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Simulation tools are critical to control system development and design. Simulation of knock control systems, however, is complicated both by the stochastic nature of knock, and by the wide range of signal bandwidth and dimensionality within the feedback loop. The aim of this paper is therefore to provide a review, and in some cases an extension, of knock simulation methods from a control-oriented perspective, focusing particularly on the statistical properties of knock intensity and knock events. Deterministic notions of closed-loop performance can be misleading in this context, and recent work using Markov- and Monte-Carlo-based methods is briefly summarized as a means to obtain a more rigorous and complete description of closed-loop behavior. The methods are illustrated using a classical knock controller design.

This paper collates and summarizes recent advances in knock analysis, simulation and control. The statistical properties of knock intensity and knock events are reviewed showing in particular that knock intensity behaves as an independent random process, and that knock events conform to a binomial distribution. These properties have a significant impact on knock control and simulation. Traditional and recently proposed cumulative-summation-based and Likelihood-based knock control strategies are reviewed and illustrated in this context. Efficient tools for simulating both specific instances of the closed loop time response, and the evolution of the distribution of these responses based on a Markov-like approach, are also briefly reviewed. Finally, it is shown how an optimization of the knock threshold and an associated retuning of the controller parameters can result in significantly improved closed loop performance without any other modification of the control algorithm.