Output Regulation of Linearized Column Froth Flotation Process

This article explores the output regulation problem of the linearized column froth flotation process consisting of collection and froth regions that are modeled by a set of linear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs) with time delay. Collection and froth regions are combined through PDE boundary conditions and time-delay models the interconnections between PDE boundary and ODEs representing well-stirred reactor dynamics. The linearization of the original nonlinear system is carried out to obtain a linearized PDE-ODE system. To complete the output regulation of resulting PDE-ODE systems, one challenge is the design of an observer and stabilization controller. We proposed to obtain the stabilization feedback gains and the observer injection gains by solving operator Riccati equations; in particular, these gains can also assign a specific exponential decay rate. Another challenge is the solvability of regulator equations that arise during the regulator design for the linearized PDE-ODE systems. In particular, we consider the tracking control of more general reference signals, including step, ramp, harmonic, and arbitrary polynomial signals, and novelty lies in the necessity to investigate the solvability of the corresponding regulator equations. In this article, the development of state feedback and error feedback regulators are designed and the regulator performance is demonstrated by simulation studies.