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Summary A robust discrete terminal sliding mode repetitive controller is proposed for a class of nonlinear positioning systems with parameter uncertainties and nonlinear friction. The terminal sliding mode control (TSMC) part is designed to improve the transient characteristics of the system, as well as the robustness against parameter uncertainties, nonperiodic nonlinearities, and disturbances. The repetitive control (RC) part is then integrated to eliminate the effects of the periodic uncertainties present in the system. Moreover, a pure phase lead compensator is incorporated into the RC to improve the tracking at high frequencies. A robust stability analysis and an analysis of the finite time convergence properties of the proposed controller are also provided in this paper. Simulation testing and an experimental validation using a linear actuator system with nonlinear friction and parameter uncertainties are conducted to verify the effectiveness of the proposed controller.

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A sliding mode based repetitive control system is proposed, to improve reference tracking performance, as well as compensate output disturbances. The design algorithm is based on the concept of sliding mode controller (SMC), feedback controller, and modified repetitive controller (MRC). With two tuning parameters, the sliding mode based RC provides a simple and convenient method to solve the complex engineering problems. The comparison study was conducted to demonstrate the effectiveness of sliding mode based RC over state feedback based RC.