A 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.

中文翻译：

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混合柱浮选的建模及边界最优控制设计

一个三相连续混合浮选塔，其目的是同时获得机械池和浮选塔的好处，其建模方法是将代表充分混合区的CSTR与代表纸浆和泡沫区的两个推流反应器（PFR）互连。植物模型考虑了微观过程，例如气泡与颗粒的碰撞和附着以及气泡的出现和破裂。这种复杂的分布参数系统（DPS）由一组非线性耦合守恒逆流双曲偏微分方程（PDE）和一组常微分方程（ODE）来描述。在基于模型的最佳控制器设计中，采用了基于动态守恒律的连续混合浮选塔模型，包括搅拌良好的，纸浆（气泡）和泡沫区。这种基于线性二次调节器（LQR）的控制器考虑了最优性，稳定性和性能。控制器设计利用在感兴趣的工作稳态下通过线性化获得的线性模型。设计了一种全状态最优反馈控制律，并通过对物理意义和相关工厂运行条件的数值模拟，证明了控制器的性能。基于LQR的最优控制器在初始状态发生扰动后恢复到稳态方面比基于比例积分（PI）的控制性能高出一个数量级。设计了一种全状态最优反馈控制律，并通过对物理意义和相关工厂运行条件的数值模拟，证明了控制器的性能。基于LQR的最优控制器在初始状态发生扰动后恢复到稳态方面比基于比例积分（PI）的控制性能高出一个数量级。设计了一种全状态最优反馈控制律，并通过对物理意义和相关工厂运行条件的数值模拟，证明了控制器的性能。基于LQR的最优控制器在初始状态发生扰动后恢复到稳态方面比基于比例积分（PI）的控制性能高出一个数量级。