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

Abstract

Proportional integral derivative (PID) controllers are important and widely used tools of system control. Tuning their gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time an engineer spends tuning the gains in a simulation software, we propose to formulate a part of the problem as a black-box optimization task. In this paper, we summarize the properties and practical limitations of gain tuning in this particular application. We investigate the latest methods of black-box optimization and conclude that the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with bi-population restart strategy, elitist parent selection and active covariance matrix adaptation is best suited for this task. Details of the algorithm's experiment-based calibration are explained as well as derivation of a suitable objective function. The method's performance is compared with that of PSO and SHADE. Finally, its usability is verified on six models of real engines.