This paper analyzes the robustness of a two-scale command shaping strategy for reducing vibrations in hybrid electric vehicle (HEV) powertrains during engine restart. Propagation of HEVs through the automobile market depends on their perceived quality and performance. In this work, a two-scale command shaping strategy addresses the drivability of the vehicle by focusing on the reduction of noise, vibration, and harshness (NVH) issues associated with restarting the internal combustion engine (ICE) during a mode transition. The strategy tailors the electric machine (EM) torque profile, which consists of a linear and time-varying component, to significantly mitigate the powertrain and chassis vibrations for a smoother ICE startup. The time-varying EM torque component is calculated by applying a perturbation technique for separating the scales of an analytical ICE model, which isolates the ICE nonlinear response. Command shaping is then applied to the linear problem governed by the remaining scale. Simulations confirm that the two-scale command shaping strategy is a straightforward technique for reducing powertrain and chassis vibrations during ICE restart. In real-time implementation, inaccuracies or variations in system parameters and initial conditions arising from the operating condition or from general wear during a vehicle’s life cycle will occur. Therefore, successful implementation of the two-scale command shaping strategy relies upon the robustness of the perturbation technique and command shaping to these variations. This paper validates the perturbation technique’s robustness to variations in the ICE parameters and initial conditions. Robust command shaping methods are also explored to decrease the impact of system parameter variations on the efficacy of command shaping. Improving the overall robustness of the two-scale command shaping strategy will increase the applicability to consumer HEVs by ensuring its performance under variations in system parameters.

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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Above all else I would like to thank the endless support from my family; especially, my mother, Lori Wilbanks, and father, Jamie Wilbanks. The advice and support received from my parents was invaluable in completing my doctoral studies. The time spent around my grandfather, A. C. Whitten, served as the impetus for my pursuit of a degree in mechanical engineering, and without his advice throughout the years I would not have the practical knowledge and ideals that have served me so well through my studies and life. In addition, I would also like to thank my grandmother, Jan Whitten, for providing mental support as well as amazing meals throughout the years. Additionally, I would like to thank my uncle, Barry Whitten, who provided me with a good taste in music, taught me to drive a manual transmission, and showed me the need for a good proofreader. I would also like to thank my advisor Dr. Leamy for his support throughout the pursuit of my PhD. The indispensable feedback and motivation provided throughout my time in graduate school kept me pushing forward. He also provided me time to prepare for qualifying examinations, presentation opportunities, deadlines to drive me forward, funding opportunities, and the all-important discussions about college football or cars.Without his guidance, I do not believe I would have been able to successfully navigate the completion of my PhD.

Vibration testing of complex aerospace structures requires substantial pretest planning. Ground and flight testing of structures can be costly to execute in terms of time and money, so it is pertinent that tests are properly set up to capture mode shapes or dynamics of interest. One of the most important planning tasks is the placement of sensors to acquire measurements for control and characterization of the results. In this paper, we will examine two techniques that can leverage available output from finite element modeling to intelligently place accelerometers for a vibration test to capture the structural dynamics throughout a specified frequency range with a data acquisition channel budget. These two techniques are effective independence (EI) and optimal experimental design (OED). Both methods will be applied to an aerospace structure. Effects of the chosen sets on system equivalent reduction and expansion process (SEREP) is detailed alongside simpler comparison metrics, like the Auto-Modal Assurance Criterion (Auto-MAC). In addition to comparing the resulting instrumentation sets, the application of the two approaches will be compared in terms of the inputs required, the information obtained from their application, and the computation time requirements. Both OED and EI offer an effective method for selecting an instrumentation set for a given vibration test. EI is a straightforward, computationally inexpensive approach that provides effective instrumentation sets. OED provides an effective alternative that is less sensitive to the impact of local modes and leads to a natural ranking of importance for each chosen degree of freedom (DOF).