Presented in this paper is the conversion of NARMAX models to describing function based models for the purpose of robust feedback controller design. This investigation develops discrete NARMAX models to represent the nonlinear dynamics of a Ford 4.6L V-8 fuel injection engine operating at a preset idle speed. A SISO NARMAX model of the engine is developed between the By-Pass Idle Air Valve (BPAV) and engine speed. From this model, a describing function is obtained for the purpose of controller design. The objective of the controller design is to regulate engine speed within a 100 rpm tolerance about 700 rpm despite external torque disturbances. The design is executed in the frequency domain which incorporates model uncertainty and the transport delay of the engine. A controller is designed and verified using both numerical simulations and experimental verification.

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