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Robust repetitive control for a class of uncertain nonlinear systems

This paper presents an output‐feedback repetitive control method for a class of systems with nonlinearities, unknown state‐dependent uncertainties, and external disturbances. An additive‐state‐decomposition approach is used to decompose the system under study into a primary linear periodic system in charge of repetitive‐control tracking task and a secondary linearized system in charge of robustly stabilization task. Such a treatment not only significantly simplifies system analysis and controller design, but also provides an effective method to cope with the intrinsic constraints between tracking and disturbance rejection. Another attractive point lies in two aspects. On one hand, a periodic term from the nonlinearity in the plant is extracted to be treated in the primary system and the known plant information is used to design controller parameters, which greatly improves the disturbance rejection ability of the system. On the other hand, repetitive control gain, feedback control gain, and the observer gain are optimized through an optimization algorithm by introducing an index to evaluate the overall system performance. System stability criteria and design procedure are developed. Finally, a case study on the tracking control of a chuck‐piece system demonstrates the validity of the proposed method. Comparisons with some existing methods show that the proposed method achieves better performances in both signal tracking and disturbance rejection.