  Cascaded controller tuning is a multi-step iterative procedure that needs to
be performed routinely upon maintenance and modification of mechanical systems.
An automated data-driven method for cascaded controller tuning based on
Bayesian optimization is proposed. The method is tested on a linear axis drive,
modeled using a combination of first principles model and system
identification. A custom cost function based on performance indicators derived
from system data at different candidate configurations of controller parameters
is modeled by a Gaussian process. It is further optimized by minimization of an
acquisition function which serves as a sampling criterion to determine the
subsequent candidate configuration for experimental trial and improvement of
the cost model iteratively, until a minimum according to a termination
criterion is found. This results in a data-efficient procedure that can be
easily adapted to varying loads or mechanical modifications of the system. The
method is further compared to several classical methods for auto-tuning, and
demonstrates higher performance according to the defined data-driven
performance indicators. The influence of the training data on a cost prior on
the number of iterations required to reach optimum is studied, demonstrating
the efficiency of the Bayesian optimization tuning method.
