Adaptive Fuzzy Hysteresis Internal Model Tracking Control of Piezoelectric Actuators With Nanoscale Application

• Published in: IEEE transactions on fuzzy systems Vol. 24; no. 5; pp. 1246 - 1254
• Main Authors: Li, Pengzhi, Li, Peiyue, Sui, Yongxin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Autoregressive processes; Chlorine; Fuzzy adaptive internal model (FAIM); Fuzzy sets; Hysteresis; piezoelectric actuator; Piezoelectric actuators; Takagi–Sugeno (T–S); trajectory tracking
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2015.2502282

In this paper, a novel Takagi-Sugeno (T-S) fuzzy-system-based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the developed fuzzy hysteresis model (FHM) can be identified online through uniform partition approach and recursive least squares (RLS) algorithm, respectively. With respect to the controller design, the inverse of FHM is used to develop a fuzzy internal model (FIM) controller. Decreasing the hysteresis effect, the FIM controller has a good performance of high-speed trajectory tracking. To achieve nanometer-scale tracking precision, the novel fuzzy adaptive internal model (FAIM) controller is uniquely developed. Based on real-time input and output data to update FHM, the FAIM controller is capable of compensating for the hysteresis effect of the piezoelectric actuator in real time. Finally, the experimental results for two cases are shown: the first is with 50 Hz and the other with multiple-frequency (50 + 25 Hz) sinusoidal trajectories tracking that demonstrate the efficiency of the proposed controllers. Especially, being 0.32% of the maximum desired displacement, the maximum error of 50-Hz sinusoidal tracking is greatly reduced to 6 nm. This result clearly indicates the nanometer-scale tracking performance of the novel FAIM controller.