Joint Estimation of Nonlinear Dynamics and Resistance Torque for Integrated Motor-Transmission Systems via Switched ℓ_∞ Observers With Smoothness Guarantee

The information of the shaft torque and the resistance torque is crucial to develop advanced control and fault diagnosis/detection schemes for electrified powertrain systems. However, reliable physical sensors for torque measurement are not affordable for commercial vehicle applications. This article investigates the simultaneous estimation problem of the state dynamics and the resistance torque for integrated motor-transmission (IMT) systems of electric vehicles. To this end, the IMT system is first reformulated as a nonlinear switched model, where the resistance torque is considered as an unknown input (UI). This modeling reformulation allows taking into account not only the nonlinear nature of IMT dynamics but especially also the intrinsic discontinuity of the gear-shifting process. Then, we propose a nonlinear switched observer (NSO) structure to simultaneously estimate the nonlinear IMT dynamics, thus the shaft torque, and the unknown resistance torque. The observer design does not require any a priori information on the unknown resistance torque as for the classical proportional-integral observer design, nor the well-known matching condition for UI decoupling techniques. Using the Lyapunov stability theory, we derive sufficient conditions, expressed in terms of linear matrix inequality (LMI) constraints, to design an NSO with a guaranteed $\ell _{\infty }$ performance to mitigate the negative effect of sensor noises and disturbances. In particular, we propose to incorporate LMI-based bumps limitation conditions in the optimization-based observer design to reduce the impacts of expressive discontinuities at switching instants. Comparative studies are performed between the related estimation methods to show the practical effectiveness of the proposed solution.