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We propose a performance-based autotuning method for cascade control systems, where the parameters of a linear axis drive motion controller from two control loops are tuned jointly. Using Bayesian optimization as all parameters are tuned simultaneously, the method is guaranteed to converge asymptotically to the global optimum of the cost. The data-efficiency and performance of the method are studied numerically for several training configurations and compared numerically to those achieved with classical tuning methods and to the exhaustive evaluation of the cost. On the real system, the tracking performance and robustness against disturbances are compared experimentally to nominal tuning. The numerical study and the experimental data both demonstrate that the proposed automated tuning method is efficient in terms of required tuning iterations, robust to disturbances, and results in improved tracking.