Constrained optimal control of multi-dynamometer internal combustion engine test benches

Dynamical internal combustion engine test benches are commonly used in automotive development to enforce reproducible operating conditions for testing and calibration. The associated control problem consists in tracking simultaneously speed references and torque references and can be described in terms of a nonlinear optimal control problem. In most cases, only one internal combustion engine and one dynamometer are used, either an electrical dynamometer or a hydrodynamic dynamometer, each offering different advantages. In some cases, a so called tandem configuration is meaningful, using a small electrical load machine for baseline operation and a hydrodynamic dynamometer for peak demands, or vice versa. Due to the asymmetric properties of the hydrodynamic dynamometer, the problem cannot be stated directly in terms of a Hamilton-Bellman-Equation, but needs an extension. This paper presents such a solution based on a nonlinear mapping of the asymmetric input constraints and a dynamic extension to the state of the system and examines the usefulness of such an approach. Measurements at a test bench are used to evaluate the performance of the proposed control approach for typical cases.