Analysis of Multistage Hybrid Powertrains Using Multistage Mixed-Integer Trajectory Optimization

Huayi Li, Dominic Liao-Mcpherson, Ilya Kolmanovsky, Shinhoon Kim, Ken Butts

Research output: Contribution to journalConference articlepeer-review


Increasingly complex hybrid electric vehicle (HEV) powertrains are being developed to address the growing stringency of emissions regulations, fuel economy standards and drivability/performance requirements. Early in their design process, it is desirable to rapidly evaluate powertrain architectures and components using simulation models before committing to costly physical prototyping. However, HEV powertrains have multiple controlled degrees of freedom, such as power split, engine on/off and gear selection, the operation of which needs to be pre-determined before a meaningful performance evaluation can be carried out. In this paper, we describe a multistage mixed integer trajectory optimization methodology that allows design engineers to rapidly perform performance analyses of complex powertrains. The methodology can generate optimal input signals for both continuous (engine torque or motor power) and discrete (engine on/off or gear selection) degrees of freedom for a given scenario. Moreover, the method is computationally efficient; it exploits characteristics of powertrain control problems, builds on existing nonlinear programming solvers and is highly parallelizable. We illustrate the utility of this technique by applying it to a Toyota multistage hybrid powertrain of the type used in 2018 LC500h vehicles. We consider several driving scenarios and perform a jerk/acceleration time tradeoff study. Our results indicate that the proposed methodology is effective for performing these kinds of analyses.

Original languageEnglish
JournalSAE Technical Papers
Issue numberApril
StatePublished - Apr 14 2020
EventSAE 2020 World Congress Experience, WCX 2020 - Detroit, United States
Duration: Apr 21 2020Apr 23 2020

Bibliographical note

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ASJC Scopus subject areas

  • Automotive Engineering
  • Safety, Risk, Reliability and Quality
  • Pollution
  • Industrial and Manufacturing Engineering


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