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Operating charts for continuous sedimentation. IV: Limitations for control of dynamic behaviour. (English) Zbl 1154.76047
Summary: The nonlinear behaviour of a one-dimensional idealized model of continuous sedimentation has been investigated in this series of papers [for parts I, II, III see the author, ibid. 41, No. 2–3, 117–144 (2001; Zbl 1128.76370); 53, No. 2, 139–185 (2005; Zbl 1086.76069); 54, No. 3, 225–259 (2006; Zbl 1189.76667), respectively]. The model is a scalar hyperbolic conservation law with a space-discontinuous flux function and a point source. Parameters in the equation are two input variables (concentration and flux) and the control variable (a volume flow). The most desired type of solution contains a large concentration discontinuity and is referred to as ‘optimal operation’. Operating charts (concentration-flux diagrams) have proved to be a means for classifying the nonlinear behaviour. In this paper, some fundamental results on the dynamic behaviour are presented, which give information on the limitations of the range of the control variable. When this is used together with the previously introduced optimal control strategies for step inputs, the process can be controlled.

MSC:
76N25 Flow control and optimization for compressible fluids and gas dynamics
76T20 Suspensions
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