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This paper presents original concepts of control systems for an electrical drive with an elastic mechanical coupling between the motor and the driven mechanism. The synthesis procedure of the speed controller uses a proposed quality index (cost function) of system operation ensures the minimization of both tracking errors and torsional vibrations. Proper selection of the cost function focusses more on the reduction of torsional vibrations due to their negative influence on the drive's mechanical coupling vitality. The omission of the plant identification of an adaptive fuzzy controller was proposed. Two types of fuzzy controllers were analyzed, namely with type I and type II fuzzy membership functions. The novelty of the presented approach is in the application of a Petri transition layer in a type II fuzzy controller which reduces the numerical complexity in case of a large number of complicated type II fuzzy sets. The presented simulation and experimental results prove that the best dumping of mechanical vibrations ensures the adaptive fuzzy controller with type II functions and a Petri transition layer. [ABSTRACT FROM AUTHOR]