Stability and performance robustness analysis of repetitive control systems using structured singular values

The structured singular value method is applied to continuous-time SISO repetitive control systems in order to determine their stability and performance robustness in the presence of structured parametric modeling error in the plant. Performance measures for repetitive control systems are introduced and the robust performance analysis using structured singular values is modified, taking the alternating magnitude behaviour of the sensitivity function of a repetitive control system into account. The analysis procedure is simplified considerably in the case of large time delay by noting that the upper and lower envelopes of the structured singular value plots are obtained from corresponding finite dimensional systems without any time delay. The analysis procedures developed are applied to an example on repetitive control of an electrohydraulic material testing machine, available in the literature, to demonstrate their usefulness.