A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters

Abstract

In this paper a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous consideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using Linear Matrix Inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable.

Repetitive process based iterative learning control design using frequency domain analysis

“…Application of the result of Lemma 1 to the ILC model (14), where the model matrices are given by (15), yields matrix inequalities which are not convex. This difficulty is removed by the following result expressed in terms of LMIs and provides an algorithm for designing the control law, that is, the matrices K 1 and K 2 in (13).…”

“…Theorem 2: Consider an ILC scheme written as a discrete linear repetitive process of the form (14). Then stability along the pass, that is, pass-to-pass error convergence, holds if there exist matrices Q 0 N , K 2 such that the following LMIs are feasible…”

“…Theorem 2 can be only applied to systems with CB = 0 because the LMI (18) not feasible when CB = 0, since in this case D 0 = I. To remove this limitation, the analysis that follows introduces a low-pass filter with unity dc-gain and sufficiently high cut-off frequency into the ILC scheme (14), where the input to this filter is the current trial error (e k+1 defined by (14)). (This ideas was also suggested in [8] for non-ILC applications.…”

Design of iterative learning control schemes for systems with zero Markov parameters

“…Each axis of the gantry robot was modeled based on the frequency response function method where, since the axes are orthogonal, it is assumed that there is minimal interaction between them. In [15], [16] the following continuous-time transfer-function has been obtained for one of the axes G(s) = 15.8869(s + 850.3) s(s 2 + 707.6s + 3.377 × 10 5 ) .…”

A 2D Hopfield Neural Network approach to mechanical beam damage detection

“…Note that the damage detection problem is treated in a 2D framework in spite of the beam length being finite. This type of approach is also frequent in repetitive processes, in the sense that it is also common to see a system that is finite in one of the directions to be treated as a 2D system (see [19], for instance). Looking at the damage detection problem in a 2D context allows us to choose di↵erent discretization steps in both directions, time and one-dimensional space, which is an advantage.…”