Abstract
Showing superior performance in many areas, interval type-2 (IT2) fuzzy control has received wide acceptability in the last few years. The improved performance is mainly by virtue of the footprint of uncertainty (FoU) underlying the IT2 fuzzy sets. But the design of IT2 fuzzy controllers remains a challenging task since the FoU increases the computational complexity. We propose in this paper a simplified structure of a novel three-input IT2 Takagi–Sugeno (TS) fuzzy PID controller, a parallel combination of fuzzy PI and fuzzy PD controllers having two inputs, respectively. A novel TS rule base is presented which incorporates uncertainty in both input IT2 fuzzy sets and the rule consequent parameters. The rule base consists of two rules that are logically connected with algebraic product (AP) triangular norm and bounded sum (BS) triangular co-norm. AP and BS operators enable the simplification of the input plane, which in turn reduces the complexity of the controller structure. The effect of FoU on the controller structure is fully investigated. Further, we present the simulation studies on magnetic levitation (MagLev) and cart-pole systems to demonstrate the applicability of the proposed fuzzy PID controller.
| Original language | English |
|---|---|
| Pages (from-to) | 589-603 |
| Number of pages | 15 |
| Journal | Soft Computing |
| Volume | 26 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 2022 |
Keywords
- Analytical structure
- Interval type-2 fuzzy control
- Takagi–Sugeno (TS)controller
- Three-term controller
- Variable structure controller