Iterative learning control of multivariable uncertain nonlinear systems with nonrepetitive trajectory

• Published in: Nonlinear dynamics Vol. 95; no. 3; pp. 2197 - 2208
• Main Authors: Boudjedir, Chems Eddine, Boukhetala, Djamel, Bouri, Mohamed
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2019; Springer Nature B.V
• Subjects: Asymptotic methods; Automotive Engineering; Classical Mechanics; Control; Control systems; Control theory; Convergence; Dynamical Systems; Engineering; Learning; Mechanical Engineering; Multivariable control; Nonlinear systems; Original Paper; Robots; Tracking errors; Trajectory control; Vibration; Delta robot; Nonrepetitive trajectory; Alignment condition; Iterative learning control; MIMO uncertain system
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-018-4685-0

Iterative learning control (ILC) theory is based on the traditional assumptions of resetting condition and repetitive trajectory. To overcome these restrictions, a novel ILC is developed in this paper for MIMO uncertain nonlinear systems subject to external disturbances and performing nonrepetitive trajectory. The proposed ILC scheme works under alignment condition and nonrepetitive trajectory that can be varied from iteration to iteration in time interval length, in magnitude scale as well as in initial and final positions. A time-scale transformation is introduced and combined with Lyapunov method to synthesise the control law and to prove the asymptotic convergence. The tracking error converges to zero as the number of iterations increases. Simulation of pick-and-place operations is carried out on a parallel Delta robot in order to show the feasibility and the effectiveness of the proposed approach.