In even the simplest recycling system with a first-order plus dead time model for the direct and recycling paths, the characteristic equation for the open-loop transfer function contains an infinite number of poles. This is due to the presence of time delays in the internal dynamics. The task of designing a controller is therefore challenging from the perspective of control. This paper considers the problem of stabilising a high-order delayed recycling system (with a possible unstable direct path) through the use of a reduced model in conjunction with a new PID (proportional-integral-derivative)-type delayed controller. We state the condition under which the stability of the closed-loop system is guaranteed and determine the sets of stabilising control parameters. The performance of our proposed strategy is illustrated using several numerical simulations of industrial processes, including an industrial quench column, two continuous stirred tank reactor systems with recycling and a reactor–separator process.

中文翻译：

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基于模型约简的时滞高阶回收系统的延迟PID型控制器设计

即使在具有用于直接路径和再循环路径的一阶加死区时间模型的最简单的再循环系统中，开环传递函数的特征方程也包含无限个极点。这是由于内部动力学中存在时间延迟。因此，从控制的角度来看，设计控制器的任务具有挑战性。本文考虑了通过使用简化模型结合新的PID来稳定高阶延迟回收系统（具有可能不稳定的直接路径）的问题（比例-积分-微分）型延迟控制器。我们陈述了保证闭环系统稳定性的条件，并确定了稳定控制参数的集合。我们提出的策略的性能通过几个工业过程的数值模拟来说明，包括一个工业骤冷塔、两个带循环的连续搅拌釜反应器系统和一个反应器-分离器过程。