In this paper, two non-singleton interval type-2 fuzzy PID (NIT2F-PID) controllers for the high precision electro-optical tracking system (ETS) are presented to improve anti-interference ability. Specifically, two types of non-singleton fuzzifiers, including type-1 (T1) and type-2 (T2), are considered to construct the proposed NIT2F-PID (N1IT2F-PID and N2IT2F-PID) controllers. Faced with the optimization problem of parameters, particle swarm optimization (PSO), quantum-behaved PSO (QPSO), weighted QPSO (WQPSO) and improved QPSO with adaptive coefficients (LTQPSO) are employed for comparison of convergence performance to optimize the parameters of controllers. In addition, to demonstrate the superiority of the proposed NIT2F-PID controllers, PID, singleton T1 fuzzy PID (ST1F-PID), singleton interval T2 fuzzy PID (SIT2F-PID), T1 non-singleton interval T2 fuzzy (N1IT2F) and T2 non-singleton interval T2 fuzzy (N2IT2F) controllers are also designed. All of these controllers are tested under the circumstances of step disturbance and sinusoidal disturbance. At last, a series of simulation analyses and experimental results explicitly show performance of proposed NIT2F-PID controllers are superior to their counterparts.

本文提出了两种用于高精度光电跟踪系统（ETS）的非单区间2型模糊PID（NIT2F-PID）控制器，以提高抗干扰能力。具体来说，考虑构建所提出的 NIT2F-PID（N1IT2F-PID 和 N2IT2F-PID）控制器的两种类型的非单例模糊器，包括类型 1（T1）和类型 2（T2）。面对参数优化问题，采用粒子群优化（PSO）、量子行为PSO（QPSO）、加权QPSO（WQPSO）和带自适应系数的改进QPSO（LTQPSO）比较收敛性能来优化控制器参数. 此外，为了展示所提出的 NIT2F-PID 控制器的优越性，PID、单例 T1 模糊 PID (ST1F-PID)、单例区间 T2 模糊 PID (SIT2F-PID)、还设计了T1非单区间T2模糊(N1IT2F)和T2非单区间T2模糊(N2IT2F)控制器。所有这些控制器都在阶跃扰动和正弦扰动的情况下进行了测试。最后，一系列仿真分析和实验结果明确表明，所提出的 NIT2F-PID 控制器的性能优于同类控制器。