Stochastic Control Of Air-fuel Ratio Considering Effect Of Residual Gas For Spark Ignition Engines

With the increase of environmental pollution and energy crisis, decreasing thehazardous substances in vehicle exhaust and enhancing fuel economy as the purpose of theengine control are becoming the focus of widespread concern. Air-fuel ratio control is oneof the important control problems of the engine, the accuracy of the air-fuel ratio controldirectly affects the hazardous substances in vehicle exhaust and fuel economy, and theresidual gas which is trapped in the cylinder at the end of the exhaust stroke is one of theimportant factors which affects the accuracy of the air-fuel ratio control. Therefore, on thebackground of spark ignition engines, this paper investigates the problem of the air-fuelratio control considering the affection from the residual gas. The main works of this paperis around establishing models of the residual gas and control strategies of the air-fuel ratio,and its specific research content is as follows:For the establishing of models of the residual gas fraction (RGF), the measurement ofthe RGF, the one-step predictive model of the RGF and the dynamic model of air-fuelratio control with RGF are given, respectively. The measurement of the RGF is expressedas a function of the cylinder pressures at the beginning and the end of the exhaust stroke,which is derived from the ideal gas equation and the law of thermodynamics, and it makesthe RGF to be a physical quantity which can be measured in real time, using for feedbackcontroller design. The one-step predictive model of the RGF is a predictive model whichis obtained by analyzing the statistical properties of the RGF samples and employing themaximum likelihood estimation, and it makes the one-step predictive value of the RGFcan be given in the mean value sense in the controller design. Meanwhile, for thecontroller design, the dynamic model of the air-fuel ratio control with RGF is developedwhich describes the dynamic of air path, fuel path and combustion products path in thecylinder, based on the definition of the RGF and the assumption of uniform emission.Considering the stochasticity of the RGF and the established models of the residualgas, the stochastic optimal control problem, the stochastic disturbance attenuation problemand the stochastic adaptive control problem of air-fuel ratio are investigated, respectively.As the air-fuel ratio control causing the fluctuation of the fuel injection affects theperformance of the engine (such as the fluctuation of the torque output), the air-fuel ratiocontrol problem with consideration of the fuel injection fluctuation is transformed into the stochastic optimal control problem of the discrete-time system. The stochastic optimalcontroller which is designed by employing the dynamic programming theory of thediscrete-time linear systems with Markovian jumping parameters, makes the wholeclosed-loop system mean square stable, and achieves the tradeoff between the controlaccuracy of the air-fuel ratio and the fuel injection fluctuation. Fresh air charge can beseen as the composition of the fluctuation and the nominal value, the fluctuation affectsthe accuracy of the air-fuel ratio control and the nominal value is obtained by thecorresponding sensors, whose estimation will be affected by the measurement noise. Thetwo aspects are researched by the stochastic disturbance attenuation problem andstochastic adaptive control problem, respectively. The purpose of the stochasticdisturbance attenuation problem is to attenuate the fluctuation of the fresh air charge, andthe controller accomplished by using the robust control theory of discrete-time jumpinglinear system makes the whole closed-loop system mean square stable. The nominal valueof the fresh air charge is estimated on-line by the adaptive law in the stochastic adaptivecontrol problem. Comparing to the measurement model-based air charge estimation, theadaptive law need not using additional sensors, and it is not affected by the measurementnoise from the sensors. The effectiveness of the stochastic optimal controller, thestochastic robust controller and the stochastic adaptive controller are verified by thenumerical simulation and the test bench.Finally, as an extension of the main research, the stabilization problem of the residualgas mass is also considered. The dynamic model of the residual gas mass is derived fromthe definition of the RGF. The validation of the stabilization controller is verified by thecomparison of its control performance and the one of the open-loop controller on the testbench.