Robust H∞ control of an observer-based repetitive-control system

• DOI: 10.1016/j.jfranklin.2018.05.024
• Publication Date: 2018-05-26T12:18:21Z
• Authors: Lan Zhou; Jinhua She; Shaowu Zhou
• Keywords: Aperiodic graph; Repetitive Control; Linear matrix inequality; Observer (physics); Lyapunov stability

Abstract This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.