Closed loop statistical performance analysis of N-K knock controllers

The closed loop performance of engine knock controllers cannot be rigorously assessed from single experiments or simulations because knock behaves as a random process and therefore the response belongs to a random distribution also. In this work a new method is proposed for computing the distributions and expected values of the closed loop response, both in steady state and in response to disturbances. The method takes as its input the control law, and the knock propensity characteristic of the engine which is mapped from open loop steady state tests. The method is applicable to the 'n-k' class of knock controllers in which the control action is a function only of the number of cycles n since the last control move, and the number k of knock events that have occurred in this time. A Cumulative Summation (CumSum) based controller falls within this category, and the method is used to investigate the performance of the controller in a deeper and more rigorous way than has previously been possible. The results are validated using onerous Monte Carlo simulations, which confirm both the validity of the method and its high computational efficiency.