Stochastic Simulation and Performance Analysis of Classical Knock Control Algorithms

Computing the closed-loop characteristics of a generalized multi-threshold knock controller

“…where T ([ i A , i B ]) denotes a column vector whose i th element is T ([ i A , i B ], i ), and c is an identically sized vector containing all ones apart from the elements i ∈ [ i A , i B ] which are zero. Note that the form of equation (21) is very similar to previous results for the response time of a conventional single-threshold controller, 12 but in this case, the matrix M * is defined by the more general expression…”

“…Such a ‘stochastic simulator’, for example, has been developed for a (single-threshold) classical knock controller and for the class of ‘ n − k ’ knock controllers. 12,13 These algorithms may be used to obtain the expected values, and in some cases the complete distribution of a variety of performance measures. The aim of this article is to extend the approach to the general multi-threshold knock control case, and to apply it in particular to assess the performance of a dual-threshold knock controller in a much more complete and rigorous way than previously has been possible.…”

A comparative study of fixed-gain classical knock control strategies

“…By contrast, stochastic simulation methods provide a way to compute the closed loop distribution from which such individual instances or experiments are drawn. 23,24 The statistical properties or parameters characterizing this distribution then provide a much more complete and repeatable quantification of closed loop performance.…”

“…To avoid having to conduct and process thousands of engine tests or simulations, methods have been developed to enable these closed loop distributions to be calculated analytically from the knock probability characteristic of the engine and the control law that is applied. 23,24 In this paper such methods are adapted and extended in order to encompass the classical control variants discussed above. The resulting stochastic analysis provides a more general complement to the more instance-specific time domain experiment or simulation results.…”

Bayesian Estimation and Control of Engine Knocking Level for Transient Operation

“…Considering the stochastic nature of the knocking phenomena, feedback loop controllers built on a probabilistic approach have already been developed [3]- [12]. Instead of acting immediately to a punctual high knock intensity measurement, actions can be taken only if their relevance is supported by accumulated measurements stored in a buffer memory.…”