Fixed-Time Adaptive Control With Predefined Tracking Accuracy for Piezoactuators Subject to Stochastic Disturbances

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 72; no. 7; pp. 3543 - 3555
• Main Authors: Lai, Guanyu, Li, Liang, Wang, Yonghua, Xiao, Hanzhen, Chen, C. L. Philip
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Adaptive control; adaptive fuzzy control; Asymptotic stability; Circuit stability; Convergence; Disturbances; fixed-time control; Fuzzy control; Fuzzy logic; High speed; Hysteresis; Integrated circuit modeling; Mathematical models; Nonlinear systems; Nonlinearity; Piezoactuators; Piezoelectric actuators; Preisach hysteresis; Preisach's theory; Robust control; Stability; Stability criteria; stochastic disturbances; Stochastic processes; Stochastic systems; Tracking control
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2024.3488791

The work aims to solve the high-speed high-precision tracking control problem of piezoactuators in the presence of stochastic disturbances. First, a cascade model composed of the Preisach operator and a class of stochastic nonlinear systems is proposed to describe the sophisticated actuator dynamics during high-speed operation, and then a hysteresis decomposition strategy is developed to transform the Preisach model into an appropriate form tractable to control design so that a robust adaptive fuzzy control framework can be constructed successfully to suppress the hysteresis nonlinearities, and to robustify bounded stochastic disturbances. More importantly, based on such a framework, the fixed-time stability (instead of practical fixed-time stability), and the prescribed steady-state tracking performance can be established simultaneously. Besides theoretical analysis, some experimental tests are also conducted to illustrate the effectiveness of the proposed scheme.