Analysis of Modified Repetitive Control Schemes: the Port-Hamiltonian Approach

Repetitive Control (RC) schemes are described by systems of coupled PDEs and ODEs and, in this paper, their stability analysis relies on the modularity of the port-Hamiltonian framework to characterise a family of linear plants for which this control technique can be successfully applied. To achieve this, the regulator, that is in fact an infinite dimensional system, is treated as a boundary control system in port-Hamiltonian form, and novel results dealing with the exponential stabilisation of this class of infinite dimensional systems are exploited. The focus here is on plants that are strictly proper and, as a consequence, on Modified Repetitive Control (MRC) schemes, i.e. RC schemes in which a low-pass filter is in series with the pure delay block. The result is a characterisation of a class of linear systems for which MRC schemes converge.