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Abstract：
A methodology is developed to systematically design the membership functions of fuzzy-logic controllers for multivariable systems. The methodology consists of a systematic derivation of the critical points of the membership functions as a function of predefined control objectives. Several constrained optimization problems corresponding to different qualitative operation states of the system are defined and solved to identify, in a consistent manner, the critical points of the membership functions for the input variables. The consistently identified critical points, together with the linguistic rules, determine the long term reachability of the control objectives by the fuzzy logic controller. The methodology is highlighted using a single-stage side-stream partial nitritation/Anammox reactor as a case study. As a result, a new fuzzy-logic controller for high and stable total nitrogen removal efficiency is designed. Rigorous simulations are carried out to evaluate and benchmark the performance of the controller. The results demonstrate that the novel control strategy is capable of rejecting the long-term influent disturbances, and can achieve a stable and high TN removal efficiency. Additionally, the controller was tested, and showed robustness, against measurement noise levels typical for wastewater sensors. A feedforward-feedback configuration using the present controller would give even better performance. In comparison, a previously developed fuzzy-logic controller using merely expert and intuitive knowledge performed worse. This proved the importance of using a systematic methodology for the derivation of the membership functions for multivariable systems. These results are promising for future applications of the controller in real full-scale plants. Furthermore, the methodology can be used as a tool to help systematically design fuzzy logic control applications for other biological processes.
摘要：
开发了一种方法来系统地设计多变量系统的模糊逻辑控制器的隶属函数。该方法包括根据预定义的控制目标系统地推导隶属函数的临界点。定义并求解对应于系统不同定性运行状态的若干约束优化问题,以一致的方式，输入变量的隶属函数的临界点。一致确定的临界点，连同语言规则，通过模糊逻辑控制器确定控制目标的长期可达性。以单级侧流部分亚硝化/Anammox反应器为例，重点介绍了该方法。因此,设计了一种新的模糊逻辑控制器，用于实现高而稳定的总氮去除效率。进行严格的仿真以评估和基准控制器的性能。结果表明，新的控制策略能够拒绝长期的流入干扰，并能实现稳定、高的TN去除效率。此外,对控制器进行了测试，并显示出鲁棒性，针对废水传感器典型的测量噪声水平。使用本控制器的前馈-反馈配置将给出甚至更好的性能。相比之下,以前开发的模糊逻辑控制器仅使用专家和直觉知识表现更差。这证明了使用系统方法推导多变量系统隶属函数的重要性。这些结果对于控制器在实际的全尺寸工厂中的未来应用是有希望的。此外，该方法可以作为一种工具来帮助系统地设计其他生物过程的模糊逻辑控制应用。
