Non-singleton interval type-2 fuzzy PID control for high precision electro-optical tracking system

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.