Tracking control of periodic signals with varying magnitude and its application to hybrid powertrain

Internal model based repetitive control for linear time invariant (LTI) system has been widely applied to track or reject periodic signals with only the period known. It is well understood that the discrete generating dynamics of the periodic signal can be obtained by finite sampling, and embedding it as the internal model will yield asymptotic performance. However, the traditional repetitive control framework will no longer work for periodic signals with varying peak to peak amplitude. As will be revealed in this paper, the generating dynamics of this kind of signals is time varying, and thus simply embedding its generating dynamics as the internal model will no longer ensure asymptotic performance. The necessity of investigating tracking or rejecting varying magnitude periodic signals comes from a wide class of anticipated applications, one example of which is the hybrid vehicle powetrain vibration reduction. In the hybrid vehicles, engine starting and stopping occur frequently to switch between power sources, which could cause driveline vibration. With proper formulation, the oscillation signal becomes periodic with varying magnitude. To suppress such vibration, in this paper, the generating dynamics of this unique signal is first derived, and then its corresponding controller design method is presented. After a series of simulations and case studies, the proposed control framework is demonstrated to be a promising solution for the hybrid powertrain vibration reduction problem.