A regulator for continuous sedimentation in ideal clarifier-thickener units.

*(English)*Zbl 1133.76045Summary: The purpose is to present a regulator for control of continuous-sedimentation process in a clarifier-thickener unit when this is modelled in one space dimension and when the settling properties of the solids obey Kynch’s assumption. The model is a scalar hyperbolic conservation law with space-discontinuous flux function and point source. The most desired type of solution contains a large discontinuity. A common objective is to control the movement of this discontinuity subject to the requirement that the effluent of the process have zero concentration of particles. In addition, there may be a requirement that the underflow concentration of the thickened suspension lie above a predefined value. Based on previous results on the nonlinear behaviour of the process [the author, SIAM J. Appl. Math. 56, No. 2, 388–419 (1996; Zbl 0849.35142)], a nonlinear regulator is presented. It controls the location of the large discontinuity indirectly by controlling the total mass. The process is stabilized significantly and large input oscillations can be handled.

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