Kumar Anupam, Kumar Vijay
Indian Institute of Technology, Department of Electronics and communication Engineering, Roorkee 247667, India.
ISA Trans. 2017 May;68:251-275. doi: 10.1016/j.isatra.2017.03.022. Epub 2017 Mar 31.
In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.
本文提出了一种新型的区间二型分数阶模糊PID（IT2FO - FPID）控制器概念，该控制器需要分数阶积分器和分数阶微分器。研究了将Takagi - Sugeno - Kang（TSK）型区间二型模糊逻辑控制器（IT2FLC）与PID型分数阶控制器相结合，用于单位阶跃响应和单位负载扰动下的时间响应测量。在不同的延迟线性和非线性基准工厂上对所得的IT2FO - FPID控制器进行了测试，并进行了鲁棒性分析。为了设计该控制器，将分数阶积分 - 微分算子视为设计变量，包括输入 - 输出比例因子。一种名为人工蜂群 - 遗传算法（ABC - GA）的新型混合算法用于优化控制器的参数，同时最小化时间绝对误差积分（ITAE）和控制输出平方积分（ISCO）的加权和。为了评估IT2FO - FPID的比较性能，作者将其与现有控制器进行了比较，即区间二型模糊PID（IT2 - FPID）、一型分数阶模糊PID（T1FO - FPID）、一型模糊PID（T1 - FPID）和传统PID控制器。此外，为了展示所提出控制器的有效性，对具有较大死区时间的受扰过程进行了测试。此外，所提出的控制器还在存在未建模动态的多输入多输出（MIMO）、耦合且高度复杂的非线性双连杆机器人操纵器系统上实现。最后，仿真结果明确表明，在大多数情况下，所提出的IT2FO - FPID控制器的性能优于其传统对应物。
