Modelling and boundary optimal control design of hybrid column flotation

Abstract

AbstractA three‐phase continuous hybrid flotation column that seeks to obtain the benefits of both mechanical cells and flotation columns is modelled as the interconnection of a CSTR representing the well‐mixed zone and two plug‐flow reactors (PFR) representing pulp and froth zones. The plant model accounts for the micro‐scale processes such as bubble‐particle collision and attachment and the appearance and breakage of bubbles. This complex distributed parameter system (DPS) is described by sets of nonlinear coupled conservation counter‐current hyperbolic partial differential equations (PDEs) and one set of ordinary differential equations (ODEs). The dynamic conservation law‐based model for the continuous hybrid flotation column including well‐stirred, pulp (bubbly), and froth zones, is utilized in an optimal model‐based controller design. This linear quadratic regulator (LQR)‐based controller accounts for optimality, stability, and performance. The controller design utilizes a linear model obtained by linearization at operating steady states of interest. A full‐state optimal feedback control law is designed and controller performance has been demonstrated through a numerical simulation of physically meaningful and relevant plant operating conditions. The LQR‐based optimal controller outperforms proportional‐integral (PI)‐based control by more than an order of magnitude in terms of a return to steady state after a perturbation in the initial condition.