Using CMA-ES for tuning coupled PID controllers within models of combustion engines

Proportional integral derivative (PID) controllers are important and widely used tools of system control. In this paper, we deal with the problem of tuning multiple coupled PID controllers within the practical context of combustion engine simulations, where no information about the controlled system is provided. We formulate the problem as a black-box optimization problem and, based on its properties and practical limitations, we find and tune the appropriate optimization algorithm: Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with bi-population restart strategy, elitist parent selection and active covariance matrix adaptation. Details of the algorithm's experiment-based calibration are explained as well as derivation of a suitable objective function. Finally, the method's usability is verified on six models of real engines.