A cumulative-summation-based stochastic knock controller

Abstract

In this paper, an analysis of knock signals suggests that the knock intensity is a cyclically uncorrelated random process, and that it is therefore not possible to control individual cycles to a specified knock intensity in a deterministic manner. A new knock control algorithm is therefore developed on the basis of a stochastic interpretation of the knock signal, and on the basis of a control objective specified as a certain percentage of knocking cycles. Unlike traditional controllers, the new algorithm does not respond to knock events provided that these are occurring within a specified tolerance of the target knock rate. The new controller uses the cumulative summation of knock events to make this determination, thereby avoiding the slow transient response times sometimes associated with ‘stochastic’ knock controllers. When a spark adjustment is deemed necessary, the magnitude of the control action is scaled according to the likelihood ratio of the observed events since the last spark adjustment was made. A theoretical analysis of the new controller is presented and a simulation tool which is closely based on experimental data is used to assess its performance. The results show that the new controller is able to achieve the same target knock rate as a traditional controller while operating at a more advanced mean spark angle. There is also less cyclic variance about this mean and the regulatory response is significantly improved. The transient response to overly advanced or retarded conditions is similar to the traditional controller. These results suggest that the new controller will deliver increased torque and engine efficiency under knock-limited conditions without increasing the risk of engine damage.

Stochastic simulation and analysis of a classical knock controller

“…In the case of knock probability, however, this relationship is known explicitly (Figure 4), and it is therefore possible to transform the spark advance distributions into distributions for the instantaneous knock probability according to equation (19).…”

“…A similar histogram can be constructed from the experimental data by dividing the data into non-overlapping samples of n = 30 engine cycles each and computing the empirical frequency of knock events according tô The results, shown as the leftmost bars in Figure 5, all lie within a 2 SD interval of the theoretical results, confirming that knock event counts are consistent with a binomial distribution. The binomial properties of knock events are useful both in the design of stochastic knock controllers [17][18][19][20] and in the simulation of statistically representative sequences of knocking/non-knocking cycles. 25 In this latter context, the knock characteristic of Figure 4 can be encapsulated in a lookup table and used as the basis for the knock event simulator shown in Figure 6.…”

“…[13][14][15][16] In particular, a recent emphasis on knock as a stochastic cyclic process has proved fruitful in the development of new likelihood or cumulative-summation-based knock control strategies and their optimization. [17][18][19][20][21] Despite these developments, however, there currently exist no tools that embrace the stochastic nature of knock when quantifying and comparing the performance of knock controllers. Such quantification is not trivial since repeating an experiment, whether on an engine test bed, or in simulation, is likely to yield a different response according to the random arrival of knock events in that particular instance.…”

Knock Intensity Distribution and a Stochastic Control Framework for Knock Control

“…Studies by Peyton Jones et al [13][14][15] concluded that significant improvements in the performance of standard knock controllers may be possible if the properties of the knock process are better characterized and exploited in knock controller designs. Several studies have indeed shown that a more stochastic approach of knock control considering the statistical properties of combustion intensity can offer better spark timing control (and thereby better knock control) [16][17][18].…”

Tuning and experimental evaluation of a likelihood-based engine knock controller

“…Another approach, using a cumulative-summation-based controller, has been presented in [16], and improved in [17,18]. This controller reacts quickly to changes in knock rate while having less cyclic variability compared to the conventional controller, achieving a mean spark advance closer to the knock limit.…”