This paper develops PD-type iterative learning control schemes for a class of uncertain batch processes subject to nonrepetitive disturbances. By means of two-dimensional/repetitive setting the conditions for batch-to-bach error convergence and H ∞ disturbance attenuation are formulated and analyzed. Subsequently, the procedure for computing the desired control law matrices is formulated in terms of solvability of linear matrix inequalities. The proposed control law is able to fulfil the imposed design specifications, i.e., they are suitable for the batch processes with time-varying uncertainties as well as non-repetitive disturbances. An illustrative example is used to validate the proposed control scheme and demonstrates a possible applicability of the developed results.
The paper develops new results on stability analysis and stabilization of linear repetitive processes. Repetitive processes are a distinct subclass of two-dimensional (2D) systems, whose origins are in the modeling for control of mining and metal rolling operations. The reported systems theory for them has been applied in other areas such iterative learning control, where, uniquely among 2D systems based designs, experimental validation results have been reported. This paper uses a version of the Kalman–Yakubovich–Popov Lemma to develop new less conservative conditions for stability in terms of linear matrix inequalities, with an extension to control law design. Differential and discrete dynamics are analysed in an unified manner, and supporting numerical examples are given.
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