  Control algorithms such as model predictive control (MPC) and state
estimators rely on a number of different parameters. The performance of the
closed loop usually depends on the correct setting of these parameters. Tuning
is often done manually by experts based on a simulation model of the system.
Two problems arise with this procedure. Firstly, experts need to be skilled and
still may not be able to find the optimal parametrization. Secondly, the
performance of the simulation model might not be able to be carried over to the
real world application due to model inaccuracies within the simulation. With
this contribution, we demonstrate on an industrial milling process how Bayesian
optimization can automate the tuning process and help to solve the mentioned
problems. Robust parametrization is ensured by perturbing the simulation with
arbitrarily distributed model plant mismatches. The objective is to minimize
the expected integral reference tracking error, guaranteeing acceptable worst
case behavior while maintaining real-time capability. These verbal requirements
are translated into a constrained stochastic mixed-integer black-box
optimization problem. A two stage min-max-type Bayesian optimization procedure
is developed and compared to benchmark algorithms in a simulation study of a
CNC machining center. It is showcased how the empirical performance model
obtained through Bayesian optimization can be used to analyze and visualize the
results. Results indicate superior performance over the case where only the
nominal model is used for controller synthesis. The optimized parametrization
improves the initial hand-tuned parametrization notably.
