  This paper presents an automated, model-free, data-driven method for the safe
tuning of PID cascade controller gains based on Bayesian optimization. The
optimization objective is composed of data-driven performance metrics and
modeled using Gaussian processes. We further introduce a data-driven constraint
that captures the stability requirements from system data. Numerical evaluation
shows that the proposed approach outperforms relay feedback autotuning and
quickly converges to the global optimum, thanks to a tailored stopping
criterion. We demonstrate the performance of the method in simulations and
experiments. For experimental implementation, in addition to the introduced
safety constraint, we integrate a method for automatic detection of the
critical gains and extend the optimization objective with a penalty depending
on the proximity of the current candidate points to the critical gains. The
resulting automated tuning method optimizes system performance while ensuring
stability and standardization
