A comparative study of fixed-gain classical knock control strategies

Abstract

Classical knock control strategies are still widely used in production vehicles but exist in several variant forms whose performance with respect to one another, and to engine efficiency, ease of calibration and analytical tractability has not been rigorously evaluated. This paper examines the absolute and relative performance of these strategies subject to both transient and systematic disturbances using both time history simulation methods and analytical methods. The former illustrates the response to specific instances of the knock process, while the latter enables the statistical properties of the closed loop response to be computed and compared.

A critical analysis of classical severity-based knock control strategies

“…where the min/max constraints and different knock conditions in (10) are subsumed within signed, constrained, and variable control moves m 0 r defined by,…”

“…Finally, note that once the state distribution is known, it is straightforward to compute related metrics such as the expected mean knock rate, m p , the expected ''weak'' IMEP rate, m q , and expected value of the closed loop cost function m J . 10 Stochastic simulation for a multi-threshold controller is more complex than the single threshold case considered previously. In this case, the state transition matrix M is given by the sum of r separate matrices…”

“…As noted above, one advantage of classifying knock intensities in this way is that the simulation technique used by Peyton Jones and Patel 10 can now be extended to simulate different knock intensity events. In this case, the set of curves shown in Figure 3 is embedded in a look-up table and used to obtain the prevailing probabilities p ( θ ) ( r ) , for any simulated spark advance condition, (see Figure 5).…”

“…As in the case of the other classical controllers considered in Peyton Jones and Patel, 10 it is also convenient to discretize the angular state i of the controller, such that,…”

“…A recent study of classical fixed-gain controllers, for example, analyzed and compared the performance of the classical advance-retard strategy with retard-only strategies or periodic-advance strategies. 10 Fixed-gain control strategies, however, make no distinction between knock events that only just exceed the knock threshold, and other much more severe and potentially damaging high knock intensity cycles; the controller response to all events, regardless of severity, is defined by the constant retard gain. Some strategies, however, scale the magnitude of the control action according to the knock intensity or severity observed during the prior cycle.…”