ABSTRACT

Over the last three decades, finding the mathematical models of fuzzy controllers has become an interesting area of research in the control community. The mathematical model of a controller gives a clear insight into the analytical structure of a controller and helps to understand the control problem in the framework of well-defined control theory. Because of modelling and computational complexities, from the literature, it seems to the authors that modelling of three-input fuzzy PID controller has rarely been attempted using the Center of Gravity (CoG) defuzzification. The purpose of the present manuscript is to unveil the exact mathematical model of a nonlinear fuzzy three-input PID controller using CoG defuzzification and to investigate its properties. To justify the theoretical development made in this manuscript, the applicability of the proposed controller is shown through simulation and real-time studies. In the simulation, a nonlinear plant, an unstable plant with large time-delay, and a higher-order plant with dead-time and inverse response are controlled. Whereas in real-time an unstable nonlinear Magnetic levitation (Maglev) plant is controlled. As the proposed controller structure does not depend on plant dynamics, it can easily be implemented for other control applications also.

摘要

在过去的三年中，寻找模糊控制器的数学模型已成为控制界的一个有趣的研究领域。控制器的数学模型可以清楚地了解控制器的分析结构，并有助于在明确定义的控制理论框架内理解控制问题。由于建模和计算的复杂性，从文献来看，作者似乎很少尝试使用重心 (CoG) 去模糊化对三输入模糊 PID 控制器进行建模。本手稿的目的是揭示使用 CoG 去模糊化的非线性模糊三输入 PID 控制器的精确数学模型并研究其性质。为了证明本手稿中的理论发展，通过仿真和实时研究显示了所提出控制器的适用性。在仿真中，对非线性被控对象、具有大时滞的不稳定被控对象和具有死区时间和逆响应的高阶被控对象进行控制。而实时控制不稳定的非线性磁悬浮 (Maglev) 设备。由于所提出的控制器结构不依赖于工厂动态，因此它也可以很容易地用于其他控制应用程序。