科研之友
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摘要
A method of designing a robust observer-based modified repetitive-control system for a class of strictly proper linear plants with periodic uncertainties has been developed. These plants have no direct path from the input to the output. First, the periodicity and continuity of repetitive control are exploited to construct a continuous-discrete two-dimensional (2D) model that allows the preferential adjustment of control and learning through regulation of the 2D feedback gains. Next, Lyapunov stability theory and the singular-value decomposition of the output matrix are used to establish two stability conditions. The conditions convert (a) the problem of designing the maximum cut-off angular frequency of the low-pass filter into a standard generalised eigenvalue optimisation problem, and (b) the problem of independently designing a state observer and a stabilising controller into a feasibility problem for linear matrix inequalities (LMIs). Two tuning parameters in one of the LMIs determine the selection of the 2D feedback gains. Then, the combination of two design conditions yields an iterative algorithm that simultaneously optimises the maximum cut-off angular frequency of the low-pass filter and the gains of the stabilising controller. It solves the trade-off problem between stability and tracking performance. Finally, a simulation example demonstrates the validity of the method.
