NARMAX modeling and robust controller design of internal combustion engines

Presented in this paper is robust controller design procedure utilizing a discrete nonlinear model. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. For the engine idle speed control of this study, a SISO NARMAX model of the engine is given between the By-Pass Idle Air Valve (BPAV) and engine speed. From this model, a describing function representation is obtained for controller design subject to the time domain tolerance \Delta rpm\ less than or equal to 100 rpm on idle speed perturbations despite nonmeasurable 20 Nm external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.