Output feedback control of discrete linear repetitive processes

Abstract

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an LMI setting. These results are for the sub-class of the so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control.

H∞ and guaranteed cost control of discrete linear repetitive processes

“…If this is the case then one option is to use the dynamic output controller of the next section, where again the structure of the process dynamics (and, in particular, the 2D transfer function matrix G yw (z 1 , z 2 ), which arises directly from the underlying dynamics of these processes (as opposed to an assumption made)) allows us to obtain, relative to Roesser model analysis, simpler and hence more effective results. Note also that it should be possible to replace the current pass state vector in the control law here with the current pass profile vectorsee [17] where this problem is solved for the problem of computing a control law to ensure stability along the pass with the control law applied.…”

“…In what follows, we assume that the current pass state vector is not available for control purposes and instead we consider the use of a full dynamic pass profile controller of the form (17) to ensure stability along the pass with a guaranteed bound on the associated cost function.…”

Delay-dependent guaranteed cost control for uncertain 2-D discrete systems with state delay in the FM second model

“…then for any delays d 1 and d 2 satisfying 0od 1 pd à 1 and 0od 2 pd à 2 , uði; jÞ ¼ NP À1 xði; jÞ is a guaranteed cost controller, and the cost function (6) of the resulting closed-loop system (8) satisfies…”

“…Many physical processes, such as image processing [4], signal filtering [5], and thermal processes in chemical reactors, head exchangers and pipe furnaces [3], have a clear 2-D structure. The 2-D system theory is frequently used as an analysis tool to solve some problems, e.g., iterative learning control [6,7] and repetitive process control [8,9]. However, the analysis and synthesis approaches for 2-D systems cannot simply extend from existing standard (1-D) system techniques because there are many 2-D system phenomena which have no 1-D system counterparts.…”

An SQP trust region method for solving the discrete-time linear quadratic control problem

“…Several methods have been proposed in the literature based on Lyapunov and Riccati equations, linear matrix inequalities, or eigenstructure assignment; see, e.g., the surveys of Mäkilä and Toivonen (1987) and Syrmos et al (1997) as well as later ones, e.g., those by Varga and Pieters (1998), Garcia et al (2001), Sulikowski et al (2004), Zhai et al (2005), Lee and Khargonekar (2007), Mostafa (2008), and the references therein.…”