In recent years technology development for the design of electric and hybrid-electric vehicle systems has reached a peak, due to ever increasing restrictions on fuel economy and reduced vehicle emissions. An international race among car manufacturers to bring production hybrid-electric vehicles to market has generated a great deal of interest in the scientific community. The design of these systems requires development of new simulation and optimization tools. In this paper, a description of a real-time numerical environment for Virtual Proving Grounds studies for hybrid-electric vehicles is presented. Within this environment, vehicle models are developed using a recursive multibody dynamics formulation that results in a set of Differential-Algebraic Equations (DAE), and vehicle subsystem models are created using Ordinary Differential Equations (ODE). Based on engineering knowledge of vehicle systems, two time scales are identified. The first time scale, referred to as slow time scale, contains generalized coordinates describing the mechanical vehicle system that includs the chassis, steering rack, and suspension assemblies. The second time scale, referred to as fast time scale, contains the hybrid-electric powertrain components and vehicle tires. Multirate techniques to integrate the combined set of DAE and ODE in two time scales are used to obtain computational gains that will allow solution of the system’s governing equations for state derivatives, and efficient numerical integration in real time.

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