Automatic calibration of control parameters based on merit function spectral analysis

The number of actuations influencing the combustion is increasing, and, as a consequence, the calibration of control parameters is becoming challenging. One of the most effective factors influencing performance and efficiency is the combustion phasing: for gasoline engines control variables such as Spark Advance (SA), Air-to-Fuel Ratio (AFR), Variable Valve Timing (VVT), Exhaust Gas Recirculation (EGR) are mostly used to set the combustion phasing. The optimal control setting can be chosen according to a cost function, taking into account performance indicators, such as Indicated Mean Effective Pressure (IMEP), Brake Specific Fuel Consumption (BSFC), pollutant emissions, or other indexes inherent to reliability issues, such as exhaust gas temperature, or knock intensity. The paper proposes the use of the extremum seeking approach during the calibration process. The main idea consists in changing the values of each control parameter at the same time, identifying its effect on the monitored cost function, allowing to shift automatically the control setting towards the optimum solution throughout the calibration procedure. Obviously, the nodal point is to establish how the various control parameters affect the monitored cost function and to determine the direction of the required variation, in order to approach the optimum. This task is carried out by means of a spectral analysis of the cost function: each control variable is varied according to a sine wave, thus its effect on the cost function can be determined by evaluating the amplitude of the Fast Fourier Transform (FFT) of the cost function, for the given excitation frequency. The FFT amplitude is representative of the cost function sensitivity to the control variable variations, while the phase can be used to assess the direction of the variation that must be applied to the control settings in order to approach the optimum configuration. Each control parameter is excited with a different frequency, thus it is possible to recognize the effect of a single parameter by analyzing the spectrum of the cost function for the given excitation frequency. The methodology has been applied to data referring to a PFI engine, trying to maximize IMEP, while limiting the knock intensity and exhaust gas temperature, using SA and AFR as control variables. The approach proved to be efficient in reaching the optimum control setting, showing that the optimal setting can be achieved rapidly and consistently.