NARMAX modelling and robust control of internal combustion engines

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engin e. The methodology begins with the identification of a NARMAX model that ca ptures the non-linear dynamics relating the input to the output of a system . This model is converted to a describing function representation for the p urpose of robust feedback controller design. The ideology for the describin g function recovery is developed in the form of an algorithm which can be e xtended to other NARMAX model structures not considered here. The controlle r design is executed in the frequency domain where the output performance s pecification is \y(t)\ less than or equal to beta For All t > 0 and the act uator saturation constraint is \u(t)\ less than or equal to kappa For All t > 0. For the engine idle speed control application of this study, a SISO N ARMAX model of the engine is developed between the by-pass idle air valve ( BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of \Delta rpm\ less than or equal to 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.