A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

Abstract

Abstract-The Interval Type-2 Fuzzy PI controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance which could be potentially due to the robust performance as a result of the smoother control surface around the steady state [1]. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison to the Type-1 Fuzzy PI (T1-FPI) counterpart [1]. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a trade-off between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices based general Type-2 Fuzzy PI controller (zT2-FPI) where the Secondary Membership Functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an on-line manner. We will examine the effect of the SMF on the closed system control performance to investigate their induced performance improvements. The paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared to the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems in addition to real-world experiments which were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared to the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise and uncertainties when compared to the type-1 and interval type-2 fuzzy counterparts.

Landing on the moon with type-2 fuzzy logic

“…That lies because the design of the IT2-FLC has been accomplished as an extension of its T1 counterpart. Moreover, this also coincides with the results presented in [23] where it has been stated that the IT2-FLCs result in smoother control surfaces in comparison with its T1 counterpart. Thus, the resulting system response might be relatively slower but potentially more robust against uncertainties.…”

Using a 3D Interval Type-2 Fuzzy Interpolation System to Improve Modeless Robots Measurement and Calibration Accuracy

“…Similar to type 1 fuzzy inference system, the type 2 fuzzy inference systems still use the input and output membership functions, combined with the control rules, to derive the outputs [13][14][15][16][17][18][19][20][21]. However, the fuzzy sets used in the type 2 fuzzy logic or the membership grades involved in each membership function are not crisp values, but another fuzzy sets.…”

Type 2 fuzzy logic-based robust control strategy for power sharing in microgrids with uncertainties in operating conditions

“…Unlike the type 1 sets, the type 2 FLSs are described with a 3‐dimensional fuzzy MF that includes a footprint of uncertainty (FOU). The third dimension of MFs and FOU together provide an additional degree of freedom in the controller design that makes it possible to directly model and handle the uncertainties associated with the rules and MFs . The IT2‐FLC can be designed for a smoother control surface, which enables it to behave like a variable gain PI controller.…”