A systematic study of fuzzy PID controllers-function-based evaluation approach
A systematic study of fuzzy PID controllers-function-based evaluation approach
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DOI：
10.1109/91.963756
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发表时间：
2001-10
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通讯作者：
Bao-Gang Hu;G. Mann;R. Gosine
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作者：
Bao-Gang Hu;G. Mann;R. Gosine
提出了一种基于函数的评估方法，用于系统研究模糊比例积分微分（PID）类控制器。该方法用于通过解决两个问题来导出与过程无关的设计指南：简单性和非线性。为了检验模糊 PID 控制器的简单性，我们得出结论，直接作用控制器比增益调度控制器表现出更简单的设计特性。然后，我们按照五个标准评估直接动作控制器的推理结构：控制动作组合、输入耦合、增益依赖性、增益角色变化和规则/参数增长。分析了使用一输入、二输入和三输入推理结构的三种类型的模糊PID控制器。根据标准，结果表明 Mamdani 的双输入控制器存在一些缺陷。为了保持线性 PID 控制器的简单性，建议使用具有“一对三”映射推理引擎的单输入模糊 PID 控制器。我们讨论非线性近似研究中的三种评估方法：基于函数估计、基于泛化能力和基于非线性变化的近似。本研究重点关注最后一种方法。然后基于非线性变化指标和线性逼近指标这两个指标对多个单输入模糊PID控制器进行非线性评估。利用这些定量指标，可以在不需要任何过程信息的情况下合理选择模糊推理机制和隶属函数。从研究中我们观察到，Zadeh-Mamdani 的“最大-最小重力”方案在非线性变化方面产生最高分数，优于其他方案，例如 Mizumoto 的“乘积和重力”和“Takagi-Sugeno-Kang”方案。
A function-based evaluation approach is proposed for a systematic study of fuzzy proportional-integral-derivative (PID)-like controllers. This approach is applied for deriving process-independent design guidelines from addressing two issues: simplicity and nonlinearity. To examine the simplicity of fuzzy PID controllers, we conclude that direct-action controllers exhibit simpler design properties than gain-scheduling controllers. Then, we evaluate the inference structures of direct-action controllers in five criteria: control-action composition, input coupling, gain dependency, gain-role change, and rule/parameter growth. Three types of fuzzy PID controllers, using one-, two- and three-input inference structures, are analyzed. The results, according to the criteria, demonstrate some shortcomings in Mamdani's two-input controllers. For keeping the simplicity feature like a linear PID controller, a one-input fuzzy PID controller with "one-to-three" mapping inference engine is recommended. We discuss three evaluation approaches in a nonlinear approximation study: function-estimation-based, generalization-capability-based and nonlinearity-variation-based approximations. The study focuses on the last approach. A nonlinearity evaluation is then performed for several one-input fuzzy PID controllers based on two measures: nonlinearity variation index and linearity approximation index. Using these quantitative indices, one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information. From the study we observed that the Zadeh-Mamdani's "max-min-gravity" scheme produces the highest score in terms of nonlinearity variations, which is superior to other schemes, such as Mizumoto's "product-sum-gravity" and "Takagi-Sugeno-Kang" schemes.