Control of a surface of discontinuity in continuous thickness.

*(English)*Zbl 0758.35009Summary: This paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration \(C(x,t)\) of particles. The controlled variable is the height \(H^*\) of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.

##### MSC:

35B37 | PDE in connection with control problems (MSC2000) |

76T99 | Multiphase and multicomponent flows |

35F30 | Boundary value problems for nonlinear first-order PDEs |

35R35 | Free boundary problems for PDEs |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

65N99 | Numerical methods for partial differential equations, boundary value problems |

76M20 | Finite difference methods applied to problems in fluid mechanics |