简化通用型 2 型模糊 PID 控制器的数学分析。
Mathematical analysis of a simplified general type-2 fuzzy PID controller.
机构信息
School of Energy and Power Engineering, Nanjing Institute of Technology, Nanjing 211167, China.
出版信息
Math Biosci Eng. 2020 Nov 12;17(6):7994-8036. doi: 10.3934/mbe.2020406.
For the type reduction of general type-2 fuzzy PID controller is time consuming and the mathematical expression of general type-2 fuzzy PID controller is difficult to derived. So, a simplified general type-2 fuzzy PID (SGT2-FPID) controller is studied in this article. The SGT2-FPID controller adopts triangular function as the primary and secondary membership function. Then the primary membership degree of apex for the secondary membership degree will be applied to get the output of SGT2-FPID controller, which can reduce the computation complexity of general type-2 fuzzy controller type reduction. Furthermore, the mathematical expressions of SGT2-FPID controller, type-1 fuzzy PID controller and interval type-2 fuzzy PID controller are discussed. Finally, 4 plants are applied to demonstrate the effectiveness and robustness of SGT2-FPID controller. The simulation results show that when the plants have uncertainty in model structure, measurement and external disturbance, the SGT2-FPID controller can achieve better control performances in contrast to compared controllers.
对于通用型 2 型模糊 PID 控制器的简化，其类型减少是耗时的，并且通用型 2 型模糊 PID 控制器的数学表达式难以推导。因此，本文研究了简化的通用型 2 型模糊 PID（SGT2-FPID）控制器。SGT2-FPID 控制器采用三角形函数作为主要和次要隶属度函数。然后，将二次隶属度的顶点的主要隶属度应用于获得 SGT2-FPID 控制器的输出，这可以降低通用型 2 型模糊控制器类型减少的计算复杂度。此外，还讨论了 SGT2-FPID 控制器、1 型模糊 PID 控制器和区间型 2 模糊 PID 控制器的数学表达式。最后，应用 4 个植物来证明 SGT2-FPID 控制器的有效性和鲁棒性。仿真结果表明，当植物在模型结构、测量和外部干扰方面存在不确定性时，与比较控制器相比，SGT2-FPID 控制器可以实现更好的控制性能。
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