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In this study, the problem of regulation of air-fuel ratio (AFR) in gasoline engines under different engine operating conditions is discussed. Firstly, the mean value mathematical model of the AFR system has been created. Then, two different approaches named with classical proportional-integral-derivative (PID) and a fuzzy logic gain scheduling PID controller combined with gray system modelling approach (Gray GS-PID)have been used to improve the performance of the engine to monitor stoichiometric conditions. The parameters of classical PID parameters are determined by the pattern search algorithm. The design procedures for both controllers have been presented in detail. In order to evaluate the performance analysis for both of the proposed controllers, variable conditions were established based on engine speed and throttle opening ratios in the US06 and UDDS driving conditions and validated by simulation results. According to the results, Gray GS_PID is more powerful than optimally adjusted PID in terms of reducing the amount of deviation of AFR from stoichiometric value under variable engine operating conditions. The most important contribution of this study is that, unlike conventional AFR regulation, the prediction of future error value relative to the previous AFR error values ​​using the gray prediction algorithm, and the design of the control algorithm that determines the control action for the next step depending on the predicted error value before the error occurs and sets the gain parameters.

Gray based Fuzzy Gain-Scheduling PID Controller Design for Air-Fuel System Under Variable Engine Operating Conditions