This paper develops recursive least-squares (RLS) and extended Kalman filtering (EKF) approaches for estimating uncertain engine friction (and other) parameters necessary for successful implementation of a two-scale command shaping (TSCS) engine restart strategy. The TSCS strategy has been developed for mitigating vibrations in conventional and hybrid electric vehicle (HEV) powertrains during internal combustion engine (ICE) restart. Implementing the TSCS strategy increases the drivability of a HEV by reducing noise, vibration, and harshness (NVH) issues associated with ICE restart during a powertrain mode transition. This is accomplished primarily, by modifying the electric machine (EM) torque profile with linear and time-varying components over multiple time scales. For full implementation, the TSCS strategy requires input parameters characterizing the ICE which may be a) difficult to quantify, and/or b) uncertain due to their dependence on engine operating temperature and other environmental considerations. RLS and EKF algorithms tailored to TSCS are presented herein for estimating these parameters. It is shown that both the RLS and EKF algorithms can be used to estimate the necessary ICE parameters and increase effectiveness of the TSCS strategy. The EKF algorithm, in particular, estimates uncertain ICE parameters with minimal measurement requirements, giving it an advantage over the presented RLS algorithm.

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