a conventional adaptive controller (Astrtlm and Wittenmark, 1989) could be considered. However, for mode-switch processes the 195 timeneeded foradaptation may be toolong, i.e. larger than theaverage residence timeina process mode. For instance. because the closed-loop process signals are not sufficiently exciting. Although theaddition oftest signals can increase theadaptation speed. it obviously disturbs the process and hence induces performance loss. Ontheother hand, it seems notto benecessary to repeat thewhole adaptation cycle each time theprocess returns to a certain process mode. Theproblem is that conventional adaptive controllers forget theuseful information which was ...