Interval Type-2 Beta Fuzzy Basis Functions: Some Properties and their First-Order Derivatives

2015 ◽  
Author(s):  
Nesrine Baklouti ◽  
Adel M. Alimi ◽  
Ajith Abraham
Keyword(s):  
Basis Functions ◽  
First Order ◽  
Interval Type

Influence of different fuzzy operators on analytical structure and variable gains of typical interval type-2 fuzzy PI controller

2020 ◽  
Vol 39 (3) ◽  
pp. 4319-4329
Author(s):  
Haibo Zhou ◽  
Chaolong Zhang ◽  
Shuaixia Tan ◽  
Yu Dai ◽  
Ji’an Duan ◽  
...  
Keyword(s):  
Pi Controller ◽  
Real Time Control ◽  
Fuzzy Operators ◽  
Fuzzy Operator ◽  
Analytical Structure ◽  
Product Operator ◽  
Pi Controllers ◽  
Fuzzy Pi Controller ◽  
Interval Type

The fuzzy operator is one of the most important elements affecting the control performance of interval type-2 (IT2) fuzzy proportional-integral (PI) controllers. At present, the most popular fuzzy operators are product fuzzy operator and min() operator. However, the influence of these two different types of fuzzy operators on the IT2 fuzzy PI controllers is not clear. In this research, by studying the derived analytical structure of an IT2 fuzzy PI controller using typical configurations, it is proved mathematically that the variable gains, i.e., proportional and integral gains of typical IT2 fuzzy PI controllers using the min() operator are smaller than those using the product operator. Moreover, the study highlights that unlike the controllers based on the product operator, the controllers based on the min() operator have a simple analytical structure but provide more control laws. Real-time control experiments on a linear motor validate the theoretical results.

scholarly journals Social spider optimization algorithm for tuning parameters in PD-like Interval Type-2 Fuzzy Logic Controller applied to a parallel robot

2021 ◽  
Vol 54 (3-4) ◽  
pp. 303-323
Author(s):  
Amjad J Humaidi ◽  
Huda T Najem ◽  
Ayad Q Al-Dujaili ◽  
Daniel A Pereira ◽  
Ibraheem Kasim Ibraheem ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Trajectory Tracking ◽  
Fuzzy Logic Controller ◽  
Optimization Technique ◽  
Parallel Robot ◽  
Design Parameters ◽  
Social Spider ◽  
Social Spider Optimization ◽  
Interval Type

This paper presents control design based on an Interval Type-2 Fuzzy Logic (IT2FL) for the trajectory tracking of 3-RRR (3-Revolute-Revolute-Revolute) planar parallel robot. The design of Type-1 Fuzzy Logic Controller (T1FLC) is also considered for the purpose of comparison with the IT2FLC in terms of robustness and trajectory tracking characteristics. The scaling factors in the output and input of T1FL and IT2FL controllers play a vital role in improving the performance of the closed-loop system. However, using trial-and-error procedure for tuning these design parameters is exhaustive and hence an optimization technique is applied to achieve their optimal values and to reach an improved performance. In this study, Social Spider Optimization (SSO) algorithm is proposed as a useful tool to tune the parameters of proportional-derivative (PD) versions of both IT2FLC and T1FLC. Two scenarios, based on two square desired trajectories (with and without disturbance), have been tested to evaluate the tracking performance and robustness characteristics of proposed controllers. The effectiveness of controllers have been verified via numerical simulations based on MATLAB/SIMULINK programming software, which showed the superior of IT2FLC in terms of robustness and tracking errors.

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