This paper presents an integrated interval type-2 fuzzy logic approach that simultaneously models and controls an underactuated mobile two-wheeled inverted pendulum (MTWIP), which suffers from modeling uncertainties and external disturbances. The control objective is to attain the desired position and direction while keeping the MTWIP balanced. It is achieved by integrating four interval type-2 fuzzy logic systems (IT2 FLSs): the first IT2 FLS describes the dynamics of the MTWIP using a Takagi-Sugeno model, the second IT2 FLS controls the balance of the MTWIP using also a Takagi-Sugeno model, and the third and fourth IT2 FLSs control its position and direction, respectively, using a Mamdani model. A linear matrix inequality based design approach is also proposed to guarantee the stability of the balance controller. The proposed approach is compared with a type-1 FLS in real-world experiments. All results demonstrate that the IT2 FLS outperforms the type-1 FLS, especially under modeling uncertainties and external disturbances.

中文翻译：

---

移动两轮倒立摆的区间2型模糊逻辑建模与控制


本文提出了一种集成区间 2 型模糊逻辑方法，可同时对欠驱动移动两轮倒立摆 (MTWIP) 进行建模和控制，该方法受到建模不确定性和外部干扰的影响。控制目标是获得所需的位置和方向，同时保持 MTWIP 平衡。它是通过集成四个区间类型 2 模糊逻辑系统 (IT2 FLS) 来实现的：第一个 IT2 FLS 使用 Takagi-Sugeno 模型描述 MTWIP 的动态，第二个 IT2 FLS 也使用 Takagi-Sugeno 模型控制 MTWIP 的平衡。 Sugeno 模型，第三和第四个 IT2 FLS 分别使用 Mamdani 模型控制其位置和方向。还提出了基于线性矩阵不等式的设计方法来保证平衡控制器的稳定性。所提出的方法与实际实验中的 1 型 FLS 进行了比较。所有结果都表明，IT2 FLS 优于 1 类 FLS，特别是在建模不确定性和外部干扰下。