Comprehensive Energy Footprint Benchmarking Algorithm for Electrified Powertrains

Electrification in automotive control systems has made powertrains a complex cyber-physical system. This article presents a benchmark algorithm to quantify the performance of complex automotive systems exhibiting mechanical, electrical, and thermal interactions at various timescales. Traditionally, dynamic programming (DP) has been used for benchmarking performance; however, it fails to deliver results for a system with a higher number of states and control levers due to the curse of dimensionality. We propose “PS3,” a three-step algorithm for mixed-integer nonlinear optimal control problems (OCP) with application to powertrain energy management. PS3 uses pseudospectral collocation (PSC) theory for accurate modeling of dynamics with fast and slow dynamic states, discontinuous behaviors, nondifferentiable and linearly interpolated 1-D and 2-D maps, as well as combinatorial constraints. We give a feasibility analysis along with a discussion on the convergence and optimality gap of the proposed algorithm. Based on the validated powertrain component models, we have addressed simultaneous optimization of electrical [state of charge (SOC)], vehicular (eco-driving), and thermal (after-treatment and battery temperatures) dynamics along with an integer (gear and engine on/off) control and its corresponding (dwell time) constraints. Six powertrain control problems are given to benchmark the accuracy and computational effort against DP. Our analysis shows that this algorithm does not scale computational burden as DP does and can handle highly complex interactions that occur in modern-day powertrains, without compromising nonlinear and complex plant modeling.