Bayesian Optimization for automatic tuning of digital multi-loop PID controllers

In recent years, the use of Bayesian optimization (BO) for efficient automatic tuning of general controller structures through iterative closed-loop experiments, has been attracting increasing interest. However, its potential for tuning interactive multi-loop PID controllers in Multi Input Multi Output (MIMO) processes remains largely unexplored. Even though the optimization domain greatly affects closed-loop performance and safety, it is usually defined manually, through expert knowledge or experimentation. This paper presents a novel systematic methodology for defining the optimization domain for automatic multi-loop PID tuning using BO. Sequential loop closing, system identification and tuning relations are used to constrain the bounds on controller parameters to meaningful ranges, including gains and sampling times. This provides an effective way to improve the convergence of BO and secure process safety during closed-loop experiments, without requiring a MIMO process model or extensive prior knowledge. The methodology can be applied "as is" to single-loop PID controllers.