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首页> 外文期刊>Journal of computational science >Simulation and control of a complex nonlinear dynamic behavior of multi-stage evaporator using PID and Fuzzy-PID controllers
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Simulation and control of a complex nonlinear dynamic behavior of multi-stage evaporator using PID and Fuzzy-PID controllers

机译：基于PID和Fuzzy-PID控制器的多级蒸发器复杂非线性动力学行为的仿真与控制

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The dynamic model of heptads' stage evaporative unit employed in concentrating black liquor in paper industry show tremendous complexity. In this work, linearization of such a complex nonlinear model consisting of 14 first order nonlinear differential equations and determination of the system transfer functions has been explored through an exhaustive state space representation technique. The transfer functions that relate the product concentration change to liquor flow rate deviation have been evaluated and presented through this work for the first time. These serve as an input to design a PID controller and study its response for a set point change in product concentration. The response analysis indicated a noticeable overshoot, undershoot and Integral Square Error (ISE), that may collectively influence the product quality. To overcome this issue and to make controlling of product concentration more robust, an intelligent Mamdani type Fuzzy Logic-Proportional-Integral-Derivative (FLC-PID) controller has been additionally designed and its response simulated. A comparison of response of FLC-PID and PID indicated that the rise time of former is larger than the latter. However, FLC-PID response settles faster with 49% smaller settling time than PID, possesses zero undershoot, a 93% reduced overshoot and 21% reduced ISE. The results demonstrate improved tracking capability, and hence, better control performance of FLC-PID for transient changes in product concentration. (C) 2017 Elsevier B.V. All rights reserved.
机译：造纸工业中用于浓缩黑液的七步阶段蒸发装置的动力学模型显示出极大的复杂性。在这项工作中，已经通过穷举状态空间表示技术探索了由14个一阶非线性微分方程组成的复杂非线性模型的线性化，并确定了系统传递函数。首次通过这项工作评估并提出了将产品浓度变化与液体流速偏差相关的传递函数。这些用作设计PID控制器并研究其对产品浓度设定值变化的响应的输入。响应分析表明明显的过冲，下冲和积分平方误差（ISE），可能共同影响产品质量。为了克服此问题并使产品浓度控制更加可靠，已另外设计了智能的Mamdani型模糊逻辑比例积分微分（FLC-PID）控制器并对其响应进行了仿真。 FLC-PID和PID响应的比较表明，前者的上升时间大于后者。但是，FLC-PID响应的建立时间比PID更快，建立时间比PID小，下冲为零，过冲为93％，ISE减小为21％。结果证明了改进的跟踪能力，因此，对于产品浓度的瞬时变化，FLC-PID的控制性能更好。 （C）2017 Elsevier B.V.保留所有权利。

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