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One of the building blocks of the Stellantis hybrid powertrain embedded control software computes the maximum and minimum values of objective functions, such as output torque, as a function of engine torque, hybrid motor torque and other variables. To test such embedded software, an offline reference function was created. The reference function calculates the ideal minimum and maximum values to be compared with the output of the embedded software. This article presents the offline reference function with an emphasis on mathematical novelties. The reference function computes the minimum and maximum points of a linear objective function as a function of six independent variables, subject to 42 linear and two nonlinear constraints. Concave domains, curved surfaces, disjoint domains and multiple local extremum points challenge the algorithm. As a theorem, the conditions and methods for running trigonometric calculations in 6D Euclidean space are presented.

Modern powertrains are highly complex systems whose development requires careful tuning of hundreds of parameters, called calibrations. These calibrations determine essential vehicle attributes such as performance, dynamics, fuel consumption, emissions, noise, vibrations, harshness, etc. This paper presents a methodology for automatic generation of calibrations for a powertrain-abstraction software module within the powertrain software of hybrid electric vehicles. This module hides the underlying powertrain architecture from the remaining powertrain software. The module encodes the powertrain’s torque-speed equations as calibrations. The methodology commences with modeling the powertrain in MapleSim, a multi-domain modeling and simulation tool. Then, the underlying mathematical representation of the modeled powertrain is generated from the MapleSim model using Maple, MapleSim’s symbolic engine.