Motion control with high accuracy for each axial system is the fundamental requirement to reduce a synchronous motion error of a multi-axis system. Especially, designing a model-based controller for an uncertainty system with unknown parameters is not easy without using system identification. To overcome the mentioned issue, this article proposes a cross-coupling synchronous velocity controller using a backstepping-based model reference adaptive control scheme in an unsymmetrical biaxial winding system called a transformer winding system. The proposed controller deals not only with the uncertainty but also with the recursive structure of the system. The backstepping technique for the recursive structural system and the model reference adaptive control method for the uncertainty of the system are designed to stabilize two axial systems with unknown parameters. An auxiliary system is added to build the proposed controller for coping with input constraints of physical actuators. To improve the proposed controller’s ability to cope with external disturbances, a dead-zone modification is utilized to modify the adaptation laws to avoid the drift phenomenon. Moreover, a cross-coupling mechanism is integrated into the proposed controller to reduce the synchronous velocity error between the velocities of the biaxial winding system. The proposed controller is also transformed into discrete time to be run on a digital signal processor alone chip. The experimental results are shown to verify the high performance and efficiency of the proposed controller for practical applications.
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