Gain scheduled linear quadratic tracking system tuned optimally by covariance matrix adaption evolutionary strategy for automotive engine coldstart control

Abstract

In this paper, a gain scheduled linear quadratic tracking system (LQTS) tuned optimally by an evolutionary strategy (ES) is devised to reduce the total tailpipe hydrocarbon (HC) emissions of an automotive engine over the coldstart period. As the engine’s behavior during coldstart operations is nonlinear, the system dynamics is clearly analyzed and represented by a number of separate linear models generated based on a coldstart model verified by experimental data. An independent LQTS is then implemented for each of these linear models. In this way, several control laws are created, and the corresponding gains are calculated for each of the independent control laws. ES is then used to tune the adjustable parameters of LQTSs to calculate the control inputs, namely air/fuel ratio (AFR) and spark timing (Δ), such that the resulting exhaust gas temperature (Texh) and engine-out HC emissions (HCraw) be close to a set of optimum profiles. This enables the controller reduce the cumulative tailpipe hydrocarbon emissions (HCcum) to the highest possible extent. To demonstrate the acceptable performance of the proposed controller, an optimal controller derived from the Pontryagin’s minimum principle (PMP) is also taken into account. Based on the results of the conducted comparative study, it is shown that the proposed control technique has a very good performance, and also, can be easily used for real-time applications, as it consumes a remarkably trivial computational time for calculating the controlling commands.