Iterative Learning Control Based on Relaxed 2-D Systems Stability Criteria

Abstract

Abstract-This brief develops a new algorithm for the design of iterative learning control law algorithms in a 2-D systems setting. This algorithm enables control law design for error convergence and performance, and is actuated by process output information only. Results are also given from the experimental application to a gantry robot.Index Terms-2-D systems design, iterative learning control, repetitive processes.

Parameter‐dependent Lyapunov function‐based robust iterative learning control for discrete systems with actuator faults

“…A multi-axis gantry robot [29], which executes the pick and place task, has been used to test the performance of ILC laws designed in the repetitive process setting [12,13,14]. The robot has three separate axes that are mounted perpendicular to each other and hence each of them can be treated as a single-input single-output system.…”

“…Research in this area has resulted in ILC laws that have been experimentally verified on a gantry robot, e.g., [12]. In this last paper, a constant parameter Lyapunov function based sufficient condition for stability along the pass was used to derive ILC control law matrices, with more recent follow on results in, for example, [13,14,15]. Use of the repetitive process for analysis and design applies to both analog and digital model based design in contrast to the lifted setting, see, for example, the relevant papers cited in [2,3], which applies only to digital design.…”

Singular Distributed Parameter System Iterative Learning Control with Forgetting Factor with Time- Delay

“…Since then, ILC becomes a very important issue of control field. A lot of achievements have been published [2][3][4]. Many of the discussed systems described by ordinary differential equations.…”

Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings

“…In the past few decades, discrete-time two-dimensional (2-D) systems have gained considerable attention since a large number of practical systems can be modeled as 2-D systems, such as those in repetitive processes, image data processing and transmission, thermal processes, gas absorption, water stream heating Dymkov & Dymkou, 2012;Kaczorek, 1985;Marszalek, 1984), and iterative learning control (Cichy, Galkowski, Rogers, & Kummert, 2011;Dabkowski et al, 2013), where one direction of information is from trial-to-trial and the other is along a trial. So far, many important results have been reported in the literature, see for example, Bouagada and Dooren (2013), Gao, Lam, Xu, and Wang (2004), Li and Gao (2012), Paszke, Lam, Gałkowski, Xu, and Lin (2004), Wu, Shi, Gao, and Wang (2008), Wu, Yao, and Zheng (2012), Xiang and Huang (2013), Yang, Xie, and Zhang (2006) and ✩ The material in this paper was not presented at any conference.…”