Relative rate observer-based online tuning mechanism for single-input interval type-2 fuzzy PID controllers
Turkish Journal of Electrical Engineering and Computer Sciences, cilt.34, sa.5, ss.809-832, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0632.4277
- Dergi Adı: Turkish Journal of Electrical Engineering and Computer Sciences
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, TR DİZİN (ULAKBİM), Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
- Sayfa Sayıları: ss.809-832
- Anahtar Kelimeler: footprint of uncertainty, IT2-FPID controller, Online adjustment for MFs, relative rate observer
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
The characteristics of the footprint of uncertainty (FOU) in interval type-2 membership functions (IT2-MFs) are crucial to the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). However, existing IT2-FC design approaches mostly use fixed FOU structures. This study proposes an online membership function (MF) adjustment mechanism for a single-input interval type-2 fuzzy PID controller (SIT2-FPID) that adjusts the FOU of the antecedent MFs and the weights of the consequent MFs, respectively, to achieve high performance and robustness. The proposed online adjustment mechanism consists of a relative rate observer (RRO), a two-input rule-base adjustment system, and a first-order smoothing filter. The RRO provides the “normalized acceleration R_v(k)” value, which provides relative information on the speed of the system response. The two inputs of the rule-base adjustment system are “error e(k)” and R_v(k). The raw output of the adjustment mechanism, denoted by γ_raw(k), is filtered to generate the effective tuning signal γ(k), which is then used as a tuning variable for the FOU of the antecedent IT2-MFs and the weights of the consequent crisp MFs. The SIT2-FPID with a proposed adjustment mechanism is compared with the conventional PID controller and an SIT2-FPID with fixed MFs through simulations. Simulation results demonstrate that the proposed SIT2-FPID controller outperforms the conventional PID and SIT2-FPID with fixed MFs controllers in all performance measures and is effective in compensating for input and output disturbances within a short time. These improvements are observed in both linear and nonlinear systems.