MPC with learning properties applied to finite-horizon repetitive systems

Abstract

A repetitive system is one that continuously repeats a finite-duration procedure (operation) along the time. This kind of systems can be found in several industrial fields such as robot manipulation ((Tan, Huang, Lee & Tay, 2003)), injection molding ((Yao, Gao & Allgöwer, 2008)), batch processes ((Bonvin et al., 1984; Lee & Lee, 1999)) and semiconductor processes ((Moyne, Castillo, & Hurwitz, 2003)). Because of the repetitive characteristic, these systems have two count indexes or time scales: o e for the time running within the interval each operation lasts, and the other for the number of operations or repetitions in the continuous sequence. Consequently, it can be said that a control strategy for repetitive systems requires accounting for two different objectives: a short-term disturbance rejection during a finite-duration single operation in the continuous sequence (this frequently means the tracking of a predetermined optimal trajectory) and the long-term disturbance rejection from operation to operation (i.e., considering each operation as a single point of a continuous process1). The MPC proposed in this Chapter is formulated under a closed-loop paradigm ((Rossiter, 2003)). The basic idea of a closed-loop paradigm is to choose a stabilizing control law and assume that this law (underlying input sequence) is present throughout the predictions. More precisely, the MPC propose here is an Infinite Horizon MPC (IHMPC) that includes an underlying control sequence as a (deficient) reference candidate to be improved for the tracking control. Then, by solving on line a constrained optimization problem, the input sequence is corrected, and so the learning updating is performed.