This paper studies the design of a robust discrete-time sliding mode control (DT-SMC) for a high precision electro-hydraulic actuator (EHA) system with nonlinear actuator friction. Nonlinear friction in the hydraulic actuator can greatly influence the performance and accuracy of the hydraulic actuators; however, it is difficult to accurately model nonlinear friction characteristics. In this paper, it is proposed to characterize frictions as an uncertainty in the system matrices. Indeed, the effects of variations of the nonlinear friction coefficients are considered as norm bounded uncertainties that span a bounded region to cover a wide range of real actuator friction. For such a discrete-time dynamic model for the EHA system with system matrices uncertainties and a nonlinear term, a sufficient condition for the existence of stable sliding surfaces is proposed by using the linear matrix inequality (LMI) approach. Based on this existence condition, a discrete-time sliding mode controller is developed such that the reaching motion satisfies the discrete-time sliding mode reaching condition for uncertain systems. Simulation and comparison studies on the EHA system model illustrate the effectiveness of the proposed method. The study is simulation based only as it is important to establish the feasibility and stability of the controller before attempting to apply the controller to a physical system.

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