Robust Parametrization of a Model Predictive Controller for a CNC Machining Center Using Bayesian Optimization

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.