2D systems based robust iterative learning control using noncausal finite-time interval data

Abstract

a b s t r a c tThis paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.

Multidimensional control systems: case studies in design and evaluation

“…One option is to use the GKYP lemma [Paszke et al (2013)] to permit design over finite frequency ranges of interest and again these designs have been experimentally benchmarked on the gantry robot. As another problem demonstrating the scope of repetitive process models in ILC design, [Cichy et al (2014)] has used the wave repetitive process setting to examine how best to make use of previous pass data.…”

Robust fault-tolerant iterative learning control for discrete systems via linear repetitive processes theory

“…Finally, there are alternative 2D systems based designs that could be employed, e.g., [28], but the form of the control law to be implemented is much less transparent in terms of actual implementation. Moreover, the analysis in [22] uses a repetitive process model that has no 2D discrete linear systems counterpart. Finally, the repetitive process setting for design can be undertaken for differential dynamics, i.e., where design by emulation is the preferred or only option for a given application.…”

“…Also, the repetitive process setting has been used [22] to develop results on how to make the most effective use of previous trial information.…”

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

“…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.…”