Stochastic simulation and analysis of a classical knock controller

Knock control remains a critical issue in modern engine powertrains, and a renewed emphasis on knock as a stochastic process has proved beneficial in the development of new controller designs. However, the random nature of knock also makes it hard to evaluate the closed-loop performance of a knock controller in a rigorous, repeatable way. This work therefore focuses particularly on the statistical properties of knock intensities and knock events, and a new Markov-based analysis is used to compute the corresponding statistical properties and distribution of the closed-loop response. The method is applied to a conventional knock controller, revealing new aspects of its behavior. In particular, the closed-loop spark advance distribution is found to be periodic initially, only collapsing to an invariant steady-state distribution as a result of limits applied to the spark advance actuation. The stochastic response of the controller to different initial conditions is also investigated, providing a more rigorous insight into its performance. The results of the Markov-based analysis are confirmed using Monte Carlo simulations.