Robust two-scale command shaping for residual vibration mitigation in nonlinear systems

Abstract

This paper develops robust two-scale command shaping (TSCS) for vibration mitigation in nonlinear systems. Recursive least-squares (RLS) and extended Kalman filtering (EKF) approaches are used to estimate uncertain system parameters alongside robust command shaping methods to decrease the impact of vibration mode variations on TSCS efficacy. For full implementation, the TSCS strategy requires input parameters to characterize the nonlinear system for which it is being applied, which may be a) difficult to quantify, and/or b) uncertain due to their dependence on environmental considerations or operating conditions. To alleviate these issues a parameter estimation technique can be used to help define these required input parameters. Additionally, robust command shaping methods can be leveraged to decrease the impact of variations in system vibration modes on the efficacy of the command shaping portion of TSCS. A motivating problem for adding robustness to TSCS is the mitigation of vibration-related issues during internal combustion engine (ICE) restart. TSCS applied to engine restart is used as an example to develop the techniques to add robustness to the strategy. 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. Robust command shaping is then used to reduce the effect of variations in the chassis and powertrain vibration modes on the efficacy of TSCS during ICE restart.