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This paper presents a modified sliding-mode structure implemented for the speed control of a two-mass drive. A characteristic feature of the presented control method is the higher rank of the switching function caused by the application of an integral element (sliding mode with an integral function control). The proposed control system is a combination of a sliding-mode controller and a linear controller. Furthermore, to eliminate the chattering phenomenon related to the sliding-mode control, a switching function with a variable slope based on the fuzzy system is implemented. This solution ensures the robustness and dynamics of a two-mass drive better than with a linear speed controller. The main stages of the design methodology of the presented speed control structure are described in the initial sections of this paper. In the subsequent sections, simulation and experimental tests for the proposed control structure are presented and discussed.