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

TL;DR

This paper explores using CMA-ES, a black-box optimization algorithm, to efficiently tune PID controllers in combustion engine models, demonstrating its advantages over other methods through experiments on real engine models.

Contribution

It introduces CMA-ES with specific strategies for tuning PID controllers in combustion engines and compares its performance with other optimization algorithms.

Findings

CMA-ES outperforms PSO and SHADE in tuning efficiency.

The method is effective across six real engine models.

CMA-ES provides a practical solution for complex system control tuning.

Abstract

Proportional integral derivative (PID) controllers are important and widely used tools in system control. Tuning of the controller gains is a laborious task, especially for complex systems such as combustion engines. To minimize the time of an engineer for tuning of 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 tuning of the gains 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.